NTA JEE Main 12th May 2012 Online

NTA JEE Main 12th May 2012 Online - Question 1

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A student measured the diameter of a wire using a screw gauge with the least count $$0.001$$ cm and listed the measurements. The measured value should be recorded as

A

$$5.3200$$ cm

B

$$5.3$$ cm

C

$$5.32$$ cm

D

$$5.320$$ cm

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NTA JEE Main 12th May 2012 Online - Question 2

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The distance travelled by a body moving along a line in time $$t$$ is proportional to $$t^3$$. The acceleration-time $$(a, t)$$ graph for the motion of the body will be

A

B

C

D

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NTA JEE Main 12th May 2012 Online - Question 3

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An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $$1/3$$. If the line joining the centre of the hemispherical surface to the insect makes an angle $$\alpha$$ with the vertical, the maximum possible value of $$\alpha$$ so that the insect does not slip is given by

A

$$\cot\alpha = 3$$

B

$$\sec\alpha = 3$$

C

$$\csc\alpha = 3$$

D

$$\cos\alpha = 3$$

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NTA JEE Main 12th May 2012 Online - Question 4

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A projectile moving vertically upwards with a velocity of $$200$$ ms$$^{-1}$$ breaks into two equal parts at a height of $$490$$ m. One part starts moving vertically upwards with a velocity of $$400$$ ms$$^{-1}$$. How much time it will take, after the break up with the other part to hit the ground?

A

$$2\sqrt{10}$$ s

B

$$5$$ s

C

$$10$$ s

D

$$\sqrt{10}$$ s

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NTA JEE Main 12th May 2012 Online - Question 5

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Two bodies $$A$$ and $$B$$ of mass $$m$$ and $$2m$$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. A third body $$C$$ of mass $$m$$ is placed on the floor. The body $$C$$ moves with a velocity $$v_0$$ along the line joining $$A$$ and $$B$$ and collides elastically with $$A$$. At a certain time after the collision it is found that the instantaneous velocities of $$A$$ and $$B$$ are same and the compression of the spring is $$x_0$$. The spring constant $$k$$ will be

A

$$m\dfrac{v_0^2}{x_0^2}$$

B

$$m\dfrac{v_0}{2x_0}$$

C

$$2m\dfrac{v_0}{x_0}$$

D

$$\dfrac{2}{3}m\left(\dfrac{v_0}{x_0}\right)^2$$

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NTA JEE Main 12th May 2012 Online - Question 6

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A spring is compressed between two blocks of masses $$m_1$$ and $$m_2$$ placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of $$v_1$$ and $$v_2$$ as shown. The blocks travel distances $$x_1$$ and $$x_2$$ respectively before coming to rest. The ratio $$\left(\dfrac{x_1}{x_2}\right)$$ is

A

$$\dfrac{m_2}{m_1}$$

B

$$\dfrac{m_1}{m_2}$$

C

$$\sqrt{\dfrac{m_2}{m_1}}$$

D

$$\sqrt{\dfrac{m_1}{m_2}}$$

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NTA JEE Main 12th May 2012 Online - Question 7

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A solid sphere is rolling on a surface as shown in figure, with a translational velocity $$v$$ ms$$^{-1}$$. If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is

A

$$\sqrt{2gh}$$

B

$$\sqrt{\dfrac{7}{5}gh}$$

C

$$\sqrt{\dfrac{7}{2}gh}$$

D

$$\sqrt{\dfrac{10}{7}gh}$$

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NTA JEE Main 12th May 2012 Online - Question 8

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This question has Statement 1 and Statement 2. Out of the four choices given after the Statements, choose the one that best describes the two Statements.

Statement 1: When moment of inertia $$I$$ of a body rotating about an axis with angular speed $$\omega$$ increases, its angular momentum $$L$$ is unchanged but the kinetic energy $$K$$ increases if there is no torque applied on it. 

Statement 2: $$L = I\omega$$, kinetic energy of rotation $$= \dfrac{1}{2}I\omega^2$$

A

Statement 1 is true, Statement 2 is true, 2 is not the correct explanation of Statement 1.

B

Statement 1 is false, Statement 2 is true.

C

Statement 1 is true, Statement 2 is true, 2 is correct explanation of the Statement 1.

D

Statement 1 is true, Statement 2 is false.

