NTA JEE Main 9th April 2016 Online

NTA JEE Main 9th April 2016 Online - Question 1

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In the following $$I$$ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity:

A

$$M^{-1}L^{-3}T^3I$$

B

$$M^{-1}L^{-3}T^3I^2$$

C

$$M^{-1}L^3T^3I$$

D

$$ML^{-3}T^{-3}I^2$$

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NTA JEE Main 9th April 2016 Online - Question 2

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A rocket is fired vertically from the earth with an acceleration of 2g, where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $$\theta$$ with the horizontal, a point object of mass m is kept. The minimum coefficient of friction $$\mu_{min}$$ between the mass and the inclined surface such that the mass does not move is:

A

$$\tan 2\theta$$

B

$$\tan \theta$$

C

$$3\tan \theta$$

D

$$2\tan \theta$$

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NTA JEE Main 9th April 2016 Online - Question 3

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Which of the following option correctly describes the variation of the speed v and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force $$F = -kv$$, where 'k' is a constant, on the body? (Graphs are schematic and not drawn to scale)

A

B

C

D

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NTA JEE Main 9th April 2016 Online - Question 4

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A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force $$\frac{W}{20}$$ on the car. While moving uphill on the road at a speed of 10 ms$$^{-1}$$, the car needs power P. If it needs power $$\frac{P}{2}$$ while moving downhill at speed v then the value of v is:

A

20 ms$$^{-1}$$

B

5 ms$$^{-1}$$

C

15 ms$$^{-1}$$

D

10 ms$$^{-1}$$

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NTA JEE Main 9th April 2016 Online - Question 5

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A cubical block of side 30 cm is moving with velocity 2 m s$$^{-1}$$ on a smooth horizontal surface. The surface has a bump at a point O as shown in the figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is:

A

13.3

B

5.0

C

9.4

D

6.7

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NTA JEE Main 9th April 2016 Online - Question 6

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The figure shows an elliptical path $$ABCD$$ of a planet around the sun $$S$$ such that the area of triangle $$CSA$$ is $$\frac{1}{4}^\text{th}$$ the area of the ellipse (see the figure below) with $$DB$$ as the major axis, and $$CA$$ as the minor axis. If $$t_1$$ is the time taken for the planet to go over the path $$ABC$$ and $$t_2$$ for the path taken over $$CDA$$ then:

A

$$t_1 = 4t_2$$

B

$$t_1 = 2t_2$$

C

$$t_1 = 3t_2$$

D

$$t_1 = t_2$$

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NTA JEE Main 9th April 2016 Online - Question 7

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A uniformly tapering conical wire is made from a material of Young's modulus $$Y$$ and has a normal, unextended length $$L$$. The radii, at the upper and lower ends of this conical wire, have values $$R$$ and $$3R$$, respectively. The upper end of the wire is fixed to a rigid support and a mass $$M$$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal:

A

$$L\left(1 + \frac{2}{9}\frac{Mg}{\pi YR^2}\right)$$

B

$$L\left(1 + \frac{1}{9}\frac{Mg}{\pi YR^2}\right)$$

C

$$L\left(1 + \frac{1}{3}\frac{Mg}{\pi YR^2}\right)$$

D

$$L\left(1 + \frac{2}{3}\frac{Mg}{\pi YR^2}\right)$$

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NTA JEE Main 9th April 2016 Online - Question 8

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Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h. Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x, then:

A

$$x = r\left(\frac{H}{H+h}\right)^{1/4}$$

B

$$x = r\left(\frac{H}{H+h}\right)$$

C

$$x = r\left(\frac{H}{H+h}\right)^2$$

D

$$x = r\left(\frac{H}{H+h}\right)^{1/2}$$

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NTA JEE Main 9th April 2016 Online - Question 9

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A simple pendulum made of a bob of mass m and a metallic wire of a negligible mass has a time period of 2 s at $$T = 0°C$$. If the temperature of the wire is increased, and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope $$S$$. If the coefficient of linear expansion of metal is $$\alpha$$, then the value of $$S$$ is

A

$$\frac{\alpha}{2}$$

B

$$2\alpha$$

C

$$\alpha$$

D

$$\frac{1}{\alpha}$$

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NTA JEE Main 9th April 2016 Online - Question 10

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The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is

A

$$\frac{2}{5}$$

B

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

C

$$\frac{3}{5}$$

D

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

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NTA JEE Main 9th April 2016 Online - Question 11

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200 g water is heated from 40°C to 60°C. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J kg$$^{-1}$$ K$$^{-1}$$):

A

167.4 kJ

B

8.4 kJ

C

4.2 kJ

D

16.7 kJ

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NTA JEE Main 9th April 2016 Online - Question 12

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Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and T, respectively. At time $$t = 0$$ one particle has displacement A while the other one has displacement $$-\frac{A}{2}$$ and they are moving towards each other. If they cross each other at time t, then t is:

A

$$\frac{5T}{6}$$

B

$$\frac{T}{3}$$

C

$$\frac{T}{4}$$

D

$$\frac{T}{6}$$

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NTA JEE Main 9th April 2016 Online - Question 13

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Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they pass each other. Speed of sound is 330 m/sec:

A

450 Hz

B

540 Hz

C

270 Hz

D

648 Hz

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NTA JEE Main 9th April 2016 Online - Question 14

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The potential (in volts) of a charge distribution is given by
$$V(z) = 30 - 5z^2$$ for $$|z| \leq 1$$ m
$$V(z) = 35 - 10|z|$$ for $$|z| \geq 1$$ m.
$$V(z)$$ does not depend on x and y. If this potential is generated by a constant charge per unit volume $$\rho_0$$ (in units of $$\epsilon_0$$) which is spread over a certain region, then choose the correct statement.

A

$$\rho_0 = 20\,\epsilon_0$$ in the entire region

B

$$\rho_0 = 10\,\epsilon_0$$ for $$|z| \leq 1$$ m and $$\rho_0 = 0$$ else where

C

$$\rho_0 = 20\,\epsilon_0$$ for $$|z| \leq 1$$ m and $$\rho_0 = 0$$ else where

D

$$\rho_0 = 40\,\epsilon_0$$ in the entire region

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NTA JEE Main 9th April 2016 Online - Question 15

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Three capacitors each of 4 $$\mu$$F are to be connected in such a way that the effective capacitance is 6 $$\mu$$F. This can be done by connecting them

A

all in series

B

all in parallel

C

two in parallel and one in series

D

two in series and one in parallel

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NTA JEE Main 9th April 2016 Online - Question 16

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In the circuit shown, the resistance r is a variable resistance. If for $$r = fR$$, the heat generation in r is maximum then the value of f is

A

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

B

1

C

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

D

$$\frac{3}{4}$$

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NTA JEE Main 9th April 2016 Online - Question 17

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To know the resistance $$G$$ of a galvanometer by half deflection method, a battery of emf $$V_E$$ and resistance $$R$$ is used to deflect the galvanometer by angle $$\theta$$. If a shunt of resistance $$S$$ is needed to get half deflection the $$G$$, $$R$$ and $$S$$ are related by the equation:

A

$$S(R + G) = RG$$

B

$$2S(R + G) = RG$$

C

$$2G = S$$

D

$$2S = G$$

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NTA JEE Main 9th April 2016 Online - Question 18

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A 50 $$\Omega$$ resistance is connected to a battery of 5 V. A galvanometer of resistance 100 $$\Omega$$ is to be used as an ammeter to measure current through the resistance, for this a resistance $$r_S$$ is connected to the galvanometer. Which of the following connections should be employed if the measured current is with in 1% of the current without the ammeter in the circuit?

A

$$r_S = 0.5\Omega$$ in series with galvanometer

B

$$r_S = 1\,\Omega$$ in series with galvanometer

C

$$r_S = 1\,\Omega$$ in parallel with galvanometer

D

$$r_S = 0.5\,\Omega$$ in parallel with the galvanometer

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NTA JEE Main 9th April 2016 Online - Question 19

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A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75°. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30° with this field. The magnitude of the other field (in mT) is close to

A

1

B

11

C

36

D

1060

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NTA JEE Main 9th April 2016 Online - Question 20

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A series $$LR$$ circuit is connected to a voltage source with $$V(t) = V_0\sin(\omega t)$$. After a very large time, current $$I(t)$$ behaves as $$(t_0 \gg \frac{L}{R})$$:

A

B

C

D

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NTA JEE Main 9th April 2016 Online - Question 21

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Microwave oven acts on the principle of:

A

giving rotational energy to water molecules

B

giving translational energy to water molecules

C

giving vibrational energy to water molecules

D

transferring electrons from lower to higher energy levels in water molecule

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NTA JEE Main 9th April 2016 Online - Question 22

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To find the focal length of a convex mirror, a student records the following data:
Object pin: 22.2 cm, Convex Lens: 32.2 cm, Convex Mirror: 45.8 cm, Image Pin: 71.2 cm
The focal length of the convex lens is $$f_1$$ and that of mirror is $$f_2$$. Then taking index correction to be negligibly small, $$f_1$$ and $$f_2$$ are close to:

A

$$f_1 = 7.8$$ cm, $$f_2 = 12.7$$ cm

B

$$f_1 = 12.7$$ cm, $$f_2 = 7.8$$ cm

C

$$f_1 = 15.6$$ cm, $$f_2 = 25.4$$ cm

D

$$f_1 = 7.8$$ cm, $$f_2 = 25.4$$ cm

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NTA JEE Main 9th April 2016 Online - Question 23

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A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of:

A

60 cm from the convex lens

B

60 cm from the concave lens

C

70 cm from the convex lens

D

70 cm from the concave lens

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NTA JEE Main 9th April 2016 Online - Question 24

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In Young's double-slit experiment, the distance between slits and the screen is 1 m and monochromatic light of wavelength 600 nm is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance $$d_0$$ between the slits. If the angular resolution of the eye is $$\frac{1}{60}°$$, then the value of $$d_0$$ is close to

A

1 mm

B

3 mm

C

2 mm

D

4 mm

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NTA JEE Main 9th April 2016 Online - Question 25

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When photons of wavelength $$\lambda_1$$ are incident on an isolated sphere, the corresponding stopping potential is found to be $$V$$. When photons of wavelength $$\lambda_2$$ are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength $$\lambda_3$$ is used then find the stopping potential for this case:

A

$$\frac{hc}{e}\left[\frac{1}{\lambda_3} + \frac{1}{\lambda_2} - \frac{1}{\lambda_1}\right]$$

B

$$\frac{hc}{e}\left[\frac{1}{\lambda_3} + \frac{1}{2\lambda_2} - \frac{1}{\lambda_1}\right]$$

C

$$\frac{hc}{e}\left[\frac{1}{\lambda_3} - \frac{1}{\lambda_2} - \frac{1}{\lambda_1}\right]$$

D

$$\frac{hc}{e}\left[\frac{1}{\lambda_3} + \frac{1}{2\lambda_2} - \frac{3}{2\lambda_1}\right]$$

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NTA JEE Main 9th April 2016 Online - Question 26

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An electron in a hydrogen atom makes a transition from $$n = 2$$ to $$n = 1$$ and emits a photon. This photon strikes a doubly ionized lithium atom which was already in an excited state and completely removes the orbiting electron. The least quantum number for the excited state of the lithium-ion for the process is

A

2

B

4

C

5

D

3

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NTA JEE Main 9th April 2016 Online - Question 27

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An unknown transistor needs to be identified as a npn or pnp type. A multimeter, with +ve and -ve terminals, is used to measure resistance between different terminals of transistor. If terminal 2 is the base of the transistor then which of the following is correct for a pnp transistor?

A

+ve terminal 2, -ve terminal 3, resistance low

B

+ve terminal 2, -ve terminal 1, resistance high

C

+ve terminal 1, -ve terminal 2, resistance high

D

+ve terminal 3, -ve terminal 2, resistance high

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NTA JEE Main 9th April 2016 Online - Question 28

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A Zener diode with a breakdown voltage of 4 V is connected in series with a resistance $$R$$ to a battery of emf 10 V. The maximum power dissipation rating for the Zener diode is 1 W. The value of $$R$$ to ensure maximum power dissipation across the diode is

A

12 $$\Omega$$

B

24 $$\Omega$$

C

36 $$\Omega$$

D

6 $$\Omega$$

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NTA JEE Main 9th April 2016 Online - Question 29

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The truth table given in fig. represents:

A	B	Y
0	0	0
0	1	1
1	0	1
1	1	1

A

OR-Gate

B

NAND-Gate

C

AND-Gate

D

NOR-Gate

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NTA JEE Main 9th April 2016 Online - Question 30

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An audio signal consists of two distinct sounds: one a human speech signal in the frequency band of 200 Hz to 2700 Hz, while the other is a high frequency music signal in the frequency band of 10200 Hz to 15200 Hz. The ratio of the AM signal band width required to send both the signals together to the AM signal band width required to send just the human speech is:

A

3

B

5

C

6

D

2

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NTA JEE Main 9th April 2016 Online - Question 31

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An organic compound contains C, H and S. The minimum molecular weight of the compound containing 8% Sulphur is

A

600 g mol$$^{-1}$$

B

200 g mol$$^{-1}$$

C

400 g mol$$^{-1}$$

D

300 g mol$$^{-1}$$

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NTA JEE Main 9th April 2016 Online - Question 32

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The amount of arsenic pentasulphide that can be obtained when 35.5 g arsenic acid is treated with excess $$H_2S$$ in the presence of conc. HCl (assuming 100% conversion) is

A

0.25 mol

B

0.50 mol

C

0.333 mol

D

0.125 mol

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NTA JEE Main 9th April 2016 Online - Question 33

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The total number of orbitals associated with the principal quantum number 5 is:

A

20

B

25

C

10

D

5

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NTA JEE Main 9th April 2016 Online - Question 34

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The group of molecules having identical shape is:

A

$$PCl_5$$, $$IF_5$$, $$XeO_2F_2$$

B

$$BF_3$$, $$PCl_3$$, $$XeO_3$$

C

$$SF_4$$, $$XeF_4$$, $$CCl_4$$

D

$$ClF_3$$, $$XeOF_2$$, $$XeF_3^+$$

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NTA JEE Main 9th April 2016 Online - Question 35

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At very high pressures, the compressibility factor of one mole of a gas is given by:

A

$$1 + \frac{Pb}{RT}$$

B

$$\frac{Pb}{RT}$$

C

$$1 - \frac{Pb}{RT}$$

D

$$1 - \frac{b}{(VRT)}$$

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NTA JEE Main 9th April 2016 Online - Question 36

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Which intermolecular force is most responsible in allowing xenon gas to liquefy?

