JEE MAIN-2019 Online CBT Mode Dt. 12.01.2019 Evening Question Paper With Answer Key

JEE MAIN-2019 Online CBT Mode Dt. 12.01.2019 Evening

PHYSICS

1. 

In the figure, given that VBB supply can vary from 0 to 5.0 V, VCC = 5V,  βdc= 200, RB = 100 KΩ, RC = 1 KΩ and VBE= 1.0V. The minimum base

current and the input voltage at which the transistor

will go to saturation, will be respectively:

(1) 25 μ A and 3.5 V

(2) 20 μ A and 2.8 V

(3) 25 μ A and 2.8 V

(4) 20 μ A and 3.5 V

Answer: (1)

2. A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is I1, and hat below the piston isI2, such that I1> I2. Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m will be given by :

(R is universal gas constant and g is the acceleration due to gravity)

(1)    

(2) 

(3)   

(4)   

Answer: (1)

3. A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 × 10–4 A passes through it, its needle(pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance of:

(1)  6250 ohm

(2)  250 ohm

(3)  200 ohm

(4)  6200 ohm

Answer: (3)

4. In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 μ All values in the circuit are in μF.

(1)   

(2)   

(3)   

(4)   

Answer: (1)

5. The mean intensity of radiation on the surface of the Sun is about 108 W/m2. The rms value of the corresponding magnetic field is closet to:

(1)  102\T

(2)  104 T

(3)  1 T

(4)  102 T

Answer: (2)

6. In a radioactive decay chain, the initial nucleus is  At the end there are 6 α-particles and particles which are emitted. If the end nucleus is  A and Z are given by :

(1) A = 200; Z = 81

(2) A = 202; Z = 80

(3) A = 208; Z = 80

(4) A = 208; Z = 82

Answer: (4)

7. The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is ‘I(x)’. Which one of the graphs represents the variation of I(x) with x correctly?

(1)  

(2) 

(3) 

(4) 

Answer: (3)

8. A simple harmonic motion is represented by :

The amplitude and time period of the motion are:

(1)    

(2)    

(3)   

(4)   

Answer: (1)

9. In the given circuit diagram, the currents, I1 = −3 A, I4 = 0.8 A and I5 = 0.4 A, are flowing as shown. The currents I2, I3 and I6, respectively, are :

(1) 1.1 A, 0.4 A, 0.4 A

(2) 1.1 A, – 0.4 A, 0.4 A

(3) 0.4 A, 1.1 A, 0.4 A

(4) –0.4 A, 0.4 A, 1.1 A

Answer: (1)

10. When a certain photosensistive surface is illuminated with monochromatic light of frequency v, the stopping potential for the photo current is –V0/2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is –V0 . The threshold frequency for photoeletric emission is:

(1)  3v/2

(2)   

(3)  5v/3

(4)  2 v

Answer: (1)

11. A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle’s apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now th load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8.

The new value of increase in length of the steel wire is:

(1)  4.0 mm

(2)  zero

(3)  5.0 mm

(4)  3.0 mm

Answer: (4)

12. A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is a height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be:

(Take g = 10 m/s2)

(1)  2 kg-m2/s

(2)  3 kg-m2/s

(3)  8 kg-m2/s

(4)  6 kg-m2/s

Answer: (4)

13. Formation of real image using a biconvex lens is shown below:

If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

(1) Erect real image

(2) No change

(3) Image disappears

(4) Magnified image

Answer: (3)

14. A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 ms–1, at right angles to the horizontal component of the earth’s magnetic field, of 0.3×10–4 Wb/m2. The value of the induced emf in wire is:

(1)  1.1 × 103 V

(2)  0.3 × 103 V

(3)  2.5 × 103 V

(4)  1.5 × 103 V

Answer: (1)

15. An alpha-particle of mass m suffers 1-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is:

(1)  1.5 m

(2)  3.5 m

(3)  4 m

(4)  2 m

Answer: (3)

16. To double the covering range of a TV transmission tower, its height should be multiplied by:

(1)  √2

(2)  2

(3)  1/√2

(4)  4

Answer: (4)

17. A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is:

[Take g = 10 m/s2]

(1)  1/2

(2)  √3/2

(3)  √3/4

(4)  2/3

Answer: (2)

18. A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by:

(1) 

(2) 

(3) 

(4) 

Answer: (*)

19. A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be:

(1)  1.2

(2)  0.1

(3)  0.4

(4)  2.0

Answer: (4)

20. A plano-convex lens (focal length f2 , refractive index μ2, radius of curvature R) fits exactly into a planoconcave lens(focal length f1 , refractive index μ 1 radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:

(1)  f1 – f2

(2)   

(3)   

(4)  f1 + f2

Answer: (2)

21. In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to

(1)  1700 nm

(2)  2020 nm

(3)  250 nm

(4)  220 nm

Answer: ()

22. Two satellites, A and B, have masses m and 2 m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2 R around the earth. The ratio of their kinetic energies, T­A/TB is

(1)  1

(2)  1/2

(3)  2

(4)   

Answer: (1)

23. An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is 6 × 10–8 If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to

(1)  2 × 107 s

(2)  3 × 106 s

(3)  0.5 × 108 s

(4)  4 × 108 s

Answer: (4)

24. 

In the above circuit,  R2 = 20 Ω,  and R1 = 10 Ω. Current in L-R1 path is I1 and in C-R2 path it is I2. The voltage of A.C. source is given by

V = 200√2 sin(100 t) volts. The phase difference between I1and I2 is

(1)  0°

(2)  60°

(3)  30°

(4)  90°

Answer: ()

25. A paramagnetic material has 1028 atoms/m3. Its magnetic susceptibility at temperature 350 K is 2.8 × 10–4. Its susceptibility at 300 K is

(1)  3.726 × 104

(2)  3.672 × 104

(3)  2.672 × 104

(4)  3.267 × 104

Answer: (4)

26. Let I, r, c and v represent inductance, resistance, capacitance and voltage, respectively. The dimension of 1/rcv in SI units will be

(1)  [A1]

(2)  [LA−2]

(3)  [LT2]

(4)  [LTA]

Answer: (1)

27. The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure

What is the value of current at t = 4 s?

(1)  2 μA

(2)  zero

(3)  3 μA

(4)  1.5 μA

Answer: (2)

28. A parallel plate capacitor with plates of area 1 m2 each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is:

(1)  8.85 × 1010 C

(2)  9.85 × 1010 C

(3)  6.85 × 1010 C

(4)  7.85 × 1010 C

Answer: (1)

29. Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure

The relative velocity   

(1)    

(2)    

(3)  

(4)   

Answer: ()

30. A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is   repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to

(1)  322 ms1

(2)  341 ms1

(3)  328 ms1

(4)  335 ms1

Answer: (3)

CHEMISTRY

1. An open vessel at 27°C is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is

(1)  750°C

(2)  750 K

(3)  500°C

(4)  500 K

Answer: (4)

2. Given

Based on the above thermochemical equations, find out which one of the following algebraic relationships is correct?

(1) x = y – z

(2) x = y + z

(3) y = 2z – x

(4)  z = x + y

Answer: (2)

3. The increasing order of the reactivity of the following with LiAlH4 is

(1) (A) < (B) < (C) < (D)

(2) (B) < (A) < (D) < (C)

(3) (A) < (B) < (D) < (C)

(4) (B) < (A) < (C) < (D)

Answer: (3)

4. Among the following, the false statement is

(1) Tyndall effect can be used to distinguish between a colloidal solution and a true solution.

(2) Latex is a colloidal solution of rubber particles which are positively charged

(3) Lyophilic sol can be coagulated by adding an electrolyte.

(4) It is possible to cause artificial rain by throwing electrified sand carrying charge opposite to the one on clouds from an aeroplane.

Answer: (2)

5. The major product of the following reaction is

Answer: (4)

6. The magnetic moment of an octahedral homoleptic Mn(II) complex is 5.9 BM. The suitable ligand for this complex is

(1)  CO

(2)  Ethylenediamine

(3)  NCS

(4)  CN

Answer: (3)

7. The major product of the following reaction is

(1) 

(2) 

(3) 

(4) 

Answer: (2)

8. If Ksp of Ag2CO3 is 8 × 1012, the molar solubility of Ag2CO3 in 0.1 M AgNO3 is

(1)  8 × 1011 M

(2)  8 × 1012 M

(3)  8 × 1013 M

(4)  8 × 1010 M

Answer: (4)

9. for NaCl, HCl and NaA are 126.4, 425.9 and 100.5 S cm2mol–1, respectively. If the conductivity of 0.001 M HA is 5 × 10–5 S cm–1, degree of dissociation of HA is

(1)  0.25

(2)  0.125

(3)  0.50

(4)  0.75

Answer: (2)

10. The major product of the following reaction is

Answer: ()

11. The aldehydes which will not form Grignard product with one equivalent Grignard reagent are

(1) (B), (C)

(2) (B), (D)

(3) (B), (C), (D)

(4) (C), (D)

Answer: (2)

12. For a reaction, consider the plot of In k versus 1/T given in the figure. If the rate constant of this reaction at 400 K is 10–5 s–1, then the rate constant at 500 K is

(1) 4 × 10–4 s–1

(2) 10–6 s–1

(3) 2 × 10–4 s–1

(4) 10–4 s–1

Answer: (4)

13. The major product of the following reaction is

Answer: (4)

14. The compound that is NOT a common component of photochemical smog is:

(1)   

(2)  CH2 = CHCHO

(3)  CF2Cl2

(4)  O3

Answer: (3)

15. The major product in the following conversion is

Answer: (3)

16. The major product of the following reaction is

Answer: (3)

17. Molecules of benzoic acid (C6H5 COOH) dimerise in benzene. ‘w’ g of the acid dissolved in 30 g of benzene shows a depression in freezing point equal to 2 K. If the percentage association of the acid to form dimer in the solution is 80, then w is

(Given that Kf =5 K kg mol1, Molar mass of benzoic acid = 122 g mol1)

(1)  1.5 g

(2)  2.4 g

(3)  1.8 g

(4)  1.0 g

Answer: (2)

18. Chlorine on reaction with hot and concentrated sodium hydroxide gives

(1)  Cl and ClO

(2)  Cl and ClO2

(3)  ClO3 and ClO2

(4)  Cl and ClO3

Answer: (4)

19. The correct statement(s) among I to III with respect to potassium ions that are abundant within the cell fluids is/are

I. They activate many enzymes

II. They participate in the oxidation of glucose to produce ATP

III. Along with sodium ions, they are responsible for the transmission of nerve signals

(1) I and III only

(2) I, II and III

(3) III only

(4) I and II only

Answer: (2)

20. If the de Broglie wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5 πa0 (a0 is Bohr radius), then the value of n/z is

(1)  0.40

(2)  1.50

(3)  0.75

(4)  1.0

Answer: (3)

21. The volume strength of 1M H2O2 is

(Molar mass of H2O2 = 34 g mol1)

(1)  11.35

(2)  22.4

(3)  5.6

(4)  16.8

Answer: (1)

22. The correct order of atomic radii is

(1) Ce > Eu > Ho > N

(2) N > Ce > Eu > Ho

(3) Eu > Ce > Ho > N

(4) Ho > N > Eu > Ce

Answer: (3)

23. The element that does NOT show catenation is

(1)  Sn

(2)  Ge

(3)  Pb

(4)  Si

Answer: (3)

24. The two monomers for the synthesis of nylon 6, 6 are

(1)  HOOC(CH2)6COOH, H2N(CH2)4NH2

(2)  HOOC(CH2)6COOH, H2N(CH2)6NH

(3)  HOOC(CH2)4COOH, H2MN(CH2)6NH2

(4)  HOOC(CH2)4COOH, H2N(CH2)4NH2

Answer: (3)

25. The pair that does NOT require calcination is

(1)  Fe2O3 and CaCO3 ∙ MgCO3

(2)  ZnCO3 and CaO

(3)  ZnO and MgO

(4)  ZnO and Fe2O3 ∙ xH2O

Answer: (3)

26. The upper stratosphere consisting of the ozone layer protects us from the sun’s radiation that falls in the wavelength region of

(1)  200 – 315 nm

(2)  600 – 750 nm

(3)  400 – 500 nm

(4)  0.8 – 1.5 nm

Answer: (1)

27. The combination of plots which does not represent isothermal expansion of an ideal gas is

(1) (A) and (C) (2)

(A) and (D)

(3) (B) and (C)

(4) (B) and (D)

Answer: (4)

28. 8 g of NaOH is dissolved in 18 g of H2 Mole fraction of NaOH in solution and molality (in mol kg–1) of the solution respectively are

(1)  0.2, 22.20

(2)  0.167, 22.20

(3)  0.167, 11.11

(4)  0.2, 11.11

Answer: (3)

29. The element that shows greater ability of form pπ – pπ multipole bonds, is

(1)  Sn

(2)  Si

(3)  Ge

(4)  C

Answer: (4)

30. The correct structure of histidine in a strongly acidic solution (pH = 2) is

(1) 

(2) 

(3) 

(4) 

Answer: (4)

MATHEMATICS

1. In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither of NCC nor for NSS is

(1)  5/6

(2)  1/3

(3)  1/6

(4)  2/3

Answer: (3)

2. Let  be three unit vectors, out of which vectors  are non-parallel. If α and β are the angles which vector  makes with vectors  respectively and  the |α – β| is equal to

(1)  90°

(2)  45°

(3)  30°

(4)  60°

Answer: (3)

3. If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30° and the angle of depression of reflection of the cloud in the lake from P be 60°, then the height of the cloud (in meters) from the surface of the lake is

(1)  45

(2)  50

(3)  42

(4)  60

Answer: (2)

4. The tangent to the curve y = x2 – 5x + 5, parallel to the line 2y = 4x + 1, also passes through the point

(1)  (1/4, 7/2)

(2)  (1/8, −7)

(3)  (7/2, 1/4)

(4)  (−1/8, 7)

Answer: (2)

5. If  ; then for all  det (A) lies in the interval:

(1)  (1, 5/2]

(2)  (0, 3/2]

(3)  [5/2, 4)

(4)  (3/2, 3]

Answer: (4)

6. In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is

(1)    

(2)  0

(3)    

(4)   

Answer: (2)

7. If a curve passes through the point (1, –2) and has slope of the tangent at any point (x, y) on it as  then the curve also passes through the point

(1)  (−1, 2)

(2)  (√3, 0)

(3)  (3, 0)

(4)  (−√2, 1)

Answer: (2)

8. If sin4α + 4 cos4β + 2 = 4√2 sin α cos β; α, β ∈[0, π], then cos(α + β) – cos(α – β) is equal to

(1)  √2

(2)  −√2

(3)  −1

(4)  0

Answer: (2)

9. The integral  is equal to

(1)   

(2)   

(3)    

(4)   

Answer: (1)

10. Let S and Sʹ be the foci of an ellipse and B be any one of the extremities of its minor axis. If ∆SʹBS is a right angled triangle with right angle at B and area (∆SʹBS) = 8 sq. units, then the length of a latus rectum of the ellipse is

(1)  4√2

(2)  4

(3)  2√2

(4)  2

Answer: (2)

11. Let f be a differentiable function such that f (1) = 2 and f ʹ(x) = f(x) for all x ∈ If h(x) = f(f (x)), then hʹ (1) is equal to

(1)  2e

(2)  2e2

(3)  4e

(4)  4e2

Answer: (3)

