NTA JEE Main 12th April 2019 Shift 2

NTA JEE Main 12th April 2019 Shift 2 - Question 1

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A particle is moving with speed $$v = b\sqrt{x}$$ along positive x-axis. Calculate the speed of the particle at time $$t = \tau$$ (assume that the particle is at origin at t = 0)

A

$$b^2\tau$$

B

$$\frac{b^2\tau}{\sqrt{2}}$$

C

$$\frac{b^2\tau}{2}$$

D

$$\frac{b^2\tau}{4}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 2

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Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h$$_1$$ and h$$_2$$. Which of the following is correct?

A

R$$^2$$ = h$$_1$$h$$_2$$

B

R$$^2$$ = 4h$$_1$$h$$_2$$

C

R$$^2$$ = 2h$$_1$$h$$_2$$

D

R$$^2$$ = 16h$$_1$$h$$_2$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 3

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A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an angle of 30° with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $$\mu$$ = 0.2. The difference between the accelerations of the block, in case (B) and case (A) will be: (g = 10 m s$$^{-2}$$)

A

3.2 m s$$^{-2}$$

B

0 m s$$^{-2}$$

C

0.8 m s$$^{-2}$$

D

0.4 m s$$^{-2}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 4

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A spring whose unstretched length is $$l$$ has a force constant k. The spring is cut into two pieces of unstretched lengths $$l_1$$ and $$l_2$$ where, $$l_1 = nl_2$$ and n is an integer. The ratio $$k_1/k_2$$ of the corresponding force constants, k$$_1$$ and k$$_2$$ will be:

A

$$\frac{1}{n^2}$$

B

$$n^2$$

C

n

D

$$\frac{1}{n}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 5

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Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be:

A

$$\left(\frac{7}{12}\text{ m},\; \frac{\sqrt{3}}{4}\text{ m}\right)$$

B

$$\left(\frac{7}{12}\text{ m},\; \frac{\sqrt{3}}{8}\text{ m}\right)$$

C

$$\left(\frac{\sqrt{3}}{4}\text{ m},\; \frac{5}{12}\text{ m}\right)$$

D

$$\left(\frac{\sqrt{3}}{8}\text{ m},\; \frac{7}{12}\text{ m}\right)$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 6

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A smooth wire of length $$2\pi r$$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $$\omega$$ about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of $$\omega^2$$ is equal to:

A

$$2g/r$$

B

$$\frac{\sqrt{3}g}{2r}$$

C

$$2g/(r\sqrt{3})$$

D

$$(g\sqrt{3})/r$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 7

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The ratio of the weights of a body on Earth's surface to that on the surface of a planet is 9:4. The mass of the planet is $$\frac{1}{9}$$th of that of the Earth. If R is the radius of the Earth, what is the radius of the planet? (Take the planets to have the same mass density)

A

$$\frac{R}{4}$$

B

$$\frac{R}{2}$$

C

$$\frac{R}{3}$$

D

$$\frac{R}{9}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 8

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A solid sphere, of radius R acquires a terminal velocity $$v_1$$ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $$\eta$$. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, $$v_2$$, when falling through the same fluid, the ratio $$\left(\frac{v_1}{v_2}\right)$$ equals:

A

$$\frac{1}{9}$$

B

27

C

$$\frac{1}{27}$$

D

9

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NTA JEE Main 12th April 2019 Shift 2 - Question 9

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A uniform cylindrical rod of length L and radius r, is made from a material whose Young's modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to:

A

$$F/(3\pi r^2 YT)$$

B

$$9F/(\pi r^2 YT)$$

C

$$6F/(\pi r^2 YT)$$

D

$$3F/(\pi r^2 YT)$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 10

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1 kg of water, at 20°C is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20 Ω. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully is close to
[Specific heat of water = 4200 J kg$$^{-1}$$ °C$$^{-1}$$ Latent heat of water = 2260 kJ kg$$^{-1}$$]

A

3 min

B

16 min

C

22 min

D

10 min

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NTA JEE Main 12th April 2019 Shift 2 - Question 11

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A Carnot engine has an efficiency of $$\frac{1}{6}$$. When the temperature of the sink is reduced by 62°C, its efficiency is doubled. The temperatures of the source and the sink are, respectively,

A

124 °C, 62 °C

B

37 °C, 99 °C

C

99 °C, 37 °C

D

62 °C, 124 °C

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NTA JEE Main 12th April 2019 Shift 2 - Question 12

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A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process?