A

London forces

B

Ion-dipole

C

Ionic

D

Dipole-dipole

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NTA JEE Main 9th April 2016 Online - Question 37

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For the reaction,
$$A(g) + B(g) \to C(g) + D(g)$$, $$\Delta H°$$ and $$\Delta S°$$ are, respectively, $$-29.8$$ kJ mol$$^{-1}$$ and $$-0.100$$ kJ K$$^{-1}$$ mol$$^{-1}$$ at 298 K. The equilibrium constant for the reaction at 298 K is:

A

$$1.0 \times 10^{-10}$$

B

10

C

1

D

$$1.0 \times 10^{10}$$

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NTA JEE Main 9th April 2016 Online - Question 38

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A reaction at 1 bar is non-spontaneous at low temperature but becomes spontaneous at high temperature. Identify the correct statement about the reaction among the following:

A

$$\Delta H$$ is negative while $$\Delta S$$ is positive

B

Both $$\Delta H$$ and $$\Delta S$$ are negative

C

$$\Delta H$$ is positive while $$\Delta S$$ is negative

D

Both $$\Delta H$$ and $$\Delta S$$ are positive

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NTA JEE Main 9th April 2016 Online - Question 39

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Identify the incorrect statement regarding heavy water:

A

It reacts with $$SO_3$$ to form deuterated sulphuric acid $$(D_2SO_4)$$.

B

It is used as a coolant in nuclear reactors.

C

It reacts with $$CaC_2$$ to produce $$C_2D_2$$ and $$Ca(OD)_2$$.

D

It reacts with $$Al_4C_3$$ to produce $$CD_4$$ and $$Al(OD)_3$$.

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NTA JEE Main 9th April 2016 Online - Question 40

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The correct order of the solubility of alkaline-earth metal sulphates in water is:

A

Mg > Ca > Sr > Ba

B

Mg > Sr > Ca > Ba

C

Mg < Ca < Sr < Ba

D

Mg < Sr < Ca < Ba

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NTA JEE Main 9th April 2016 Online - Question 41

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Match the items in Column I with its main use listed in Column II:

A

A - iii, B - i, C - iv, D - ii

B

A - iv, B - i, C - ii, D - iii

C

A - ii, B - i, C - iv, D - iii

D

A - ii, B - iv, C - i, D - iii

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NTA JEE Main 9th April 2016 Online - Question 42

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The hydrocarbon with seven carbon atoms containing a neopentyl and a vinyl group is:

A

2,2-dimethyl-4-pentene

B

4,4-dimethylpent-1-ene

C

Isopropyl-2-butene

D

2,2-dimethyl-3-pentene

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NTA JEE Main 9th April 2016 Online - Question 43

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5 L of an alkane requires 25 L of oxygen for its complete combustion. If all volumes are measured at constant temperature and pressure, the alkane is

A

Isobutane

B

Ethane

C

Butane

D

Propane

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NTA JEE Main 9th April 2016 Online - Question 44

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BOD stands for:

A

Bacterial Oxidation Demand

B

Biological oxygen demand

C

Biochemical oxygen demand

D

Both A and B

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NTA JEE Main 9th April 2016 Online - Question 45

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The solubility of $$N_2$$ in water at 300 K and 500 torr partial pressure is 0.01 g L$$^{-1}$$. The solubility (in g L$$^{-1}$$) at 750 torr partial pressure is:

A

0.0075

B

0.005

C

0.02

D

0.015

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NTA JEE Main 9th April 2016 Online - Question 46

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What will happen when a block of copper metal is dropped into a beaker containing a solution of 1 M $$ZnSO_4$$?

A

The copper metal will dissolve with evolution of oxygen gas.

B

The copper metal will dissolve with evolution of hydrogen gas.

C

No reaction will occur.

D

The copper metal will dissolve and zinc metal will be deposited.