12. If the function f given by f (x) = x3 – 3 (a – 2)x2 + 3ax + 7, for some a ∈ R is increasing in (0, 1] and decreasing n [1, 5), then a root of the equation,  is:

(1)  −7

(2)  5

(3)  6

(4)  7

Answer: (4)

13. There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is

(1)  9

(2)  7

(3)  11

(4)  12

Answer: (4)

14. Let Z be the set of integers.

If  and

B = {x ∈ Z : −3 < 2x – 1 < 9}, then the number of subsets of the set A × B is

(1)  215

(2)  212

(3)  218

(4)  210

Answer: (1)

15. The expression ~(~p → q) is logically equivalent to

(1)  p ⋀ q

(2)  p ⋀ ~ q

(3)  ~ p ⋀ ~ q

(4)  ~ p ⋀ ~ q

Answer: (3)

16. The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations, is

(1)  5

(2)  7

(3)  3

(4)  1

Answer: (2)

17. Let S be the set of all real values of λ such that a plane passing through the points (−λ2, 1, 1), (1, −λ2, 1) and (1, 1, −λ2) also passes through the point (–1, –1, 1). Then S is equal to

(1)  {1, −1}

(2)  {√3}

(3)  {√3, −√3}

(4)  {3, −3}

Answer: (3)

18. If an angle between the line,  and the plane, x – 2y – kz = 3 is  then a value of k is

(1)   

(2)    

(3)  −5/3

(4)  −3/5

Answer: (2)

19. Let z1 and z2 be two complex numbers satisfying |z1| = 9 and |z2 – 3 – 4i | = 4. Then the minimum value of |z1 – z2| is

(1)  0

(2)  √2

(3)  1

(4)  2

Answer: (1)

20. The number of integral values of m for which the quadratic expression, (1 + 2m)x2 – 2(1 + 3m)x + 4(1 + m), x ∈ R, is always positive, is:

(1)  8

(2)  3

(3)  6

(4)  7

Answer: (4)

21. If nC4, nC5 and nC6 are in A.P., then n can be :

(1)  12

(2)  9

(3)  14

(4)  11

Answer: (3)

22. If a circle of radius R pases through the origin O and intersects the coordinate axes at A and B, then the locus of the foot of perpendicular from O on AB is:

(1) (x2 + y2)2 = 4Rx2y2

(2) (x2 + y2)2 = 4R2x2y2

(3) (x2 + y2)3 = 4R2x2y2

(4) (x2 + y2)(x + y) = R2xy

Answer: (3)

23.  is equal to:

(1)  π/4

(2)  tan1(3)

(3)  tan1 (2)

(4)  π/2

Answer: (3)

24. The integral  is equal to (where C is a constant of integration)

(1)    

(2)    

(3)    

(4)   

Answer: (3)

25. The equation of a tangent to the parabola, x2 = 8y, which makes an angle θ with the positive direction of x-axis, is:

(1) x = y cot θ – 2tan θ

(2) y = x tan θ + 2cot θ

(3) x = y cot θ + 2tan θ

(4) y = x tan θ – 2cot θ

Answer: (3)

26. If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is:

(1)  3x – 4y + 25 = 0

(2) 4x – 3y + 24 = 0

(3) x – y + 7 = 0

(4) 4x + 3y = 0

Answer: (2)

27. is equal to :

(1)    

(2)    

(3)    

(4)    

Answer: (1)

28. If the sum of the first 15 terms of the series  is equal to 225 k, then k is equal to :

(1)  108

(2)  27

(3)  9

(4)  54

Answer: (2)

29. The total number of irrational terms in the binomial expansion of (71/5 – 31/10)60 is :

(1)  48

(2)  49

(3)  54

(4)  55

Answer: (3)

30. The set of all values of λ for which the system of linear equations

x – 2y – 2z = λx

x + 2y + z = λy

–x – y = λz

(has a non-trivial solution)

(1) Contains exactly two elements

(2) Contains more than two elements

(3) Is a singleton

(4) Is an empty set

Answer: (3)

JEE MAIN-2019 Online CBT Mode Dt. 11.01.2019 Morning Question Paper With Answer Key

JEE MAIN-2019 Online CBT Mode Dt. 11.01.2019 Morning

PHYSICS

1. An amplitude modulated signal is given by V(t) = 10 [1 + 0.3cos (2.2 × 104t)] sin(5.5 × 105t). Here t is in seconds. The sideband frequencies (in kHz) are, [Given π =22/7]

(1)  1785 and 1715

(2)  178.5 and 171.5

(3)  89.25 and 85.75

(4)  892.5 and 857.5

Answer: (3)

2. In the circuit shown,

the switch S1 is closed at time t = 0 and the switch S2 is kept open. At some later time(t0), the switch S1 is opened and S2 is closed. The behaviour of the

current I as a function of time ‘t ’ is given by

(1)  

(2) 

(3) 

(4) 

Answer: (3)

3. The force of interaction between two atoms is given by  where x is the distance, k is the Boltzmann constant and T is temperature and α and β are two constants. The dimension of β is

(1)  M0L2T4

(2)  M2LT4

(3)  MLT2

(4)  M2L2T2

Answer: (2)

4. The given graph shows variation (with distance r from centre) of

(1) Potential of a uniformly charged spherical shell

(2) Electric field of a uniformly charged sphere

(3) Electric field of uniformly charged spherical shell

(4) Potential of a uniformly charged sphere

Answer: (1)

5. A particle is moving along a circular path with a constant speed of 10 ms–1. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60° around the centre of the circle?

(1)  10 m/s

(2)  Zero

(3)  10√3 m/s

(4)  10√2 m/s

Answer: (1)

6. A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980 Å. The radius of the atom in the excited state, in terms of Bohr radius a0, will be

(hc = 12500 eV-Å)

(1)  4a0

(2)  9a0

(3)  25a0        

(4)  16a0

Answer: (4)

7. Two equal resistances when connected in series to a battery, consume electric power of 60 W. If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be

(1)  60 W

(2)  30 W

(3)  120 W

(4)  240 W

Answer: (4)

8. Three charges Q, +q and +q are placed at the vertices of a right-angle isosceles triangles as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is

(1)    

(2)  +q

(3)  −2q

(4)    

Answer: (1)

9. In a Wheatstone bridge (see fig.), Resistances P and Q are approximately equal. When R = 400 Ω, the bridge is balanced. On interchanging P and Q, the value of R, for balance, is 405 Ω. The value of X is close to

(1)  404.5 ohm

(2)  401.5 ohm

(3)  402.5 ohm

(4)  403.5 ohm

Answer: (3)

10. There are two long co-axial solenoids of same length l. The inner and outer coils have radii r1 and r2 and number of turns per unit length n1 and n2, respectively. The ratio of mutual inductance to the self inductance of the inner-coil is

(1)    

(2)   

(3)    

(4)   

Answer: (2)

11. The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if Dm is the angle of minimum deviation?

(1)  

(2) 

(3) 

(4)  

Answer: (1)

12. A particle undergoing simple harmonic motion has time dependent displacement given by  The ratio of kinetic to potential energy of this particle at t = 210 s will be

(1)  1

(2)  3

(3)  2   

(4)  1/9

Answer: (*)

13. In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6 × 10–19 C, Mass of the electron = 9.1 × 10–31 kg]

(1)  7.5 × 103 m

(2)  7.5 m

(3)  7.5 × 102 m

(4)  7.5 × 104 m

Answer: (2)

14. An equilateral triangle ABC is cut from a thin solid sheet of wood. (See figure) D, E and F are the midpoints of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I0. If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. Then

(1)    

(2)    

(3)    

(4)   

Answer: (2)

15. A body is projected at t = 0 with a velocity 10 ms–1 at an angle of 60° with the horizontal. The radius of curvature of its trajectory at t = 1 s is R. Neglecting air resistance and taking acceleration due to gravity g = 10 ms–2, the value of R is

(1)  5.1 m

(2)  2.5 m

(3)  2.8 m

(4)  10.3 m

Answer: (3)

16. Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450t – 9x) where distance and time are measured in SI units. The tension in the string is

(1)  10 N

(2)  7.5 N

(3)  5 N

(4)  12.5 N

Answer: (4)

17. A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only translational and rotational modes, the total internal energy of the system is

(1)  4RT

(2)  12RT

(3)  15RT

(4)  20 RT

Answer: (3)

18. In the figure shown below, the charge on the left plate of the 10 μF capacitor is –30 μ The charge on the right plate of the 6 μF capacitor is

(1)  +18 μC

(2)  −12 μC

(3)  +12 μC

(4)  −18 μC

Answer: (1)

19. An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be

(1) 0.92 × 10–3 m/s away from the lens

(2) 2.26 × 10–3 m/s away from the lens

(3) 1.16 × 10–3 m/s towards the lens

(4) 3.22 × 10–3 m/s towards the lens

Answer: (3)

20. A slab is subjected to two forces  of same magnitude F as shown in the figure. Force  is in XY-plane while force F1 acts along z-axis at the point  moment of these forces about point O will be

(1)   

(2)    

(3)    

(4)    

Answer: (1)

21. An electromagnetic wave of intensity 50 Wm–2 enters in a medium of refractive index ‘n’ without any loss. The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by

(1)   

(2)   

(3)     

(4)    

Answer: (2)

22. A liquid of density ρ is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be

(1)    

(2)   

(3)    

(4)    

Answer: (1)

23. The resistance of the metre bridge AB in given figure is 4 Ω. With a cell of emf ε = 0.5 V and rheostat resistance Rh = 2 Ω the null point is obtained at some point J. When the cell is replaced by another one of emf ε = ε2 the same null point J is found for Rh = 6 Ω.The emf ε2 is

(1)  0.6 V

(2)  0.5 V

(3)  0.3 V

(4)  0.4 V

Answer: (3)

24. A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25 × 106 N/m. The body sticks to the platform and the spring’s maximum compression is found to be x. Given that g = 10 ms–2, the value of x will be close to

(1)  80 cm

(2)  8 cm

(3)  4 cm

(4)  40 cm

Answer: (*)

25. In a Young’s double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is 1/8th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to

(1)  0.74

(2)  0.94

(3)  0.80

(4)  0.85

Answer: (4)

26. A satellite is revolving in a circular orbit at a height h from the earth surface, such that h << R where R is the radius of the earth. Assuming that the effect of earth’s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is

(1)    

(2)   

(3)    

(4)    

Answer: (2)

27. In the given circuit the current through Zener Diode is close to

(1)  6.7 mA

(2)  0.0 mA

(3)  4.0 mA

(4)  6.0 mA

Answer: (2)

28. A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TVx = constant, then x is

(1)  2/5

(2)  2/3

(3)  5/3

(4)  3/5

Answer: (1)

29. Ice at –20°C is added to 50 g of water at 40°C. When the temperature of the mixture reaches 0°C, it is found that 20 g of ice is still unmelted. The amount off ice added to the water was close to (Specific heat of water = 4.2 J/g/°C Specific heat of Ice = 2.1 J/g/°C Heat of fusion of water at 0°C = 334 J/g)

(1)  100 g

(2)  40 g

(3)  50 g

(4)  60 g

Answer: (2)

30. If the deBroglie wavelength of an electron is equal to 10–3 times the wavelength of a photon of frequency 6 × 1014 Hz, then the speed of electron is equal to :

(Speed of light = 3 × 108 m/s

Planck’s constant = 6.63 × 10–34 J-s

Mass of electron = 9.1 × 10–31 kg)

(1)  1.7 × 106 m/s

(2)  1.45 × 106 m/s

(3)  1.8 × 106 m/s

(4)  1.1 × 106 m/s

Answer: (2)

CHEMISTRY

1. Match the ores (column A) with the metals (column B):

(Column A)            (Column B)

Ores                        Metals

(I) Siderite               (a) Zinc

(II) Kaolinite           (b) Copper

(III) Malachite         (c) Iron

(IV) Calamine         (d) Aluminium

(1) (I) – (a); (II) – (b); (III) – (c); (IV) – (d)

(2) (I) – (c); (II) – (d); (III) – (a); (IV) – (b)

(3) (I) – (c); (II) – (d); (III) – (b); (IV) – (a)

(4) (I) – (b); (II) – (c); (III) – (d); (IV) – (a)

Answer: (3)

2. The concentration of dissolved oxygen (DO) in cold water can go upto:

(1)  14 ppm

(2)  16 ppm

(3)  10 ppm

(4)  8 ppm

Answer: (3)

3. The freezing point of a diluted milk sample is found to be –0.2°C, while it should have been –0.5°C for pure milk. How much water has been added to pure milk to make the diluted sample?

(1) 3 cups of water and 2 cups of pure milk

(2) 1 cup of water and 2 cups of pure milk

(3) 2 cups of water to 3 cups of pure milk

(4) 1 cup of water to 3 cups of pure milk

Answer: (1)

4. The correct match between item (I) and item (II) is:

Item – I                             Item – II

(A) Norethindrone            (P) Anti-biotic

(B) Ofloxacin                   (Q) Anti-fertility

(C) Equanil                       (R) Hypertension

(S) Analgesics

(1) (A) → (R) ; (B) → (P) ; (C) → (R)

(2) (A) → (R) ; (B) → (P) ; (C) → (S)

(3) (A) → (Q) ; (B) → (P) ; (C) → (R)

(d) (A) → (Q) ; (B) → (R) ; (C) → (S)

Answer: (3)

5. The major product of the following reaction is

Answer: (2)

6. The major product of the following reaction is:

 

(2)

(3) 

(4) 

Answer: (1)

7. The chloride that CANNOT get hydrolysed is:

(1)  PbCl4

(2)  CCl4

(3)  SnCl4

(4)  SiCl4

Answer: (2)

8. If a reaction follows the Arrhenius equation, the plot Ink vs  gives straight line with a gradient (–y) unit. The energy required to activate the reactant is:

(1)  yR unit

(2)  y/R unit

(3)  −y unit

(4)  y unit

Answer: (4)

9. The major product of the following reaction is

(1)  

(2) 

(3)  

(4)  

Answer: (3)

10. The major product of the following reaction is:

Answer: (4)

11. A solid having density of 9 × 103 kg m–3 forms face centred cubic crystals of edge length 200√2 pm. What is the molar mass of the solid?

[Avogadro constant ≅ 6 × 1023 mol–1, π ≅ 3 ]

(1)  0.0305 kg mol1

(2)  0.4320 kg mol1

(3)  0.0432 kg mol1

(4)  0.0216 kg mol1

Answer: (1)

12. The correct match between items I and II is

Item-I (Mixture)                                 Item-II

(Separation method)

(A) H2O : Sugar                                  (P) Sublimation

(B) H2O : Aniline                                (Q) Recrystallization

(C) H2O : Toluene                               (R) Steam distillation

(S) Differential extraction

(1) (A) → (R), (B) → (P), (C) → (S)

(2) (A) → (S), (B) → (R), (C) → (P)

(3) (A) → (Q), (B) → (R), (C) → (P)

(4) (A) → (Q), (B) → (R), (C) → (S)

Answer: (4)

13. The correct order of the atomic radii of C, Cs, Al, and S is

(1) S < C < Al < Cs

(2) C < S < Cs < Al

(3) S < C < Cs < Al

(4) C < S < Al < Cs

Answer: (4)

14. For the cell Zn(s)|Zn2+(aq)||Mx+(aq)| M(s), different half cells and their standard electrode potentials are given below

If  which cathode will give a maximum value of

cell per electron transferred?

