NTA JEE Main 11th April 2014 Online

NTA JEE Main 11th April 2014 Online - Question 1

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In terms of resistance R and time T, the dimensions of ratio $$\frac{\mu}{\varepsilon}$$ of the permeability $$\mu$$ and permittivity $$\varepsilon$$ is:

A

$$[RT^{-2}]$$

B

$$[R^2T^{-1}]$$

C

$$[R^2]$$

D

$$[R^2T^2]$$

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NTA JEE Main 11th April 2014 Online - Question 2

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The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target must the rifle be aimed in order to hit the target?

A

1.0 m

B

4.2 m

C

6.1 m

D

9.8 m

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NTA JEE Main 11th April 2014 Online - Question 3

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A body of mass 5 kg under the action of constant force $$\vec{F} = F_x\hat{i} + F_y\hat{j}$$ has velocity at t = 0 s as $$\vec{v} = (6\hat{i} - 2\hat{j})$$ m/s and at t = 10 s as $$\vec{v} = +6\hat{j}$$ m/s. The force $$\vec{F}$$ is:

A

$$(-3\hat{i} + 4\hat{j})$$ N

B

$$\left(-\frac{3}{5}\hat{i} + \frac{4}{5}\hat{j}\right)$$ N

C

$$(3\hat{i} - 4\hat{j})$$ N

D

$$\left(\frac{3}{5}\hat{i} - \frac{4}{5}\hat{j}\right)$$ N

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NTA JEE Main 11th April 2014 Online - Question 4

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A small ball of mass m starts at a point A with speed $$v_o$$ and moves along a frictionless track AB as shown. The track BC has coefficient of friction $$\mu$$. The ball comes to stop at C after travelling a distance L which is:

A

$$\frac{2h}{\mu} + \frac{v_o^2}{2\mu g}$$

B

$$\frac{h}{\mu} + \frac{v_o^2}{2\mu g}$$

C

$$\frac{h}{2\mu} + \frac{v_o^2}{\mu g}$$

D

$$\frac{h}{2\mu} + \frac{v_o^2}{2\mu g}$$

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NTA JEE Main 11th April 2014 Online - Question 5

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A thin bar of length L has a mass per unit length $$\lambda$$, that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is $$\lambda_0$$, then the distance of the centre of mass from the lighter end is:

A

$$\frac{L}{2} - \frac{\lambda_0 L^2}{4M}$$

B

$$\frac{L}{3} + \frac{\lambda_0 L^2}{8M}$$

C

$$\frac{L}{3} + \frac{\lambda_0 L^2}{4M}$$

D

$$\frac{2L}{3} - \frac{\lambda_0 L^2}{6M}$$

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NTA JEE Main 11th April 2014 Online - Question 6

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From a sphere of mass M and radius R, a smaller sphere of radius $$\frac{R}{2}$$ is carved out such that the cavity made in the original sphere is between its centre and the periphery (see the figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two spheres is:

A

$$\frac{41GM^2}{3600R^2}$$

B

$$\frac{41GM^2}{450R^2}$$

C

$$\frac{59GM^2}{450R^2}$$

D

$$\frac{GM^2}{225R^2}$$

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NTA JEE Main 11th April 2014 Online - Question 7

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The bulk moduli of ethanol, mercury and water are given as 0.9, 25 and 2.2 respectively in units of $$10^9$$ Nm$$^{-2}$$. For a given value of pressure, the fractional compression in volume is $$\frac{\Delta V}{V}$$. Which of the following statements about $$\frac{\Delta V}{V}$$ for these three liquids is correct?

A

Ethanol > Water > Mercury

B

Water > Ethanol > Mercury

C

Mercury > Ethanol > Water

D

Ethanol > Mercury > Water

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NTA JEE Main 11th April 2014 Online - Question 8

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The average mass of rain drops is $$3.0 \times 10^{-5}$$ kg and their average terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.

A

$$3.5 \times 10^5$$ J

B

$$4.05 \times 10^4$$ J

C

$$3.0 \times 10^5$$ J

D

$$9.0 \times 10^4$$ J

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NTA JEE Main 11th April 2014 Online - Question 9

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A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3 m and that of kerosene is 2 m. When the hole is opened, the velocity of fluid coming out from it is nearly: (take g = 10 ms$$^{-2}$$ and density of water = $$10^3$$ kg m$$^{-3}$$)

A

10.7 ms$$^{-1}$$

B

9.6 ms$$^{-1}$$

C

8.5 ms$$^{-1}$$

D

7.6 ms$$^{-1}$$

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NTA JEE Main 11th April 2014 Online - Question 10