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NTA JEE Main 12th May 2012 Online - Question 9

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Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a distance of $$r$$ from the centre is proportional to

A

$$r$$

B

$$r^{-1}$$

C

$$r^2$$

D

$$r^{-2}$$

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NTA JEE Main 12th May 2012 Online - Question 10

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Water is flowing through a horizontal tube having cross-sectional areas of its two ends being $$A$$ and $$A'$$ such that the ratio $$A/A'$$ is $$5$$. If the pressure difference of water between the two ends is $$3\times 10^5$$ N m$$^{-2}$$, the velocity of water with which it enters the tube will be (neglect gravity effects)

A

$$5$$ m s$$^{-1}$$

B

$$10$$ m s$$^{-1}$$

C

$$25$$ m s$$^{-1}$$

D

$$50\sqrt{10}$$ m s$$^{-1}$$

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NTA JEE Main 12th May 2012 Online - Question 11

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A given ideal gas with $$\gamma = \dfrac{C_p}{C_v} = 1.5$$ at a temperature $$T$$. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be

A

$$2\sqrt{2}T$$

B

$$4T$$

C

$$2T$$

D

$$8T$$

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NTA JEE Main 12th May 2012 Online - Question 12

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$$n$$ moles of an ideal gas undergo a process $$A \to B$$ as shown in the figure. Maximum temperature of the gas during the process is

A

$$\dfrac{9P_0V_0}{nR}$$

B

$$\dfrac{3P_0V_0}{2nR}$$

C

$$\dfrac{9P_0V_0}{2nR}$$

D

$$\dfrac{9P_0V_0}{4nR}$$

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NTA JEE Main 12th May 2012 Online - Question 13

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This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: Bats emitting ultrasonic waves can detect the location of a prey by hearing the waves reflected from it. Statement 2: When the source and the detector are moving, the frequency of reflected waves is changed.

A

Statement 1 is false, Statement 2 is true.

B

Statement 1 is true, Statement 2 is false.

C

Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

D

Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

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NTA JEE Main 12th May 2012 Online - Question 14

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A wave represented by the equation $$y_1 = a\cos(kx - \omega t)$$ is superimposed with another wave to form a stationary wave such that the point $$x = 0$$ is a node. The equation for the other wave is

A

$$a\cos(kx - \omega t + \pi)$$

B

$$a\cos(kx + \omega t + \pi)$$

C

$$a\cos\left(kx + \omega t + \dfrac{\pi}{2}\right)$$

D

$$a\cos\left(kx - \omega t + \dfrac{\pi}{2}\right)$$

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NTA JEE Main 12th May 2012 Online - Question 15

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A series combination of $$n_1$$ capacitors, each of capacity $$C_1$$ is charged by source of potential difference $$4V$$. When another parallel combination of $$n_2$$ capacitors each of capacity $$C_2$$ is charged by a source of potential difference $$V$$, it has the same total energy stored in it as the first combination has. The value of $$C_2$$ in terms of $$C_1$$ is then

A

$$16\dfrac{n_2}{n_1}C_1$$

B

$$\dfrac{2C_1}{n_1 n_2}$$

C

$$2\dfrac{n_2}{n_1}C_1$$

D

$$\dfrac{16C_1}{n_1 n_2}$$

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NTA JEE Main 12th May 2012 Online - Question 16

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Three resistors of $$4\Omega, 6\Omega$$ and $$12\Omega$$ are connected in parallel and the combination is connected in series with a $$1.5$$ V battery of $$1\Omega$$ internal resistance. The rate of Joule heating in the $$4\Omega$$ resistor is

A

$$0.55$$ W

B

$$0.33$$ W

C

$$0.25$$ W

D

$$0.86$$ W

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NTA JEE Main 12th May 2012 Online - Question 17

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It is preferable to measure the e.m.f. of a cell by potentiometer than by a voltmeter because of the following possible reasons. (i) In case of potentiometer, no current flows through the cell. (ii) The length of the potentiometer allows greater precision. (iii) Measurement by the potentiometer is quicker. (iv) The sensitivity of the galvanometer, when using a potentiometer is not relevant. Which of these reasons are correct?

A

(i),(iii),(iv)

B

(i),(iii),(iv) only

C

(i),(ii)

D

(i),(ii),(iii),(iv)

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NTA JEE Main 12th May 2012 Online - Question 18

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In a sensitive meter bridge apparatus the bridge wire should possess

A

high resistivity and low temperature coefficient.

B

low resistivity and high temperature coefficient.

C

low resistivity and low temperature coefficient.

D

high resistivity and high temperature coefficient.

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NTA JEE Main 12th May 2012 Online - Question 19

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The magnetic force acting on charged particle of charge $$2\mu C$$ in magnetic field of $$2T$$ acting in $$y$$-direction, when the particle velocity is $$(2\hat{i} + 3\hat{j})\times 10^6$$ ms$$^{-1}$$ is

A

$$8$$ N in z-direction

B

$$8$$ N in y-direction

C

$$4$$ N in y-direction

D

$$4$$ N in z-direction

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NTA JEE Main 12th May 2012 Online - Question 20

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The circuit in figure consists of wires at the top and bottom and identical springs as the left and right sides. The wire at the bottom has a mass of $$10$$ g and is $$5$$ cm long. The wire is hanging as shown in the figure. The springs stretch $$0.5$$ cm under the weight of the wire and the circuit has a total resistance of $$12\Omega$$. When the lower wire is subjected to a static magnetic field, the springs, stretch an additional $$0.3$$ cm. The magnetic field is