(1)  Fe2+/Fe

(2)  Ag+/Ag

(3)  Fe3+/Fe2+

(4)  Au3+/Au

Answer: (4)

15. Consider the reaction

N2(g) + 3H2(g) ⇌ 2NH3 (g)

The equilibrium constant of the above reaction is KP. If pure ammonia is left to dissociate, the partial pressure of ammonia at equilibrium is given by (Assume that  at equilibrium)

(1)    

(2)    

(3)    

(4)    

Answer: (4)

16. For the chemical reaction X ⇌ Y, the standard reaction Gibbs energy depends on temperature T (in K) as 

The major component of the reaction mixture at T is

(1) Y if T = 280 K

(2) X if T = 315 K

(3) X if T = 300 K

(4) X if T = 350 K

Answer: (2)

17. An organic compound is estimated through Dumas method and was found to evolve 6 moles of CO2, 4 moles of H2O and 1 mole of nitrogen gas. The formula of the compound is

(1)  C6H8N

(2)  C­12H8N

(3)  C6H8N

(4)  C12H8N2

Answer: (1)

18. Match the metals (column I) with the coordination compound(s)/enzyme(s) (column II)

(Column I)                                (Column II)

                                                      Metals Coordination

                                                       compound(s)/

                                                       enzyme(s)

(A) Co                                        (i) Wilkinson catalyst

(B) Zn                                        (ii) Chlorophyll

(C) Rh                                        (iii) Vitamin B12

(D) Mg                                       (iv) Carbonic anhydrase

(1)  (A) – (iv), (B) – (iii), (C) – (i), (D) – (ii)

(2) (A) – (i), (B) – (ii), (C) – (iii), (D) – (iv)

(3) (A) – (ii), (B) – (i), (C) – (iv), (D) – (iii)

(4) (A) – (iii), (B) – (iv), (C) – (i), (D) – (ii)

Answer: (4)

19. Two blocks of the same metal having same mass and at temperature T1 and T2, respectively, are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure. The change in entropy, ∆S, for this process is

(1)    

(2)    

(3)    

(4)    

Answer: (2)

20. The correct statements among (a) to (d) regarding H2 as a fuel are

(a) It produces less pollutants than petrol.

(b) A cylinder of compressed dihydrogen weighs ~ 30 times more than a petrol tank producing the same amount of energy.

(c) Dihydrogen is stored in tanks of metal alloys like NaNi5.

(d) On combustion, values of energy released per gram of liquid dihydrogen and LPG are 50 and 142 kJ, respectively.

(1)  (b) and (d) only

(2) (a) and (c) only

(3) (b), (c) and (d) only

(4)  (a), (b) and (c) only

Answer: (4)

21. The element that usually does NOT show variable oxidation states is

(1)  Cu

(2)  Ti

(3)  V

(4)  Sc

Answer: (4)

22. Among the following compounds, which one is found in RNA?

Answer: (4)

23. The polymer obtained from the following reactions is

Answer: (1)

24. NaH is an example of

(1)  Metallic hydride

(2)  Electron –rich hydride

(3)  Molecular hydride

(4)  Saline hydride

Answer: (4)

25. The amphoteric hydroxide is

(1)  Mg(OH)2

(2)  Be(OH)2

(3)  Sr(OH)2

(4)  Ca(OH)2

Answer: (2)

26. Which compound(s) out of following is/are not aromatic?

(1) (B), (C) and (D)

(2) (A) and (C)

(3) (C) and (D)

(4) (B)

Answer: (1)

27. Peroxyacetyl nitrate (PAN), an eye irritant is produced by

(1)  Classical smog

(2)  Acid rain

(3)  Organic waste

(4)  Photochemical smog

Answer: (4)

28. A 10 mg effervescent tablet containing sodium bicarbonate and oxalic acid releases 0.25 ml of CO2 at T = 298.15 K and p = 1 bar. If molar volume of CO2 is 25.0 L under such condition, what is the percentage of sodium bicarbonate in each tablet?

[Molar mass of NaHCO3 = 84 g mol–1]

(1)  33.6

(2)  8.4

(3)  0.84

(4)  16.8

Answer: (2)

29. Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this purpose?

[RH= 1 × 105 cm, h = 6.6 × 10–34 Js, c = 3 × 108 ms–1]

(1)  Balmer, ∞ → 2

(2)  Lyman, ∞ → 1

(3)  Paschen, 5 → 3

(4)  Paschen, ∞ → 3

Answer: (4)

30. An example of solid sol is.

(1)  Butter

(2)  Hair cream

(3)  Paint

(4)  Gem stones

Answer: (4)

MATHEMATICS

1. Let  and g(x) = | f(x)|+f(|x|). Then, in the interval (–2, 2), g is

(1) not differentiable at two points

(2) not differentiable at one point

(3) not continuous

(4) differentiable at all points

Answer: (2)

2. The plane containing the line  and also containing its projection on the plane 2x + 3y – z = 5, contains which one of the following points?

(1) (0, –2, 2)

(2) (2, 2, 0)

(3) (–2, 2, 2)

(4) (2, 0, –2)

Answer: (4)

3. Let f : R → R be defined by  Then the range of f is

(1)  R – [−1/2, 1/2]

(2)  [−1/2, 1/2]

(3)  [–1, 1) – {0}

(4)  R – [–1, 1]

Answer: (2)

4. The outcome of each of 30 items was observed; 10 items gave an outcome  each, 10 items gave outcome 1/2 each and the remaining 10 items gave outcome . If the variance of this outcome data is 4/3 then |d| equals.

(1)  √2

(2)  √5/2

(3)  2/3

(4)  2

Answer: (1)

5. Let  and  be coplanar vectors. Then the none-zero vector  is:

(1)   

(2)   

(3)    

(4)   

Answer: (4)

6. The area (in sq. units) of the region bounded by the curve x2 = 4y and the straight line x = 4y – 2 is

(1)  7/8

(2)  5/4

(3)  9/8

(4)  3/4

Answer: (3)

7. Let a1, a2, …, a10 be a G.P. If  equals

(1)  53

(2)  54

(3)  2(52)

(4)  4(52)

Answer: (2)

8. If the system of linear equations

2x + 2y + 3z = a

3x – y + 5z = b

x – 3y + 2z = c

where a, b, c are non-zero real numbers, has more than one solution, then

(1) b – c + a = 0

(2)  b + c – a = 0

(3) a + b + c = 0

(4) b – c – a = 0

Answer: (4)

9. The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is

(1)  √5/4

(2)  √5/2

(3)  4√5

(4)  2√5

Answer: (2)

10 Let [x] denote the greatest integer less than or equal to x. Then

(1)  equals 0

(2)  equals π + 1

(3)  equals π

(4)  does not exist

Answer: (4)

11. Let  If AAT = I3, then |p| is:

(1)  1/√3

(2)  1/√6

(3)  1/√5

(4)  1/√2

Answer: (4)

12. Two circles with equal radii are intersecting at the points (0, 1) and (0, –1). The tangent at the point (0, 1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is:

(1)  1

(2)  √2

(3)  2√2

(4)  2

Answer: (4)

13. The value of r for which 20Cr 20C0 + 20Cr – 1 20C1 + 20Cr – 2 20C2+ … + 20C0 20Cr is maximum, is :

(1)  10

(2)  20

(3)  15

(4)  11

Answer: (2)

14. If x loge (loge x) – x2 + y2 = 4 (y > 0), then dy/dx at x = e is equal to :

(1)   

(2)    

(3)    

(4)    

Answer: (1)

15. If  for a suitable chosen integer m and a function A(x), where C is a constant of integration, then (A(x))m equals:

(1)  −1/3x3

(2)  1/27x6

(3)  1/9x4

(4)  −1/27x9

Answer: (4)

16. Two integers are selected at random from the set {1, 2, …, 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:

(1)  3/5

(2)  7/10

(3)  1/2

(4)  2/5

Answer: (4)

17. Equation of a common tangent to the parabola y2 = 4x and the hyperbola xy = 2 is:

(1)  4x + 2y + 1 = 0

(2)  x + 2y + 4 = 0

(3)  x – 2y + 4 = 0

(4)  x + y + 1 = 0

Answer: (2)

18. If tangents are drawn to the ellipse x2 + 2y2 = 2 at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve:

(1)    

(2)    

(3)    

(4)   

Answer: (4)

19. A square is inscribed in the circle x2 + y2 – 6x + 8y – 103 = 0 with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is:

(1)  6

(2)  √41

(3)  13

(4)  √137

Answer: (2)

20. In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If x2 – c2 = y, where c is the length of the third side of the triangle, then the circum radius of the triangle is:

(1)  c/√3

(2)   

(3)  c/3

(4)  y/√3

Answer: (1)

21. Let  where x and y are real numbers, the y – x equals

(1)  −85

(2)  −91

(3)  85

(4)  91

Answer: (4)

22. If q is false and p ⋀ q ↔ r is true, then which one of the following statements is a tautology?

(1)  p ⋁ r

(2)  (p ⋀ r) → (p ⋁ r)

(3)  (p ⋁ r) → (p ⋀ r)

(4)  p ⋀ r

Answer: (2)

23. If y(x) is the solution of the differential equation  then

(1)  y(x) is decreasing in (1/2, 1)

(2)   

(3)  y(loge 2) = log­e 4

(4)  y(x) is decreasing in (0, 1)

Answer: (1)

24. The direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) and making an angle π/4 with the plane y – z + 5 = 0 are

(1)  2√3, 1, −1

(2)  2, √2, −√2

(3)  2, −1, 1

(4)  √2, 1, −1

Answer: (2, 4)

25. The maximum value of the function f(x) = 3x3 – 18x2 + 27x – 40 on the set S = {x ∈ R: x2 + 30 ≤ 11x} is

(1)  122

(2)  −122

(3)  222

(4)  −222

Answer: (1)

26. Let  for k = 1, 2, 3, …. Then for all x ∈ R, the value of f4(x) – f6(x) is equal to

(1)  −1/12

(2)  1/12

(3)  5/12

(4)  1/4

Answer: (2)

27. The sum of the real values of x for which the middle term in the binomial expansion of  equals 5670 is

(1)  4

(2)  8

(3)  0

(4)  6

Answer: (3)

28. The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is 27/19. Then the common ratio of this series is

(1)  1/3

(2)  2/9

(3)  2/3

(4)  4/9

Answer: (3)

29. The value of the integral  (where [x] denotes the greatest integer less than or equal to x) is

(1)  sin 4

(2)  4 – sin 4

(3)  0

(4)  4

Answer: (3)

30. If one real root of the quadratic equation 81x2 + kx + 256 = 0 is cube of the other root, then a value of k is

(1)  −300

(2)  144

(3)  −81

(4)  100

Answer: (1)

JEE MAIN-2019 Online CBT Mode Dt. 11.01.2019 Evening Question Paper With Answer Key

JEE MAIN-2019 Online CBT Mode Dt. 11.01.2019 Evening

PHYSICS

1. A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 × 10–6 J/T when a magnetic intensity of 60 × 103 A/m is applied. Its magnetic susceptibility is

(1)  3.3 × 102

(2)  2.3 × 102

(3)  3.3 × 104

(4)  4.3 × 102

Answer: (3)

2. An electric field of 1000 V/m is applied to an electric dipole at angle of 45°. The value of electric dipole moment is 10–29 Cm. What is the potential energy of the electric dipole?

(1)  –9 × 10–20 J

(2)  –10 × 10–29 J

(3)  –7 × 10–27 J

(4)  –20 × 10–18 J

Answer: (3)

3. A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is

(1) 

(2)   

(3)    

(4)   

Answer: (2)

4. A metal ball of mass 0.1 kg is heated upto 500°C and dropped into a vessel of heat capacity 800 JK–1 and containing 0.5 kg water. The initial temperature of water and vessel is 30°C. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, 4200 Jkg–1K–1 and 400 Jkg–1K–1]

(1)  25%

(2)  20%

(3)  30%

(4)  15%

Answer: (2)

5. The region between y = 0 and y = d contains a magnetic field  A particle of mass m and charge q enters the region with a velocity  if  the acceleration of the charged particle at the point of its emergence at the other side is

(1)   

(2)   

(3)    

(4)    

Answer: (Bonus)

6. A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string) :

(1)  16 rad/s2

(2)  20 rad/s2

(3)  12 rad/s2

(4)  10 rad/s2

Answer: (1)

7. A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of 10–2 The relative change in the angular frequency of the pendulum is best given by

(1)  103 rad/s

(2)  10−1 rad/s

(3)  10−5 rad/s

(4)  1 rad/s

Answer: (1)

8. If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young’s modulus will be

(1)  V2A2F2

(2)  V2A2F2

(3)  V4A2F

(4)  V4A2F

Answer: (3)

9. When 100 g of a liquid A at 100°C is added to 50 g of a liquid B at temperature 75°C, the temperature of the mixture becomes 90°C. The temperature of the mixture, if 100 g of liquid A at 100°C is added to 50 g of liquid B at 50°C, will be

(1)  85°C

(2)  80°C

(3)  70°C

(4)  60°C

Answer: (2)

10. A 27 mW laser beam has a cross-sectional area of 10 mm2. The magnitude of the maximum electric field in this electromagnetic wave is given by:

[Given permittivity of space ∈0 = 9 × 1012 SI units, Speed of light c = 3 × 108 m/s]

(1)  1.4 kV/m

(2)  1 kV/m

(3)  2 kV/m

(4)  0.7 kV/m

Answer: (1)

11. The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be:

(1)    

(2)   

(3) 

(4)   

Answer: (4)

12. In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is λ. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:

(1)    

(2)    

(3)   

(4)    

Answer: (3)

13. In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to : 

(1)  1.0 V

(2)  2.0 V

(3)  1.5 V

(4)  0.5 V

Answer: (1)

14. Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180°C and B upto T°C, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value f T is:

(1)  270°C

(2)  230°C

(3)  250°C

(4)  200°C

Answer: (2)

15. In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process, the temperature of the gas is increased by ∆ The amount of heat absorbed by gas is (R is gas constant):

(1)    

(2)    

(3)    

(4)   

Answer: (2)

16. A galvanometer having a resistance of 20 Ω and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is:

(1)  100 Ω

(2)  125 Ω

(3)  80 Ω

(4)  120 Ω

Answer: (3)

17. A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and x0 /3 when in contact with ice. What is the temperature of an object in °C, if this thermometer in the contact with the object reads x0 /2?

(1)  40

(2)  60

(3)  35

(4)  25

Answer: (4)

18. In the circuit shown, the potential difference between A and B is:

(1)  6 V

(2)  3 V

(3)  2 V

(4)  1 V

Answer: (3)

19. An amplitude modulated signal is plotted below:

Which one of the following best describes the above signal?

