NTA JEE Main 19th April 2014 Online

NTA JEE Main 19th April 2014 Online - Question 1

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A bullet loses $$\left(\frac{1}{n}\right)^{th}$$ of its velocity passing through one plank. Considering uniform retardation, the number of such planks that are required to stop the bullet can be:

A

Infinite

B

$$n$$

C

$$\frac{n^2}{(2n-1)}$$

D

$$\frac{2n^2}{(n-1)}$$

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NTA JEE Main 19th April 2014 Online - Question 2

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A heavy box is to be dragged along a rough horizontal floor. To do so, the person A pushes it at an angle 30° from the horizontal and requires a minimum force $$F_A$$, while the person B pulls the box at an angle 60° from the horizontal and needs minimum force $$F_B$$. If the coefficient of friction between the box and the floor is $$\frac{\sqrt{3}}{5}$$, the ratio $$\frac{F_A}{F_B}$$ is:

A

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

B

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

C

$$\sqrt{3}$$

D

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

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NTA JEE Main 19th April 2014 Online - Question 3

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A particle is released on a vertical smooth semicircular track from point X so that, OX makes an angle $$\theta$$ from the vertical (see the figure). The normal reaction of the track on the particle vanishes at point Y, where OY makes an angle $$\phi$$ with the horizontal. Then:

A

$$\sin\phi = \frac{2}{3}\cos\theta$$

B

$$\sin\phi = \frac{3}{4}\cos\theta$$

C

$$\sin\phi = \frac{1}{2}\cos\theta$$

D

$$\sin\phi = \cos\theta$$

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NTA JEE Main 19th April 2014 Online - Question 4

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Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is $$F_{friction}$$ at point P? It is assumed that the cylinder does not slip.

A

Ma

B

$$\frac{Ma}{2}$$

C

$$\frac{Ma}{3}$$

D

Mg

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NTA JEE Main 19th April 2014 Online - Question 5

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A ball of mass 160 g is thrown up at an angle of 60° to the horizontal at a speed of 10 m s$$^{-1}$$. The angular momentum of the ball at the highest point of the trajectory with respect to the point from which the ball is thrown is nearly (g = 10 m s$$^{-2}$$)

A

1.73 kg m$$^2$$ s$$^{-1}$$

B

3.46 kg m$$^2$$ s$$^{-1}$$

C

3.0 kg m$$^2$$ s$$^{-1}$$

D

6.0 kg m$$^2$$ s$$^{-1}$$

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NTA JEE Main 19th April 2014 Online - Question 6

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Match List-I (Event) with List-II (Order of the time interval for the happening of the event) and select the correct option from the options given below the lists.

List-I:                                                             List-II:
(a) The rotation period of earth             (i) 10$$^5$$ s
(b) Revolution period of earth               (ii) 10$$^7$$ s
(c) Period of a light wave                      (iii) 10$$^{-15}$$ s
(d) Period of a sound wave                    (iv) 10$$^{-3}$$ s

A

(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)

B

(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)

C

(a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)

D

(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)

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NTA JEE Main 19th April 2014 Online - Question 7

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The gravitational field in a region is given by $$\vec{g} = (5\hat{i} + 12\hat{j})$$ N kg$$^{-1}$$. The change in the gravitational potential energy of a particle of mass 2 kg when it is taken from the origin to a point (7 m, $$-3$$ m) is:

A

71 J

B

$$13\sqrt{58}$$ J

C

2 J

D

1 J

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NTA JEE Main 19th April 2014 Online - Question 8

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The velocity of water in a river is 18 km h$$^{-1}$$ near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water = $$10^{-2}$$ poise.

A

$$10^{-4}$$ N m$$^{-2}$$

B

$$10^{-3}$$ N m$$^{-2}$$

C

$$10^{-2}$$ N m$$^{-2}$$

D

$$10^{-1}$$ N m$$^{-2}$$

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NTA JEE Main 19th April 2014 Online - Question 9

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A large number of liquid drops each of radius r coalesce to form a single drop of the radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of the liquid T, density $$\rho$$)

A

$$\sqrt{\frac{2T}{\rho}\left(\frac{1}{r} - \frac{1}{R}\right)}$$

B

$$\sqrt{\frac{6T}{\rho}\left(\frac{1}{r} - \frac{1}{R}\right)}$$

C

$$\sqrt{\frac{4T}{\rho}\left(\frac{1}{r} - \frac{1}{R}\right)}$$

D

$$\sqrt{\frac{T}{\rho}\left(\frac{1}{r} - \frac{1}{R}\right)}$$

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NTA JEE Main 19th April 2014 Online - Question 10