A

40 J

B

35 J

C

25 J

D

30 J

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NTA JEE Main 12th April 2019 Shift 2 - Question 13

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The number density of molecules of a gas depends on their distance r from the origin as, $$n(r) = n_0 e^{-\alpha r^4}$$. Then the numer of molecules is proportional to:

A

$$n_0 \alpha^{-3}$$

B

$$\sqrt{n_0} \alpha^{\frac{1}{2}}$$

C

$$n_0 \alpha^{\frac{-3}{4}}$$

D

$$n_0 \alpha^{\frac{1}{4}}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 14

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A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? [Given reference intensity of sound as $$10^{-12}$$ W/m$$^2$$]

A

40 cm

B

20 cm

C

10 cm

D

30 cm

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NTA JEE Main 12th April 2019 Shift 2 - Question 15

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Two sources of sound S$$_1$$ and S$$_2$$ produce sound waves of same frequency 660 Hz. A listener is moving from source S$$_1$$ towards S$$_2$$ with a constant speed u$$_0$$ m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u$$_0$$ equals:

A

10.0 m/s

B

2.5 m/s

C

5.5 m/s

D

15.0 m/s

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NTA JEE Main 12th April 2019 Shift 2 - Question 16

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Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $$\rho(r) = kr$$, where r is the distance from the centre. Two charges A and B, of -Q each, are placed on diametrically opposite points, at equal distance, a, from the centre. If A and B do not experience any force, then:

A

a = $$\frac{3R}{2^{\frac{1}{4}}}$$

B

a = $$\frac{R}{\sqrt{3}}$$

C

a = $$2^{\frac{-1}{4}}R$$

D

a = $$8^{\frac{-1}{4}}R$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 17

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In the given circuit, the charge on 4 μF capacitor will be:

A

9.6 μC

B

5.4 μC

C

24 μC

D

13.4 μC

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NTA JEE Main 12th April 2019 Shift 2 - Question 18

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A moving coil galvanometer, having a resistance G, produces full scale deflection when a current I$$_G$$ flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to I$$_0$$ (I$$_0$$ > I$$_g$$) by connecting a shunt resistance R$$_A$$ to it and (ii) into a voltmeter of range 0 to V (V = GI$$_0$$) by connecting a series resistance R$$_V$$ to it. Then,

A

R$$_A$$R$$_V$$ = G$$^2\left(\frac{I_0 - I_g}{I_g}\right)$$ and $$\frac{R_A}{R_V} = \left(\frac{I_g}{I_0-I_g}\right)^2$$

B

R$$_A$$R$$_V$$ = G$$^2$$ and $$\frac{R_A}{R_V} = \frac{I_g}{(I_0 - I_g)}$$

C

R$$_A$$R$$_V$$ = G$$^2\left(\frac{I_g}{I_0 - I_g}\right)$$ and $$\frac{R_A}{R_V} = \left(\frac{I_0 - I_g}{I_g}\right)^2$$

D

R$$_A$$R$$_V$$ = G$$^2$$ and $$\frac{R_A}{R_V} = \left(\frac{I_g}{I_0 - I_g}\right)^2$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 19

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An electron, moving along the x-axis with an initial energy of 100 eV, enters a region of magnetic field $$\vec{B} = (1.5 \times 10^{-3}$$ T)$$\hat{k}$$ at S (see figure). The field extends between x = 0 and x = 2 cm. The electron is detected at the point Q on a screen placed 8 cm away from the point S. The distance d between P and Q (on the screen) is:
(electron’s charge $$1.6 ×10^{−19} C$$, mass of electron $$=9.1×10^{−31} kg$$)

A

1.22 cm

B

12.87 cm

C

11.65 cm

D

2.25 cm

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NTA JEE Main 12th April 2019 Shift 2 - Question 20

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Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5 A. (See figure) ($$\mu_0 = 4\pi \times 10^{-7}$$ NA$$^{-2}$$)

A

$$1.5 \times 10^{-5}$$ T

B

$$2.0 \times 10^{-5}$$ T

C

$$3.0 \times 10^{-5}$$ T

D

$$2.5 \times 10^{-5}$$ T

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NTA JEE Main 12th April 2019 Shift 2 - Question 21

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Consider the LR circuit shown in the figure. If the switch S is closed at t = 0 then the amount of charge that passes through the battery between t = 0 and t = $$\frac{L}{R}$$ is:

A

$$\frac{7.3EL}{R^2}$$

B

$$\frac{EL}{7.3R^2}$$

C

$$\frac{2.7EL}{R^2}$$

D

$$\frac{EL}{2.7R^2}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 22

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A plane electromagnetic wave having a frequency f = 23.9 GHz propagates along the positive z-direction in free space. The peak value of the Electric Field is 60 V/m. Which among the following is the acceptable magnetic field component in the electromagnetic wave?