A

$$0.6$$ T and directed out of page

B

$$1.2$$ T and directed into the plane of page

C

$$0.6$$ T and directed into the plane of page

D

$$1.2$$ T and directed out of page

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NTA JEE Main 12th May 2012 Online - Question 21

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Magnetic flux through a coil of resistance $$10\Omega$$ is changed by $$\Delta\phi$$ in $$0.1$$ s. The resulting current in the coil varies with time as shown in the figure. Then $$|\Delta\phi|$$ is equal to (in weber)

A

$$6$$

B

$$4$$

C

$$2$$

D

$$8$$

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NTA JEE Main 12th May 2012 Online - Question 22

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A resistance $$R$$ and a capacitance $$C$$ are connected in series to a battery of negligible internal resistance through a key. The key is closed at $$t = 0$$. If after $$t$$ sec the voltage across the capacitance was seven times the voltage across $$R$$, the value of $$t$$ is

A

$$3RC\ln 2$$

B

$$2RC\ln 2$$

C

$$2RC\ln 7$$

D

$$3RC\ln 7$$

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NTA JEE Main 12th May 2012 Online - Question 23

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We wish to make a microscope with the help of two positive lenses both with a focal length of $$20$$ mm each and the object is positioned $$25$$ mm from the objective lens. How far apart the lenses should be so that the final image is formed at infinity?

A

$$20$$ mm

B

$$100$$ mm

C

$$120$$ mm

D

$$80$$ mm

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NTA JEE Main 12th May 2012 Online - Question 24

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The first diffraction minimum due to the single slit diffraction is seen at $$\theta = 30°$$ for a light of wavelength $$5000\text{\AA}$$ falling perpendicularly on the slit. The width of the slit is

A

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

B

$$1.25\times 10^{-5}$$ cm

C

$$10\times 10^{-5}$$ cm

D

$$5\times 10^{-5}$$ cm

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NTA JEE Main 12th May 2012 Online - Question 25

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The maximum number of possible interference maxima for slit separation equal to $$1.8\lambda$$, where $$\lambda$$ is the wavelength of light used, in a Young's double slit experiment is

A

zero

B

$$3$$

C

infinite

D

$$5$$

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NTA JEE Main 12th May 2012 Online - Question 26

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A hypothetical atom has only three energy levels. The ground level has energy, $$E_1 = -8$$ eV. The two excited states have energies, $$E_2 = -6$$ eV and $$E_3 = -2$$ eV. Then which of the following wavelengths will not be present in the emission spectrum of this atom?

A

$$207$$ nm

B

$$465$$ nm

C

$$310$$ nm

D

$$620$$ nm

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NTA JEE Main 12th May 2012 Online - Question 27

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A doubly ionised Li atom is excited from its ground state ($$n = 1$$) to $$n = 3$$ state. The wavelengths of the spectral lines are given by $$\lambda_{32}$$, $$\lambda_{31}$$ and $$\lambda_{21}$$. The ratio $$\lambda_{32}/\lambda_{31}$$ and $$\lambda_{21}/\lambda_{31}$$ are, respectively

A

$$8.1, 0.67$$

B

$$8.1, 1.2$$

C

$$6.4, 1.2$$

D

$$6.4, 0.67$$

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NTA JEE Main 12th May 2012 Online - Question 28

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Which of the following Statements is correct?

A

The rate of radioactive decay cannot be controlled but that of nuclear fission can be controlled.

B

Nuclear forces are short range, attractive and charge dependent.

C

Nuclei of atoms having same number of neutrons are known as isobars.

D

Wavelength of matter waves is given by de Broglie formula but that of photons is not given by the same formula.

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NTA JEE Main 12th May 2012 Online - Question 29

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This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: A pure semiconductor has negative temperature coefficient of resistance. Statement 2: On raising the temperature, more charge carriers are released into the conduction band.

A

Statement 1 is false, Statement 2 is true.

B

Statement 1 is true, Statement 2 is false.

C

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

D

Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

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NTA JEE Main 12th May 2012 Online - Question 30

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A $$10$$ kW transmitter emits radio waves of wavelength $$500$$ m. The number of photons emitted per second by the transmitter is of the order of

A

$$10^{37}$$

B

$$10^{31}$$

C

$$10^{25}$$

D

$$10^{43}$$

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NTA JEE Main 12th May 2012 Online - Question 31

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An aqueous solution of oxalic acid dihydrate contains its $$6.3$$ g in $$250$$ ml. The volume of $$0.1$$ N NaOH required to completely neutralize $$10$$ ml of this solution

A

$$4$$ ml

B

$$20$$ ml

C

$$2$$ ml

D

$$40$$ ml

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NTA JEE Main 12th May 2012 Online - Question 32

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$$5$$ g of benzene on nitration gave $$6.6$$ g of nitrobenzene. The theoretical yield of the nitrobenzene will be

A

$$4.5$$ g

B

$$5.6$$ g

C

$$8.09$$ g

D

$$6.6$$ g

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NTA JEE Main 12th May 2012 Online - Question 33

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If the radius of first orbit of H atom is $$a_0$$, the deBroglie wavelength of an electron in the third orbit is

A

$$4\pi a_0$$

B

$$8\pi a_0$$

C

$$6\pi a_0$$

D

$$2\pi a_0$$

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NTA JEE Main 12th May 2012 Online - Question 34

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Which among the following elements has the highest first ionization enthalpy?