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In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross-section of the tube at A and B is 6 mm$$^2$$ and 10 mm$$^2$$ respectively. The rate at which water flows through the tube is (g = 10 m s$$^{-2}$$)

A

7.5 cc s$$^{-1}$$

B

12.5 cc s$$^{-1}$$

C

8.0 cc s$$^{-1}$$

D

10.0 cc s$$^{-1}$$

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NTA JEE Main 19th April 2014 Online - Question 11

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A black coloured solid sphere of radius R and mass M is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature $$T_0$$. The initial temperature of the sphere is $$3T_0$$. If the specific heat of the material of the sphere varies as $$\alpha T^3$$ per unit mass with the temperature T of the sphere, where $$\alpha$$ is a constant, then the time taken for the sphere to cool down to temperature $$2T_0$$ will be ($$\sigma$$ is Stefan Boltzmann constant)

A

$$\frac{M\alpha}{16\pi R^2\sigma}\ln\left(\frac{3}{2}\right)$$

B

$$\frac{M\alpha}{16\pi R^2\sigma}\ln\left(\frac{16}{3}\right)$$

C

$$\frac{M\alpha}{4\pi R^2\sigma}\ln\left(\frac{3}{2}\right)$$

D

$$\frac{M\alpha}{4\pi R^2\sigma}\ln\left(\frac{16}{3}\right)$$

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NTA JEE Main 19th April 2014 Online - Question 12

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A monoatomic gas is compressed from a volume of 2 m$$^3$$ to a volume of 1 m$$^3$$ at a constant pressure of 100 N m$$^2$$. Then it is heated at constant volume by supplying 150 J of energy. As a result, the internal energy of the gas:

A

Decreases by 50 J

B

Increases by 250 J

C

Decreases by 250 J

D

0 J

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NTA JEE Main 19th April 2014 Online - Question 13

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A gas molecule of mass M at the surface of the earth has kinetic energy equivalent to 0 °C. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than the radius of the earth. (k$$_B$$ is Boltzmann constant)

A

$$\frac{273k_B}{2Mg}$$

B

$$\frac{819k_B}{2Mg}$$

C

0

D

$$\frac{546k_B}{3Mg}$$

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NTA JEE Main 19th April 2014 Online - Question 14

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A body is in simple harmonic motion with time period $$T = 0.5$$ s and amplitude $$A = 1$$ cm. Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

A

16 cm/s

B

6 cm/s

C

4 cm/s

D

12 cm/s

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NTA JEE Main 19th April 2014 Online - Question 15

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The total length of a sonometer wire fixed between two bridges is 110 cm. Now, two more bridges are placed to divide the length of the wire in the ratio 6 : 3 : 2. If the tension in the wire is 400 N and the mass per unit length of the wire is 0.01 kg m$$^{-1}$$, then the minimum common frequency with which all the three parts can vibrate, is:

A

1000 Hz

B

1100 Hz

C

100 Hz

D

110 Hz

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NTA JEE Main 19th April 2014 Online - Question 16

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The electric field in a region of space is given by, $$\vec{E} = E_0\hat{i} + 2E_0\hat{j}$$ where $$E_0 = 100$$ N C$$^{-1}$$. The flux of this field through a circular surface of radius 0.02 m parallel to the Y-Z plane is nearly:

A

0.02 N m$$^2$$ C$$^{-1}$$

B

0.005 N m$$^2$$ C$$^{-1}$$

C

0.125 N m$$^2$$ C$$^{-1}$$

D

3.14 N m$$^2$$ C$$^{-1}$$

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NTA JEE Main 19th April 2014 Online - Question 17

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The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose relative permittivity varies linearly from $$\epsilon_1$$ at one plate to $$\epsilon_2$$ at the other. The capacitance of the capacitor is:

A

$$\frac{\epsilon_0(\epsilon_2-\epsilon_1)A}{d\ln(\epsilon_2/\epsilon_1)}$$

B

$$\frac{\epsilon_0(\epsilon_2+\epsilon_1)A}{2d}$$

C

$$\frac{\epsilon_0(\epsilon_1+\epsilon_2)A}{d}$$

D

$$\frac{\epsilon_0 A}{[d\ln(\epsilon_2/\epsilon_1)]}$$

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NTA JEE Main 19th April 2014 Online - Question 18

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Four bulbs B$$_1$$, B$$_2$$, B$$_3$$ and B$$_4$$ of 100 W each are connected to 220 V main as shown in the figure. The reading in the ideal ammeter will be:

A

0.90 A

B

1.35 A

C

0.45 A

D

1.80 A

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NTA JEE Main 19th April 2014 Online - Question 19

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An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity B, the magnetic field $$B_s$$ inside the superconductor will be such that:

A

$$B_s = B$$

B

$$B_s = 0$$

C

$$B_s < B$$ but $$B_s \neq 0$$

D

$$B_s = -B$$

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NTA JEE Main 19th April 2014 Online - Question 20

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A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of 10 m s$$^{-1}$$ (see figure). The e.m.f induced at the time the left arm of the frame is at x = 10 cm from the wire is:

A

0.75 $$\mu$$V

B

1 $$\mu$$V

C

2 $$\mu$$V

D

0.5 $$\mu$$V

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NTA JEE Main 19th April 2014 Online - Question 21

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The figure shows a circular area of radius R where a uniform magnetic field $$\vec{B}$$ is going into the plane of the paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?

A

B

C

D

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NTA JEE Main 19th April 2014 Online - Question 22

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If microwaves, X-rays, infrared, gamma rays, ultraviolet, radio waves and visible parts of the electromagnetic spectrum are denoted respectively by M, X, I, G, U, R and V the following is the arrangement in ascending order of the wavelength:

A

I, M, R, U, V, X and G

B

R, M, I, V, U, X and G

C

M, R, V, X, U, G and I

D

G, X, U, V, I, M and R

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NTA JEE Main 19th April 2014 Online - Question 23

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The diameter of the objective lens of the microscope makes an angle $$\beta$$ at the focus of the microscope. Further, the medium between the object and the lens is the oil of the refractive index n. Then the resolving power of the microscope:

A

Increases with decreasing value of $$\beta$$

B

Increases with increasing value of $$n\sin 2\beta$$

C

Increases with increasing value of $$\frac{1}{n\sin 2\beta}$$

D

Increases with decreasing value of $$n$$

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NTA JEE Main 19th April 2014 Online - Question 24

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A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is $$\theta_{iC}$$ and Brewster's angle of incidence is $$\theta_{iB}$$, such that $$\frac{\sin\theta_{iC}}{\sin\theta_{iB}} = \eta = 1.28$$. The relative refractive index of the two media is:

A

0.4

B

0.2

C

0.9

D

0.8

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NTA JEE Main 19th April 2014 Online - Question 25

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In Young's double-slit experiment, the distance between the two identical slits is 6.1 times larger than the slit width. Then the number of intensity maxima observed within the central maximum of the single-slit diffraction pattern is:

A

3

B

6

C

24

D

12

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NTA JEE Main 19th April 2014 Online - Question 26

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Match List-I (Experiment performed) with List-II (Phenomena discovered/associated) and select the correct option from the options given below the lists.

List-I:                                                                  List-II:
(a) Davisson and Germer experiment                    (i) Wave nature of electrons
(b) Millikan's oil drop experiment                         (ii) Charge of an electron
(c) Rutherford experiment                                   (iii) Quantisation of energy levels
(d) Franck-Hertz experiment                               (iv) Existence of the nucleus

A

(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

B

(a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)

C

(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

D

(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)

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NTA JEE Main 19th April 2014 Online - Question 27

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A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If the half-life of C$$^{14}$$ is 5730 years, then the age of the wooden piece placed in the museum is approximately: [This question was awarded a bonus and proper correction was made to avoid that]

A

10439 years

B

39049 years

C

19042 years

D

13094 years

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NTA JEE Main 19th April 2014 Online - Question 28

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Given, A and B are input terminals. Logic 1 is > 5 V, Logic 0 is < 1 V. Which logic gate operation, the following circuit does?

Note: This question was awarded a bonus. C option changed.

A

OR gate

B

NOR gate

C

Output will always be one

D

XOR gate

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NTA JEE Main 19th April 2014 Online - Question 29

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Long-range radio transmission is possible when the radio waves are reflected from the ionosphere. For this to happen the frequency of the radio waves must be in the range:

A

150 $$-$$ 500 kHz

B

80 $$-$$ 150 MHz

C

1 $$-$$ 3 MHz

D

8 $$-$$ 25 MHz

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NTA JEE Main 19th April 2014 Online - Question 30

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In an experiment to determine the gravitational acceleration g of a place with the help of a simple pendulum, the measured time period squared is plotted against the string length of the pendulum in the figure. What is the value of g at the place?

A

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

B

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

C

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

D

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

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NTA JEE Main 19th April 2014 Online - Question 31

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The ionization energy of gaseous Na atoms is 495.5 kJ mol$$^{-1}$$. The lowest possible frequency of light that ionizes a sodium atom is (h = $$6.626 \times 10^{-34}$$ Js, N$$_A$$ = $$6.022 \times 10^{23}$$ mol$$^{-1}$$)

A

$$1.24 \times 10^{15}$$ s$$^{-1}$$

B

$$7.50 \times 10^4$$ s$$^{-1}$$

C

$$4.76 \times 10^{14}$$ s$$^{-1}$$

D

$$3.15 \times 10^{15}$$ s$$^{-1}$$

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NTA JEE Main 19th April 2014 Online - Question 32

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Which one of the following has the largest ionic radius?