A

$$\vec{B} = 2 \times 10^{-7}\sin(0.5 \times 10^3 z - 1.5 \times 10^{11}t)\hat{i}$$

B

$$\vec{B} = 2 \times 10^{-7}\sin(1.5 \times 10^3 x + 0.5 \times 10^{11}t)\hat{j}$$

C

$$\vec{B} = 2 \times 10^7\sin(0.5 \times 10^3 z + 1.5 \times 10^{11}t)\hat{i}$$

D

$$\vec{B} = 60\sin(0.5 \times 10^3 x + 1.5 \times 10^{11}t)\hat{i}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 23

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A transparent cube of side d, made of a material of refractive index $$\mu_2$$, is immersed in a liquid of refractive index $$\mu_1$$ ($$\mu_1 < \mu_2$$). A ray is incident on the face AB at an angle $$\theta$$ (shown in the figure). Total internal reflection takes place at point E on the face BC.

Then $$\theta$$ must satisfy

A

$$\theta < \sin^{-1}\sqrt{\frac{\mu_2^2}{\mu_1^2} - 1}$$

B

$$\theta > \sin^{-1}\frac{\mu_1}{\mu_2}$$

C

$$\theta < \sin^{-1}\frac{\mu_1}{\mu_2}$$

D

$$\theta > \sin^{-1}\sqrt{\frac{\mu_2^2}{\mu_1^2} - 1}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 24

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A system of three polarizers P$$_1$$, P$$_2$$, P$$_3$$ is set up such that the pass axis of P$$_3$$ is crossed with respect to that of P$$_1$$. The pass axis of P$$_2$$ is inclined at 60° to the pass axis of P$$_3$$. When a beam of unpolarized light of intensity I$$_0$$ is incident on P$$_1$$, the intensity of light transmitted by the three polarizers is I. The ratio (I$$_0$$/I) equals (nearly):

A

5.33

B

16.00

C

1.80

D

10.67

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NTA JEE Main 12th April 2019 Shift 2 - Question 25

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Consider an electron in a hydrogen atom, revolving in its second excited state (having radius 4.65 Å). The de-Broglie wavelength of this electron is:

A

12.9 Å

B

6.6 Å

C

9.7 Å

D

3.5 Å

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NTA JEE Main 12th April 2019 Shift 2 - Question 26

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The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, $$\frac{\lambda_1}{\lambda_2}$$, of the photons emitted in this process is:

A

$$\frac{7}{5}$$

B

$$\frac{20}{7}$$

C

$$\frac{9}{7}$$

D

$$\frac{27}{5}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 27

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Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be:

A

3 : 8

B

8 : 1

C

1 : 8

D

9 : 8

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NTA JEE Main 12th April 2019 Shift 2 - Question 28

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Figure shows a DC voltage regulator circuit, with a Zener diode of breakdown voltage = 6 V. If the unregulated input voltage varies between 10 V to 16 V, then what is the maximum Zener current?

A

1.5 mA

B

3.5 mA

C

7.5 mA

D

2.5 mA

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NTA JEE Main 12th April 2019 Shift 2 - Question 29

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In a CE transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 2 V, if the base resistance is 1 kΩ and the current amplification of the transistor is 100 then the input signal voltage is

A

10 mV

B

1 mV

C

0.1 V

D

1 V

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NTA JEE Main 12th April 2019 Shift 2 - Question 30

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A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, l$$_1$$ = 30 cm and l$$_2$$ = 70 cm. Then, v is equal to:

A

384 m s$$^{-1}$$

B

332 m s$$^{-1}$$

C

338 m s$$^{-1}$$

D

379 m s$$^{-1}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 31

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25 g of an unknown hydrocarbon upon burning produces 88 g of CO$$_2$$ and 9 g of H$$_2$$O. This unknown hydrocarbon contains:

A

24 g of carbon and 1 g of hydrogen

B

18 g of carbon and 7 g of hydrogen

C

22 g of carbon and 3 g of hydrogen

D

20 g carbon and 5 g of hydrogen

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NTA JEE Main 12th April 2019 Shift 2 - Question 32

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Among the following, the energy of 2s orbital is lowest in:

A

K

B

H

C

Na

D

Li

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NTA JEE Main 12th April 2019 Shift 2 - Question 33

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In comparison to boron, beryllium has:

A

greater nuclear charge and lesser first ionisation enthalpy

B

lesser nuclear charge and greater first ionisation enthalpy

C

lesser nuclear charge and lesser first ionisation enthalpy.

D

greater nuclear charge and greater first ionisation enthalpy.