A

Nitrogen

B

Boron

C

Carbon

D

Oxygen

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NTA JEE Main 12th May 2012 Online - Question 35

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The formation of molecular complex $$\text{BF}_3 - \text{NH}_3$$ results in a change in hybridization of boron

A

from $$sp^2$$ to $$dsp^2$$

B

from $$sp^2$$ to $$sp^3$$

C

from $$sp^3$$ to $$sp^2$$

D

from $$sp^3$$ to $$sp^3d$$

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NTA JEE Main 12th May 2012 Online - Question 36

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Although CN$$^-$$ ion and N$$_2$$ molecule are isoelectronic, yet N$$_2$$ molecule is chemically inert because of

A

presence of more number of electrons in bonding

B

lone bond energy orbitals

C

absence of bond polarity

D

uneven electron distribution.

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NTA JEE Main 12th May 2012 Online - Question 37

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Among the following chloro-compound having the lowest dipole moment is

A

B

C

D

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NTA JEE Main 12th May 2012 Online - Question 38

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$$\alpha$$, $$v$$ and $$u$$ represent most probable velocity, average velocity and root mean square velocity respectively of a gas at a particular temperature. The correct order among the following is

A

$$u > v > \alpha$$

B

$$v > u > \alpha$$

C

$$\alpha > u > v$$

D

$$u > \alpha > v$$

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NTA JEE Main 12th May 2012 Online - Question 39

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The difference between the reaction enthalpy change ($$\Delta_r H$$) and reaction internal energy change ($$\Delta_r U$$) for the reaction: $$$2\text{C}_6\text{H}_6(l) + 15\text{O}_2(g) \longrightarrow$$$ at $$300$$ K is ($$R = 8.314$$ J mol$$^{-1}$$ K$$^{-1}$$)

A

$$0$$ J mol$$^{-1}$$

B

$$2490$$ J mol$$^{-1}$$

C

$$-2490$$ J mol$$^{-1}$$

D

$$-7482$$ J mol$$^{-1}$$

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NTA JEE Main 12th May 2012 Online - Question 40

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$$8$$ mol of $$AB_3(g)$$ are introduced into a $$1.0$$ dm$$^3$$ vessel. If it dissociates as $$2AB_3(g) \rightleftharpoons A_2(g) + 3B_2(g)$$. At equilibrium, $$2$$ mol of $$A_2$$ are found to be present. The equilibrium constant of this reaction is

A

$$2$$

B

$$3$$

C

$$27$$

D

$$36$$

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NTA JEE Main 12th May 2012 Online - Question 41

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Given
(i) $$\text{HCN}(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{H}_3\text{O}^+(aq) + \text{CN}^-(aq)$$, $$K_a = 6.2\times 10^{-10}$$
(ii) $$\text{CN}^-(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{HCN}(aq) + \text{OH}^-(aq)$$, $$K_b = 1.6\times 10^{-5}$$.
These equilibria show the following order of the relative base strength,

A

$$\text{OH}^- > \text{H}_2\text{O} > \text{CN}^-$$

B

$$\text{OH}^- > \text{CN}^- > \text{H}_2\text{O}$$

C

$$\text{H}_2\text{O} > \text{CN}^- > \text{OH}^-$$

D

$$\text{CN}^- > \text{H}_2\text{O} > \text{OH}^-$$

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NTA JEE Main 12th May 2012 Online - Question 42

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In the following balanced reaction,

values of $$X, Y$$ and $$Z$$ respectively are

A

$$2, 5, 16$$

B

$$8, 2, 5$$

C

$$5, 2, 16$$

D

$$5, 8, 4$$

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NTA JEE Main 12th May 2012 Online - Question 43

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A metal $$M$$ on heating in nitrogen gas gives $$Y$$. $$Y$$ on treatment with $$\text{H}_2\text{O}$$ gives a colourless gas which when passed through $$\text{CuSO}_4$$ solution gives a blue colour. $$Y$$ is

A

$$\text{NH}_3$$

B

$$\text{Mg}(\text{NO}_3)_2$$

C

$$\text{Mg}_3\text{N}_2$$

D

$$\text{MgO}$$

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NTA JEE Main 12th May 2012 Online - Question 44

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In the below mentioned compounds the decreasing order of reactivity towards electrophilic substitution is

(i)

(ii)