A

F$$^-$$

B

B$$^{3+}$$

C

O$$^{2-}$$

D

Li$$^+$$

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NTA JEE Main 19th April 2014 Online - Question 33

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Which one of the following molecules is paramagnetic?

A

N$$_2$$

B

O$$_3$$

C

CO

D

NO

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NTA JEE Main 19th April 2014 Online - Question 34

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Sulphur dioxide and oxygen were allowed to diffuse through a porous partition. 20 dm$$^3$$ of SO$$_2$$ diffuses through the porous partition in 60 seconds. The volume of O$$_2$$ in dm$$^3$$ which diffuses under the similar condition in 30 seconds will be (atomic mass of sulphur = 32 u):

A

28.2

B

10.0

C

14.1

D

7.09

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NTA JEE Main 19th April 2014 Online - Question 35

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For the decomposition of the compound, represented as NH$$_2$$COONH$$_4$$(s) $$\rightleftharpoons$$ 2NH$$_3$$(g) + CO$$_2$$(g), the K$$_p$$ = $$2.9 \times 10^{-5}$$ atm$$^3$$. If the reaction is started with 1 mole of the compound, the total pressure at equilibrium would be:

A

$$7.66 \times 10^{-2}$$ atm

B

$$38.8 \times 10^{-2}$$ atm

C

$$5.82 \times 10^{-2}$$ atm

D

$$1.94 \times 10^{-2}$$ atm

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NTA JEE Main 19th April 2014 Online - Question 36

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Zirconium phosphate [Zr$$_3$$(PO$$_4$$)$$_4$$] dissociates into three zirconium cations of charge +4 and four phosphate anions of charge $$-3$$. If molar solubility of zirconium phosphate is denoted by s and its solubility product by K$$_{sp}$$ then which of the following relationship between s and K$$_{sp}$$ is correct?

A

$$S = \{K_{sp}/6912\}^7$$

B

$$S = \{K_{sp}/144\}^{1/7}$$

C

$$S = \{K_{sp}/(6912)^{1/7}\}$$

D

$$S = (K_{sp}/6912)^{1/7}$$

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NTA JEE Main 19th April 2014 Online - Question 37

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How many electrons are involved in the following redox reaction?
Cr$$_2$$O$$_7^{2-}$$ + Fe$$^{2+}$$ + C$$_2$$O$$_4^{2-}$$ → Cr$$^{3+}$$ + Fe$$^{3+}$$ + CO$$_2$$ (Unbalanced)

A

6

B

5

C

3

D

4

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NTA JEE Main 19th April 2014 Online - Question 38

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Consider the reaction: H$$_2$$SO$$_{3(aq)}$$ + Sn$$^{4+}_{(aq)}$$ + H$$_2$$O$$_{(l)}$$ → Sn$$^{2+}_{(aq)}$$ + HSO$$^-_{4(aq)}$$ + 3H$$^+_{(aq)}$$. Which of the following statements is correct?

A

Sn$$^{4+}$$ is the oxidizing agent because it undergoes oxidation

B

Sn$$^{4+}$$ is the reducing agent because it undergoes oxidation

C

H$$_2$$SO$$_3$$ is the reducing agent because it undergoes reduction

D

H$$_2$$SO$$_3$$ is the reducing agent because it undergoes oxidation

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NTA JEE Main 19th April 2014 Online - Question 39

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Amongst LiCl, RbCl, BeCl$$_2$$ and MgCl$$_2$$ the compounds with the greatest and the least ionic character, respectively are:

A

MgCl$$_2$$ and BeCl$$_2$$

B

RbCl and MgCl$$_2$$

C

LiCl and RbCl

D

RbCl and BeCl$$_2$$

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NTA JEE Main 19th April 2014 Online - Question 40

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Example of a three-dimensional silicate is:

A

Ultramarines

B

Feldspars

C

Zeolites

D

All of these

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NTA JEE Main 19th April 2014 Online - Question 41

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Which of these statements is not true?

A

LiAlH$$_4$$ is versatile reducing agent in organic synthesis.