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NTA JEE Main 9th April 2016 Online - Question 47

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The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process shown below:
$$O_3(g) + Cl^\bullet \to O_2(g) + ClO^\bullet(g)$$ ...(i)
$$k_i = 5.2 \times 10^9$$ L mol$$^{-1}$$ s$$^{-1}$$
$$ClO^\bullet(g) + O^\bullet(g) \to O_2(g) + Cl^\bullet(g)$$ ...(ii)
$$k_{ii} = 2.6 \times 10^{10}$$ L mol$$^{-1}$$ s$$^{-1}$$
The closest rate constant for the overall reaction
$$O_3(g) + O^\bullet(g) \to 2O_2(g)$$ is:

A

$$1.4 \times 10^{20}$$ L mol$$^{-1}$$ s$$^{-1}$$

B

$$3.1 \times 10^{10}$$ L mol$$^{-1}$$ s$$^{-1}$$

C

$$5.2 \times 10^{9}$$ L mol$$^{-1}$$ s$$^{-1}$$

D

$$2.6 \times 10^{10}$$ L mol$$^{-1}$$ s$$^{-1}$$

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NTA JEE Main 9th April 2016 Online - Question 48

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A particular adsorption process has the following characteristics: (i) It arises due to van der Waals forces and (ii) it is reversible. Identify the correct statement that describes the above adsorption process:

A

Adsorption is monolayer

B

Adsorption increases with increase in temperature

C

Enthalpy of adsorption is greater than 100 kJ mol$$^{-1}$$

D

Energy of activation is low

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NTA JEE Main 9th April 2016 Online - Question 49

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The most appropriate method of making egg-albumin sol is:

A

Break an egg carefully and transfer the transparent part of the content to 100 mL of 5% w/V saline solution and stir well

B

Keep the egg in boiling water for 10 minutes. After removing the shell, transfer the yellow part of the content to 100 mL of 5% w/V saline solution and homogenize with a mechanical shaker

C

Keep the egg in boiling water for 10 minutes. After removing the shell, transfer the white part of the content to 100 mL of 5% w/V saline solution and homogenize with a mechanical shaker

D

Break an egg carefully and transfer only the yellow part of the content to 100 mL of 5% w/V saline solution and stir well

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NTA JEE Main 9th April 2016 Online - Question 50

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The plot shows the variation of $$-\ln K_P$$ versus temperature for the two reactions.
$$M(s) + \frac{1}{2}O_2(g) \to MO(s)$$ and
$$C(s) + \frac{1}{2}O_2(g) \to CO(s)$$

Identify the correct statement:

A

At T < 1200 K, oxidation of carbon is unfavourable

B

Oxidation of carbon is favourable at all temperatures

C

At T < 1200 K, the reaction $$MO(s) + C(s) \to M(s) + CO(g)$$ is spontaneous

D

At T > 1200 K, carbon will reduce $$MO_{(s)}$$ to $$M_{(s)}$$.

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NTA JEE Main 9th April 2016 Online - Question 51

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The non-metal that does not exhibit positive oxidation state is:

A

Chlorine

B

Iodine

C

Fluorine

D

Oxygen

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NTA JEE Main 9th April 2016 Online - Question 52

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Which one of the following species is stable in aqueous solution?

A

$$Cr^{2+}$$

B

$$MnO_4^{2-}$$

C

$$MnO_4^{3-}$$

D

$$Cu^+$$

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NTA JEE Main 9th April 2016 Online - Question 53

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Which one of the following complexes will consume more equivalents of aqueous solution of $$AgNO_3$$?

A

$$Na_2[CrCl_5(H_2O)]$$

B

$$Na_3[CrCl_6]$$

C

$$[Cr(H_2O)_5Cl]Cl_2$$

D

$$[Cr(H_2O)_6]Cl_3$$

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NTA JEE Main 9th April 2016 Online - Question 54

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Identify the correct trend given below:
(Atomic No. = Ti : 22, Cr : 24 and Mo : 42)

A

$$\Delta$$ of $$[Cr(H_2O)_6]^{2+} > [Mo(H_2O)_6]^{2+}$$ and $$\Delta$$ of $$[Ti(H_2O)_6]^{3+} > [Ti(H_2O)_6]^{2+}$$

B

$$\Delta$$ of $$[Cr(H_2O)_6]^{2+} > [Mo(H_2O)_6]^{2+}$$ and $$\Delta$$ of $$[Ti(H_2O)_6]^{3+} < [Ti(H_2O)_6]^{2+}$$

C

$$\Delta$$ of $$[Cr(H_2O)_6]^{2+} < [Mo(H_2O)_6]^{2+}$$ and $$\Delta$$ of $$[Ti(H_2O)_6]^{3+} > [Ti(H_2O)_6]^{2+}$$

D

$$\Delta$$ of $$[Cr(H_2O)_6]^{2+} < [Mo(H_2O)_6]^{2+}$$ and $$\Delta$$ of $$[Ti(H_2O)_6]^{3+} < [Ti(H_2O)_6]^{2+}$$

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NTA JEE Main 9th April 2016 Online - Question 55

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The gas evolved on heating $$CH_3MgBr$$ in methanol is:

A

Methane

B

Ethane

C

Propane

D

HBr

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NTA JEE Main 9th April 2016 Online - Question 56

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Bouveault-Blanc reduction reaction involves:

A

Reduction of an acyl halide with $$H_2/Pd$$.