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An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density $$10^3$$ kg/m$$^3$$. The pressure inside the bubble is 1100 Nm$$^{-2}$$ greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? ($$g = 9.8$$ ms$$^{-2}$$)

A

0.1 m

B

0.15 m

C

0.20 m

D

0.25 m

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NTA JEE Main 11th April 2014 Online - Question 11

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A hot body, obeying Newton's law of cooling is cooling down from its peak value 80°C to an ambient temperature of 30°C. It takes 5 minutes in cooling down from 80°C to 40°C. How much time will it take to cool down from 62°C to 32°C? (Given ln 2 = 0.693, ln 5 = 1.609)

A

3.75 minutes

B

8.6 minutes

C

9.6 minutes

D

6.5 minutes

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NTA JEE Main 11th April 2014 Online - Question 12

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During an adiabatic compression, 830 J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly: (R = 8.3 JK$$^{-1}$$ mol$$^{-1}$$)

A

40 K

B

33 K

C

20 K

D

14 K

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NTA JEE Main 11th April 2014 Online - Question 13

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An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section $$8.0 \times 10^{-3}$$ m$$^2$$. Initially the gas is at 300 K and occupies a volume of $$2.4 \times 10^{-3}$$ m$$^3$$ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is $$1.0 \times 10^5$$ N/m$$^2$$. The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible).

A

300 K

B

800 K

C

500 K

D

1000 K

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NTA JEE Main 11th April 2014 Online - Question 14

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The angular frequency of the damped oscillator is given by, $$\omega = \sqrt{\left(\frac{k}{m} - \frac{r^2}{4m^2}\right)}$$ where k is the spring constant, m is the mass of the oscillator and r is the damping constant. If the ratio $$\frac{r^2}{mk}$$ is 8%, the change in time period compared to the undamped oscillator is approximately as follows:

A

increases by 1%

B

increases by 8%

C

decreases by 1%

D

decreases by 8%

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NTA JEE Main 11th April 2014 Online - Question 15

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Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be:

A

2

B

4

C

8

D

10

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NTA JEE Main 11th April 2014 Online - Question 16

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A cone of base radius R and height h is located in a uniform electric field $$\vec{E}$$ parallel to its base. The electric flux entering the cone is:

A

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

B

EhR

C

2EhR

D

4EhR

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NTA JEE Main 11th April 2014 Online - Question 17

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A parallel plate capacitor is made of two plates of length l, width w and separated by a distance d. A dielectric slab (dielectric constant K) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force $$F = -\frac{\partial U}{\partial x}$$, where U is the energy of the capacitor when dielectric is inside the capacitor up to distance x (see the figure). If the charge on the capacitor is Q then the force on the dielectric when it is near the edge is:

A

$$\frac{Q^2 d}{2wl^2\varepsilon_0}K$$

B

$$\frac{Q^2 w}{2dl^2\varepsilon_0}(K-1)$$

C

$$\frac{Q^2 d}{2wl^2\varepsilon_0}(K-1)$$

D

$$\frac{Q^2 w}{2dl^2\varepsilon_0}K$$

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NTA JEE Main 11th April 2014 Online - Question 18

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In the circuit shown, current (in A) through 50 V and 30 V batteries are, respectively:

A

2.5 and 3

B

3.5 and 2

C

4.5 and 1

D

3 and 2.5

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NTA JEE Main 11th April 2014 Online - Question 19

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In the circuit diagrams (A, B, C and D) shown below, R is a high resistance and S is a resistance of the order of galvanometer resistance G. The correct circuit, corresponding to the half deflection method for finding the resistance and figure of merit of the galvanometer, is the circuit labelled as:

(a)

(b)

(c)

(d)

A

Circuit A with $$G = \frac{RS}{(R-S)}$$

B

Circuit B with G = S

C

Circuit C with G = S

D

Circuit D with $$G = \frac{RS}{(R-S)}$$

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NTA JEE Main 11th April 2014 Online - Question 20

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Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as follows:

Make the correspondence of these bars with their material being diamagnetic (D), ferromagnetic (F) and paramagnetic (P):

A

A ↔ D, B ↔ P, C ↔ F

B

A ↔ F, B ↔ D, C ↔ P

C

A ↔ P, B ↔ F, C ↔ D

D

A ↔ F, B ↔ P, C ↔ D

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NTA JEE Main 11th April 2014 Online - Question 21

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Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length 25 cm is:

A

$$3 \times 10^{-4}$$ N toward right

B

$$6 \times 10^{-4}$$ N toward right

C

$$9 \times 10^{-4}$$ N toward right

D

Zero

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NTA JEE Main 11th April 2014 Online - Question 22