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NTA JEE Main 12th April 2019 Shift 2 - Question 34

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The incorrect match in the following is:

A

$$\Delta G^0 < 0, K > 1$$

B

$$\Delta G^0 > 0, K < 1$$

C

$$\Delta G^0 = 0, K = 1$$

D

$$\Delta G^0 < 0, K < 1$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 35

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In which one of the following equilibria, K$$_p$$ ≠ K$$_c$$?

A

2HI(g) ⇌ H$$_2$$(g) + I$$_2$$(g)

B

2C(s) + O$$_2$$(g) ⇌ 2CO(g)

C

2NO(g) ⇌ N$$_2$$(g) + O$$_2$$(g)

D

NO$$_2$$(g) + SO$$_2$$(g) ⇌ NO(g) + SO$$_3$$(g)

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NTA JEE Main 12th April 2019 Shift 2 - Question 36

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The molar solubility of Cd(OH)$$_2$$ is $$1.84 \times 10^{-5}$$ M in water. The expected solubility of Cd(OH)$$_2$$ in a buffer solution of pH = 12 is:

A

$$2.49 \times 10^{-10}$$ M

B

$$\frac{2.49}{1.84} \times 10^{-9}$$ M

C

$$1.84 \times 10^{-9}$$ M

D

$$6.23 \times 10^{-11}$$ M

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NTA JEE Main 12th April 2019 Shift 2 - Question 37

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The temporary hardness of a water sample is due to compound X. Boiling this sample converts X to compound Y. X and Y, respectively, are:

A

Mg(HCO$$_3$$)$$_2$$ and MgCO$$_3$$

B

Ca(HCO$$_3$$)$$_2$$ and Ca(OH)$$_2$$

C

Mg(HCO$$_3$$)$$_2$$ and Mg(OH)$$_2$$

D

Ca(HCO$$_3$$)$$_2$$ and CaO

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NTA JEE Main 12th April 2019 Shift 2 - Question 38

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The incorrect statement is:

A

LiNO$$_3$$ decomposes on heating to give LiNO$$_2$$ and O$$_2$$.

B

LiCl crystallises from aqueous solution as LiCl - 2H$$_2$$O.

C

Lithium is the strongest reducing agent among the alkali metals.

D

Lithium is least reactive with water among the alkali metals.

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NTA JEE Main 12th April 2019 Shift 2 - Question 39

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The C - C bond length is maximum in:

A

C$$_{70}$$

B

C$$_{60}$$

C

graphite

D

diamond

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NTA JEE Main 12th April 2019 Shift 2 - Question 40

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The IUPAC name for the following compound is:

A

3-methyl-4-(1-methylprop-2-ynyl)-1-heptene

B

3, 5-dimethyl-4-propylhept-6-en-1-yne

C

3, 5-dimethyl-4-propyl hept-1-en-6-yne

D

3-methyl-4-(3-methylprop-1-enhyl)-1-heptyne

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NTA JEE Main 12th April 2019 Shift 2 - Question 41

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Which one of the following is likely to give a precipitate with AgNO$$_3$$ solution?

A

CH$$_2$$ = CH - Cl

B

(CH$$_3$$)$$_3$$CCl

C

CCl$$_4$$

D

CHCl$$_3$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 42

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In the following skew conformation of ethane, H' - C - C - H'' dihedral angle is:

A

58°

B

120°

C

149°

D

151°

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NTA JEE Main 12th April 2019 Shift 2 - Question 43

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Heating of 2-chloro-1-phenylbutane with EtOK/EtOH gives X as the major product. Reaction X with Hg(OAc)$$_2$$/H$$_2$$O followed by NaBH$$_4$$ gives Y as the major product. Y is:

A

B

C

D

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NTA JEE Main 12th April 2019 Shift 2 - Question 44

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The primary pollutant that leads to photochemical smog is:

A

nitrogen oxides

B

ozone

C

acrolein

D

Sulphur dioxide

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NTA JEE Main 12th April 2019 Shift 2 - Question 45

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The ratio of number of atoms present in a simple cubic, body centered cubic and face centered cubic structure are, respectively:

A

4 : 2 : 1

B

1 : 2 : 4

C

4 : 2 : 3

D

8 : 1 : 6

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NTA JEE Main 12th April 2019 Shift 2 - Question 46

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A solution is prepared by dissolving 0.6 g of urea (molar mass = 60 g mol$$^{-1}$$) and 1.8 g of glucose (molar mass = 180 g mol$$^{-1}$$) in 100 mL of water at 27°C. The osmotic pressure of the solution is:
(R = 0.08206 L atm K$$^{-1}$$ mol$$^{-1}$$)

A

8.2 atm

B

2.46 atm

C

4.92 atm

D

1.64 atm

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NTA JEE Main 12th April 2019 Shift 2 - Question 47

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The decreasing order of electrical conductivity of the following aqueous solutions is:
(A) 0.1 M Formic acid,
(B) 0.1 M Acetic acid,
(C) 0.1 M Benzoic acid.