B

Reduction of an anhydride with $$LiAlH_4$$

C

Reduction of an ester with $$Na/C_2H_5OH$$.

D

Reduction of a carbonyl compound with Na/Hg and HCl.

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NTA JEE Main 9th April 2016 Online - Question 57

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The test to distinguish primary, secondary and tertiary amines is:

A

Sandmeyer's reaction

B

Carbylamine reaction

C

Idoform test

D

$$C_6H_5SO_2Cl$$

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NTA JEE Main 9th April 2016 Online - Question 58

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Assertion: Rayon is a semisynthetic polymer whose properties are better than natural cotton.
Reason: Mechanical and aesthetic properties of cellulose can be improved by acetylation.

A

Both assertion and reason are correct, but the reason is not the correct explanation for the assertion.

B

Both assertion and reason are correct, and the reason is the correct explanation for the assertion.

C

Assertion is incorrect statement, but the reason is correct.

D

Both assertion and reason are incorrect.

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NTA JEE Main 9th April 2016 Online - Question 59

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The artificial sweetener that has the highest sweetness value in comparison to cane sugar is:

A

Sucralose

B

Aspartame

C

Saccharin

D

Alitame

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NTA JEE Main 9th April 2016 Online - Question 60

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Consider the following sequence for aspartic acid:

The pH (Isoelectric point) of aspartic acid is:

A

3.65

B

2.77

C

5.74

D

1.88

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NTA JEE Main 9th April 2016 Online - Question 61

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If the equations $$x^2 + bx - 1 = 0$$ and $$x^2 + x + b = 0$$ have a common root different from $$-1$$, then $$|b|$$ is equal to:

A

2

B

3

C

$$\sqrt{3}$$

D

$$\sqrt{2}$$

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NTA JEE Main 9th April 2016 Online - Question 62

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The point represented by $$2 + i$$ in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there $$2\sqrt{2}$$ units in the south-west wards direction. Then its new position in the Argand plane is at the point represented by:

A

$$1 + i$$

B

$$2 + 2i$$

C

$$-2 - 2i$$

D

$$-1 - i$$

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NTA JEE Main 9th April 2016 Online - Question 63

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If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is:

A

110

B

59

C

$$\frac{11!}{(2!)^3}$$

D

56

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NTA JEE Main 9th April 2016 Online - Question 64

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Let $$x$$, $$y$$, $$z$$ be positive real numbers such that $$x + y + z = 12$$ and $$x^3y^4z^5 = (0.1)(600)^3$$. Then $$x^3 + y^3 + z^3$$ is equal to

A

342

B

216

C

258

D

270

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NTA JEE Main 9th April 2016 Online - Question 65

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The value of $$\sum_{r=1}^{15} r^2 \left(\frac{^{15}C_r}{{}^{15}C_{r-1}}\right)$$ is equal to:

A

1240

B

560

C

1085

D

680

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NTA JEE Main 9th April 2016 Online - Question 66

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For $$x \in R$$, $$x \neq -1$$, if $$(1+x)^{2016} + x(1+x)^{2015} + x^2(1+x)^{2014} + \ldots + x^{2016} = \sum_{i=0}^{2016} a_i x_i$$, then $$a_{17}$$ is equal to

A

$$\frac{2017!}{17!2000!}$$

B

$$\frac{2016!}{17!1999!}$$

C

$$\frac{2016!}{16!}$$

D

$$\frac{2017!}{2000!}$$

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NTA JEE Main 9th April 2016 Online - Question 67

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If $$m$$ and $$M$$ are the minimum and the maximum values of $$4 + \frac{1}{2}\sin^2 2x - 2\cos^4 x$$, $$x \in R$$, then $$M - m$$ is equal to:

A

$$\frac{15}{4}$$

B

$$\frac{9}{4}$$

C

$$\frac{7}{4}$$

D

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

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NTA JEE Main 9th April 2016 Online - Question 68

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The number of $$x \in [0, 2\pi]$$ for which $$\left|\sqrt{2\sin^4 x + 18\cos^2 x} - \sqrt{2\cos^4 x + 18\sin^2 x}\right| = 1$$ is:

A

2

B

6

C

4

D

8

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NTA JEE Main 9th April 2016 Online - Question 69

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If a variable line drawn through the intersection of the lines $$\frac{x}{3} + \frac{y}{4} = 1$$ and $$\frac{x}{4} + \frac{y}{3} = 1$$, meets the coordinate axes at A and B, $$(A \neq B)$$, then the locus of the midpoint of AB is:

A

$$7xy = 6(x + y)$$

B

$$4(x+y)^2 - 28(x+y) + 49 = 0$$

C

$$6xy = 7(x + y)$$

D

$$14(x+y)^2 - 97(x+y) + 168 = 0$$

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NTA JEE Main 9th April 2016 Online - Question 70