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A coil of circular cross-section having 1000 turns and 4 cm$$^2$$ face area is placed with its axis parallel to a magnetic field which decreases by $$10^{-2}$$ Wb m$$^{-2}$$ in 0.01 s. The e.m.f. induced in the coil is:

A

400 mV

B

200 mV

C

4 mV

D

0.4 mV

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NTA JEE Main 11th April 2014 Online - Question 23

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An electromagnetic wave of frequency $$1 \times 10^{14}$$ hertz is propagating along z-axis. The amplitude of electric field is 4 V/m. If $$\varepsilon_0 = 8.8 \times 10^{-12}$$ C$$^2$$/N-m$$^2$$, then average energy density of electric field will be:

A

$$35.2 \times 10^{-10}$$ J/m$$^3$$

B

$$35.2 \times 10^{-11}$$ J/m$$^3$$

C

$$35.2 \times 10^{-12}$$ J/m$$^3$$

D

$$35.2 \times 10^{-13}$$ J/m$$^3$$

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NTA JEE Main 11th April 2014 Online - Question 24

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An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 3. What is the distance between the screen and the object?

A

124.5 cm

B

144.5 cm

C

65.0 cm

D

99.0 cm

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NTA JEE Main 11th April 2014 Online - Question 25

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In a compound microscope the focal length of objective lens is 1.2 cm and focal length of eye piece is 3.0 cm. When object is kept at 1.25 cm in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be:

A

200

B

100

C

400

D

150

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NTA JEE Main 11th April 2014 Online - Question 26

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Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright and dark parts of the resultant pattern is:

A

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

B

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

C

$$\frac{7}{1}$$

D

$$\frac{49}{1}$$

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NTA JEE Main 11th April 2014 Online - Question 27

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A photon of wavelength $$\lambda$$ is scattered from an electron, which was at rest. The wavelength shift $$\Delta\lambda$$ is three times of $$\lambda$$ and the angle of scattering $$\theta$$ is 60°. The angle at which the electron recoiled is $$\phi$$. The value of $$\tan \phi$$ is: (electron speed is much smaller than the speed of light)

A

0.16

B

0.22

C

0.25

D

0.28

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NTA JEE Main 11th April 2014 Online - Question 28

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Match the List-I (Phenomenon associated with electromagnetic radiation) with List-II (Part of electromagnetic spectrum) and select the correct code from the choices given below this lists:

A

(I)-(A), (II)-(B), (III)-(B), (IV)-(C)

B

(I)-(A), (II)-(B), (III)-(C), (IV)-(C)

C

(I)-(D), (II)-(C), (III)-(A), (IV)-(B)

D

(I)-(B), (II)-(A), (III)-(D), (IV)-(A)

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NTA JEE Main 11th April 2014 Online - Question 29

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A radioactive nuclei with decay constant 0.5/s is being produced at a constant rate of 100 nuclei/s. If at t = 0 there were no nuclei, the time when there are 50 nuclei is:

A

1 s

B

$$2\ln\left(\frac{4}{3}\right)$$ s

C

$$\ln 2$$ s

D

$$\ln\left(\frac{4}{3}\right)$$ s

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NTA JEE Main 11th April 2014 Online - Question 30

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A Zener diode is connected to a battery and a load as shown below:

The currents, I, I$$_Z$$ and I$$_L$$ are respectively.

A

15 mA, 5 mA, 10 mA

B

15 mA, 7.5 mA, 7.5 mA

C

12.5 mA, 5 mA, 7.5 mA

D

12.5 mA, 7.5 mA, 5 mA

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NTA JEE Main 11th April 2014 Online - Question 31

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A gaseous compound of nitrogen and hydrogen contains 12.5% (by mass) of hydrogen. The density of the compound relative to hydrogen is 16. The molecular formula of the compound is:

A

NH$$_2$$

B

N$$_3$$H

C

NH$$_3$$

D

N$$_2$$H$$_4$$

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NTA JEE Main 11th April 2014 Online - Question 32

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If $$\lambda_0$$ and $$\lambda$$ be threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected from the metal surface is:

A

$$\sqrt{\frac{2h}{m}(\lambda_0 - \lambda)}$$

B

$$\sqrt{\frac{2hc}{m}(\lambda_0 - \lambda)}$$

C

$$\sqrt{\frac{2hc}{m}\left(\frac{\lambda_0 - \lambda}{\lambda \lambda_0}\right)}$$

D

$$\sqrt{\frac{2h}{m}\left(\frac{1}{\lambda_0} - \frac{1}{\lambda}\right)}$$

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NTA JEE Main 11th April 2014 Online - Question 33