(iii)

(iv)

A

(iv) > (i) > (ii) > (iii)

B

(ii) > (iii) > (i) > (iv)

C

(iii) > (i) > (iv) > (ii)

D

(i) > (ii) > (iii) > (iv)

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NTA JEE Main 12th May 2012 Online - Question 45

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The reaction, $$\text{CH}_3\text{CHO} \xrightarrow[\text{Zn(Hg)/Conc. HCl}]{[\text{H}]} \text{CH}_3\text{CH}_3$$

A

Cannizaro's reaction

B

Rosenmund reduction

C

Wolf-Kishner reduction

D

Clemmenson reduction

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NTA JEE Main 12th May 2012 Online - Question 46

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Water sample is reported to be highly polluted if BOD (Biological Oxygen Demand) value of sample becomes

A

more than $$17$$ ppm

B

equal to $$10$$ ppm

C

equal to $$5$$ ppm

D

less than $$5$$ ppm

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NTA JEE Main 12th May 2012 Online - Question 47

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The radius of a calcium ion is $$94$$ pm and of the oxide ion is $$146$$ pm. The possible crystal structure of calcium oxide will be

A

tetrahedral

B

trigonal

C

octahedral

D

pyramidal

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NTA JEE Main 12th May 2012 Online - Question 48

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A solution containing $$0.85$$ g of $$\text{ZnCl}_2$$ in $$125.0$$ g of water freezes at $$-0.23°$$C. The apparent degree of dissociation of the salt is ($$K_f$$ for water $$= 1.86$$ K kg mol$$^{-1}$$, atomic mass: Zn $$= 65.3$$ and Cl $$= 35.5$$)

A

$$1.36\%$$

B

$$73.5\%$$

C

$$7.35\%$$

D

$$2.47\%$$

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NTA JEE Main 12th May 2012 Online - Question 49

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The ppm level of F$$^-$$ in a $$500$$ g sample of a tooth paste containing $$0.2$$ g F$$^-$$ is

A

$$400$$

B

$$1000$$

C

$$250$$

D

$$200$$

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NTA JEE Main 12th May 2012 Online - Question 50

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In a chemical reaction $$A$$ is converted into $$B$$. The rates of reaction, starting with initial concentrations of $$A$$ as $$2\times 10^{-3}$$ M and $$1\times 10^{-3}$$ M, are equal to $$2.40\times 10^{-4}$$ Ms$$^{-1}$$ and $$0.60\times 10^{-4}$$ Ms$$^{-1}$$ respectively. The order of reaction with respect to reactant $$A$$ will be

A

$$0$$

B

$$1.5$$

C

$$1$$

D

$$2$$

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NTA JEE Main 12th May 2012 Online - Question 51

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The correct statement for both the processes of physisorption and chemisorption is

A

both are endothermic

B

chemisorption is endothermic but physisorption is exothermic

C

both are exothermic

D

physisorption is endothermic but chemisorption is exothermic.

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NTA JEE Main 12th May 2012 Online - Question 52

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In the electrolysis of alumina to obtain aluminium metal, cryolite is added mainly to

A

lower the melting point of alumina

B

dissolve alumina in molten cryolite

C

remove the impurities of alumina

D

increase the electrical conductivity

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NTA JEE Main 12th May 2012 Online - Question 53

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Magnetic moment of $$\text{Gd}^{3+}$$ ion ($$Z = 64$$) is

A

$$3.62$$ BM

B

$$9.72$$ BM

C

$$7.9$$ BM

D

$$10.60$$ BM

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NTA JEE Main 12th May 2012 Online - Question 54

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Which of the following complex ions will exhibit optical isomerism? (en = 1, 2-diamine ethane).

A

$$[\text{Cr}(\text{NH}_3)_2\text{Cl}_2]^+$$

B

$$[\text{Co}(\text{en})_2\text{Cl}_2]^+$$

C

$$[\text{Co}(\text{NH}_3)_4\text{Cl}_2]^+$$

D

$$[\text{Zn}(\text{en})_2]^{2+}$$

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NTA JEE Main 12th May 2012 Online - Question 55

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Which of the following statements is wrong?

A

Ethyl chloride on reduction with $$\text{Zn}-\text{Cu}$$ couple and alcohol gives ethane.

B

The reaction of methyl magnesium bromide with acetone gives butanol-2.