(1) (9 + sin(2π × 104t))sin(2.5π × 105t) V

(2) (9 + sin(4π × 104t))sin(5π × 105t) V

(3) (1 + 9sin(2π × 104t))sin(2.5π × 105t) V

(4) (9 + sin(2.5π  × 105t))sin(2π × 104t) V

Answer: (1)

20. In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance of 40 cm from A. If a 10 Ω resistor is connected in series with R1, the null point shifts by 10 cm. The resistance that should be connected in parallel with (R1 + 10) Ω such that the null point shifts back to its initial position is:

(1)  60 Ω

(2)  30 Ω

(3)  40 Ω

(4)  20 Ω

Answer: (1)

21. A particle of mass m and charge q is in an electric and magnetic field given by

The charged particle is shifted from the origin to the point P(x = 1 ; y = 1) along a straight path. The magnitude of the total work done is:

(1)  (0.15)q

(2)  (5q)

(3)  (0.35)q

(4)  (2.5)q

Answer: (2)

22. Seven capacitors, each of capacitance 2 μF, are to be connected in a configuration to obtain an effective capacitance of (6/13) μ Which of the combinations, shown in figures below, will achieve the desired value?

(1) 

(2)  

(3) 

(4) 

Answer: (1)

23. A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K2. Then

(1)  K2 = 2K1

(2)  K2 = K1/4

(3)  K2 = K1

(4)  K2 = K1/2

Answer: (1)

24. A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is √3, then the angle of incidence is:

(1)  90°

(2)  30°

(3)  45°

(4)  60°

Answer: (4)

25. In a double-slit experiment, green light (5303 Å) falls on a double slit having a separation of 19.44 μm and a width of 4.05 μ The number of bright fringes between the first and the second diffraction minima is

(1)  05

(2)  09

(3)  10

(4)  04

Answer: (4)

26. A particle moves from the point  at t = 0, with an initial velocity   It is acted upon by a constant force which  produces a constant acceleration  What is the distance of the particle form the origin at time 2 s

(1)  20√2 m

(2)  15 m

(3)  10√2 m

(4)  5 m

Answer: (1)

27. The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N, and the distance of the particle from the origin is 5 m, the angle between the force and the position vector is (in radians):

(1)  π/8

(2)  π/6

(3)  π/3

(4)  π/4

Answer: (2)

28. A circular disc D1 of mass M and radius R has two identical discs D2 and D3 of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OOʹ, passing through the centre of D1 as shown in the figure, will be:

(1)  3MR2

(2)   

(3)  MR2

(4)   

Answer: (1)

29. The circuit shown below contains two ideal diodes, each with a forward resistance of 50Ω. If the battery voltage is 6 V, the current through the 100 Ω resistance (in amperes) is:

(1)  0.036

(2)  0.020

(3)  0.030

(4)  0.027

Answer: (2)

30. A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil:

(1) Increases by a factor of 3

(2) Decreases by a factor of 9√3

(3) Decreases by a factor of 9

(4) Increases by a factor of 27

Answer: (1)

CHEMISTRY

1. Given the equilibrium constant :

KC of the reaction :

Cu(s) + 2Ag+ (aq) → Cu2+ (aq) + 2Ag(s) is 10 × 1015, calculate the E0 cell of this reaction at 298 K

(1)  0.4736 mV

(2)  0.4736 V

(3)  0.04736 V

(4)  0.04736 mV

Answer: (2)

2. Among the colloids cheese (C), milk (M) and smoke (S), the correct combination of the dispersed phase and dispersion medium, respectively is :

(1) C : solid in liquid; M : liquid in liquid; S : gas in solid

(2) C : liquid in solid; M : liquid in solid; S : solid in gas

(3) C : liquid in solid; M : liquid in liquid; S : solid in gas

(4) C : solid in liquid; M : solid in liquid; S : solid in gas

Answer: (3)

3. The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is : (Edge length is represented by ‘a’)

(1)  0.027 a

(2)  0.047 a

(3)  0.067 a

(4)  0.134 a

Answer: (3)

4. The reaction 2X → B is a zeroth order reaction. If the initial concentration of X is 0.2 M, the half-life is 6 h. When the initial concentration of X is 0.5 M, the time required to reach its final concentration of 0.2 M will be :

(1)  12.0 h

(2)  7.2 h

(3)  9.0 h

(4)  18.0 h

Answer: (4)

5. In the following compound,

the favourable site/s protonation is/are :

(1) (a)

(2) (b), (c) and (d)

(3) (a) and (d)

(4)  (a) and (e)

Answer: (2)

6. The major product obtained in the following conversion is :

(1) 

(2)  

(3)  

(4)  

Answer: ()

7. K2 HgI4 is 40% ionised in aqueous solution. The value of its van’t Hoff factor (i) is :

(1)  1.6

(2)  2.0

(3)  2.2

(4)  1.8

Answer: (4)

8. Match the following items in column I with the corresponding items in column II.

Column-I                         Column-II

(i) Na2CO3.10H2O   (A) Portland cement ingredient

(ii) Mg(HCO3)2             (B) Castner-Kellner process

(iii) NaOH               (C) Solvay process

(iv) Ca3Al2O6                    (D) Temporary hardness

(1) (i)(B), (ii)(C), (iii)(A), (iv)(D)

(2) (i)(C), (ii)(D), (iii)(B), (iv)(A)

(3) (i)(D), (ii)(A), (iii)(B), (iv)(C)

(4) (i)(C), (ii)(B), (iii)(D), (iv)(A)

Answer: (2)

9. The de Broglie wavelength (λ) associated with a photoelectron varies with the frequency (ν) of the incident radiation as, [ν0is threshold frequency]:

(1)    

(2)    

(3)   

(4)    

Answer: (3)

10. The correct option with respect to the Pauling electronegativity values of the elements is:

(1)  Si < Al

(2)  P > S

(3)  Te > Se

(4)  Ga < Ge

Answer: (4)

11. The correct match between Item I and Item II is:

Item I                               Item II

(A) Ester test                             (P) Tyr

(B) Carbylamine test        (Q) AsP

(C) Phthalein dye test       (R) Ser

(S) Lys

(1) (A) → (Q); (B) →  (S); (C) → (P)

(2) (A) → (R); (B) → (Q); (C) → (P)

(3) (A) → (Q); (B) → (S); (C) → (R)

(4) (A) → (R); (B) → (S); (C) → (Q)

Answer: (1)

12. The correct match between Item I and Item II is:

Item I

(A) Allosteric effect

(B) Competitive

(C) Receptor

(D) Poison

Item II

(P) Molecule binding to the active site of enzyme

(Q) Molecule crucial for inhibitor communication in the body

(R) Molecule binding to a site other than the active site of  enzyme

(S) Molecule binding to the enzyme covalently

(1)  (A) → (P); (B) → (R); (C) → (S); (D) → (Q)

(2)  (A) → (R); (B) → (P); (C) → (Q); (D) → (S)

(3)  (A) → (P); (B) → (R); (C) → (Q); (D) → (S)

(4)  (A) → (R); (B) → (C); (C) → (D); (D) → (Q)

Answer: (2)

13. Which of the following compounds will produce a precipitate with AgNO3 ?

(1) 

(2)  

(3)  

(4) 

Answer: (4)

14. The number of bridging CO ligand(s) and Co-Co bond(s) in Co2(CO)8, respectively are:

(1)  2 and 1

(2)  0 and 2

(3)  2 and 0

(4)  4 and 0

Answer: (1)

15. The major product obtained in the following reaction is:

(1) 

(2)  

(3) 

(4) 

Answer: (1)

16. 

In the above sequence of reactions, A and D, respectively, are :

(1)  KI and K2MnO4

(2)  KIO3 and MnO2

(3)  MnO2 and KIO3

(4)  KI and KMnO4

Answer: (3)

17. The major product of the following reaction is :

(1)  

(2)  

(3) 

(4)  

Answer: (1)

18. Taj Mahal is being slowly disfigured and discoloured. This is primarily due to :

(1)  Acid rain

(2)  Water pollution

(3)  Global warming

(4)  Soil pollution

Answer: (1)

19. The relative stability of +1 oxidation state of group 13 elements follows the order :

(1) Tl < In < Ga < Al

(2) Al < Ga < Tl < In

(3) Al < Ga < In < Tl

(4) Ga < Al < In < Tl

Answer: (3)

20. The homopolymer formed from 4-hydroxy-butanoic acids is :

(1)    

(2)    

(3)    

(4)    

Answer: (1)

21. The reaction that does NOT define calcination is:

Answer: (4)

22. Which of the following compounds reacts with ethylmagnesium bromide and also decolourizes bromine water solution?

(1)  

(2)  

(3) 

(4) 

Answer: (1 and 2)

23. The hydride that is NOT electron deficient is

(1)  SiH4

(2)  GaH3

(3)  B2H6

(4)  AlH3

Answer: (1)

24. For the equilibrium

2H2O ⇌ H3O+ + OH, the value of ∆G° at 298 K is approximately

(1)  −80 kJ mol1

(2)  −100 kJ mol1

(3)  80 kJ mol1

(4)  100 kJ mol1

Answer: (3)

25. The coordination number of Th in K4[Th(C2O4)4(OH2)2] is

(C2O42 = Oxalato)

(1)  10

(2)  6

(3)  14

(4)  8

Answer: (1)

26. A compound ‘X’ on treatment with Br2/NaOH, provided C3H9N, which gives positive carbylamines test. Compound ‘X’ is

(1)  CH3CH2CH2CONH2

(2)  CH3COCH2NHCH3

(3)  CH3CH2COCH2NH2

(4)  CH3CON(CH3)2

Answer: (1)

27. The higher concentration of which gas in air can cause stiffness of flower buds?

(1)  SO2

(2)  CO

(3)  CO2

(4)  NO2

Answer: (1)

28. The reaction

MgO(s) + C(s) → Mg(s) + CO(g), for, which ∆rH° = +491.1 kJ mol−1 and ∆sH° = 198.0 JK−1 mol−1, is not feasible at 298 K. Temperature above which reaction will be feasible is

(1)  2040.5 K

(2)  1890.0 K

(3)  2480.3 K

(4)  2380.5 K

Answer: (3)

29. 25 ml of the given HCl solution requires 30 mL of 0.1 M sodium carbonate solution. What is the volume of this HCl solution required to titrate 30 mL of 0.2 M aqueous NaOH solution

(1)  25 mL

(2)  12.5 mL

(3)  50 mL

(4)  75 mL

Answer: (1)

30. The standard reaction Gibbs energy for a chemical reaction at an absolute temperature T is given by

rG° A – BT

Where A and B are non-zero constants. Which of the following is true about this reaction?

(1) Exothermic if B < 0

(2) Endothermic if A > 0

(3) Endothermic if A < 0 and B > 0

(4) Exothermic if A > 0 and B < 0

Answer: (2)

MATHEMATICS

1. Let A and B be two invertible matrices of order 3 × 3. If det(ABAT) = 8 and det(AB–1) = 8, then det(BA–1BT) is equal to :

(1)  1

(2)  16

(3)  1/16

(4)  1/4

Answer: (3)

2. A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is :

(1)  A hyperbola

(2)  A parabola

(3)  An ellipse

(4)  A straight line

Answer: (2)

3. Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression  is

(1)  1/2

(2)    

(3)  1

(4)  1/4

Answer: (4)

4. If  (a + b + c) (x + a + b + c)2, x ≠ 0 and a + b + c ≠ 0, then x is equal to :

(1)  2(a + b+ c)

(2)  −(a + b +c)

(3)  abc

(4)  −2(a + b +c)

Answer: (4)

5. Let a function f : (0, ∞) → (0, ∞) be defined by  Then f is :

(1) Injective only

(2) Both injective as well as surjective

(3) Not injective but it is surjective

(4) Neither injective nor surjective

Answer: (*)

6. If  where C is a constant of integration, then f(x) is equal to :

(1)   

(2)    

(3)   

(4)   

Answer: (2)

7. If the area of the triangle whose one vertex is at the vertex of the parabola, y2 + 4(x – a2) = 0 and the other two vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of ‘a’ is :

(1)  5√5

(2)  (10)2/3

(3)  5(213)

(4)  5

Answer: (4)

8. Let z be a complex number such that |z| + z = 3 + i (where i = √−1).

Then |z| is equal to :

(1)  √41/4

(2)  5/4

(3)  5/3

(4)  √34/3

Answer: (3)

9. Let  where a, b and d are non-zero constants. Then :

(1) f is an increasing function of x

(2) f is a decreasing function of x

(3) f is neither increasing nor decreasing function of x

(4) fʹ is not a continuous function of x

Answer: (1)

10. Contrapositive of the statement

“If two numbers are not equal, then their squares are not equal.” is :

(1) If the squares of two numbers are equal, then the numbers are equal

(2) If the squares of two numbers are not equal, then the numbers are equal

(3) If the squares of two numbers are equal, then the numbers are not equal

(4) If the squares of two numbers are not equal, then the numbers are not equal

Answer: (1)

11. If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is :

(1) 5x + 3y – 11 = 0

(2) 3x + 5y – 13 = 0

(3) 3x – 5y + 7 = 0

(4) 5x – 3y + 1 = 0

Answer: (4)

12. is equal to :

(1)  2

(2)  4

(3)  1

(4)  0

Answer: (3)

13. Two lines  and  intersect at the point R. The reflection of R in the xy-plane has coordinates :

(1)  (–2, 4, 7)

(2) (2, 4, 7)

(3) (2, –4, –7)

 (4)  (2, –4, 7)

Answer: (3)

14. Let (x + 10)50 + (x – 10)50 = a0 + a1x + a2x2 + … + a50­x50. for all x ∈ R; then a2/a0 is equal to

(1)  12.25

(2)  12.75

(3)  12.00

(4)  12.50

Answer: (1)

15. Given  for ∆ABC with usual notation. If  then the ordered triplet (α, β, γ) has a value :

(1)  (3, 4, 5)

(2)  (7, 19, 25)

(3)  (19, 7, 25)

(4)  (5, 12, 13)

Answer: (2)

16. If 19th term of a non-zero A.P. is zero, then its (49th term) : (29th term) is :

(1)  2 : 1

(2)  1 : 3

(3)  4 : 1

(4)  3 : 1

Answer: (4)

17. The number of function f from {1, 2, 3, …,20} onto {1, 2, 3, …, 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :

(1)  56 × 15

(2)  65 × (15)!

(3)  5! × 6!

(4)  (15)! × 6!

Answer: (4)

18. The integral  equals :

(1)    

(2)   

(3)    

(4)    

Answer: (1)

19. Let α and β the roots of the quadratic equation x2 sin θ – x(sin θ cos θ +1) + cos θ = 0 (0 < θ > 45°), and α < β. Then  is equal to :

(1)   

(2)    

(3)   

(4)    

Answer: (2)

20. A bag contains 30 white ball and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then  is equal to :

(1)  3√2

(2)  4√3

(3)  4√3/3

(4)  4

Answer: (2)

21. If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :

(1)  2

(2)  13/8

(3)  13/6

(4)  13/12

Answer: (4)

22. Let Sn = 1 + q + q2 + … + qn and  where q is a real number and q ≠

If 101C1 + 101C2 ∙ S1 + … + 101C101 S100 = α T100.