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Based on the equation: $$\Delta E = -2.0 \times 10^{-18}$$ J $$\left(\frac{1}{n_2^2} - \frac{1}{n_1^2}\right)$$, the wavelength of the light that must be absorbed to excite hydrogen electron from level n = 1 to level n = 2 will be: (h = $$6.625 \times 10^{-34}$$ Js, C = $$3 \times 10^8$$ ms$$^{-1}$$)

A

$$1.325 \times 10^{-7}$$ m

B

$$1.325 \times 10^{-10}$$ m

C

$$2.650 \times 10^{-7}$$ m

D

$$5.300 \times 10^{-10}$$ m

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NTA JEE Main 11th April 2014 Online - Question 34

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Which of the following series correctly represents relations between the elements from X to Y? X → Y

A

$$_3$$Li → $$_{19}$$K Ionization enthalpy increases

B

$$_9$$F → $$_{35}$$Br Electron gain enthalpy (negative sign) increases

C

$$_6$$C → $$_{32}$$Ge Atomic radii increases

D

$$_{18}$$Ar → $$_{54}$$Xe Noble character increases

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NTA JEE Main 11th April 2014 Online - Question 35

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The correct order of bond dissociation energy among N$$_2$$, O$$_2$$, O$$_2^-$$ is shown in which of the following arrangements?

A

N$$_2$$ > O$$_2^-$$ > O$$_2$$

B

O$$_2^-$$ > O$$_2$$ > N$$_2$$

C

N$$_2$$ > O$$_2$$ > O$$_2^-$$

D

O$$_2$$ > O$$_2^-$$ > N$$_2$$

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NTA JEE Main 11th April 2014 Online - Question 36

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Which one of the following does not have a pyramidal shape?

A

(CH$$_3$$)$$_3$$ N

B

(SiH$$_3$$)$$_3$$ N

C

P(CH$$_3$$)$$_3$$

D

P(SiH$$_3$$)$$_3$$

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NTA JEE Main 11th April 2014 Online - Question 37

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In allene (C$$_3$$H$$_4$$), the type(s) of hybridization of the carbon atoms is (are):

A

sp and sp$$^3$$

B

sp$$^2$$ and sp

C

only sp$$^2$$

D

sp$$^2$$ and sp$$^3$$

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NTA JEE Main 11th April 2014 Online - Question 38

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The initial volume of a gas cylinder is 750.0 mL. If the pressure of gas inside the cylinder changes from 840.0 mmHg to 360.0 mmHg, the final volume the gas will be:

A

1.750 L

B

3.60 L

C

4.032 L

D

7.50 L

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NTA JEE Main 11th April 2014 Online - Question 39

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The molar heat capacity (C$$_p$$) of CD$$_2$$O is 10 cals at 1000 K. The change of entropy associated with cooling of 32 g of CD$$_2$$O vapour from 1000 K to 100 K at constant pressure will be: (D = deuterium, atomic mass = 2u)

A

23.03 cal deg$$^{-1}$$

B

$$-23.03$$ cal deg$$^{-1}$$

C

2.303 cal deg$$^{-1}$$

D

$$-2.303$$ cal deg$$^{-1}$$

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NTA JEE Main 11th April 2014 Online - Question 40

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Consider the following equilibrium:
$$AgCl \downarrow + 2NH_3 \rightleftharpoons [Ag(NH_3)_2]^+ + Cl^-$$
White precipitate of AgCl appears on adding which of the following?

A

NH$$_3$$

B

aqueous NaCl

C

aqueous HNO$$_3$$

D

aqueous NH$$_4$$Cl

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NTA JEE Main 11th April 2014 Online - Question 41

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Assuming that the degree of hydrolysis is small, the pH of 0.1M solution of sodium acetate (K$$_a$$ = $$1.0 \times 10^{-5}$$) will be:

A

5.0

B

6.0

C

8.0

D

9.0

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NTA JEE Main 11th April 2014 Online - Question 42

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Which of the following statements about Na$$_2$$O$$_2$$ is not correct?

A

It is diamagnetic in nature

B

It is derivative of H$$_2$$O$$_2$$

C

Na$$_2$$O$$_2$$ oxidises Cr$$^{3+}$$ to CrO$$_4^{2-}$$ in acid medium

D

It is the super oxide of sodium

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NTA JEE Main 11th April 2014 Online - Question 43

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The reagent needed for converting:

A

Cat. Hydrogenation

B

H$$_2$$/Lindlar Cat.

C

Li/NH$$_3$$

D

LiAlH$$_4$$

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NTA JEE Main 11th April 2014 Online - Question 44

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The gas liberated by the electrolysis of Dipotassium succinate solution is:

A

Ethane

B

Ethyne

C

Ethene

D

Propene

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NTA JEE Main 11th April 2014 Online - Question 45

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Which of the following statements about the depletion of ozone layer is correct?