A

(A) > (B) > (C)

B

(A) > (C) > (B)

C

(C) > (B) > (A)

D

(C) > (A) > (B)

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NTA JEE Main 12th April 2019 Shift 2 - Question 48

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NO$$_2$$ required for a reaction is produced by the decomposition of N$$_2$$O$$_5$$ in CCl$$_4$$ as per the equation, 2N$$_2$$O$$_5$$(g) $$\to$$ 4NO$$_2$$(g) + O$$_2$$(g). The initial concentration of N$$_2$$O$$_5$$ is 3.00 mol L$$^{-1}$$ and it is 2.75 mol L$$^{-1}$$ after 30 minutes. The rate of formation of NO$$_2$$ is:

A

$$1.667 \times 10^{-2}$$ mol L$$^{-1}$$ min$$^{-1}$$

B

$$8.333 \times 10^{-3}$$ mol L$$^{-1}$$ min$$^{-1}$$

C

$$4.167 \times 10^{-3}$$ mol L$$^{-1}$$ min$$^{-1}$$

D

$$2.083 \times 10^{-3}$$ mol L$$^{-1}$$ min$$^{-1}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 49

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Among the following, the incorrect statement about colloids is:

A

They are larger than small molecules and have high molar mass.

B

They can scatter light.

C

The osmotic pressure of a colloidal solution is of higher order than the true solution at the same concentration.

D

The range of diameters of colloidal particles is between 1 and 1000 nm.

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NTA JEE Main 12th April 2019 Shift 2 - Question 50

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The correct statement is:

A

Pig iron is obtained from cast iron.

B

The Hall-Heroult process is used for the production of aluminium and iron.

C

leaching of bauxite using concentrated NaOH solution gives sodium aluminate and sodium silicate.

D

the blistered appearance of copper during metallurgical process is due to the evolution of CO$$_2$$.

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NTA JEE Main 12th April 2019 Shift 2 - Question 51

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The pair that has similar atomic radii is:

A

Mo and W

B

Sc and Ni

C

Mn and Re

D

Ti and Hf

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NTA JEE Main 12th April 2019 Shift 2 - Question 52

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Thermal decomposition of a Mn compound (X) at 513 K results in compound Y, MnO$$_2$$ and a gaseous product. MnO$$_2$$ reacts with NaCl and concentrated H$$_2$$SO$$_4$$ to give a pungent gas Z. X, Y and Z, respectively, are:

A

K$$_3$$MnO$$_4$$, K$$_3$$MnO$$_4$$ and Cl$$_2$$

B

K$$_2$$MnO$$_4$$, KMnO$$_4$$ and Cl$$_2$$

C

K$$_2$$MnO$$_4$$, KMnO$$_4$$ and SO$$_2$$

D

KMnO$$_4$$, K$$_2$$MnO$$_4$$ and Cl$$_2$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 53

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The coordination numbers of Co and Al in [Co(Cl)(en)$$_2$$]Cl and K$$_3$$[Al(C$$_2$$O$$_4$$)$$_3$$], respectively are:
(en = ethane-1, 2-diamine)

A

3 and 3

B

5 and 3

C

5 and 6

D

6 and 6

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NTA JEE Main 12th April 2019 Shift 2 - Question 54

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The compound used in the treatment of lead poisoning is:

A

Desferrioxime B

B

EDTA

C

Cis-platin

D

D-penicillamine

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NTA JEE Main 12th April 2019 Shift 2 - Question 55

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An 'Assertion' and a 'Reason' is given below. Choose the correct answer from the following options:
Assertion (A): Vinyl halides do not undergo nucleophilic substitution easily.
Reason (R): Even though the intermediate carbocation is stabilized by loosely held $$\pi$$-electrons, the cleavage is difficult because of the strong bonding.

A

Both (A) and (R) are correct statements but (R) is not the correct explanation of (A).

B

Both (A) and (R) are wrong statements.

C

Both (A) and (R) are wrong statements and (R) is the correct explanation of (A).

D

(A) is a correct statement but (R) is a wrong statement.

