## 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 V_{BB} supply can vary from 0 to 5.0 V, V_{CC} = 5V, β_{dc}= 200, R_{B} = 100 KΩ, R_{C} = 1 KΩ and V_{BE}= 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

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 I_{1}, and hat below the piston isI_{2}, such that I_{1}> I_{2}. 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)

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

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)

5. The mean intensity of radiation on the surface of the Sun is about 10^{8} W/m^{2}. The rms value of the corresponding magnetic field is closet to:

(1) 10^{2\}T

(2) 10^{−}^{4} T

(3) 1 T

(4) 10^{−}^{2} T

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

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)

8. A simple harmonic motion is represented by :

The amplitude and time period of the motion are:

(1)

(2)

(3)

(4)

9. In the given circuit diagram, the currents, I_{1} = −3 A, I_{4} = 0.8 A and I_{5} = 0.4 A, are flowing as shown. The currents I_{2}, I_{3} and I_{6}, 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

10. When a certain photosensistive surface is illuminated with monochromatic light of frequency v, the stopping potential for the photo current is –V_{0}/2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is –V_{0} . The threshold frequency for photoeletric emission is:

(1) 3v/2

(2)

(3) 5v/3

(4) 2 v

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

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/s^{2})

(1) 2 kg-m^{2}/s

(2) 3 kg-m^{2}/s

(3) 8 kg-m^{2}/s

(4) 6 kg-m^{2}/s

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

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/m^{2}. The value of the induced emf in wire is:

(1) 1.1 × 10^{−}^{3} V

(2) 0.3 × 10^{−}^{3} V

(3) 2.5 × 10^{−}^{3} V

(4) 1.5 × 10^{−}^{3} V

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

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

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/s^{2}]

(1) 1/2

(2) √3/2

(3) √3/4

(4) 2/3

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)

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

20. A plano-convex lens (focal length f_{2} , refractive index μ_{2}, radius of curvature R) fits exactly into a planoconcave lens(focal length f_{1} , 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) f_{1} – f_{2}

(2)

(3)

(4) f_{1} + f_{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

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, T_{A}/T_{B} is

(1) 1

(2) 1/2

(3) 2

(4)

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 × 10^{−}^{7} s

(2) 3 × 10^{−}^{6} s

(3) 0.5 × 10^{−}^{8} s

(4) 4 × 10^{−}^{8} s

24.

In the above circuit, R_{2} = 20 Ω, and R_{1} = 10 Ω. Current in L-R_{1} path is I_{1} and in C-R_{2} path it is I_{2}. The voltage of A.C. source is given by

V = 200√2 sin(100 t) volts. The phase difference between I_{1}and I_{2} is

(1) 0°

(2) 60°

(3) 30°

(4) 90°

25. A paramagnetic material has 10^{28} atoms/m^{3}. Its magnetic susceptibility at temperature 350 K is 2.8 × 10^{–4}. Its susceptibility at 300 K is

(1) 3.726 × 10^{−}^{4}

(2) 3.672 × 10^{−}^{4}

(3) 2.672 × 10^{−}^{4}

(4) 3.267 × 10^{−}^{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) [A^{−}^{1}]

(2) [LA^{−2}]

(3) [LT^{2}]

(4) [LTA]

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

28. A parallel plate capacitor with plates of area 1 m^{2 }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 × 10^{−}^{10} C

(2) 9.85 × 10^{−}^{10} C

(3) 6.85 × 10^{−}^{10} C

(4) 7.85 × 10^{−}^{10} C

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)

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 ms^{−}^{1}

(2) 341 ms^{−}^{1}

(3) 328 ms^{−}^{1}

(4) 335 ms^{−}^{1}

**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

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

3. The increasing order of the reactivity of the following with LiAlH_{4} is

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

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

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

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

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.

5. The major product of the following reaction is

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^{−}

7. The major product of the following reaction is

(1)

(2)

(3)

(4)

8. If K_{sp} of Ag_{2}CO_{3} is 8 × 10^{−}^{12}, the molar solubility of Ag_{2}CO_{3} in 0.1 M AgNO_{3} is

(1) 8 × 10^{−}^{11} M

(2) 8 × 10^{−}^{12} M

(3) 8 × 10^{−}^{13} M

(4) 8 × 10^{−}^{10} M

9. for NaCl, HCl and NaA are 126.4, 425.9 and 100.5 S cm^{2}mol^{–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

10. The major product of the following reaction is

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)