C

Alkyl halides follow the following reactivity sequence on reaction with alkenes. $$\text{R}-\text{I} > \text{R}-\text{Br} > \text{R}-\text{Cl} > \text{R}-\text{I}$$

D

$$\text{C}_2\text{H}_4\text{Cl}_2$$ may exist in two isomeric forms

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NTA JEE Main 12th May 2012 Online - Question 56

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In the given reaction, the product 'A' is

A

B

C

D

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NTA JEE Main 12th May 2012 Online - Question 57

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The conversion of benzene diazonium chloride to bromobenzene can be accomplished by

A

Reimer-Tiemann reaction

B

Friedel-Crafts reaction

C

Gattermann reaction

D

Azo-coupling reaction

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NTA JEE Main 12th May 2012 Online - Question 58

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Synthetic polymer bakelite can be prepared from following compounds

A

Styrene and vinyl chloride

B

Acrylonitrile and vinyl chloride

C

Adipic acid and ethylene glycol

D

Phenol and formaldehyde

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NTA JEE Main 12th May 2012 Online - Question 59

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Chemically heroin is

A

morphine monoacetate

B

morphine dibenzoate

C

morphine diacetate

D

morphine monobenzoate

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NTA JEE Main 12th May 2012 Online - Question 60

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Amylopectin is a polymer of

A

$$\alpha - D - $$ glucose

B

amino acid

C

$$\beta - D - $$ glucose

D

amylase.

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NTA JEE Main 12th May 2012 Online - Question 61

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If $$a, b, c, d$$ and $$p$$ are distinct real numbers such that $$(a^2+b^2+c^2)p^2 - 2p(ab+bc+cd) + (b^2+c^2+d^2) \le 0$$, then

A

$$a, b, c, d$$ are in A.P.

B

$$ab = cd$$

C

$$ac = bd$$

D

$$a, b, c, d$$ are in G.P.

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NTA JEE Main 12th May 2012 Online - Question 62

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If the sum of the square of the roots of the equation $$x^2 - (\sin\alpha - 2)x - (1 + \sin\alpha) = 0$$ is least, then $$\alpha$$ is equal to

A

$$\dfrac{\pi}{6}$$

B

$$\dfrac{\pi}{4}$$

C

$$\dfrac{\pi}{3}$$

D

$$\dfrac{\pi}{2}$$

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NTA JEE Main 12th May 2012 Online - Question 63

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The area of the triangle whose vertices are complex numbers $$z, iz, z + iz$$ in the Argand diagram is

A

$$2|z|^2$$

B

$$\dfrac{1}{2}|z|^2$$

C

$$4|z|^2$$

D

$$|z|^2$$

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NTA JEE Main 12th May 2012 Online - Question 64

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The sum of the series $$\dfrac{1}{1+\sqrt{2}} + \dfrac{1}{\sqrt{2}+\sqrt{3}} + \dfrac{1}{\sqrt{3}+\sqrt{4}} + \ldots$$ upto $$15$$ terms is

A

$$1$$

B

$$2$$

C

$$3$$

D

$$4$$

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NTA JEE Main 12th May 2012 Online - Question 65

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The number of terms in the expansion of $$\left(y^{1/5} + x^{1/10}\right)^{55}$$, in which powers of $$x$$ and $$y$$ are free from radical signs are

A

six

B

twelve

C

seven

D

five

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NTA JEE Main 12th May 2012 Online - Question 66

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If the point $$(1, a)$$ lies between the straight lines $$x + y = 1$$ and $$2(x+y) = 3$$ then $$a$$ lies in interval

A

$$\left(\dfrac{3}{2}, \infty\right)$$

B

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

C

$$(-\infty, 0)$$

D

$$\left(0, \dfrac{1}{2}\right)$$

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NTA JEE Main 12th May 2012 Online - Question 67

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If two vertices of a triangle are $$(5, -1)$$ and $$(-2, 3)$$ and its orthocentre is at $$(0, 0)$$, then the third vertex is

A

$$(4, -7)$$

B

$$(-4, -7)$$

C

$$(-4, 7)$$

D

$$(4, 7)$$

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NTA JEE Main 12th May 2012 Online - Question 68

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The area of triangle formed by the lines joining the vertex of the parabola, $$x^2 = 8y$$, to the extremities of its latus rectum is

A

$$2$$

B

$$8$$

C

$$1$$

D

$$4$$

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NTA JEE Main 12th May 2012 Online - Question 69

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If $$P_1$$ and $$P_2$$ are two points on the ellipse $$\dfrac{x^2}{4} + y^2 = 1$$ at which the tangents are parallel to the chord joining the points $$(0, 1)$$ and $$(2, 0)$$, then the distance between $$P_1$$ and $$P_2$$ is

A

$$2\sqrt{2}$$

B

$$\sqrt{5}$$

C

$$2\sqrt{3}$$

D

$$\sqrt{10}$$

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NTA JEE Main 12th May 2012 Online - Question 70

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The logically equivalent proposition of $$p \Leftrightarrow q$$ is

A

$$(p \Rightarrow q) \wedge (q \Rightarrow p)$$

B

$$p \wedge q$$

C

$$(p \wedge q) \vee (q \neq p)$$

D

$$(p \wedge q) \Rightarrow (q \vee p)$$

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NTA JEE Main 12th May 2012 Online - Question 71

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If the mean of $$4, 7, 2, 8, 6$$ and $$a$$ is $$7$$, then the mean deviation from the median of these observations is