B

NO$$^+$$ is isoelectronic with O$$_2$$

C

Boron is always covalent in its compounds

D

In aqueous solution, the Tl$$^+$$ ion is much more stable than Tl (III)

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NTA JEE Main 19th April 2014 Online - Question 42

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The correct IUPAC name of the following compound is:

A

4-methyl-3-ethylhexane

B

3-ethyl-4-methylhexane

C

4-ethyl-3-methylhexane

D

3,4-ethylmethylhexane

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NTA JEE Main 19th April 2014 Online - Question 43

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The total number of octahedral void(s) per atom present in a cubic close packed structure is:

A

1

B

2

C

3

D

4

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NTA JEE Main 19th April 2014 Online - Question 44

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For an ideal solution of two components A & B, which of the following is true?

A

$$\Delta H_{mixing} > 0$$ (zero)

B

A $$-$$ B interaction is stronger than A $$-$$ A & B $$-$$ B interactions

C

A $$-$$ A, B $$-$$ B & A $$-$$ B interactions are identical

D

$$\Delta H_{mixing} < 0$$ (zero)

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NTA JEE Main 19th April 2014 Online - Question 45

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The observed osmotic pressure for a 0.10 M solution of Fe(NH$$_4$$)$$_2$$(SO$$_4$$)$$_2$$ at 25 °C is 10.8 atm. The expected and experimental (observed) values of Van't Hoff factor 'i' will be respectively; (R = 0.082 L atm k$$^-$$ mol$$^{-1}$$)

A

4 and 4.00

B

3 and 5.42

C

5 and 4.42

D

5 and 3.42

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NTA JEE Main 19th April 2014 Online - Question 46

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Choose the correct statement with respect to the vapour pressure of a liquid among the following:

A

Increases non-linearly with increasing temperature

B

Decreases non-linearly with increasing temperature

C

Decreases linearly with increasing temperature

D

Increases linearly with increasing temperature

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NTA JEE Main 19th April 2014 Online - Question 47

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For the reaction, 3A + 2B → C + D, the differential rate law can be written as:

A

$$+\frac{1}{3}\frac{d[A]}{dt} = -\frac{d[C]}{dt} = k[A]^n[B]^m$$

B

$$\frac{1}{3}\frac{d[A]}{dt} = \frac{d[C]}{dt} = k[A]^n[B]^m$$

C

$$-\frac{1}{3}\frac{d[A]}{dt} = \frac{d[C]}{dt} = k[A]^n[B]^m$$

D

$$-\frac{d[A]}{dt} = \frac{d[C]}{dt} = k[A]^n[B]^m$$

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NTA JEE Main 19th April 2014 Online - Question 48

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Which one of the following ores is known as Malachite:

A

Cu$$_2$$S

B

Cu$$_2$$O

C

Cu(OH)$$_2$$ · CuCO$$_3$$

D

CuFeS$$_2$$

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NTA JEE Main 19th April 2014 Online - Question 49

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An octahedral complex with molecular composition M.5NH$$_3$$.Cl.SO$$_4$$ has two isomers, A and B. The solution of A gives a white precipitate with AgNO$$_3$$ solution and the solution of B gives white precipitate with BaCl$$_2$$ solution. The type of isomerism exhibited by the complex is:

A

Coordinate isomerism

B

Geometrical isomerism

C

Ionisation isomerism

D

Linkage isomerism

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NTA JEE Main 19th April 2014 Online - Question 50

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Nickel (Z = 28) combines with a uninegative monodentate ligand to form a diamagnetic complex [NiL$$_4$$]$$^{2-}$$. The hybridisation involved and the number of unpaired electrons present in the complex are respectively:

A

dsp$$^2$$, zero

B

sp$$^3$$, zero

C

dsp$$^2$$, one

D

sp$$^3$$, two

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NTA JEE Main 19th April 2014 Online - Question 51

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Amongst the following, identify the species with an atom in +6 oxidation state.

A

CrO$$_2$$Cl$$_2$$

B

[Cr(CN)$$_6$$]$$^{3-}$$

C

Cr$$_2$$O$$_3$$

D

[MnO$$_4$$]$$^-$$

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NTA JEE Main 19th April 2014 Online - Question 52

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The major product formed when 1, 1, 1-trichloropropane is treated with aqueous potassium hydroxide is:

A

2-Propanol

B

Propyne

C

Propionic acid

D

1-Propanol

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NTA JEE Main 19th April 2014 Online - Question 53

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Which of the following compounds will not be soluble in sodium bicarbonate?

A

2, 4, 6-Trinitrophenol

B

Benzene sulphonic acid

C

o-Nitrophenol

D

Benzoic acid

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NTA JEE Main 19th April 2014 Online - Question 54

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Which one of the following substituents at para-position is most effective in stabilizing the phenoxide ion?