A

The problem of ozone depletion is less serious at poles because NO$$_2$$ solidifies and is not available for consuming ClO• radicals.

B

The problem of ozone depletion is more serious at poles because ice crystals in the clouds over poles act as catalyst for photochemical reactions involving the decomposition of ozone of Cl• and ClO• radicals.

C

Freons, chlorofluorocarbons, are inert. Chemically, they do not react with ozone in stratosphere.

D

Oxides of nitrogen also do not react with ozone in stratosphere.

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NTA JEE Main 11th April 2014 Online - Question 46

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The appearance of colour in solid alkali metal halides is generally due to:

A

Schottky defect

B

Frenkel defect

C

Interstitial position

D

F-centres

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NTA JEE Main 11th April 2014 Online - Question 47

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In some solutions, the concentration of H$$_3$$O$$^+$$ remains constant even when small amounts of strong acid or strong base are added to them. These solutions are known as:

A

Ideal solutions

B

Colloidal solutions

C

True solutions

D

Buffer solutions

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NTA JEE Main 11th April 2014 Online - Question 48

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Given:
Fe$$^{3+}$$(aq) + e$$^-$$ → Fe$$^{2+}$$(aq); E$$^0$$ = +0.77 V
Al$$^{3+}$$(aq) + 3e$$^-$$ → Al(s); E$$^0$$ = $$-1.66$$ V
Br$$_2$$(aq) + 2e$$^-$$ → 2Br$$^-$$; E$$^0$$ = +1.09 V
Considering the electrode potentials, which of the following represents the correct order of reducing power?

A

Fe$$^{2+}$$ < Al < Br$$^-$$

B

Br$$^-$$ < Fe$$^{2+}$$ < Al

C

Al < Br$$^-$$ < Fe$$^{2+}$$

D

Al < Fe$$^{2+}$$ < Br$$^-$$

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NTA JEE Main 11th April 2014 Online - Question 49

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In the reaction of formation of sulphur trioxide by contact process $$2SO_2 + O_2 \rightleftharpoons 2SO_3$$ the rate of reaction was measured as $$\frac{d[O_2]}{dt} = -2.5 \times 10^{-4}$$ mol L$$^{-1}$$ s$$^{-1}$$. The rate of reaction in terms of [SO$$_2$$] in mol L$$^{-1}$$ s$$^{-1}$$ will be:

A

$$-1.25 \times 10^{-4}$$

B

$$-2.50 \times 10^{-4}$$

C

$$-3.75 \times 10^{-4}$$

D

$$-5.00 \times 10^{-4}$$

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NTA JEE Main 11th April 2014 Online - Question 50

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For the reaction, $$2N_2O_5 \to 4NO_2 + O_2$$, the rate equation can be expressed in two ways:
$$-\frac{d[N_2O_5]}{dt} = k[N_2O_5]$$ and $$+\frac{d[NO_2]}{dt} = k'[N_2O_5]$$. k and k' are related as:

A

k = k'

B

2k = k'

C

k = 2k'

D

k = 4k'

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NTA JEE Main 11th April 2014 Online - Question 51

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Shapes of certain interhalogen compounds are stated below. Which one of them is not correctly stated?

A

IF$$_7$$: pentagonal bipyramid

B

BrF$$_5$$: trigonal bipyramid

C

BrF$$_3$$: planar T-shaped

D

ICl$$_3$$: planar dimeric

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NTA JEE Main 11th April 2014 Online - Question 52

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Which of the following name formula combinations is not correct?

A

K$$_2$$[Pt(CN)$$_4$$] - Potassium tetracyanoplatinate (II)

B

[Mn(CN)$$_5$$]$$^{2-}$$ - Pentacyanomangonate (II) ion

C

K[Cr(NH$$_3$$)$$_2$$Cl$$_4$$] - Potassium diammine tetrachlorochromate (III)

D

[Co(NH$$_3$$)$$_4$$(H$$_2$$O)I]SO$$_4$$ - Tetraammine aquaiodo cobalt (III) sulphate

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NTA JEE Main 11th April 2014 Online - Question 53

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Consider the coordination compound, [Co(NH$$_3$$)$$_6$$]Cl$$_3$$. In the formation of this complex, the species which acts as the Lewis acid is:

A

[Co(NH$$_3$$)$$_6$$]$$^{3+}$$

B

Cl$$^-$$

C

Co$$^{3+}$$

D

NH$$_3$$

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NTA JEE Main 11th April 2014 Online - Question 54

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Chlorobenzene reacts with trichloro acetaldehyde in the presence of H$$_2$$SO$$_4$$. The major product formed is:

A

B

C

D

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NTA JEE Main 11th April 2014 Online - Question 55

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Tischenko reaction is a modification of:

A

Aldol condensation

B

Claisen condensation

C

Cannizzaro reaction

D

Pinacol-pinacolon reaction

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NTA JEE Main 11th April 2014 Online - Question 56

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Which one of the following statements is not correct?

