# 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

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)

3. A conducting circular loop made of a thin wire, has area 3.5 × 10^{–3} m^{2} 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

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°

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

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

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

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%

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%

10. Surface of certain metal is first illuminated with light of wavelength λ_{1} = 350 nm and then, by light of wavelength λ_{2} = 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

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 10^{19} m^{–3} and their mobility is 1.6 m^{2}/(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

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

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

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)

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)

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 ms^{−}^{2})

(1) 25 N

(2) 32 N

(3) 18 N

(4) 23 N

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

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

(1) y^{2} = x + constant

(2) y = x^{2} + constant

(3) y^{2} = x^{2} + constant

(4) xy = constant

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

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 ∝ (a^{2}/d^{3})

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

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)

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

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

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 × 10^{28}/m^{3} 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

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 × 10^{−}^{7} T

(2) 1. 0× 10^{−}^{5} T

(3) 1.5 × 10^{−}^{5} T

(4) 1.0 × 10^{−}^{7} T

27. A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 × 10^{10} 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

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

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

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 θ_{0} and released, the tension in it when it passes through its mean position will be:

(1)

(2)

(3)

(4)

**CHEMISTRY**

1. Two complexes [Cr(H_{2}O)_{6}]Cl_{3}(A) and [Cr(NH_{3})_{6}]Cl_{3} (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

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

3. Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures T_{1 }and T_{2 }(T_{1} < T_{2}) ). The correct graphical depiction of the dependence of work done (w) on the final volume (V) is

(1)

(2)

(3)

(4)

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

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

6. The major product of the following reaction is

(1)

(2)

(3)

(4)

7. The ore that contains both iron and copper is

(1) Copper pyrites

(2) Dolomite

(3) Malachite

(4) Azurite

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

9. Which amongst the following is the strongest acid?

(1) CHBr_{3}

(2) CH(CN)_{3}

(3) CHI_{3 }

(4) CHCl_{3}

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) p^{2}

(2) p

(3) p^{1/4}

(4) p^{1/2}

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

12. According to molecular orbital theory, which of the following is true with respect to Li_{2}^{+} and Li_{2}^{−} ?

(1) Li_{2}^{+} is unstable and Li_{2}^{−} is stable

(2) Li_{2}^{+} is stable and Li_{2}^{−} is unstable

(3) Both are stable

(4) Both are unstale

13. The correct decreasing order for acid strength is

(1) FCH_{2}COOH > NCCH_{2}COOH >NO_{2}CH_{2}COOH > CICH_{2}COOH

(2) CNCH_{2}COOH > O_{2}NCH_{2}COOH>FCH_{2}COOH > CICH_{2}COOH

(3) NO_{2}CH_{2}COOH > NCCH_{2}COOH >FCH_{2}COOH > CICH_{2}COOH

(4) NO_{2}CH_{2}COOH > FCH_{2}COOH >CNCH_{2}COOH > CICH_{2}COOH

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

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

(1) Tridymite

(2) Mica

(3) Quartz

(4) Amorphous silica

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

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

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

(1) Ba(NO_{3})_{2}

(2) Ca(NO_{3})_{2}

(3) Mg(NO_{3})_{2}

(4) Sr(NO_{3})_{2}

19. Major product of the following reaction is

(1)

(2)

(3)

(4)

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

(1) Different gases have different K_{H} (Henry’s law constant) values at the same temperature

(2) The value of K_{H} increases with increase of temperature and K_{H} 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.

21. The major product of following reaction is

(1) RCH_{2}NH_{2}

(2) RCHO

(3) RCONH_{2}

(4) RCOOH

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

23. 20 ml of 0.1 M H_{2}SO_{4} solution is added to 30 mL of 0.2 M NH_{4}OH solution. The pH of the resultant mixture is : [pK_{b} of NH_{4}OH = 4.7]

(1) 9.0

(2) 5.2

(3) 5.0

(4) 9.4

24. For emission line of atomic hydrogen from n_{i} = 8 to n_{f} = n, the plot of wave number will be (The Rydberg constant, R_{H} is in wave number unit)