A

-CH$$_3$$

B

-OCH$$_3$$

C

-COCH$$_3$$

D

-CH$$_2$$OH

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NTA JEE Main 19th April 2014 Online - Question 55

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Williamson synthesis of ether is an example of:

A

Nucleophilic substitution

B

Electrophilic addition

C

Nucleophilic addition

D

Electrophilic substitution

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NTA JEE Main 19th April 2014 Online - Question 56

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The final product formed when methylamine is treated with NaNO$$_2$$ and HCl followed by hydrolysis is:

A

Nitromethane

B

Methylcyanide

C

Methyl alcohol

D

Diazomethane

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NTA JEE Main 19th April 2014 Online - Question 57

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In a set of reactions p-nitrotoluene yielded a product E.

The product E would be:

A

B

C

D

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NTA JEE Main 19th April 2014 Online - Question 58

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Which one of the following is an example of thermosetting polymer?

A

Nylon-6,6

B

Bakelite

C

Buna-N

D

Teflon

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NTA JEE Main 19th April 2014 Online - Question 59

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Among the following organic acids, the acid present in rancid butter is:

A

Pyruvic acid

B

Acetic acid

C

Butyric acid

D

Lactic acid

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NTA JEE Main 19th April 2014 Online - Question 60

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The reason for double helical structure of DNA is the operation of:

A

Van der Waals forces

B

Electrostatic attractions

C

Hydrogen bonding

D

Dipole-Dipole interactions

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NTA JEE Main 19th April 2014 Online - Question 61

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The equation $$\sqrt{3x^2 + x + 5} = x - 3$$, where x is real, has:

A

no solution

B

exactly four solutions

C

exactly one solution

D

exactly two solutions

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NTA JEE Main 19th April 2014 Online - Question 62

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For all complex numbers z of the form $$1 + i\alpha$$, $$\alpha \in R$$, if $$z^2 = x + iy$$, then:

A

$$y^2 - 4x + 4 = 0$$

B

$$y^2 + 4x - 4 = 0$$

C

$$y^2 - 4x + 2 = 0$$

D

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

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NTA JEE Main 19th April 2014 Online - Question 63

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Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval:

A

(11, 13]

B

(14, 17)

C

[10, 12)

D

[8, 9]

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NTA JEE Main 19th April 2014 Online - Question 64

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Let $$f(n) = \left[\frac{1}{3} + \frac{3n}{100}\right]n$$, where $$[n]$$ denotes the greatest integer less than or equal to n. Then $$\sum_{n=1}^{56} f(n)$$ is equal to:

A

56

B

1287

C

1399

D

689

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NTA JEE Main 19th April 2014 Online - Question 65

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The number of terms in an A.P. is even, the sum of the odd terms in it is 24 and that of the even terms is 30. If the last term exceeds the first term by $$10\frac{1}{2}$$, then the number of terms in the A.P. is:

A

4

B

8

C

16

D

12

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NTA JEE Main 19th April 2014 Online - Question 66

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The coefficient of $$x^{1012}$$ in the expansion of $$(1 + x^n + x^{253})^{10}$$, (where $$n \leq 22$$ is any positive integer), is:

A

$$^{253}C_4$$

B

$$^{10}C_4$$

C

4n

D

1

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NTA JEE Main 19th April 2014 Online - Question 67

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If a line L is perpendicular to the line $$5x - y = 1$$, and the area of the triangle formed by the line L and the coordinate axes is 5 sq units, then the distance of the line L from the line $$x + 5y = 0$$ is:

A

$$\frac{7}{\sqrt{13}}$$ units

B

$$\frac{7}{\sqrt{5}}$$ units

C

$$\frac{5}{\sqrt{13}}$$ units

D

$$\frac{5}{\sqrt{7}}$$ units

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NTA JEE Main 19th April 2014 Online - Question 68

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The circumcentre of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points $$(a^2 + 1, a^2 + 1)$$ and $$(2a, -2a)$$, $$a \neq 0$$. Then for any a, the orthocentre of this triangle lies on the line:

A

$$y - (a^2+1)x = 0$$

B

$$y - 2ax = 0$$

C

$$y + x = 0$$

D

$$(a-1)^2x - (a+1)^2y = 0$$

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NTA JEE Main 19th April 2014 Online - Question 69

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The equation of the circle described on the chord $$3x + y + 5 = 0$$ of the circle $$x^2 + y^2 = 16$$ as the diameter is:

A

$$x^2 + y^2 + 3x + y + 1 = 0$$

B

$$x^2 + y^2 + 3x + y - 22 = 0$$

C

$$x^2 + y^2 + 3x + y - 11 = 0$$

D

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

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NTA JEE Main 19th April 2014 Online - Question 70