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The point $$(2, 1)$$ is translated parallel to the line $$L : x - y = 4$$ by $$2\sqrt{3}$$ units. If the new point $$Q$$ lies in the third quadrant, then the equation of the line passing through $$Q$$ and perpendicular to $$L$$ is

A

$$x + y = 2 - \sqrt{6}$$

B

$$2x + 2y = 1 - \sqrt{6}$$

C

$$x + y = 3 - 3\sqrt{6}$$

D

$$x + y = 3 - 2\sqrt{6}$$

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NTA JEE Main 9th April 2016 Online - Question 71

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A circle passes through $$(-2, 4)$$ and touches the y-axis at $$(0, 2)$$. Which one of the following equations can represent a diameter of this circle?

A

$$2x - 3y + 10 = 0$$

B

$$3x + 4y - 3 = 0$$

C

$$4x + 5y - 6 = 0$$

D

$$5x + 2y + 4 = 0$$

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NTA JEE Main 9th April 2016 Online - Question 72

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If the tangent at a point on the ellipse $$\frac{x^2}{27} + \frac{y^2}{3} = 1$$ meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is

A

$$3\sqrt{3}$$

B

$$\frac{9}{2}$$

C

9

D

$$9\sqrt{3}$$

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NTA JEE Main 9th April 2016 Online - Question 73

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Let $$a$$ and $$b$$ respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation $$9e^2 - 18e + 5 = 0$$. If $$S(5, 0)$$ is a focus and $$5x = 9$$ is the corresponding directrix of this hyperbola, then $$a^2 - b^2$$ is equal to

A

$$-7$$

B

$$-5$$

C

5

D

7

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NTA JEE Main 9th April 2016 Online - Question 74

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If $$f(x)$$ is a differentiable function in the interval $$(0, \infty)$$ such that $$f(1) = 1$$ and $$\lim_{t \to x} \frac{t^2 f(x) - x^2 f(t)}{t - x} = 1$$, for each $$x \gt 0$$, then $$f\left(\frac{3}{2}\right)$$ is equal to

A

$$\frac{23}{18}$$

B

$$\frac{13}{6}$$

C

$$\frac{25}{9}$$

D

$$\frac{31}{18}$$

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NTA JEE Main 9th April 2016 Online - Question 75

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If $$\lim_{x \to \infty} \left(1 + \frac{a}{x} - \frac{4}{x^2}\right)^{2x} = e^3$$, then $$a$$ is equal to

A

2

B

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

C

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

D

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

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NTA JEE Main 9th April 2016 Online - Question 76

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Consider the following two statements:
$$P$$: If 7 is an odd number, then 7 is divisible by 2.
$$Q$$: If 7 is a prime number, then 7 is an odd number.
If $$V_1$$ is the truth value of the contrapositive of $$P$$ and $$V_2$$ is the truth value of contrapositive of $$Q$$, then the ordered pair $$(V_1, V_2)$$ equals

A

$$(F, T)$$

B

$$(F, F)$$

C

$$(T, F)$$

D

$$(T, T)$$

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NTA JEE Main 9th April 2016 Online - Question 77

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If the mean deviation of the numbers $$1, 1+d, \ldots, 1+100d$$ from their mean is 255, then a value of $$d$$ is:

A

10.1

B

5.05

C

20.2

D

10

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NTA JEE Main 9th April 2016 Online - Question 78

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If $$P = \begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix}$$, $$A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$$ and $$Q = PAP^T$$, then $$P^T Q^{2015} P$$ is:

A

$$\begin{bmatrix} 0 & 2015 \\ 0 & 0 \end{bmatrix}$$

B

$$\begin{bmatrix} 2015 & 0 \\ 1 & 2015 \end{bmatrix}$$

C

$$\begin{bmatrix} 1 & 2015 \\ 0 & 1 \end{bmatrix}$$

D

$$\begin{bmatrix} 2015 & 1 \\ 0 & 2015 \end{bmatrix}$$

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NTA JEE Main 9th April 2016 Online - Question 79

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The number of distinct real roots of the equation, $$\begin{vmatrix} \cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x \end{vmatrix} = 0$$ in the interval $$\left[-\frac{\pi}{4}, \frac{\pi}{4}\right]$$ is:

A

1

B

4

C

2

D

3

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NTA JEE Main 9th April 2016 Online - Question 80

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For $$x \in R$$, $$x \neq 0$$, $$x \neq 1$$, let $$f_0(x) = \frac{1}{1-x}$$ and $$f_{n+1}(x) = f_0(f_n(x))$$, $$n = 0, 1, 2, \ldots$$. Then the value of $$f_{100}(3) + f_1\left(\frac{2}{3}\right) + f_2\left(\frac{3}{2}\right)$$ is equal to:

A

$$\frac{8}{3}$$

B

$$\frac{4}{3}$$

C

$$\frac{5}{3}$$

D

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

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NTA JEE Main 9th April 2016 Online - Question 81

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If the function $$f(x) = \begin{cases} -x, & x < 1 \\ a + \cos^{-1}(x+b), & 1 \leq x \leq 2 \end{cases}$$ is differentiable at $$x = 1$$, then $$\frac{a}{b}$$ is equal to

A

$$\frac{\pi + 2}{2}$$

B

$$\frac{\pi - 2}{2}$$

C

$$\frac{-\pi - 2}{2}$$

D

$$-1 - \cos^{-1}(2)$$

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NTA JEE Main 9th April 2016 Online - Question 82

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The minimum distance of a point on the curve $$y = x^2 - 4$$ from the origin is

A

$$\frac{\sqrt{15}}{2}$$ units

B

$$\sqrt{\frac{19}{2}}$$ units

C

$$\sqrt{\frac{15}{2}}$$ units

D

$$\frac{\sqrt{19}}{2}$$ units

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NTA JEE Main 9th April 2016 Online - Question 83

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If the tangent at a point P, with parameter $$t$$, on the curve $$x = 4t^2 + 3$$, $$y = 8t^3 - 1$$, $$t \in R$$, meets the curve again at a point Q, then the coordinates of Q are:

A

$$(16t^2 + 3, -64t^3 - 1)$$

B

$$(4t^2 + 3, -8t^3 - 1)$$

C

$$(t^2 + 3, t^3 - 1)$$

D

$$(t^2 + 3, -t^3 - 1)$$

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NTA JEE Main 9th April 2016 Online - Question 84

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If $$\int \frac{dx}{\cos^3 x \sqrt{2\sin 2x}} = (\tan x)^A + C(\tan x)^B + k$$, where k is a constant of integration, then $$A + B + C$$ equals

A

$$\frac{16}{5}$$

B

$$\frac{27}{10}$$

C

$$\frac{7}{10}$$

D

$$\frac{21}{5}$$

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NTA JEE Main 9th April 2016 Online - Question 85

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If $$2\int_0^1 \tan^{-1} x\,dx = \int_0^1 \cot^{-1}(1 - x + x^2)\,dx$$, then $$\int_0^1 \tan^{-1}(1 - x + x^2)\,dx$$ is equal to

A

$$\frac{\pi}{2} + \ln 2$$

B

$$\ln 2$$

C

$$\frac{\pi}{2} - \ln 4$$

D

$$\ln 4$$

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NTA JEE Main 9th April 2016 Online - Question 86

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The area (in sq. units) of the region described by $$A = \{(x, y) | y \geq x^2 - 5x + 4, x + y \geq 1, y \leq 0\}$$ is

A

$$\frac{19}{6}$$

B

$$\frac{17}{6}$$

C

$$\frac{7}{2}$$

D

$$\frac{13}{6}$$

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NTA JEE Main 9th April 2016 Online - Question 87

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In a triangle $$ABC$$, right angle at vertex $$A$$, if the position vectors of $$A$$, $$B$$ and $$C$$ are respectively $$3\hat{i} + \hat{j} - \hat{k}$$, $$-\hat{i} + 3\hat{j} + p\hat{k}$$ and $$5\hat{i} + q\hat{j} - 4\hat{k}$$, then the point $$(p, q)$$ lies on a line:

A

Making an obtuse angle with the positive direction of $$x$$-axis

B

Parallel to $$x$$-axis

C

Parallel to $$y$$-axis

D

Making an acute angle with the positive direction of $$x$$-axis

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NTA JEE Main 9th April 2016 Online - Question 88

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The shortest distance between the lines $$\frac{x}{2} = \frac{y}{2} = \frac{z}{1}$$ and $$\frac{x+2}{-1} = \frac{y-4}{8} = \frac{z-5}{4}$$, lies in the interval:

A

$$(3, 4]$$

B

$$(2, 3]$$

C

$$[1, 2)$$

D

$$[0, 1)$$

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NTA JEE Main 9th April 2016 Online - Question 89

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The distance of the point $$(1, -2, 4)$$ from the plane passing through the point $$(1, 2, 2)$$ and perpendicular to the planes $$x - y + 2z = 3$$ and $$2x - 2y + z + 12 = 0$$, is:

A

2

B

$$\sqrt{2}$$

C

$$2\sqrt{2}$$

D

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

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NTA JEE Main 9th April 2016 Online - Question 90

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If A and B are any two events such that $$P(A) = \frac{2}{5}$$ and $$P(A \cap B) = \frac{3}{20}$$, then the conditional probability, $$P(A|(A' \cup B'))$$, where $$A'$$ denotes the complement of A, is equal to:

A

$$\frac{11}{20}$$

B

$$\frac{5}{17}$$

C

$$\frac{8}{17}$$

D

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

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