(1)  200

(2)  202

(3)  299

(4)  2100

Answer: (4)

23. Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

(1)  (4√3, 2√3)

(2)  (4√3, 2√2)

(3)  (4√2, 2√2)

(4)  (4√2, 2√3)

Answer: (2)

24. Let S = {1, 2, …., 20}. A subset B of S is said to be “nice”, if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is “nice” is

(1)  7/220

(2)  6/220

(3)  4/220

(4)  5/220

Answer: (4)

25. If the point (2, α, β) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2x – 5y = 15, then 2α – 3β is equal to

(1)  5

(2)  12

(3)  17

(4)  7

Answer: (4)

26. All x satisfying the inequality (cot–1x)2 – 7 (cot–1x) + 10 > 0, lie in the interval

(1)  (cot 2, ∞)

(2)  (cot 5, cot 4)

(3)  (−∞, cot 5) ∪ (cot 4, cot 2)

(4)  (−∞, cot 5) ∪ (cot 2, ∞)

Answer: (1)

27. Let  respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is 3/√2, then the sum of all possible values of β is

(1)  3

(2)  1

(3)  4

(4)  2

Answer: (2)

28. The solution of the differential equation,  when Y(1) = 1, is

(1)   

(2)   

(3)    

(4)    

Answer: (3)

29. Let K be the set of all real values of x where the function

f(x) = sin |x| – |x| + 2(x – π) is not differentiable. Then the set K is equal to

(1)  {π}

(2)  ϕ (an empty set)

(3)  {0}

(4)  {0, π}

Answer: (2)

30. The area (in sq. units) in the first quadrant bounded by the parabola, y = x2 + 1, the tangent to it at the point (2, 5) and the coordinate axes is

(1)  187/24

(2)  8/3

(3)  14/3

(4)  37/24

Answer: (4)

JEE Main-2019 Online CBT Mode Dt.10-01.2019 Morning Question Paper With Answer Key

JEE Main-2019 Online CBT Mode Dt.10-01.2019 Morning

PHYSICS

1. To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angular speed about its axis. If the force F is distributed uniformly over the mop and if coefficient of friction between the mop and the floor is μ, the torque, applied by the machine on the mop is

(1) 

(2) 

(3) 

(4) 

Answer: (4)

2. Two electric dipoles, A, B with respective dipole moments  are placed on the x-axis with a separation R, as shown in the figure

The distance from A at which both of them produce the same potential is

(1) 

(2) 

(3) 

(4) 

Answer: (2)

3. To get output ‘1’ at R, for the given logic gate circuit the input values must be

(1)  X = 1, Y = 1

(2)  X = 0, Y = 0

(3)  X = 1, Y = 0

(4)  X = 0, Y = 1

Answer: (3)

4. A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis, is

(1)  12 mV

(2)  2 mV

(3)  6 mV

(4)  1 mV

Answer: (1)

5. A plano convex lens of refractive index μ1 and focal length f1is kept in contact with another plano concave lens of refractive index μ2 and focal length f2. If the radius of curvature of their spherical faces is R each and f1= 2f2, then μ1and μ2 are related as

(1)  2 μ1 – μ2 = 1

(2)  3μ2 – 2μ1 = 1

(3)  2μ1 – μ1 = 1

(4)  μ1 + μ2 = 3

Answer: (1)

6. Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to

(1)  400

(2)  360

(3)  150

(4)  200

Answer: (4)

7. Water flows into a large tank with flat bottom at the rate of 10–4 m3s–1. Water is also leaking out of a hole of area 1 cm2 at its bottom. If the height of the water in the tank remains steady, then this height is

(1)  5.1 cm

(2)  1.7 cm

(3)  2.9 cm

(4)  4 cm

Answer: (1)

8. A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum distance upto which signals can be broadcasted from this tower in LOS (Line of Sight) mode? (Given : radius of earth = 6.4 × 106 m)

(1)  65 km

(2)  80 km

(3)  40 km

(4)  48 km

Answer: (1)

9. A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in fig. Work done by normal reaction on block in time t is

(1) 

(2) 

(3)  0

(4) 

Answer: (1)

10. A magnet of total magnetic moment  is placed ina time varying magnetic field,  where B = 1 Tesla and ω = 0.125 rad/s. The work done for reversing the direction of the magnetic moment at t = 1 second, is

(1)  0.028 J

(2)  0.007 J

(3)  0.014 J

(4)  0.01 J

Answer: (BONUS)

11. A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is f1. If the speed of the train is reduced to 17 m/s, the frequency registered is f2. If speed of sound is 340 m/s, then the ratio f1/f2 is

(1)  21/20

(2)  20/19

(3)  18/17

(4)  19/18

Answer: (4)

12. In the given circuit the cells have zero internal resistance. The currents (in amperes) passing through resistance Rand R2 respectively, are

(1)  1, 2

(2)  0, 1

(3)  0.5, 0

(4)  2, 2

Answer: (3)

13. In a Young’s double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle 1/40 rad by using light of wavelength λ1 . When the light of wavelength λ2 is used a bright fringe is seen at the same angle in the same set up. Given that λ1 and λ2 are in visible range (380 nm to 740 nm), their values are

(1)  380 nm, 500 nm

(2)  625 nm, 500 nm

(3)  380 nm, 525 nm

(4)  400 nm, 500 nm

Answer: (2)

14. Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T2 and T3, as shown, with T1 > T2 > T3 > T4 . The three engines are equally efficient if

(1) 

(2) 

(3) 

(4) 

Answer: (4)

15. In the cube of side ‘a’ shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be

(1) 

(2) 

(3)

(4)

Answer: (1)

16. A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is

(1)  20 mA

(2)  0.4 mA

(3)  100 mA

(4)  63 mA

Answer: (1)

17. If the magnetic field of a plane electromagnetic wave is given by (The speed of light = 3 × 108 m/s)  then the maximum electric field associated with it is

(1)  6 × 104 N/C

(2)  3 × 104 N/C

(3)  4.5 × 104 N/C

(4)  4 × 104 N/C

Answer: (2)

18. A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is

(1)  F/2mR

(2)  2F/3mR

(3)  F/3mR

(4)  3F/2mR

Answer: (2)

19. A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is

(1)  2mv2

(2)  mv2

(3) 

(4) 

Answer: (2)

20. A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be

(1) 

(2) 

(3) 

(4) 

Answer: (1)

21. An insulating, thin rod of length l has a linear charge density  on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is

(1)  πnρl3

(2)  nρl3

(3) 

(4) 

Answer: (3)

22. In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10–12 m, the minimum electron energy required is close to

(1)  100 keV

(2)  1 keV

(3)  500 keV

(4)  25 keV

Answer: (4)

23. A heat source at T = 103 K is connected to another heat reservoir at T = 102 K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 WK–1m–1, the energy flux through it in the steady state is

(1)  200 Wm2

(2)  65 Wm2

(3)  120 Wm2

(4)  90 Wm2

Answer: (4)

24. The density of a material is SI units is 128 kg m–3. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is

(1)  640

(2)  410

(3)  40

(4)  16

Answer: (3)

25. Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is

(1)  1 : 4

(2)  1 : 8

(3)  1 : 2

(4)  1 : 16

Answer: (4)

26. A parallel plate capacitor is of area 6 cm2 and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants K1= 10, K2= 12 and K3 = 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be

(1)  36

(2)  14

(3)  12

(4)  4

Answer: (3)

27. A uniform metallic wire has a resistance of 18 Ω and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is

(1)  4 Ω

(2)  12 Ω

(3)  8 Ω

(4)  2 Ω

Answer: (1)

28. A potentiometer wire AB having length L and resistance 12r is joined to a cell D of emf ε and internal resistance r. A cell C having emf ε/2 and internal resistance 3r is connected. The length AJ at which the galvanometer as shown in fig. shows no deflection is

(1) 

(2) 

(3) 

(4) 

Answer: (4)

29. A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to

(1)  33.3 cm

(2)  10.0 cm

(3)  16.6 cm

(4)  20.0 cm

Answer: (4)

30. A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upwards, with a velocity 100 ms–1, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is (g = 10 ms–2)

(1)  30 m

(2)  40 m

(3)  20 m

(4)  10 m

Answer: (2)

CHEMISTRY

1. The major product of the following reaction is

(1) 

(2) 

(3) 

(4) 

Answer: (2)

2. The chemical nature of hydrogen peroxide is

(1) Oxidising and reducing agent in both acidic and basic medium

(2) Oxidising and reducing agent in acidic medium, but not in basic medium

(3) Reducing agent in basic medium, but not in acidic medium

(4) Oxidising agent in acidic medium, but not in basic medium

Answer: (1)

3. Consider the following reduction processes:

Zn2+ + 2e → Zn(s); Eº = –0.76 V

Ca2+ + 2e → Ca(s); Eº = –2.87 V

Mg2+ + 2e → Mg(s); Eº = –2.36 V

Ni2+ + 2e→ Ni(s); Eº = –0.25 V

The reducing power of the metals increases in the order :

(1) Ca < Mg < Zn < Ni

(2) Ni < Zn < Mg < Ca

(3) Ca < Zn < Mg < Ni

(4) Zn < Mg < Ni < Ca

Answer: (2)

4. Consider the given plots for a reaction obeying Arrhenius equation (0°C < T < 300°C) : (k and Ea are rate constant and activation energy, respectively)

Choose the correct option:

(1) I is wrong but II is right

(2) Both I and II are correct

(3) Both I and II are wrong

(4) I is right but II is wrong

Answer: (2)

5. The electronegativity of aluminium is similar to

(1)  Beryllium

(2)  Carbon

(3)  Lithium

(4)  Boron

Answer: (1)

6. The values of for the following reactions at 300 K are, respectively (At 300 K, RT = 24.62 dm3 atm mol–1)

N2(g) + O2(g) ⇌ 2NO(g)

N2O4(g) ⇌ 2NO2(g)

N2(g) + 3H2(g) ⇌ 2NH3(g)

(1) 24.62 dm3 atm mol–1, 606.0 dm6 atm2 mol–2, 1.65 × 10–3 dm–6 atm–2 mol2

(2) 1, 24.62 dm3 atm mol–1, 1.65 × 10–3 dm–6 atm–2 mol2

(3) 1, 24.62 dm3 atm mol–1, 606.0 dm6 atm2 mol–2

(4) 1, 4.1 × 10–2 dm–3 atm–1 mol, 606 dm6 atm2 mol–2

Answer: (2)

7. Liquids A and B form an ideal solution in the entire composition range. At 350 K, the vapor pressures of pure A and pure B are 7 × 103 Pa and 12 × 103 Pa, respectively. The composition of the vapor in equilibrium with a solution containing 40 mole percent of A at this temperature is

(1)  xA = 0.76; xB = 0.24

(2)  xA = 0.37; xB = 0.63

(3)  xA = 0.28; xB = 0.72

(4)  xA = 0.4; xB = 0.6

Answer: (3)

8. If dichloromethane (DCM) and water (H2O) are used for differential extraction, which one of the following statements is correct?

(1) DCM and H2O will make turbid/colloidal mixture

(2) DCM and H2O will be miscible clearly

(3) DCM and H2O would stay as upper and lower layer respectively in the separating funnel (S.F.)

(4) DCM and H2O would stay as lower and upper layer respectively in the S.F.

Answer: (4)

9. The type of hybridisation and number of lone pair(s) of electrons of Xe in XeOF4, respectively, are

(1)  sp3d and 2

(2)  sp3d2 and 2

(3)  sp3d2 and 1

(4)  sp3d and 1

Answer: (3)

10. Wilkinson catalyst is (Et = C2H5)

(1)  [(Ph3P)3lrCl]

(2)  [(Ph3P)3RhCl]

(3)  [(Et3P)3lrCl]

(4)  [(Et3P)3RhCl]

Answer: (2)

11. The metal used for making X-ray tube window is

(1)  Ca

(2)  Na

(3)  Mg

(4)  Be

Answer: (4)

12. The major product ‘X’ formed in the following reaction is

(1) 

(2) 

(3) 

(4) 

Answer: (2)

13. Hall-Heroult’s process is given by

(1) 

(2)  Cr2O3 + 2Al → Al2O3 + 2Cr

(3)  2Al2O3 + 3C → 4Al + 3CO2

(4)  Cu2+(aq) + H2(g) → Cu(s) + 2H+(aq)

Answer: (3)

14. The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively, are

(1)  2 and 1

(2)  3 and 2

(3)  2 and 0

(4)  3 and 1

Answer: (4)

15. The increasing order of the pKa values of the following compounds is

(1)  D < A < C < B

(2) B < C < D < A

(3) B < C < A < D

(4) C < B < A < D

Answer: (3)

16. The total number of isomers for a square planar complex [M(F)(Cl)(SCN)(NO2)] is

(1)  8

(2)  12

(3)  4

(4)  16

Answer: (2)

17. Which of the following is not an example of heterogeneous catalytic reaction?

(1)  Combustion of coal

(2) Ostwald’s process

(3) Hydrogenation of vegetable oils

(4) Haber’s process

Answer: (1)

18. A process had ΔH = 200 Jmol–1 and ∆S = 40 JK–1 mol–1. Out of the values given below, choose the minimum temperature above which the process will be spontaneous

(1)  4 K

(2)  12 K

(3)  5 K

(4)  20 K

Answer: (3)

19. The major product of the following reaction is

Answer: (2)

20. Which dicarboxylic acid in presence of a dehydrating agent is least reactive to give an anhydride?

(1) 

(2) 

(3) 

(4) 

Answer: (3)

21. Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface?

(1) 

(2) 

(3) 

(4) 

Answer: (4)

22. Which hydrogen in compound (E) is easily replaceable during bromination reaction in presence of light?

(1) γ-hydrogen

(2) α-hydrogen

(3) δ-hydrogen

(4) β-hydrogen

Answer: (1)

23. Water filled in two glasses A and B have BOD values of 10 and 20, respectively. The correct statement regarding them, is

(1) Both A and B are suitable for drinking

(2) A is suitable for drinking, whereas B is not

(3) B is more polluted than A

(4) A is more polluted than B

Answer: (3)

24. The major product formed in the reaction given below will be

(1) 

(2) 

(3) 

(4) 

Answer: (*)

25. The correct structure of product ‘P’ in the following reaction is

(1) 

(2) 

(3) 

(4) 

Answer: (4)

26. The effect of lanthanoid contraction in the lanthanoid series of elements by and large means

(1)  Increase in atomic radii and decrease in ionic radii

(2) Decrease in atomic radii and increase in ionic radii

(3)  Decrease in both atomic and ionic radii

(4) Increase in both atomic and ionic radii

Answer: (3)

27. A mixture of 100 m mol of Ca(OH)2 and 2 g of sodium sulphate was dissolved in water and the volume was made up to 100 mL. The mass of calcium sulphate formed and the concentration of OH in resulting solution, respectively, are (Molar mass of Ca(OH)2, Na2 SO4and CaSO4 are 74, 143 and 136 g mol–1, respectively; Ksp of Ca(OH)2 is 5.5 × 10–6)

(1)  1.9 g, 0.14 mol L1

(2)  13.6 g, 0.28 mol L1

(3)  13.6 g, 0.14 mol L1

(4)  1.9 g, 0.28 mol L1

Answer: (4)

28. Two pi and half sigma bonds are present in

(1)  O2+

(2)  O2

(3)  N2+

(4)  N2

Answer: (3)

29. Which primitive unit cell has unequal edge lengths (a ≠ b ≠ c) and all axial angles different from 90°?

(1)  Hexagonal

(2)  Monoclinic

(3)  Triclinic

(4)  Tetragonal

Answer: (3)

30. The decreasing order of ease of alkaline hydrolysis for the following esters is

(1) III > II > IV > I

(2) IV > II > III > I

(3) II > III > I > IV

(4) III > II > I > IV

Answer: (4)

MATHEMATICS

1. Let d ∈ R, and  θ ∈[0, 2π]. If the minimum value of det(A) is 8, then a value f d is

(1)  −5

(2)  2(√2 + 1)