A

$$8$$

B

$$5$$

C

$$1$$

D

$$3$$

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NTA JEE Main 12th May 2012 Online - Question 72

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If in a triangle $$ABC$$, $$\dfrac{b+c}{11} = \dfrac{c+a}{12} = \dfrac{a+b}{13}$$, then $$\cos A$$ is equal to

A

$$5/7$$

B

$$1/5$$

C

$$35/19$$

D

$$19/35$$

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NTA JEE Main 12th May 2012 Online - Question 73

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If $$A = \{x \in z^+ : x < 10$$ and $$x$$ is a multiple of $$3$$ or $$4\}$$, where $$z^+$$ is the set of positive integers, then the total number of symmetric relations on $$A$$ is

A

$$2^5$$

B

$$2^{15}$$

C

$$2^{10}$$

D

$$2^{20}$$

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NTA JEE Main 12th May 2012 Online - Question 74

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Let $$A$$ and $$B$$ be real matrices of the form $$\begin{bmatrix}\alpha & 0 \\ 0 & \beta\end{bmatrix}$$ and $$\begin{bmatrix}0 & \gamma \\ \delta & 0\end{bmatrix}$$, respectively. Statement 1: $$AB - BA$$ is always an invertible matrix. Statement 2: $$AB - BA$$ is never an identity matrix.

A

Statement 1 is true, Statement 2 is false.

B

Statement 1 is false, Statement 2 is true.

C

Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.

D

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

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NTA JEE Main 12th May 2012 Online - Question 75

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If $$\begin{vmatrix}-2a & a+b & a+c \\ b+a & -2b & b+c \\ c+a & c+b & -2c\end{vmatrix} = \alpha(a+b)(b+c)(c+a) \ne 0$$ then $$\alpha$$ is equal to

A

$$a+b+c$$

B

$$abc$$

C

$$4$$

D

$$1$$

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NTA JEE Main 12th May 2012 Online - Question 76

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Statement 1: If $$A$$ and $$B$$ be two sets having $$p$$ and $$q$$ elements respectively, where $$q > p$$. Then the total number of functions from set $$A$$ to set $$B$$ is $$q^p$$. Statement 2: The total number of selections of $$p$$ different objects out of $$q$$ objects is $$^qC_p$$.

A

Statement 1 is true, Statement 2 is false.

B

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

C

Statement 1 is false, Statement 2 is true

D

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

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NTA JEE Main 12th May 2012 Online - Question 77

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Statement 1: A function $$f: R \to R$$ is continuous at $$x_0$$ if and only if $$\lim_{x \to x_0} f(x)$$ exists and $$\lim_{x \to x_0} f(x) = f(x_0)$$. Statement 2: A function $$f: R \to R$$ is discontinuous at $$x_0$$ if and only if, $$\lim_{x \to x_0} f(x)$$ exists and $$\lim_{x \to x_0} f(x) \ne f(x_0)$$.

A

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

B

Statement 1 is false, Statement 2 is true.

C

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

D

Statement 1 is true, Statement 2 is false.

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NTA JEE Main 12th May 2012 Online - Question 78

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If $$f'(x) = \sin(\log x)$$ and $$y = f\left(\dfrac{2x+3}{3-2x}\right)$$, then $$\dfrac{dy}{dx}$$ equals

A

$$\sin\left[\log\left(\dfrac{2x+3}{3-2x}\right)\right]$$

B

$$\dfrac{12}{(3-2x^2)}$$

C

$$\dfrac{12}{(3-2x)^2}\sin\left[\log\left(\dfrac{2x+3}{3-2x}\right)\right]$$

D

$$\dfrac{12}{(3-2x)^2}\cos\left[\log\left(\dfrac{2x+3}{3-2x}\right)\right]$$

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NTA JEE Main 12th May 2012 Online - Question 79

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Consider a rectangle whose length is increasing at the uniform rate of $$2$$ m/sec, breadth is decreasing at the uniform rate of $$3$$ m/sec and the area is decreasing at the uniform rate of $$5$$ m$$^2$$/sec. If after some time the breadth of the rectangle is $$2$$ m then the length of the rectangle is

A

$$2$$ m

B

$$4$$ m

C

$$1$$ m

D

$$3$$ m

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NTA JEE Main 12th May 2012 Online - Question 80

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If $$f(x) = xe^{x(1-x)}$$, $$x \in R$$, then $$f(x)$$ is

A

decreasing on $$[-1/2, 1]$$

B

decreasing on $$R$$

C

increasing on $$[-1/2, 1]$$

D

increasing on $$R$$

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NTA JEE Main 12th May 2012 Online - Question 81

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The integral of $$\dfrac{x^2 - x}{x^3 - x^2 + x - 1}$$ w.r.t. $$x$$ is