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A chord is drawn through the focus of the parabola $$y^2 = 6x$$ such that its distance from the vertex of this parabola is $$\frac{\sqrt{5}}{2}$$, then its slope can be:

A

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

B

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

C

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

D

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

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NTA JEE Main 19th April 2014 Online - Question 71

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The tangent at an extremity (in the first quadrant) of the latus rectum of the hyperbola $$\frac{x^2}{4} - \frac{y^2}{5} = 1$$, meets the x-axis and y-axis at A and B, respectively. Then $$OA^2 - OB^2$$, where O is the origin, equals:

A

$$-\frac{20}{9}$$

B

$$\frac{16}{9}$$

C

4

D

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

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NTA JEE Main 19th April 2014 Online - Question 72

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The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is:

A

if I will go to the doctor, then I am not feeling well.

B

if I am feeling well, then I will not go to the doctor.

C

if I will not go to the doctor, then I am feeling well.

D

if I will go to the doctor, then I am feeling well.

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NTA JEE Main 19th April 2014 Online - Question 73

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Let $$\bar{x}$$, M and $$\sigma^2$$ be respectively the mean, mode and variance of n observations $$x_1, x_2, \ldots, x_n$$ and $$d_i = -x_i - a$$, i = 1, 2, ..., n, where a is any number.
Statement I: Variance of d$$_1$$, d$$_2$$, ..., d$$_n$$ is $$\sigma^2$$.
Statement II: Mean and mode of d$$_1$$, d$$_2$$, ..., d$$_n$$ are $$-\bar{x} - a$$ and $$-M - a$$, respectively.

A

Statement I and Statement II are both true

B

Statement I and Statement II are both false

C

Statement I is true and Statement II is false

D

Statement I is false and Statement II is true

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NTA JEE Main 19th April 2014 Online - Question 74

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Let A and B be any two $$3 \times 3$$ matrices. If A is symmetric and B is skew symmetric, then the matrix AB $$-$$ BA is:

A

skew symmetric

B

I or $$-I$$, where I is an identity matrix

C

symmetric

D

neither symmetric nor skew symmetric

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NTA JEE Main 19th April 2014 Online - Question 75

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If $$\Delta_r = \begin{vmatrix} r & 2r-1 & 3r-2 \\ \frac{n}{2} & n-1 & a \\ \frac{1}{2}n(n-1) & (n-1)^2 & \frac{1}{2}(n-1)(3n+4) \end{vmatrix}$$, then the value of $$\sum_{r=1}^{n-1} \Delta_r$$:

A

Is independent of both a and n

B

Depends only on a

C

Depends only on n

D

Depends both on a and n

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NTA JEE Main 19th April 2014 Online - Question 76

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The principal value of $$\tan^{-1}\left(\cot\frac{43\pi}{4}\right)$$ is:

A

$$\frac{\pi}{4}$$

B

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

C

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

D

$$-\frac{3\pi}{4}$$

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NTA JEE Main 19th April 2014 Online - Question 77

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The function $$f(x) = |\sin 4x| + |\cos 2x|$$, is a periodic function with a fundamental period:

A

$$\pi$$

B

$$2\pi$$

C

$$\frac{\pi}{4}$$

D

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

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NTA JEE Main 19th April 2014 Online - Question 78

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Let $$f : R \to R$$ be defined by $$f(x) = \frac{|x|-1}{|x|+1}$$, then f is:

A

one-one but not onto

B

neither one-one nor onto

C

both one-one and onto

D

onto but not one-one

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NTA JEE Main 19th April 2014 Online - Question 79

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If the function $$f(x) = \begin{cases} \frac{\sqrt{2+\cos x}-1}{(\pi-x)^2}, & x \neq \pi \\ k, & x = \pi \end{cases}$$ is continuous at $$x = \pi$$, then k equals:

A

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

B

0

C

2

D

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

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NTA JEE Main 19th April 2014 Online - Question 80

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Let $$f : R \to R$$ be a function such that $$|f(x)| \leq x^2$$, for all $$x \in R$$. Then, at x = 0, f is:

A

differentiable but not continuous

B

neither continuous nor differentiable

C

continuous as well as differentiable

D

continuous but not differentiable

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NTA JEE Main 19th April 2014 Online - Question 81

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If the volume of a spherical ball is increasing at the rate of $$4\pi$$ cc/sec then the rate of increase of its radius (in cm/sec), when the volume is $$288\pi$$ cc is:

A

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

B

$$\frac{1}{6}$$

C

$$\frac{1}{24}$$

D

$$\frac{1}{36}$$

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NTA JEE Main 19th April 2014 Online - Question 82