(3)  −7

(4)  2(√2 + 2)

Answer: (1)

2. If a circle C passing through the point (4, 0) touches the circle x2 + y2 + 4x – 6y = 12 externally at the point (1, –1), then the radius of C is

(1)  5

(2)  2√5

(3)  √57

(4)  4

Answer: (1)

3. If  then k equals

(1)  400

(2)  100

(3)  200

(4)  50

Answer: (2)

4. The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is

(1)  1465

(2)  1356

(3)  1365

(4)  1256

Answer: (2)

5. If  and   equals

(1) 

(2) 

(3)  1/3

(4)  −4/3

Answer: (1)

6. Consider a triangular plot ABC with sides AB = 7 m, BC = 5 m and CA = 6 m. A vertical lamp-post at the mid point D of AC subtends an angle 30° at B. The height (in m) of the lamp-post is

(1)  2√21

(2)  7√3

(3) 

(4) 

Answer: (3)

7. Let  If I is minimum then the ordered pair (a, b) is

(1)  (−√2, 0)

(2)  (0, √2)

(3)  (√2, −√2)

(4)  (−√2, √2)

Answer: (4)

8. An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1, 2, 3, …, 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is

(1)  13/36

(2)  15/72

(3)  19/36

(4)  19/72

Answer: (4)

9. Consider the quadratic equation (c – 5)x2 – 2cx + (c – 4) = 0, c ≠ Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is

(1)  11

(2)  18

(3)  12

(4)  10

Answer: (1)

10. If the line 3x + 4y – 24 = 0 intersects the x-axis at the point A and the y-axis at the point B, then the incentre of the triangle OAB, where O is the origin is

(1)  (4, 3)

(2)  (3, 4)

(3)  (4, 4)

(4)  (2, 2)

Answer: (4)

11. If the third term in the binomial expansion of  equals 2560, then a possible value of x is

(1)  2√2

(2)  1/4

(3)  4√2

(4)  1/8

Answer: (2)

12. Let z1 and z2 be any two non-zero complex numbers such that 3|z1| = 4|z2|. If  then

(1)  lm(z) = 0

(2) 

(3) 

(4)  Re(z) = 0

Answer: (*)

13. The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is

(1)  4 : 9

(2)  6 : 7

(3)  10 : 3

(4)  5 : 8

Answer: (1)

14. Let 

Let S be the set of points in the interval (–4, 4) at which f is not differentiable. Then S

(1) Equals {–2, –1, 0, 1, 2}

(2) Equals {–2, 2}

(3) Is an empty set

(4) Equals {–2, –1, 1, 2}

Answer: (1)

15. Consider the statement : “P(n) : n2 – n + 41” is prime.” Then which one of the following is true?

(1) P(5) is false but P(3) is true

(2) P(3) is false but P(5) is true

(3) Both P(3) and P(5) are false

(4) Both P(3) and P(5) are true

Answer: (4)

16. A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R(3, –2) are fixed points, then the locus of the centroid of ∆PQR is a line

(1)  Parallel to y-axis

(2)  With slope 3/2

(3)  With slope 2/3

(4)  Parallel to x-axis

Answer: (3)

17. If the parabolas y2 = 4b(x – c) and y2 = 8ax have a common normal, then which one of the following is a valid choice for the ordered triad (a, b, c)?

(1)  (1/2, 2, 0)

(2)  (1/2, 2, 3)

(3)  (1, 1, 0)

(4)  (1, 1, 3)

Answer: (4)

18. The sum of all values of θ ∈(0, π/2) satisfying sin2 2θ + cos4 2θ = 3/4 is

(1)  5π/4

(2)  π/2

(3)  3π/8

(4)  π

Answer: (2)

19. The equation of a tangent to the hyperbola 4x2 – 5y2 = 20 parallel to the line x – y = 2 is

(1) x – y + 7 = 0

(2) x – y + 1 = 0

(3) x – y – 3 = 0

(4) x – y + 9 = 0

Answer: (2)

20. Let f : R → R be a function such that f(x) = x3 + x2f ʹ(1) + xfʹʹ (2) + f ʹ ʹ ʹ (3), ∈ x R. Then f(2) equals

(1)  8

(2)  −4

(3)  −2

(4)  30

Answer: (3)

21. If the system of equations

x + y + z = 5

x + 2y + 3z = 9

x + 3y + αz = β

has infinitely many solutions, then β – α equals

(1)  18

(2)  21

(3)  8

(4)  5

Answer: (3)

22. The shortest distance between the point (3/2, 0) and the curve y = √x, (x > 0), is

(1)  3/2

(2)  5/4

(3)  √3/2

(4)  √5/2

Answer: (4)

23. In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is :

(1)  1

(2)  38

(3)  102

(4)  42

Answer: (2)

24. Let n ≥ 2 be a natural number and 0 < θ < π/2. Then  is equal to (where C is a constant of integration)

(1) 

(2) 

(3) 

(4) 

Answer: (3)

25. The plane passing through the point (4, –1, 2) and parallel to the lines  and  also passes through the point :

(1) (–1, –1, –1)

(2) (–1, –1, 1)

(3) (1, 1, 1)

(4) (1, 1, –1)

Answer: (3)

26. If 5, 5r, 5r2 are the lengths of the sides of a triangle, then r cannot be equal to :

(1)  3/4

(2)  7/4

(3)  3/4

(4)  5/4

Answer: (2)

27. For each t∈ R, let [t] be the greatest integer less than or equal to t. Then,

(1)  Equals 0

(2)  Equals 1

(3)  Equals −1

(4)  Does not exist

Answer: (1)

28. Let  and  be three vectors such that  is perpendicular to  Then a possible value of (λ1, λ2, λ3) is :

(1)  (1, 3, 1)

(2)  (1, 5, 1)

(3)  (1/2, 4, −2)

(4)  (−1/2, 4, 0)

Answer: (4)

29. If the area enclosed between the curves y = kx2 and x = ky2, (k > 0), is 1 square unit. Then k is :

(1)  √3

(2)  1/√3

(3)  √3/2

(4)  2/√3

Answer: (2)

30. Let A be a point on the line  and B(3, 2, 6) be a point in the space. Then the value of μ for which the vector  is parallel to the plane x – 4y + 3z = 1 is :

(1)  1/4

(2)  1/2

(3)  1/8

(4)  −1/4

Answer: (1)

JEE MAIN 2019 Online CBT Mode DT. 10.01.2019 Evening Question Paper With Answer Key

JEE MAIN 2019 Online CBT Mode DT. 10.01.2019 Evening

PHYSICS

1. The modulation frequency of an AM radio station is 250 kHz, which is 10% of the carrier wave. If another AM station approaches you for license what broadcast frequency will you allot?

(1)   2750 kHz

(2)   2900 kHz

(3)   2000 kHz

(4)   2250 kHz

Answer: (3)

2. At some location on earth the horizontal component of earth’s magnetic field is 18 × 10–6 At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes 45° angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is:

(1)   1.3 × 10–5 N

(2)   1.8 × 10–5 N

(3)   6.5 × 10–5 N

(4)   3.6 × 10–5 N

Answer: (3)

3. The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as R1 has the colour code (Orange, Red, Brown). The resistors R2 and R4 are 80 Ω and 40 Ω

(1)   Brown, Blue, Black

(2)   Red, Green, Brown

(3)   Grey, Black, Brown

(4)   Brown, Blue, Brown

Answer: (4)

4. Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and (0, –2). The work required to put a fifth charge Q at the origin of the coordinate system will be:

(1) 

(2) 

(3) 

(4) 

Answer: (4)

5. The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by an expression

The magnetic field  is given by : (c is the velocity of light)

(1) 

(2) 

(3) 

(4) 

Answer: (4)

6. Charges –q and +q located at A and B, respectively, constitute an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to Pʹ such that OPʹ = (y/3), the force on Q will be close to : (y/3 >> 2a)

(1)   F/3

(2)   9F

(3)   27F

(4)   3F

Answer: (3)

7. A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency ω. If the radius of the bottle is 2.5 cm then ω is close to: (density of water = 103 kg/m3)

(1)   2.50 rad s1

(2)   3.75 rad s1

(3)   5.00 rad s1

(4)   1.25 rad s1

Answer: (BONUS)

8. Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20°C to 90°C. Work done by gas is close to :

(Gas constant R = 8.31 J/mol K)

(1)   291 J

(2)   581 J

(3)   146 J

(4)   73 J

Answer: (1)

9. A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th and Tc respectively, then

(1)   Th = 0.5Tc

(2)   Th = Tc

(3)   Th = 2Tc

(4)   Th = 1.5Tc

Answer: (2)

10. For the circuit shown below, the current through the Zener diode is:

(1)   Zero

(2)   9 mA

(3)   14 mA

(4)   5 mA

Answer: (2)

11. An unknown metal of mass 192 g heated to a temperature of 100°C was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4°C. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5°C. (Specific heat of brass is 394 J kg–1K–1)

(1)   916 J kg–1K–1

(2)   1232 J kg–1K–1

(3)   654 J kg–1K–1

(4)   458 J kg–1K–1

Answer: (1)

12. The actual value of resistance R, shown in the figure is 30 Ω. This is measured in an experiment as shown using the standard formula R = V/ I, where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is 5% less, then the internal resistance of the voltmeter is:

(1)   570 Ω

(2)   600 Ω

(3)   350 Ω

(4)   35 Ω

Answer: (1)

13. The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1 s, the change in the energy of the inductance is:

(1)   437.5 J

(2)   740 J

(3)   637.5 J

(4)   540 J

Answer: (1)

14. A particle which is experiencing a force, given by  undergoes a displacement  of  If the particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement?x

(1)   15 J

(2)   9 J

(3)   12 J

(4)   10 J

Answer: (1)

15. A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is :

(1)   560 pJ

(2)   692 pJ

(3)   508 pJ

(4)   600 pJ

Answer: (3)

16. Two  vectors have equal magnitudes. The magnitude of  is ‘n’ times the magnitude of 

(1) 

(2) 

(3) 

(4) 

Answer: (2)

17. Consider the nuclear fission

Ne20 → 2He4 + C12

Given that the binding energy/nucleon of Ne20, He4 and C12 are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement:

(1)   Energy of 12.4 MeV will be supplied

(2)   8.3 MeV energy will be released

(3)   Energy of 3.6 MeV will be released

(4)   Energy of 11.9 MeV has to be supplied

Answer: (BONUS)

18. A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be : (Assume that the highest frequency a person can hear is 20,000 Hz)

(1)   7

(2)   4

(3)   6

(4)   5

Answer: (3)

19. A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11 V is connected across it is

(1)   11 × 105 W

(2)   11 × 105 W

(3)   11 × 103 W

(4)   11 × 104 W

Answer: (1)

20. A metal plate of area 1 × 10–4 m2 is illuminated by a radiation of intensity 16 mW/m2. The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only 10% of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be : [1 eV = 1.6 × 10–19 J]

(1)   1014 and 10 eV

(2)   1011 and 5 eV

(3)   1010 and 5 eV

(4)   1012 and 5 eV

Answer: (2)

21. Two kg of a monoatomic gas is at a pressure of 4 × 104 N/m2. The density of the gas is 8 kg/m3. What is the order of energy of the gas due to its thermal motion ?

(1)   103 J

(2)   105 J

(3)   104 J

(4)   106 J

Answer: (3)

22. A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be :

(1)   g/2l

(2)   g/3l

(3)   g/13l

(4)   7g/3l

Answer: (3)

23. Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is :

(1) 

(2) 

(3) 

(4) 

Answer: (4)

24. A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is

(1)   4π/3

(2) 

(3)   8π/3

(4) 

Answer: (3)

25. Consider a Young’s double slit experiment as shown in figure. What should be the slit separation d in terms wavelength λ such that the first minima occurs directly in front of the slit (S1)?

(1) 

(2) 

(3) 

(4) 

Answer: (1)

26. A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle time t = 5 s?

(1)   9 m

(2)   6 m

(3)   10 m

(4)   3 m

Answer: (1)

27. Two stars of masses 3 × 1031 kg each, and at distance 2 × 1011 m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star’s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is:

(Take Gravitational constant G = 6.67 × 10–11 Nm2 kg–2)

(1)   2.8 × 105 m/s

(2)   1.4 × 105 m/s

(3)   2.4 × 104 m/s

(4)   3.8 × 104 m/s

Answer: (1)

28. Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle θ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle θ is:

(1)   30°

(2)   90°

(3)   60°

(4)   120°

Answer: (4)

29. The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separates two media of refractive indices 1 and 1.34, Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.

(1)   4.0 cm

(2)   1 cm

(3)   3.1 cm

(4)   2 cm

Answer: (3)

30. The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1 cm and 34.2 ± 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures?

(1)   4264 ± 81 cm3

(2)   4300 ± 80 cm3

(3)   4260 ± 80 cm3

(4)   4264.4 ± 81.0 cm3

Answer: (3)

CHEMISTRY

1. The process with negative entropy change is :

(1) Sublimation of dry ice

(2) Dissociation of CaSO4 (s) to CaO(s) and SO3(g)

(3) Synthesis of ammonia from N2and H2

(4) Dissolution of iodine in water

Answer: (3)

2. An aromatic compound ‘A’ having molecular formula C7H6O2 on treating with aqueous ammonia and heating forms compound ‘B’. The compound ‘B’ on reaction with molecular bromine and potassium hydroxide provides compound ‘C’ having molecular formula C6H7 The structure ‘A’ is :

(1) 

(2) 

(3) 

(4) 

Answer: (3)

3. The ground state energy of hydrogen atom is –13.6 eV. The energy of second excited state of He+ ion in eV is :

(1)   −27.2

(2)   −6.04

(3)   −54.4

(4)   −3.4

Answer: (2)

4. In the cell

Pt(s)|H2(g,1bar)|HCl(aq)|AgCl(s)|Ag(s)|Pt(s) the cell potential is 0.92 V when a 10–6 molal HCl solution is used. The standard electrode potential of (AgCl/Ag,Cl) electrode is:

(1)   0.20 V

(2)   0.40 V

(3)   0.76 V

(4)   0.94 V

Answer: (1)

5. The correct match between item ‘I’ and item ‘II’ is :

Item ‘I’                                       Item ‘II’

(compound)                               (reagent)

(A) Lysine                        (P) 1-naphthol

(B) Furfural                      (Q) ninhydrin

(C) Benzyl alcohol            (R) KMnO4

(D) Styrene                       (S) Ceric ammonium nitrate

(1)   (A) → (R); (B) → (P); (C) → (Q); (D) → (S)

(2)   (A) → (Q); (B) → (P); (C) → (S); (D) → (R)

(3)   (A) → (Q); (B) → (R); (C) → (S); (D) → (P)

(4)   (A) → (Q); (B) → (P); (C) → (R); (D) → (S)

Answer: (2)

6. Among the following reactions of hydrogen with halogens, the one that requires a catalyst is :

(1)   H2 + Cl2 → 2HCl

(2)   H2 + I2 → 2HI

(3)   H2 + Br2 → 2HBr

(4)   H2 + F2 → 2HF

Answer: (2)

7. The electrolytes usually used in the electroplating of gold and silver, respectively, are :

(1) [Au(CN)2] and [AgCl2]

(2) [Au(NH3)2]+ and [Ag(CN)2]

(3) [Au(CN)2] and [Ag(CN)2]–

(4) [Au(OH)4] and [Ag(OH)2]

Answer: (3)

8. The major product of the following reaction is :

(1) 

(2) 

(3) 

(4) 

Answer: (1)

9. A reaction of cobalt (III) chloride and ethylenediamine in a 1 : 2 mole ratio generates two isomeric products A (violet coloured) and B (green coloured). A can show optical activity, but, B is optically inactive. What type of isomers does A and B represent?