A

$$\dfrac{1}{2}\log(x^2 + 1 + c)$$

B

$$\dfrac{1}{2}\log|x^2 - 1| + c$$

C

$$\log(x^2 + 1 + c)$$

D

$$\log|x^2 - 1| + c$$

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NTA JEE Main 12th May 2012 Online - Question 82

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If $$\dfrac{d}{dx}G(x) = \dfrac{e^{\tan x}}{x}$$, $$x \in (0, \pi/2)$$, then $$\int_{1/4}^{1/2} \dfrac{2}{x} \cdot e^{\tan(\pi x^2)} dx$$ is equal to

A

$$G(\pi/4) - G(\pi/16)$$

B

$$2[G(\pi/4) - G(\pi/16)]$$

C

$$\pi[G(1/2) - G(1/4)]$$

D

$$G(1/\sqrt{2}) - G(1/2)$$

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NTA JEE Main 12th May 2012 Online - Question 83

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The area enclosed by the curves $$y = x^2$$, $$y = x^3$$, $$x = 0$$ and $$x = p$$, where $$p > 1$$, is $$1/6$$. The $$p$$ equals

A

$$8/3$$

B

$$16/3$$

C

$$2$$

D

$$4/3$$

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NTA JEE Main 12th May 2012 Online - Question 84

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If a straight line $$y - x = 2$$ divides the region $$x^2 + y^2 \le 4$$ into two parts, then the ratio of the area of the smaller part to the area of the greater part is

A

$$3\pi - 8 : \pi + 8$$

B

$$\pi - 3 : 3\pi + 3$$

C

$$3\pi - 4 : \pi + 4$$

D

$$\pi - 2 : 3\pi + 2$$

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NTA JEE Main 12th May 2012 Online - Question 85

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Statement 1: The degrees of the differential equations $$\dfrac{dy}{dx} + y^2 = x$$ and $$\dfrac{d^2y}{dx^2} + y = \sin x$$ are equal. Statement 2: The degree of a differential equation, when it is a polynomial equation in derivatives, is the highest positive integral power of the highest order derivative involved in the differential equation, otherwise degree is not defined.

A

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

B

Statement 1 is false, Statement 2 is true.

C

Statement 1 is true, Statement 2 is false.

D

Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.

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NTA JEE Main 12th May 2012 Online - Question 86

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If $$\vec{u} = \hat{j} + 4\hat{k}$$, $$\vec{v} = \hat{i} + 3\hat{k}$$ and $$\vec{w} = \cos\theta\hat{i} + \sin\theta\hat{j}$$ are vectors in 3-dimensional space, then the maximum possible value of $$|\vec{u} \times \vec{v} \cdot \vec{w}|$$ is

A

$$\sqrt{3}$$

B

$$5$$

C

$$\sqrt{14}$$

D

$$7$$

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NTA JEE Main 12th May 2012 Online - Question 87

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Statement 1: If the points $$(1, 2, 2)$$, $$(2, 1, 2)$$ and $$(2, 2, z)$$ and $$(1, 1, 1)$$ are coplanar, then $$z = 2$$. Statement 2: If the 4 points $$P, Q, R$$ and $$S$$ are coplanar, then the volume of the tetrahedron $$PQRS$$ is $$0$$.

A

Statement 1 is false, Statement 2 is true.

B

Statement 1 is true, Statement 2 is false.

C

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

D

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

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NTA JEE Main 12th May 2012 Online - Question 88

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A unit vector which is perpendicular to the vector $$2\hat{i} - \hat{j} + 2\hat{k}$$ and is coplanar with the vectors $$\hat{i} + \hat{j} - \hat{k}$$ and $$2\hat{i} + 2\hat{j} - \hat{k}$$ is

A

$$\dfrac{2\hat{j} + \hat{k}}{\sqrt{5}}$$

B

$$\dfrac{3\hat{i} + 2\hat{j} - 2\hat{k}}{\sqrt{17}}$$

C

$$\dfrac{3\hat{i} + 2\hat{j} + 2\hat{k}}{\sqrt{17}}$$

D

$$\dfrac{2\hat{i} + 2\hat{j} - \hat{k}}{3}$$

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NTA JEE Main 12th May 2012 Online - Question 89

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The coordinates of the foot perpendicular from the point $$(1, 0, 0)$$ to the line $$\dfrac{x-1}{2} = \dfrac{y+1}{-3} = \dfrac{z+10}{8}$$ are

A

$$(2, -3, 8)$$

B

$$(1, -1, -10)$$

C

$$(5, -8, -4)$$

D

$$(3, -4, -2)$$

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NTA JEE Main 12th May 2012 Online - Question 90

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A number $$n$$ is randomly selected from the set $$\{1, 2, 3, \ldots, 1000\}$$. The probability that $$\dfrac{\sum_{i=1}^{n} i^2}{\sum_{i=1}^{n} i}$$ is an integer is

A

$$0.331$$

B

$$0.333$$

C

$$0.334$$

D

$$0.332$$

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