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NTA JEE Main 12th April 2019 Shift 2 - Question 56

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Consider the following reactions:

'A' is:

A

CH$$_2$$ = CH$$_2$$

B

CH ≡ CH

C

CH$$_3$$ - C ≡ C - CH$$_3$$

D

CH$$_3$$ - C ≡ CH

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NTA JEE Main 12th April 2019 Shift 2 - Question 57

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What will be the major product when m-cresol is reacted with propargyl bromide (HC ≡ C - CH$$_2$$Br) in presence of K$$_2$$CO$$_3$$ in acetone?

A

B

C

D

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NTA JEE Main 12th April 2019 Shift 2 - Question 58

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Benzene diazonium chloride on reaction with aniline in the presence of dilute hydrochloric acid gives:

A

B

C

D

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NTA JEE Main 12th April 2019 Shift 2 - Question 59

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The correct name of the following polymer is:

A

Polyisobutylene

B

Polytert-butylene

C

Polyisobutane

D

Polyisoprene

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NTA JEE Main 12th April 2019 Shift 2 - Question 60

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Which of the given statements is incorrect about glycogen?

A

It is present in animal cells.

B

It is a straight chain polymer similar to amylose.

C

It is present in some yeast and fungi

D

Only α-linkages are present in the molecule.

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NTA JEE Main 12th April 2019 Shift 2 - Question 61

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If $$\alpha$$, $$\beta$$ and $$\gamma$$ are three consecutive terms of a non-constant G.P. Such that the equations $$\alpha x^2 + 2\beta x + \gamma = 0$$ and $$x^2 + x - 1 = 0$$ have a common root, then $$\alpha(\beta + \gamma)$$ is equal to:

A

$$\beta\gamma$$

B

$$\alpha\beta$$

C

$$\alpha\gamma$$

D

0

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NTA JEE Main 12th April 2019 Shift 2 - Question 62

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Let $$z \in C$$ with Im(z) = 10 and it satisfies $$\frac{2z - n}{2z + n} = 2i - 1$$ for some natural number n. Then

A

n = 20 and Re(z) = 10

B

n = 40 and Re(z) = 10

C

n = 20 and Re(z) = -10

D

n = 40 and Re(z) = -10

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NTA JEE Main 12th April 2019 Shift 2 - Question 63

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A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to

A

24

B

27

C

25

D

28

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NTA JEE Main 12th April 2019 Shift 2 - Question 64

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If $$a_1, a_2, a_3, \ldots$$ are in A.P. such that $$a_1 + a_7 + a_{16} = 40$$, then the sum of the first 15 terms of this A.P is:

A

280

B

120

C

150

D

200

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NTA JEE Main 12th April 2019 Shift 2 - Question 65

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If $$^{20}C_1 + (2^2)\,^{20}C_2 + (3^2)\,^{20}C_3 + \ldots + (20^2)\,^{20}C_{20} = A(2^\beta)$$, then the ordered pair $$(A, \beta)$$ is equal to

A

(380, 19)

B

(420, 18)

C

(420, 19)

D

(380, 18)

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NTA JEE Main 12th April 2019 Shift 2 - Question 66

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The term independent of x in the expansion of $$\left(\frac{1}{60} - \frac{x^8}{81}\right) \cdot \left(2x^2 - \frac{3}{x^2}\right)^6$$ is equal to

A

-72

B

36

C

-108

D

-36

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NTA JEE Main 12th April 2019 Shift 2 - Question 67

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Let S be the set of all $$\alpha \in R$$ such that the equation, $$\cos 2x + \alpha \sin x = 2\alpha - 7$$ has a solution. Then S is equal to:

A

[3, 7]

B

[2, 6]

C

[1, 4]

D

R

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NTA JEE Main 12th April 2019 Shift 2 - Question 68

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A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (-1, 1) and (2, 3). Then the centroid of this triangle is:

A

$$\left(\frac{1}{3}, 1\right)$$

B

$$\left(1, \frac{7}{3}\right)$$

C

$$\left(\frac{1}{3}, 2\right)$$

D

$$\left(\frac{1}{3}, \frac{5}{3}\right)$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 69

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A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of 60° with the line x + y = 0. Then an equation of the line L is:

A

$$(\sqrt{3} + 1)x + (\sqrt{3} - 1)y = 8\sqrt{2}$$

B

$$x + \sqrt{3}y = 8$$

C

$$\sqrt{3}x + y = 8$$

D

$$(\sqrt{3} - 1)x + \sqrt{3}y = 8\sqrt{2}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 70

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A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point:

A

(3, 10)

B

(2, 3)

C

(3, 5)

D

(1, 5)

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NTA JEE Main 12th April 2019 Shift 2 - Question 71

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The tangents to the curve $$y = (x - 2)^2 - 1$$ at its points of intersection with the line $$x - y = 3$$, intersect at the point:

A

$$\left(\frac{5}{2}, 1\right)$$

B

$$\left(\frac{5}{2}, -1\right)$$

C

$$\left(-\frac{5}{2}, -1\right)$$

D

$$\left(-\frac{5}{2}, 1\right)$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 72

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An ellipse, with foci at (0, 2) and (0, -2) and minor axis of length 4, passes through which of the following points?