(1)   Ionisation isomers

(2)   Coordination isomers

(3)   Geometrical isomers

(4)   Linkage isomers

Answer: (3)

10. Sodium metal on dissolution in liquid ammonia gives a deep blue solution due to the formation of

(1)   Ammoniated electrons

(2)   Sodium-ammonia complex

(3)   Sodium ion-ammonia complex

(4)   Sodamide

Answer: (1)

11. In the reaction of oxalate with permanganate in acidic medium, the number of electrons involved in producing one molecule of CO2 is

(1)   1

(2)   10

(3)   2

(4)   5

Answer: (1)

12. 5.1 g NH4SH is introduced in 3.0 L evacuated flask at 327ºC. 30% of the solid NH4SH decomposed to NH3 and H2S as gases. The Kp of the reaction at 327ºC is (R = 0.082 L atm mol–1K–1, Molar mass of S = 32 g mol–1, molar mass of N = 14 g mol–1)

(1)   4.9 × 103 atm2

(2)   0.242 atm2

(3)   1 × 104 atm2

(4)   0.242 × 104 atm2

Answer: (2)

13. What will be the major product in the following mononitration reaction?

(1) 

(2) 

(3) 

(4) 

Answer: (2)

14. The number of 2-centre-2-electron and 3-centre-2-electron bonds in B2H6 respectively are:

(1)   4 and 2

(2)   2 and 2

(3)   2 and 4

(4)   2 and 1

Answer: (1)

15. The 71st electron of an element X with an atomic number of 71 enters into the orbital:

(1)   5 d

(2)   6 p

(3)   4 f

(4)   6 s

Answer: (1)

16. Which of the following tests cannot be used for identifying amino acids?

(1)   Barfoed test

(2)   Biuret test

(3)   Xanthoproteic test

(4)   Ninhydrin test

Answer: (1)

17. The amount of sugar (C12H22O11) required to prepare 2L of its 0.1 M aqueous solution is:

(1)   136.8 g

(2)   17.1 g

(3)   34.2 g

(4)   68.4 g

Answer: (4)

18. The major product obtained in the following reaction is:

(1) 

(2) 

(3) 

(4) 

Answer: (4)

19. The difference in the number of unpaired electrons of a metal ion in its high spin and low-spin octahedral complexes is two. The metal ion is:

(1)   Ni2+

(2)   Mn2+

(3)   Fe2+

(4)   Co2+

Answer: (1)

20. Haemoglobin and gold sol are examples of :

(1)   negatively charged sols

(2)   positively charged sols

(3)   positively and negatively charged

(4)   negatively and positively charged sols, respectively

Answer: (3)

21. For an elementary chemical reaction,

the expression for 

(1)   k1[A2] + k–1[A]2

(2)   2k1[A2] – 2k–1[A]2

(3)   2k1[A2] – k–1[A]2

(4)   k1[A2] – k–1[A]2

Answer: (2)

22. What is the IUPAC name of the following compound?

(1)   3-Bromo-1, 2-dimethylbut-1-ene

(2)   4-Bromo-3-methylpent-2-ene

(3)   3-Bromo-3-methyl-1, 2- dimethylprop-1-ene

(4)   2-Bromo-3-methylpent-3-ene

Answer: (2)

23. An ideal gas undergoes isothermal compression from 5 m3 to 1 m3 against a constant external pressure of 4 Nm-2. Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 J mol-1K-1, the temperature of Al increases by:

(1) 

(2)   1 K

(3)   2 K

(4) 

Answer: (4)

24. The pair that contains two P-H bond in each of the oxoacids is :

(1)   H4P2O5 and H4P2O6

(2)   H4P2O5 and H3PO3

(3)   H3PO2 and H4P2O5

(4)   H3PO3 and H3PO2

Answer: (3)

25. The major product of the following reaction

(1) 

(2) 

(3) 

(4) 

Answer: (1)

26. Elevation in the boiling point for 1 molal solution of glucose is 2 K. The depression in the freezing point for 2 molal solution of glucose in the same solvent is 2 K. The relation between Kb and Kf is :

(1)   Kb = 0.5 Kf

(2)   Kb = 2 Kf

(3)   Kb = 1.5 Kf

(4)   Kb = Kf

Answer: (2)

27. A compound of formula A2B3 has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedral voids is occupied by the other atoms:

(1)   hcp lattice – B, 1/3 Tetrahedral voids – A

(2)   hcp lattice – A, 2/3 Tetrahedral voids – B

(3)   hcp lattice – B, 2/3 Tetrahedral voids – A

(4)   hcp lattice – A, 1/3 Tetrahedral voids – B

Answer: (1)

28. The reaction that is NOT involved in the ozone layer depletion mechanism in the stratosphere is :

(1) 

(2)  

(3) 

(4) 

Answer: (2)

29. Which is the most suitable reagent for the following transformation?

(1)   I2/NaOH

(2)   Alkaline KMnO4

(3)   Tollen’s reagent

(4)   CrO2Cl2/CS2

Answer: (1)

30. The major product of the following reaction is :

Answer: (4)

MATHEMATICS

1. Let  and  be two given vectors where vectors   are non-collinear. The value of λ for which vectors  are collinear, is

(1)   −3

(2)   −4

(3)   3

(4)   4

Answer: (2)

2. If the area of an equilateral triangle inscribed in the circle, x2 + y2 + 10x + 12y + c = 0 is 27√3 sq. units

(1)   13

(2)   25

(3)   −25

(4)   20

Answer: (2)

3. The number of values of θ ∈ (0, π) for which the system of linear equations

x + 3y + 7z = 0

– x + 4y + 7z = 0

(sin3θ)x + (cos2θ)y + 2z = 0

has a non-trivial solution, is:

(1)   Four

(2)   One

(3)   Three

(4)   Two

Answer: (4)

4. The positive value of λ for which the co-efficient of x2 in the expression  is  720, is

 

(1)   3

(2)   4

(3)   √5

(4)   2√2

Answer: (2)

5. The plane which bisects the line segment joining the points (–3, –3, 4) and (3, 7, 6) at right angles, passes through which one of the following points?

(1)   (–2, 3, 5)

(2)   (4, 1, –2)

(3)   (2, 1, 3)

(4)   (4, –1, 7)

Answer: (2)

6. Let  If R(z) and I(z) respectively denote the real and imaginary parts of z, then

(1)   I(z) = 0

(2)   R(z) > 0 and I(z) > 0

(3)   R(z) < 0 and I(z) > 0

(4)   R(z) = – 3

Answer: (1)

7. If the probability of hitting a target by a shooter, in any shot, is 1/3, then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than 5/6, is

(1)   4

(2)   5

(3)   3

(4)   6

Answer: (2)

8. Let f :(–1, 1)→ R be a function defined by  If K be the set of all points at which f is not differentiable, then K has exactly

(1)   Three elements

(2)   Two elements

(3)   One element

(4)   Five elements

Answer: (1)

9. The value of 

(1)   19/21

(2)   23/22

(3)   22/23

(4)   21/19

Answer: (4)

10. Consider the following three statements:

P : 5 is a prime number.

Q : 7 is a factor of 192.

R : L.C.M. of 5 and 7 is 35.

Then the truth value of which one of the following statements is true?

(1)   (~P) ⋀ (~Q ⋀ R)

(2)   (~P) ⋁ (Q ⋀ R)

(3)   P ⋁ (~Q ⋀ R)

(4)   (P ⋀ Q) ⋁ (~R)

Answer: (3)

11. The curve amongst the family of curves represented by the differential equation, (x2 – y2)dx + 2xydy = 0 which passes through (1, 1) is

(1)   A hyperbola with transverse axis along the x-axis.

(2)   A circle with centre on the y-axis.

(3)   An ellipse with major axis along the y-axis.

(4)   A circle with centre on the x-axis.

Answer: (4)

12. The length of the chord of the parabola x2 = 4y having equation x – √2y + 4√2 = 0 is

(1)   3√2

(2)   6√3

(3)   2√11

(4)   8√2

Answer: (2)

13. If  where C is a constant of integration, then f(x) is equal to

(1)   4x3 + 1

(2)   −4x3 – 1

(3)   –2x3 + 1

(4)   –2x3 – 1

Answer: (2)

14. On which of the following lines lies the point of intersection of the line,  and the plane, x + y + z = 2?

(1) 

(2) 

(3) 

(4) 

Answer: (1)

15. Let  , where r ≠ ± then S represents

(1)   An ellipse whose eccentricity is  when r > 1.

(2)   An ellipse whose eccentricity is   when r > 1.

(3)   A hyperbola whose eccentricity is  when 0 < r < 1.

(4)   A hyperbola whose eccentricity is  when 0 < r < 1.

Answer: (2)

16. Two sides of a parallelogram are along the lines, x + y = 3 and x – y + 3 = 0. If its diagonals intersect at (2, 4) then one of its vertex is :

(1)   (2, 1)

(2)   (3, 5)

(3)   (2, 6)

(4)   (3, 6)

Answer: (4)

17. Let a1, a2, a3… , a10in G.P with ai > 0 for i = 1,2, … , 10 and S be the set of pairs (r, k), r, k ∈ N(the set of natural numbers for which

(1)   2

(2)   0

(3)   4

(4)   Infinitely many

Answer: (4)

18. With the usual notation, in ∆ABC, if ∠A + ∠B = 120°, a = √3 + 1 and b = √3 – 1, then the ration ∠A : ∠B, is :

(1)   7 : 1

(2)   3 : 1

(3)   9 : 7

(4)   5 : 3

Answer: (1)

19. Let  where b > 0. Then

(1)   −√3

(2)   √3

(3)   2√3

(4)   −2√3

Answer: (3)

20. The value of  where [t] denotes the greatest integer less than or equal to t, is :

(1) 

(2) 

(3) 

(4) 

Answer: (3)

21. Let f be a differentiable function such that  and f(1) ≠ Then 

(1)   Exist and equals 4.

(2)   Does not exist.

(3)   Exists and equals 4/7.

(4)   Exists and equals 0.

Answer: (1)

22. then K is equal to :

(1)   225 – 1

(2)   (25)2

(3)   225

(4)   224

Answer: (3)

23. Two vertices of a triangle are (0, 2) and (4, 3). If its orthocentre is at the origin, then its third vertex lies in which quadrant?

(1)   Fourth

(2)   Third

(3)   First

(4)   Second

Answer: (4)

24. Let N be the set of natural numbers and two functions f and g be defined as

f, g : N → N such that

and g(n) = n – 1(−1)n. Then fog is :

(1) One-one but not onto.

(2) Onto but not one-one.

(3) Neither one-one nor onto.

(4) Both one-one and onto.

Answer: (2)

25. The tangent to the curve  passing through the point (I, e) also passes through the point :

(1)(2, 3e)

(2)   (4/3, 2e)

(3)   (3, 6e)

(4)   (5/3, 2e)

Answer: (2)

26. A helicopter is flying along the curve given by y – x3/2 = 7, (x ≥ 0)). A soldier positioned at the point (1/2, 7) wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is :

(1) 

(2) 

(3) 

(4) 

Answer: (1)

27. If  then fʹ(1/2) is :

(1)   6/25

(2)   24/25

(3)   4/5

(4)   18/25

Answer: (2)

28. If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respectively, then the variance of 6 observations x1 , x2, …, x5 and –50 is equal to :

(1)   586.5

(2)   582.5

(3)   509.5

(4)   507.5

Answer: (4)

29. The value of  is:

(1)   1/512

(2)   1/256

(3)   1/2

(4)   1/1024

Answer: (1)

30. The value of λ such that sum of the squares of the roots of the quadratic equation, x2 + (3 – λ) x + 2 = λ has the least value is:

(1)   2

(2)   1

(3)   15/8

(4)   4/9

Answer: (1)

JEE MAIN-2019 Online CBT Mode DT. 09.01.2019 Morning Question Paper With Answer Key

JEE MAIN-2019 Online CBT Mode DT. 09.01.2019 Morning

PHYSICS

1. A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m(m << M). When the car is at rest, the speed of transverse waves in the string is 60 ms–1. When the car has acceleration a, the wave-speed increases to 60.5 ms–1. The value of a, in terms of gravitational acceleration g, is closest to

(1)   g/30

(2)   g/5

(3)   g/20

(4)   g/10

Answer: (2)

2. A parallel plate capacitor is made of two square plates of side a, separated by a distance d(d << a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is

(1)    

(2)     

(3)    

(4)     

Answer: (1)

3. A conducting circular loop made of a thin wire, has area 3.5 × 10–3 m2 and resistance 10 Ω. It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50πt). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to

(1)   7 mC

(2)   21 mC

(3)   6 mC

(4)   14 mC

Answer: (Bonus)

4. Temperature difference of 120°C is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length 3L/2, is connected across AB (see figure). In steady state, temperature difference between P and Q will be close to

(1)   35°C

(2)   45°C

(3)   60°C

(4)   75°

Answer: (2)

5. A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is

(1)   1.1 cm away from the lens

(2)   0.55 cm towards the lens

(3)   0

(4)   0.55 cm away from the lens

Answer: (4)

6. A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms  speeds is close to

(1)   2.24

(2)   0.45

(3)   3.16

(4)   0.32

Answer: (3)

7. Consider a tank made of glass (refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index μ. A student finds that, irrespective of what the incident angle i (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of μ is

(1)   4/3

(2)    

(3)   3/√5

(4)   5/√3

Answer: (3)

8. A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is

(1)   0.5%

(2)   2.0%

(3)   2.5%

(4)   1.0%

Answer: (4)

9. A resistance is shown in the figure. Its value and tolerance are given respectively by

(1)   27 kΩ, 20%

(2)   270 kΩ, 5%

(3)   27 kΩ, 10%

(4)   270 kΩ,10%

Answer: (3)

10. Surface of certain metal is first illuminated with light of wavelength λ1 = 350 nm and then, by light of wavelength λ2 = 540 nm. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to

(1)   1.8

(2)   5.6

(3)   2.5

(4)   1.4

Answer: (1)

11. Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is 1019 m–3 and their mobility is 1.6 m2/(V.s) then the resistivity of the semiconductor (since it is an n-type semiconductor contribution of holes is ignored) is close

(1)   2 Ωm

(2)   0.2 Ωm

(3)   0.4 Ωm

(4)   4 Ωm

Answer: (3)

12. A gas can be taken from A and B via two different processes ACB and ADB.

When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is

10 J. The heat Flow into the system in path ADB is

(1)   100 J

(2)   80 J

(3)   20 J

(4)   40 J

Answer: (4)

13. Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M. Block A is given an initial speed ν towards B due to which it collides with B perfectly inelastically. The combined mass collides with C, also perfectly inelastically 5/6th of the initial kinetic energy is lost in whole process. What is value of M/m?