A

Alcohols are weaker acids than water

B

Acid strength of alcohols decreases in the following order: RCH$$_2$$OH > R$$_2$$CHOH > R$$_3$$COH

C

Carbon-oxygen bond length in methanol, CH$$_3$$OH is shorter than that of C-O bond length in phenol.

D

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NTA JEE Main 11th April 2014 Online - Question 57

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The following reaction is known as:

A

Perkin reaction

B

Gatterman-Koch Formylation

C

Kolbe's reaction

D

Gattermann reaction

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NTA JEE Main 11th April 2014 Online - Question 58

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An organic compound A, C$$_5$$H$$_8$$O; reacts with H$$_2$$O, NH$$_3$$ and CH$$_3$$COOH as described below:

A

B

C

D

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NTA JEE Main 11th April 2014 Online - Question 59

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Complete reduction of benzene-diazonium chloride with Zn/HCl gives:

A

Aniline

B

Phenylhydrazine

C

Azobenzene

D

Hydrazobenzene

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NTA JEE Main 11th April 2014 Online - Question 60

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Which one of the following is used as Antihistamine?

A

Omeprazole

B

Chloranphenicol

C

Diphenhydramine

D

Norethindrone

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NTA JEE Main 11th April 2014 Online - Question 61

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If $$\alpha$$ and $$\beta$$ are roots of the equation, $$x^2 - 4\sqrt{2}kx + 2e^{4\ln k} - 1 = 0$$ for some $$k$$, and $$\alpha^2 + \beta^2 = 66$$, then $$\alpha^3 + \beta^3$$ is equal to:

A

$$248\sqrt{2}$$

B

$$280\sqrt{2}$$

C

$$-32\sqrt{2}$$

D

$$-280\sqrt{2}$$

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NTA JEE Main 11th April 2014 Online - Question 62

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If $$z_1, z_2$$ and $$z_3, z_4$$ are 2 pairs of complex conjugate numbers, then $$\arg\left(\frac{z_1}{z_4}\right) + \arg\left(\frac{z_2}{z_3}\right)$$ equals:

A

0

B

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

C

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

D

$$\pi$$

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NTA JEE Main 11th April 2014 Online - Question 63

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An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is:

A

72(7!)

B

18(7!)

C

40(7!)

D

36(7!)

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NTA JEE Main 11th April 2014 Online - Question 64

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In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is:

A

7

B

21

C

28

D

42

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NTA JEE Main 11th April 2014 Online - Question 65

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The sum of the first 20 terms common between the series 3 + 7 + 11 + 15 + ... and 1 + 6 + 11 + 16 + ... is:

A

4000

B

4020

C

4200

D

4220

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NTA JEE Main 11th April 2014 Online - Question 66

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The coefficient of $$x^{50}$$ in the binomial expansion of $$(1+x)^{1000} + x(1+x)^{999} + x^2(1+x)^{998} + \ldots + x^{1000}$$ is:

A

$$\frac{(1000)!}{(50)!(950)!}$$

B

$$\frac{(1000)!}{(49)!(951)!}$$

C

$$\frac{(1001)!}{(51)!(950)!}$$

D

$$\frac{(1001)!}{(50)!(951)!}$$

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NTA JEE Main 11th April 2014 Online - Question 67

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If $$2\cos\theta + \sin\theta = 1$$ ($$\theta \neq \frac{\pi}{2}$$), then $$7\cos\theta + 6\sin\theta$$ is equal to:

A

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

B

2

C

$$\frac{11}{2}$$

D

$$\frac{46}{5}$$

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NTA JEE Main 11th April 2014 Online - Question 68

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The base of an equilateral triangle is along the line given by $$3x + 4y = 9$$. If a vertex of the triangle is $$(1, 2)$$, then the length of a side of the triangle is:

A

$$\frac{2\sqrt{3}}{15}$$

B

$$\frac{4\sqrt{3}}{15}$$

C

$$\frac{4\sqrt{3}}{5}$$

D

$$\frac{2\sqrt{3}}{5}$$

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NTA JEE Main 11th April 2014 Online - Question 69

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The set of all real values of $$\lambda$$ for which exactly two common tangents can be drawn to the circles $$x^2 + y^2 - 4x - 4y + 6 = 0$$ and $$x^2 + y^2 - 10x - 10y + \lambda = 0$$ is the interval:

A

(12, 32)

B

(18, 42)

C

(12, 24)

D

(18, 48)

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NTA JEE Main 11th April 2014 Online - Question 70