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}

13. The major product of the following reaction is

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

(1)

(2) CH_{2} = CHCHO

(3) CF_{2}Cl_{2}

(4) O_{3}

15. The major product in the following conversion is

16. The major product of the following reaction is

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 K_{f} =5 K kg mol^{−}^{1}, Molar mass of benzoic acid = 122 g mol^{−}^{1})

(1) 1.5 g

(2) 2.4 g

(3) 1.8 g

(4) 1.0 g

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

(1) Cl ^{–} and ClO^{–}

(2) Cl^{–} and ClO_{2}^{–}

(3) ClO_{3}^{–} and ClO_{2}^{–}

(4) Cl^{–} and ClO_{3}^{–}

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

20. If the de Broglie wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5 πa_{0} (a_{0} is Bohr radius), then the value of n/z is

(1) 0.40

(2) 1.50

(3) 0.75

(4) 1.0

21. The volume strength of 1M H_{2}O_{2} is

(Molar mass of H_{2}O_{2} = 34 g mol^{−}^{1})

(1) 11.35

(2) 22.4

(3) 5.6

(4) 16.8

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

23. The element that does NOT show catenation is

(1) Sn

(2) Ge

(3) Pb

(4) Si

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

(1) HOOC(CH_{2})_{6}COOH, H_{2}N(CH_{2})_{4}NH_{2}

(2) HOOC(CH_{2})_{6}COOH, H_{2}N(CH_{2})_{6}NH

(3) HOOC(CH_{2})_{4}COOH, H_{2}MN(CH_{2})_{6}NH_{2}

(4) HOOC(CH_{2})_{4}COOH, H_{2}N(CH_{2})_{4}NH_{2}

25. The pair that does NOT require calcination is

(1) Fe_{2}O_{3} and CaCO_{3} ∙ MgCO_{3}

(2) ZnCO_{3} and CaO

(3) ZnO and MgO

(4) ZnO and Fe_{2}O_{3} ∙ xH_{2}O

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

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)

28. 8 g of NaOH is dissolved in 18 g of H_{2} 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

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

(1) Sn

(2) Si

(3) Ge

(4) C

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

(1)

(2)

(3)

(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

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°

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

4. The tangent to the curve y = x^{2} – 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)

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]

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)

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)

8. If sin^{4}α + 4 cos^{4}β + 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

9. The integral is equal to

(1)

(2)

(3)

(4)

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

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) 2e^{2}

(3) 4e

(4) 4e^{2}

12. If the function f given by f (x) = x^{3} – 3 (a – 2)x^{2} + 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

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

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) 2^{15}

(2) 2^{12}

(3) 2^{18}

(4) 2^{10}

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

(1) p ⋀ q

(2) p ⋀ ~ q

(3) ~ p ⋀ ~ q

(4) ~ p ⋀ ~ q

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

17. Let S be the set of all real values of λ such that a plane passing through the points (−λ^{2}, 1, 1), (1, −λ^{2}, 1) and (1, 1, −λ^{2}) also passes through the point (–1, –1, 1). Then S is equal to

(1) {1, −1}

(2) {√3}

(3) {√3, −√3}

(4) {3, −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

19. Let z_{1} and z_{2} be two complex numbers satisfying |z_{1}| = 9 and |z_{2} – 3 – 4i | = 4. Then the minimum value of |z_{1} – z_{2}| is

(1) 0

(2) √2

(3) 1

(4) 2

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

(1) 8

(2) 3

(3) 6

(4) 7

21. If ^{n}C_{4}, ^{n}C_{5} and ^{n}C_{6} are in A.P., then n can be :

(1) 12

(2) 9

(3) 14

(4) 11

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) (x^{2} + y^{2})^{2} = 4Rx^{2}y^{2}

(2) (x^{2} + y^{2})^{2} = 4R2x^{2}y^{2}

(3) (x^{2} + y^{2})^{3} = 4R2x^{2}y^{2}

(4) (x^{2} + y^{2})(x + y) = R^{2}xy

23. is equal to:

(1) π/4

(2) tan^{−}^{1}(3)

(3) tan^{−}^{1} (2)

(4) π/2

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

(1)

(2)

(3)

(4)

25. The equation of a tangent to the parabola, x^{2} = 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

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

27. is equal to :

(1)

(2)

(3)

(4)

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

29. The total number of irrational terms in the binomial expansion of (7^{1/5} – 3^{1/10})^{60} is :

(1) 48

(2) 49

(3) 54

(4) 55

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