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If non-zero real numbers b and c are such that $$\min f(x) > \max g(x)$$, where $$f(x) = x^2 + 2bx + 2c^2$$ and $$g(x) = -x^2 - 2cx + b^2$$, $$(x \in R)$$; then $$\left|\frac{c}{b}\right|$$ lies in the interval:

A

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

B

$$\left[\frac{1}{2}, \frac{1}{\sqrt{2}}\right)$$

C

$$(0, \frac{1}{2})$$

D

$$\left[\frac{1}{\sqrt{2}}, \sqrt{2}\right]$$

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NTA JEE Main 19th April 2014 Online - Question 83

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If m is a non-zero number and $$\int \frac{x^{5m-1}+2x^{4m-1}}{(x^{2m}+x^m+1)^3} dx = f(x) + c$$, then $$f(x)$$ is equal to:

A

$$\frac{(x^{5m}-x^{4m})}{2m(x^{2m}+x^m+1)^2}$$

B

$$\frac{1}{2m} \cdot \frac{x^{4m}}{(x^{2m}+x^m+1)^2}$$

C

$$\frac{x^{5m}}{2m(x^{2m}+x^m+1)^2}$$

D

$$\frac{2m(x^{5m}+x^{4m})}{(x^{2m}+x^m+1)^2}$$

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NTA JEE Main 19th April 2014 Online - Question 84

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Let, the function F be defined as $$F(x) = \int_1^x \frac{e^t}{t} dt$$, $$x > 0$$, then the value of the integral $$\int_1^x \frac{e^t}{t+a} dt$$, where a > 0, is:

A

$$e^a[F(x) - F(1+a)]$$

B

$$e^{-a}[F(x+a) - F(a)]$$

C

$$e^a[F(x+a) - F(1+a)]$$

D

$$e^{-a}[F(x+a) - F(1+a)]$$

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NTA JEE Main 19th April 2014 Online - Question 85

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The area of the region (in square units) above the x-axis bounded by the curve $$y = \tan x$$, $$0 \leq x \leq \frac{\pi}{2}$$ and the tangent to the curve at $$x = \frac{\pi}{4}$$ is:

A

$$\frac{1}{2}(\log 2 - \frac{1}{2})$$

B

$$\frac{1}{2}(1 + \log 2)$$

C

$$\frac{1}{2}(1 - \log 2)$$

D

$$\frac{1}{2}(\log 2 + \frac{1}{2})$$

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NTA JEE Main 19th April 2014 Online - Question 86

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If $$\frac{dy}{dx} + y\tan x = \sin 2x$$ and $$y(0) = 1$$, then $$y(\pi)$$ is equal to:

A

$$-1$$

B

5

C

1

D

$$-5$$

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NTA JEE Main 19th April 2014 Online - Question 87

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If $$\vec{x} = 3\hat{i} - 6\hat{j} - \hat{k}$$, $$\vec{y} = \hat{i} + 4\hat{j} - 3\hat{k}$$ and $$\vec{z} = 3\hat{i} - 4\hat{j} - 12\hat{k}$$, then the magnitude of the projection of $$\vec{x} \times \vec{y}$$ on $$\vec{z}$$ is:

A

14

B

12

C

15

D

10

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NTA JEE Main 19th April 2014 Online - Question 88

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If the angle between the line $$2(x+1) = y = z + 4$$ and the plane $$2x - y + \sqrt{\lambda}z + 4 = 0$$ is $$\frac{\pi}{6}$$, then the value of $$\lambda$$ is:

A

$$\frac{45}{7}$$

B

$$\frac{135}{11}$$

C

$$\frac{135}{7}$$

D

$$\frac{45}{11}$$

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NTA JEE Main 19th April 2014 Online - Question 89

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Equation of the line of the shortest distance between the lines $$\frac{x}{1} = \frac{y}{-1} = \frac{z}{1}$$ and $$\frac{x-1}{0} = \frac{y+1}{-2} = \frac{z}{1}$$ is:

A

$$\frac{x}{-2} = \frac{y}{1} = \frac{z}{2}$$

B

$$\frac{x}{1} = \frac{y}{-1} = \frac{z}{-2}$$

C

$$\frac{x-1}{1} = \frac{y+1}{-1} = \frac{z}{-2}$$

D

$$\frac{x-1}{1} = \frac{y+1}{-1} = \frac{z}{1}$$

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NTA JEE Main 19th April 2014 Online - Question 90

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Let A and E be any two events with positive probabilities.
Statement I: $$P(E/A) \geq P(A/E)P(E)$$.
Statement II: $$P(A/E) \geq P(A \cap E)$$.

A

Both the statements are false

B

Both the statements are true

C

Statement-I is false, Statement-II is true

D

Statement-I is true, Statement-II is false

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