A

$$(1, 2\sqrt{2})$$

B

$$(2, \sqrt{2})$$

C

$$(\sqrt{2}, 2)$$

D

$$(2, 2\sqrt{2})$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 73

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The equation of a common tangent to the curves, $$y^2 = 16x$$ and $$xy = -4$$, is:

A

$$x - 2y + 16 = 0$$

B

$$x - y + 4 = 0$$

C

$$2x - y + 2 = 0$$

D

$$x + y + 4 = 0$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 74

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$$\lim_{x \to 0} \frac{x + 2\sin x}{\sqrt{x^2 + 2\sin x + 1} - \sqrt{\sin^2 x - x + 1}}$$ is

A

3

B

1

C

2

D

6

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NTA JEE Main 12th April 2019 Shift 2 - Question 75

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The Boolean expression $$\sim(p \Rightarrow (\sim q))$$ is equivalent to

A

$$(\sim p) \Rightarrow q$$

B

$$q \Rightarrow \sim p$$

C

$$p \vee q$$

D

$$p \wedge q$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 76

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The angle of the top of a vertical tower standing on a horizontal plane is observed to be 45° from a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be 30°, then the distance (in m) of the foot of the tower from the point A is:

A

$$15(3 + \sqrt{3})$$

B

$$15(1 + \sqrt{3})$$

C

$$15(5 - \sqrt{3})$$

D

$$15(3 - \sqrt{3})$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 77

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Let A, B and C be sets such that $$\phi \neq A \cap B \subseteq C$$. Then which of the following statements is not true?

A

$$B \cap C \neq \phi$$

B

$$(C \cup A) \cap (C \cup B) = C$$

C

If $$(A - B) \subseteq C$$, then $$A \subseteq C$$

D

If $$(A - C) \subseteq B$$, then $$A \subseteq B$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 78

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A value of $$\theta \in \left(0, \frac{\pi}{3}\right)$$, for which $$\begin{vmatrix} 1 + \cos^2\theta & \sin^2\theta & 4\cos 6\theta \\ \cos^2\theta & 1 + \sin^2\theta & 4\cos 6\theta \\ \cos^2\theta & \sin^2\theta & 1 + 4\cos 6\theta \end{vmatrix} = 0$$, is

A

$$\frac{\pi}{9}$$

B

$$\frac{7\pi}{24}$$

C

$$\frac{7\pi}{36}$$

D

$$\frac{\pi}{18}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 79

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If [x] denotes the greatest integer $$\leq x$$, then the system of linear equations $$[\sin\theta]x + [-\cos\theta]y = 0$$, $$[\cot\theta]x + y = 0$$

A

has a unique solution if $$\theta \in \left(\frac{\pi}{2}, \frac{2\pi}{3}\right) \cup \left(\pi, \frac{7\pi}{6}\right)$$

B

have infinitely many solution if $$\theta \in \left(\frac{\pi}{2}, \frac{2\pi}{3}\right) \cup \left(\pi, \frac{7\pi}{6}\right)$$

C

has a unique if $$\theta \in \left(\frac{\pi}{2}, \frac{2\pi}{3}\right)$$ and have infinitely many solutions if $$\theta \in \left(\pi, \frac{7\pi}{6}\right)$$

D

have infinitely many solutions if $$\theta \in \left(\frac{\pi}{2}, \frac{2\pi}{3}\right)$$ and has a unique solution if $$\theta \in \left(\pi, \frac{7\pi}{6}\right)$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 80

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The derivative of $$\tan^{-1}\left(\frac{\sin x - \cos x}{\sin x + \cos x}\right)$$ with respect to $$\frac{x}{2}$$, where $$x \in \left(0, \frac{\pi}{2}\right)$$, is

A

2

B

$$\frac{1}{2}$$

C

$$\frac{2}{3}$$

D

1

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NTA JEE Main 12th April 2019 Shift 2 - Question 81

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Let $$f(x) = 5 - |x - 2|$$ and $$g(x) = |x + 1|$$, $$x \in R$$. If $$f(x)$$ attains maximum value at $$\alpha$$ and $$g(x)$$ attains minimum value at $$\beta$$, then $$\lim_{x \to -\alpha\beta} \frac{(x - 1)(x^2 - 5x + 6)}{x^2 - 6x + 8}$$ is equal to