(1) Linear with slope R_{H}

(2) Linear with intercept −R_{H}

(3) Non-linear

(4) Linear with slope −R_{H}

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

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 m^{3} at 1000 K. Given R is the gas constant in JK^{–1} mol^{–1}, x is

(1)

(2)

(3)

(4)

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

28. The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The amount of PbSO_{4} electrolyzed in g during the process is (Molar mass of PbSO_{4} = 303 g mol^{–1})

(1) 7.6

(2) 15.2

(3) 11.4

(4) 22.8

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

30. The major product of the following reaction is

(1)

(2)

(3)

(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

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

(1) 18

(2) 20

(3) 22

(4) 16

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

(1) 8

(2) 4

(3) 6

(4) 14

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)

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

(1) 5π/6

(2) π

(3) 3π/4

(4) 2π/3

6. Let α and β be two roots of the equation x^{2} + 2x + 2 = 0, then α^{15} + β^{15} is equal to

(1) −512

(2) 512

(3) 256

(4) −256

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

8. The area (in sq. units) bounded by the parabola y = x^{2} – 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

9. For x ∈ R – {0, 1}, let f_{1} (x) = 1/x, f_{2}(x) = 1 – x and be three given functions. If a function, J(x) satisfies (f_{2}°J°f_{1}) (x) = f_{3}(x) then J(x) is equal to

(1) f_{1}(x)

(2)

(3) f_{2}(x)

(4) f_{3}(x)

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, ∞)

11. The value of is :

(1) 0

(2) 2/3

(3) −4/3

(4) 4/3

12. Let a_{1}, a_{2} … a_{30} be an A.P. , If a_{5} = 27 and S – 2T = 75, then a_{10} is equal to

(1) 47

(2) 57

(3) 52

(4) 42

13. Let be a vector such that is equal to

(1) 17/2

(2) 19/2

(3) 9

(4) 8

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

(1) 13 – 4 cos^{2} θ + 6sin^{2} θ cos^{2} θ

(2) 13 – 4 cos^{2} θ + 6 cos^{4} θ

(3) 13 – 4 cos^{6} θ

(4) 13 – 4 cos^{4} θ + 2sin^{2} θ cos^{2} θ

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

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)

17. The system of linear equations

x + y + z = 2

2x + 3y + 2z = 5

2x + 3y + (a^{2} – 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

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)

19. Equation of a common tangent to the circle, x^{2} + y^{2} – 6x = 0 and the parabola, y^{2} = 4x, is

(1) √3y = x+ 3

(2) 2√3y = 12x + 1

(3) √3y = 3x + 1

(4) 2√3y = −x – 12

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

21.

(1) Exists and equals

(2) Does not exist

(3) Exists and equals

(4) Exists and equals

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

(1) 8/15

(2) 7/17

(3) 8/17

(4) 4/9

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

24. If then the matrix A^{−}^{50} when θ = π/12, is equal to:

(1)

(2)

(3)

(4)

25. The maximum volume (in cu. m) of the right circular cone having slant height 3 m is :

(1)

(2) 2√3 π

(3) 3√3 π

(4) 6 π

26. If the Boolean expression (p ⊕ q) ⋀ (~ p ⨀ q) is equivalent to p ⋀ q, where ⊕, ⨀ ∈ {⋀, ⋁}, then the ordered pair (⨁, ⨀) is

(1) (⋁, ⋀)

(2) (⋁,⋁)

(3) (⋀, ⋀)

(4) (⋀,⋁)

27. If then x is equal to :

(1)

(2)

(3)

(4)

28. For x^{2} ≠ nπ + 1, n ∈ N (the set of natural numbers), the integral is equal to :

(where c is a constant of integration)

(1)

(2)

(3)

(4)

29. If a, b and c be three distinct real numbers in G.P. and a + b + c = xb, then x cannot be:

(1) 2

(2) −3

(3) −2

(4) 4

30. The equation of the line passing through (–4, 3, 1), parallel to the plane x + 2y – z – 5 = 0 and intersecting the line is :

(1)

(2)

(3)

(4)