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Let L$$_1$$ be the length of the common chord of the curves $$x^2 + y^2 = 9$$ and $$y^2 = 8x$$, and L$$_2$$ be the length of the latus rectum of $$y^2 = 8x$$, then:

A

L$$_1$$ > L$$_2$$

B

L$$_1$$ = L$$_2$$

C

L$$_1$$ < L$$_2$$

D

$$\frac{L_1}{L_2} = \sqrt{2}$$

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NTA JEE Main 11th April 2014 Online - Question 71

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A stair-case of length $$l$$ rests against a vertical wall and a floor of a room. Let P be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio 1 : 2. If the staircase begins to slide on the floor, then the locus of P is:

A

an ellipse of eccentricity $$\frac{1}{2}$$

B

an ellipse of eccentricity $$\frac{\sqrt{3}}{2}$$

C

a circle of radius $$\frac{1}{2}$$

D

a circle of radius $$\frac{\sqrt{3}}{2}l$$

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NTA JEE Main 11th April 2014 Online - Question 72

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Let P($$3\sec\theta, 2\tan\theta$$) and Q($$3\sec\phi, 2\tan\phi$$) where $$\theta + \phi = \frac{\pi}{2}$$, be two distinct points on the hyperbola $$\frac{x^2}{9} - \frac{y^2}{4} = 1$$. Then the ordinate of the point of intersection of the normals at P and Q is:

A

$$\frac{11}{3}$$

B

$$-\frac{11}{3}$$

C

$$\frac{13}{2}$$

D

$$-\frac{13}{2}$$

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NTA JEE Main 11th April 2014 Online - Question 73

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If $$\lim_{x \to 2} \frac{\tan(x - 2)\{x^2 + (k+2)x - 2k\}}{x^2 - 4x + 4} = 5$$, then k is equal to:

A

0

B

1

C

2

D

3

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NTA JEE Main 11th April 2014 Online - Question 74

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The proposition $$\sim (p \vee \sim q) \vee \sim (p \vee q)$$ is logically equivalent to:

A

p

B

q

C

$$\sim p$$

D

$$\sim q$$

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NTA JEE Main 11th April 2014 Online - Question 75

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Two ships A and B are sailing straight away from a fixed point O along routes such that $$\angle AOB$$ is always 120°. At a certain instance, OA = 8 km, OB = 6 km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/hr):

A

$$\frac{260}{\sqrt{37}}$$

B

$$\frac{260}{37}$$

C

$$\frac{80}{\sqrt{37}}$$

D

$$\frac{80}{37}$$

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NTA JEE Main 11th April 2014 Online - Question 76

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The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be $$\alpha$$. After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to $$\beta$$. Then the height (in metres) of the tower is:

A

$$\frac{2\sin\alpha\sin\beta}{\sin(\beta - \alpha)}$$

B

$$\frac{\sin\alpha\sin\beta}{\cos(\beta - \alpha)}$$

C

$$\frac{2\sin(\beta - \alpha)}{\sin\alpha\sin\beta}$$

D

$$\frac{\cos(\beta - \alpha)}{\sin\alpha\sin\beta}$$

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NTA JEE Main 11th April 2014 Online - Question 77

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Let A(2, 3, 5), B($$-1, 3, 2$$) and C($$\lambda, 5, \mu$$) be the vertices of a $$\triangle$$ABC. If the median through A is equally inclined to the coordinate axes, then:

A

$$5\lambda - 8\mu = 0$$

B

$$8\lambda - 5\mu = 0$$

C

$$10\lambda - 7\mu = 0$$

D

$$7\lambda - 10\mu = 0$$

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NTA JEE Main 11th April 2014 Online - Question 78

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Let A be a $$3 \times 3$$ matrix such that
$$A\begin{bmatrix} 1 & 2 & 3 \\ 0 & 2 & 3 \\ 0 & 1 & 1 \end{bmatrix} = \begin{bmatrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix}$$
Then A$$^{-1}$$ is:

A

$$\begin{bmatrix} 3 & 1 & 2 \\ 3 & 0 & 2 \\ 1 & 0 & 1 \end{bmatrix}$$

B

$$\begin{bmatrix} 3 & 2 & 1 \\ 3 & 2 & 0 \\ 1 & 1 & 0 \end{bmatrix}$$

C

$$\begin{bmatrix} 0 & 1 & 3 \\ 0 & 2 & 3 \\ 1 & 1 & 1 \end{bmatrix}$$

D

$$\begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 1 \\ 0 & 2 & 3 \end{bmatrix}$$

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NTA JEE Main 11th April 2014 Online - Question 79