A

$$\frac{3}{2}$$

B

$$\frac{1}{2}$$

C

$$-\frac{3}{2}$$

D

$$-\frac{1}{2}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 82

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Let $$\alpha \in \left(0, \frac{\pi}{2}\right)$$, be constant. If the integral $$\int \frac{\tan x + \tan\alpha}{\tan x - \tan\alpha} dx = A(x)\cos 2\alpha + B(x)\sin 2\alpha + C$$, where C is a constant of integration, then the functions A(x) and B(x) are respectively

A

$$x - \alpha$$ and $$\log_e|\sin(x - \alpha)|$$

B

$$x + \alpha$$ and $$\log_e|\cos(x - \alpha)|$$

C

$$x + \alpha$$ and $$\log_e|\sin(x + \alpha)|$$

D

$$x - \alpha$$ and $$\log_e|\cos(x - \alpha)|$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 83

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A value of $$\alpha$$ such that $$\int_\alpha^{\alpha+1} \frac{dx}{(x + \alpha)(x + \alpha + 1)} = \log_e\left(\frac{9}{8}\right)$$ is

A

$$-\frac{1}{2}$$

B

$$\frac{1}{2}$$

C

$$-2$$

D

2

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NTA JEE Main 12th April 2019 Shift 2 - Question 84

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If the area (in sq. units) bounded by the parabola $$y^2 = 4\lambda x$$ and the line $$y = \lambda x$$, $$\lambda > 0$$, is $$\frac{1}{9}$$, then $$\lambda$$ is equal to

A

$$4\sqrt{3}$$

B

$$2\sqrt{6}$$

C

48

D

24

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NTA JEE Main 12th April 2019 Shift 2 - Question 85

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The general solution of the differential equation $$(y^2 - x^3)dx - xy\,dy = 0$$, $$(x \neq 0)$$ is (where c is a constant of integration)

A

$$y^2 + 2x^2 + cx^3 = 0$$

B

$$y^2 - 2x^2 + cx^3 = 0$$

C

$$y^2 - 2x^3 + cx^2 = 0$$

D

$$y^2 + 2x^3 + cx^2 = 0$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 86

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Let $$\alpha \in R$$ and the three vectors $$\vec{a} = \alpha\hat{i} + \hat{j} + 3\hat{k}$$, $$\vec{b} = 2\hat{i} + \hat{j} - \alpha\hat{k}$$ and $$\vec{c} = \alpha\hat{i} - 2\hat{j} + 3\hat{k}$$. Then the set S = {$$\alpha$$: $$\vec{a}$$, $$\vec{b}$$ and $$\vec{c}$$ are coplanar}

A

is singleton

B

contains exactly two positive numbers

C

is empty

D

contains exactly two numbers only one of which is positive

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NTA JEE Main 12th April 2019 Shift 2 - Question 87

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A plane which bisects the angle between the two given planes $$2x - y + 2z - 4 = 0$$ and $$x + 2y + 2z - 2 = 0$$, passes through the point

A

(2, 4, 1)

B

(1, -4, 1)

C

(1, 4, -1)

D

(2, -4, 1)

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NTA JEE Main 12th April 2019 Shift 2 - Question 88

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The length of the perpendicular drawn from the point (2, 1, 4) to the plane containing the lines $$\vec{r} = (\hat{i} + \hat{j}) + \lambda(\hat{i} + 2\hat{j} - \hat{k})$$ and $$\vec{r} = (\hat{i} + \hat{j}) + \mu(-\hat{i} + \hat{j} - 2\hat{k})$$ is

A

$$\frac{1}{3}$$

B

3

C

$$\sqrt{3}$$

D

$$\frac{1}{\sqrt{3}}$$

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NTA JEE Main 12th April 2019 Shift 2 - Question 89

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A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is:

A

$$\frac{1}{2}$$ loss

B

$$\frac{1}{2}$$ gain

C

2 gain

D

$$\frac{1}{4}$$ loss

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NTA JEE Main 12th April 2019 Shift 2 - Question 90

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For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is $$\frac{4}{5}$$, then the probability that he is unable to solve less than two problems is

A

$$\frac{201}{5}\left(\frac{1}{5}\right)^{49}$$

B

$$\frac{164}{25}\left(\frac{1}{5}\right)^{48}$$

C

$$\frac{316}{25}\left(\frac{4}{5}\right)^{48}$$

D

$$\frac{54}{5}\left(\frac{4}{5}\right)^{49}$$

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