(1)   3

(2)   4

(3)   2

(4)   5

Answer: (2)

14. A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time,  The corresponding magnetic field  at that point will be

(1)     

(2)     

(3)    

(4)     

Answer: (2)

15. A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is

(1)     

(2)     

(3)     

(4)     

Answer: (4)

16. A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward?

(take g = 10 ms2)

(1)   25 N

(2)   32 N

(3)   18 N

(4)   23 N

Answer: (2)

17. If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is

(1)   L/m

(2)   4L/m

(3)   L/2m

(4)   2L/m

Answer: (3)

18. A particle is moving with a velocity  where K is a constant. The general equation for its path is

(1)   y2 = x + constant

(2)   y = x2 + constant

(3)   y2  = x2 + constant

(4)   xy = constant

Answer: (3)

19. A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The coercivity of the bar magnet is

(1)   520 A/m

(2)   2600 A/m

(3)   1200 A/m

(4)   285 A/m

Answer: (2)

20. An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d>>a). If the loop applies a force F on the wire then :

(1)   F = 0

(2)   F ∝ (a/d)2

(3)   F ∝ (a/d)

(4)   F ∝ (a2/d3)

Answer: (2)

21. When the switch S, in the circuit shown, is closed, then the value of current i will be

(1)   2 A

(2)   5 A

(3)   4 A

(4)   3 A

Answer: (2)

22. A rod, length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion α/°C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by ∆ Young’s modulus, Y, for this metal is

(1)    

(2)     

(3)     

(4)     

Answer: (2)

23. Three charges +Q, q, +Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by +Q, placed at x = 0, is zero then value of q is

(1)   +Q/2

(2)   −Q/2

(3)   −Q/4

(4)   +Q/4

Answer: (3)

24. An L- shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is θ, then

(1)   tan θ = 1/2

(2)   tan θ = 2/√3

(3)   tan θ = 1/3

(4)   tan θ = 1/2√3

Answer: (3)

25. Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section 5 mm2, is v. If the electron density in copper is 9 × 1028/m3 the value of v in mm/s is close to (Take charge of electron to be = 1.6 × 10–19 C)

(1)   0.02

(2)   0.2

(3)   3

(4)   2

Answer: (1)

26. A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be lose to

(1)   1.5 × 107 T

(2)   1. 0× 105 T

(3)   1.5 × 105 T

(4)   1.0 × 107 T

Answer: (4)

27. A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 × 1010 decays/s), has twice the number of nuclei as another sample of a different radioactive material B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively:

(1)   10 day and 40 days

(2)   20 day and 5 days

(3)   20 day and 10 days

(4)   5 day and 10 days

Answer: (2)

28. For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its centre. Then value of h is :

(1)   R/√2

(2)   R/√5

(3)   R

(4)   R√2

Answer: (1)

29. Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:

(1)   25 : 9

(2)   4 : 1

(3)   16 : 9

(4)   5 : 3

Answer: (1)

30. Two masses m and m/2 are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system (see figure). Because of torsional constant k, the restoring torque is τ = kθ for angular displacement θ. If the rod is rotated by θ0 and released, the tension in it when it passes through its mean position will be:

(1)     

(2)     

(3)     

(4)     

Answer: (2)

CHEMISTRY

1. Two complexes [Cr(H2O)6]Cl3(A) and [Cr(NH3)6]Cl3 (B) are violet and yellow coloured, respectively. The incorrect statement regarding them is

(1)   ∆0 values of (A) and (B) are calculated from the energies of violet and yellow light, respectively

(2)   Both are paramagnetic with three unpaired electrons

(3)   ∆0 value for (A) is less than that of (B)

(4)   Both absorb energies corresponding to their complementary colors

Answer: (1)

2. In general, the properties that decrease and increase down a group in the periodic table, respectively, are

(1)   Electronegativity and electron gain enthalpy

(2)   Atomic radius and electronegativity

(3)   Electron gain enthalpy and electronegativity

(4)   Electronegativity and atomic radius

Answer: (4)

3. Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures T1 and T2 (T1 < T2) ). The correct graphical depiction of the dependence of work done (w) on the final volume (V) is

(1)   

(2)   

(3)  

(4)  

Answer: (2)

4. The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexes is

(1)   5.92

(2)   6.93

(3)   4.90

(4)   3.87

Answer: (1)

5. The correct match between Item-I and Item-II is

Item-I (drug)                      Item-II (test)

A hloroxylenol                 P. Carbylamine test

B. Norethindrone          Q. Sodium hydrogen Carbonate test

C. Sulphapyridine         R. Ferric chloride test

D. Penicillin                    S. Bayer’s test

(1)   A → Q, B → P, C → S, D → R

(2)   A → R, B → S, C → P, D → Q

(3)   A → Q, B → S, C → P, D → R

(4)   A → R, B → P, C → S, D → Q

Answer: (2)

6. The major product of the following reaction is

(1)   

(2)   

(3)   

(4)  

Answer: (1)

7. The ore that contains both iron and copper is

(1)   Copper pyrites

(2)   Dolomite

(3)   Malachite

(4)   Azurite

Answer: (1)

8. Correct statements among a to d regarding silicones are

(a) They are polymers with hydrophobic character

(b) They are biocompatible

(c) In general, they have high thermal stability and low dielectric strength

(d) Usually, they are resistant to oxidation and used as greases

(1)   (a), (b) and (d) only

(2)   (a), (b), (c) and (d)

(3)   (a), (b) and (c) only

(4)   (a) and (b) only

Answer: (1)

9. Which amongst the following is the strongest acid?

(1)   CHBr3

(2)   CH(CN)3

(3)   CHI3

(4)   CHCl3

Answer: (2)

10. Adsorption of a gas follows Freundlich adsorption isotherm. In the given plot, x is the mass of the gas adsorbed on mass m of the adsorbent at pressure p. x/m is proportional to

(1)   p2

(2)   p

(3)   p1/4

(4)   p1/2

Answer: (4)

11. The increasing order of pKa of the following amino acids in aqueous solution is

Gly, Asp, Lys, Arg

(1)   Gly < Asp < Arg < Lys

(2)   Arg < Lys < Gly < Asp

(3)   Asp < Gly < Arg < Lys

(4)   Asp < Gly < Lys < Arg

Answer: (2)

12. According to molecular orbital theory, which of the following is true with respect to Li2+ and Li2 ?

(1)   Li2+ is unstable and Li2 is stable

(2)   Li2+ is stable and Li2 is unstable

(3)   Both are stable

(4)   Both are unstale

Answer: (3)

13. The correct decreasing order for acid strength is

(1) FCH2COOH > NCCH2COOH >NO2CH2COOH > CICH2COOH

(2) CNCH2COOH > O2NCH2COOH>FCH2COOH > CICH2COOH

(3) NO2CH2COOH > NCCH2COOH >FCH2COOH > CICH2COOH

(4) NO2CH2COOH > FCH2COOH >CNCH2COOH > CICH2COOH

Answer: (3)

14. The compounds A and B in the following reaction are, respectively

(1)   A = Benzyl alcohol, B = Benzyl isocyanide

(2)   A = Benzyl chloride, B = Benzyl cyanide

(3)   A = Benzyl chloride, B = Benzyl isocyanide

(4)   A = Benzyl alcohol, B = Benzyl cyanide

Answer: (3)

15. The one that is extensively used as a piezoelectric material is

(1)   Tridymite

(2)   Mica

(3)   Quartz

(4)   Amorphous silica

Answer: (3)

16. The isotopes of hydrogen are

(1)   Tritium and protium only

(2)   Deuterium and tritium only

(3)   Protium and deuterium only

(4)   Protium, deuterium and tritium

Answer: (4)

17. The following results were obtained during kinetic studies of the reaction ; 2 A + B → Products

The time (in minutes) required to consume half of A is

(1)   100

(2)   1

(3)   5

(4)   10

Answer: (3)

18. The alkaline earth metal nitrate that does not crystallise with water molecules, is

(1)   Ba(NO3)2

(2)   Ca(NO3)2

(3)   Mg(NO3)2

(4)   Sr(NO3)2

Answer: (1)

19. Major product of the following reaction is

(1)   

(2)  

(3)  

(4)   

Answer: (2)

20. Which one of the following statements regarding Henry’s law is not correct?

(1)   Different gases have different KH (Henry’s law constant) values at the same temperature

(2)   The value of KH increases with increase of temperature and KH is function of the nature of the gas

(3)   The partial pressure of the gas in vapour phase is proportional to the mole fraction of the gas in the solution

(4)   Higher the value of KH at a given pressure, higher is the solubility of the gas in the liquids.

Answer: (4)

21. The major product of following reaction is

(1)   RCH2NH2

(2)   RCHO

(3)   RCONH2

(4)   RCOOH

Answer: (2)

22. A water sample has ppm level concentration of the following metals: Fe = 0.2 ; Mn = 5.0 ; Cu = 3.0 ; Zn = 5.0. The metal that makes the water sample unsuitable for drinking is:

(1)   Cu

(2)   Mn

(3)   Zn

(4)   Fe

Answer: (2)

23. 20 ml of 0.1 M H2SO4 solution is added to 30 mL of 0.2 M NH4OH solution. The pH of the resultant mixture is : [pKb of NH4OH = 4.7]

(1)   9.0

(2)   5.2

(3)   5.0

(4)   9.4

Answer: (1)

24. For emission line of atomic hydrogen from ni = 8 to nf = n, the plot of wave number  will be (The Rydberg constant, RH is in wave number  unit)

(1)   Linear with slope RH

(2)   Linear with intercept −RH

(3)   Non-linear

(4)   Linear with slope −RH

Answer: (1)

25. A solution of sodium sulfate contains 92 g of Na+ ions per kilogram of water. The molality of Na+ ions in that solution in mol kg–1 is:

(1)   16

(2)   4

(3)   8

(4)   12

Answer: (2)

26. 0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume 10 m3 at 1000 K. Given R is the gas constant in JK–1 mol–1, x is

(1)     

(2)     

(3)    

(4)     

Answer: (3)

27. Arrange the following amines in the decreasing order of basicity

(1)   III > II > I

(2)   I > III > II

(3)   III > I > II

(4)   I > II > III

Answer: (3)

28. The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The amount of PbSO4 electrolyzed in g during the process is (Molar mass of PbSO4 = 303 g mol–1)

(1)   7.6

(2)   15.2

(3)   11.4

(4)   22.8

Answer: (1)

29. Aluminium is usually found in +3 oxidation state. In contrast, thallium exists in +1 and +3 oxidation states. This is due to

(1)   Lattice effect

(2)   Lanthanoid contraction

(3)   Diagonal relationship

(4)   Inert pair effect

Answer: (4)

30. The major product of the following reaction is

(1)   

(2)   

(3)   

(4)   

Answer: (4)

MATHEMATICS

1. Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements is true?

(1)   The lines are al parallel

(2)   The lines are not concurrent

(3)   The lines are concurrent at the point (3/4, 1/2)

(4)   Each line passes through the origin

Answer: (3)

2. 5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2) of the height of these six students is

(1)   18

(2)   20

(3)   22

(4)   16

Answer: (2)

3. If the fractional part of the number  then k is equal to

(1)   8

(2)   4

(3)   6

(4)   14

Answer: (1)

4. Three circles of radii a, b, c (a < b < c) touch each other externally. If they have x-axis as a common tangent, then

(1)   a, b, c are in A.P.

(2)     

(3)     

(4)    

Answer: (2)

5. Let  . Then the sum of the elements in A is

(1)   5π/6

(2)   π

(3)   3π/4

(4)   2π/3

Answer: (4)

6. Let α and β be two roots of the equation x2 + 2x + 2 = 0, then α15 + β15 is equal to

(1)   −512

(2)   512

(3)   256

(4)   −256

Answer: (4)

7. Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is

(1)   200

(2)   350

(3)   500

(4)   300

Answer: (4)

8. The area (in sq. units) bounded by the parabola y = x2 – 1, the tangent at the point (2, 3) to it and the y-axis is

(1)   32/3

(2)   8/3

(3)   56/3

(4)   14/3

Answer: (2)

9. For x ∈ R – {0, 1}, let f1 (x) = 1/x, f2(x) = 1 – x and  be three given functions. If a function, J(x) satisfies (f2°J°f1) (x) = f3(x) then J(x) is equal to

(1)   f1(x)

(2)     

(3)   f2(x)

(4)   f­3(x)

Answer: (4)

10. Let . If the eccentricity of the hyperbola  is greater than 2, then the length of its latus rectum lies in the interval

(1)   (2, 3]

(2)   (3/2, 2]

(3)   (1, 3/2]

(4)   (3, ∞)

Answer: (4)

11. The value of  is :

(1)   0

(2)   2/3

(3)   −4/3

(4)   4/3

Answer: (4)

12. Let a1, a2 … a30 be an A.P. , If a5 = 27 and S – 2T = 75, then a10 is equal to

(1)   47

(2)   57

(3)   52

(4)   42

Answer: (3)

13. Let  be a vector such that   is equal to

(1)   17/2

(2)   19/2

(3)   9

(4)   8

Answer: (2)

14. For any  the expression 3(sin θ – cos θ)4 + 6(sin θ + cos θ)2 + 4 sin6θ equals :

(1)   13 – 4 cos2 θ + 6sin2 θ cos2 θ

(2)   13 – 4 cos2 θ + 6 cos4 θ

(3)   13 – 4 cos6 θ

(4)   13 – 4 cos4 θ + 2sin2 θ cos2 θ

Answer: (3)

15. Two cards are drawn successively with replacementfrom a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P(X = 2) equals:

(1)   24/169

(2)   25/169

(3)   49/169

(4)   52/169

Answer: (2)

16. Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

(1)   (4, −4)

(2)   (5, 2√6)

(3)   (6, 4√2)

(4)   (8, 6)

Answer: (4)

17. The system of linear equations

x + y + z = 2

2x + 3y + 2z = 5

2x + 3y + (a2 – 1)z = a + 1

(1)   has infinitely many solutions for a = 4

(2)   is inconsistent when |a| = √3

(3)   has a unique solution for |a| = √3

(4)   is inconsistent when a = 4

Answer: (2)

18. The plane through the intersection of the planes x + y + z = 1 and 2x + 3y – z + 4 = 0 and parallel to y-axis also passes through the point:

(1)   (3, 2, 1)

(2)   (3, 3, −1)

(3)   (−3, 0, −1)

(4)   (−3, 1, 1)

Answer: (1)

19. Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is

(1)   √3y = x+ 3

(2)   2√3y = 12x + 1

(3)   √3y = 3x + 1

(4)   2√3y = −x – 12

Answer: (1)

20. If y = y(x) is the solution of the differential equation,  satisfying y(1) = 1, then y(1/2) is equal to

(1)   13/16

(2)   7/64

(3)   1/4

(4)   49/16

Answer: (4)

21. 

(1)   Exists and equals   

(2)   Does not exist 

(3)   Exists and equals   

(4)   Exists and equals

Answer: (3)

22. If θ denotes the acute angle between the curves, y = 10 – x2 and y = 2 + x2 at a point of their intersection, then |tan θ| is equal to :

(1)   8/15

(2)   7/17

(3)   8/17

(4)   4/9

Answer: (1)

23. Let f : R → R be a function defined as

Then, f is :

(1)   Continuous if a = –5 and b = 10

(2)   Continuous if a = 5 and b = 5

(3)   Continuous if a = 0 and b = 5

(4)   Not continuous for any values of a and b

Answer: (4)

24. If  then the matrix A50 when θ = π/12, is equal to:

(1)    

(2)