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Let for i = 1, 2, 3, $$p_i(x)$$ be a polynomial of degree 2 in $$x$$, $$p'_i(x)$$ and $$p''_i(x)$$ be the first and second order derivatives of $$p_i(x)$$ respectively. Let,
$$A(x) = \begin{bmatrix} p_1(x) & p'_1(x) & p''_1(x) \\ p_2(x) & p'_2(x) & p''_2(x) \\ p_3(x) & p'_3(x) & p''_3(x) \end{bmatrix}$$
and $$B(x) = [A(x)]^T A(x)$$. Then determinant of B(x):

A

is a polynomial of degree 6 in x

B

is a polynomial of degree 3 in x

C

is a polynomial of degree 2 in x

D

does not depend on x

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NTA JEE Main 11th April 2014 Online - Question 80

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Let f be an odd function defined on the set of real numbers such that for $$x \geq 0$$, $$f(x) = 3\sin x + 4\cos x$$. Then $$f(x)$$ at $$x = -\frac{11\pi}{6}$$ is equal to:

A

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

B

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

C

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

D

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

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NTA JEE Main 11th April 2014 Online - Question 81

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Let $$f(x) = x|x|$$, $$g(x) = \sin x$$ and $$h(x) = (g \circ f)(x)$$. Then:

A

h(x) is not differentiable at x = 0

B

h(x) is differentiable at x = 0, but h'(x) is not continuous at x = 0

C

h'(x) is continuous at x = 0 but it is not differentiable at x = 0

D

h'(x) is differentiable at x = 0

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NTA JEE Main 11th April 2014 Online - Question 82

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For the curve $$y = 3\sin\theta\cos\theta$$, $$x = e^\theta\sin\theta$$, $$0 \leq \theta \leq \pi$$, the tangent is parallel to x-axis when $$\theta$$ is:

A

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

B

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

C

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

D

$$\frac{\pi}{6}$$

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NTA JEE Main 11th April 2014 Online - Question 83

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The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius = $$\sqrt{3}$$ is:

A

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

B

$$\frac{8}{3}\sqrt{3}\pi$$

C

$$4\pi$$

D

$$2\pi$$

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NTA JEE Main 11th April 2014 Online - Question 84

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The integral $$\int x \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) dx$$ ($$x > 0$$) is equal to:

A

$$-x + (1+x^2)\tan^{-1}x + c$$

B

$$x - (1+x^2)\cot^{-1}x + c$$

C

$$-x + (1+x^2)\cot^{-1}x + c$$

D

$$x - (1+x^2)\tan^{-1}x + c$$

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NTA JEE Main 11th April 2014 Online - Question 85

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If for $$n \geq 1$$, $$P_n = \int_1^e (\log x^n) dx$$, then $$P_{10} - 90P_8$$ is equal to:

A

$$-9$$

B

10e

C

$$-9e$$

D

10

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NTA JEE Main 11th April 2014 Online - Question 86

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If the general solution of the differential equation $$y' = \frac{y}{x} + \Phi\left(\frac{x}{y}\right)$$, for some function $$\Phi$$, is given by $$y\ln|cx| = x$$, where c is an arbitrary constant, then $$\Phi(2)$$ is equal to:

A

4

B

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

C

$$-4$$

D

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

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NTA JEE Main 11th April 2014 Online - Question 87

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If $$|\vec{c}|^2 = 60$$ and $$\vec{c} \times (\hat{i} + 2\hat{j} + 5\hat{k}) = \vec{0}$$, then a value of $$\vec{c} \cdot (-7\hat{i} + 2\hat{j} + 3\hat{k})$$ is:

A

$$4\sqrt{2}$$

B

12

C

24

D

$$12\sqrt{2}$$

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NTA JEE Main 11th April 2014 Online - Question 88

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The plane containing the line $$\frac{x-1}{1} = \frac{y-2}{2} = \frac{z-3}{3}$$ and parallel to the line $$\frac{x}{1} = \frac{y}{1} = \frac{z}{4}$$ passes through the point:

A

(1, $$-2$$, 5)

B

(1, 0, 5)

C

(0, 3, $$-5$$)

D

($$-1$$, $$-3$$, 0)

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NTA JEE Main 11th April 2014 Online - Question 89

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A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that $$x \in A$$ is:

A

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

B

$$\frac{64}{127}$$

C

$$\frac{63}{128}$$

D

$$\frac{31}{128}$$

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NTA JEE Main 11th April 2014 Online - Question 90

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If X has a binomial distribution, B(n, p) with parameters n and p such that P(X = 2) = P(X = 3), then E(X), the mean of variable X, is:

A

2 $$-$$ p

B

3 $$-$$ p

C

$$\frac{p}{2}$$

D

$$\frac{p}{3}$$

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