NTA JEE Main 7th May 2012 Online

NTA JEE Main 7th May 2012 Online - Question 1

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Given that $$K$$ = energy, $$V$$ = velocity, $$T$$ = time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?

A

$$[KV^{-2}T^{-2}]$$

B

$$[K^2V^2T^{-2}]$$

C

$$[K^2V^{-2}T^{-2}]$$

D

$$[KV^2T^2]$$

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NTA JEE Main 7th May 2012 Online - Question 2

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The graph of an object's motion (along the $$x$$-axis) is shown in the figure. The instantaneous velocity of the object at points $$A$$ and $$B$$ are $$v_A$$ and $$v_B$$ respectively. Then

A

$$v_A = v_B = 0.5\ \text{m/s}$$

B

$$v_A = 0.5\ \text{m/s} < v_B$$

C

$$v_A = 0.5\ \text{m/s} > v_B$$

D

$$v_A = v_B = 2\ \text{m/s}$$

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NTA JEE Main 7th May 2012 Online - Question 3

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A car of mass 1000 kg is moving at a speed of $$30\ \text{m/s}$$. Brakes are applied to bring the car to rest. If the net retarding force is $$5000\ \text{N}$$, the car comes to stop after travelling $$d$$ m in $$t$$ s. Then

A

$$d = 150, t = 5$$

B

$$d = 120, t = 8$$

C

$$d = 180, t = 6$$

D

$$d = 90, t = 6$$

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NTA JEE Main 7th May 2012 Online - Question 4

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An engine pumps water continuously through a hose. Water leaves the hose with velocity $$v$$ and $$m$$ is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is

A

$$mv^3$$

B

$$mv^2$$

C

$$\tfrac{1}{2}mv^2$$

D

$$\tfrac{1}{2}mv^3$$

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NTA JEE Main 7th May 2012 Online - Question 5

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A particle gets displaced by $$\Delta \vec{r} = (2\hat{i} + 3\hat{j} + 4\hat{k})\ \text{m}$$ under the action of a force $$\vec{F} = (7\hat{i} + 4\hat{j} + 3\hat{k})$$. The change in its kinetic energy is

A

38 J

B

70 J

C

52.5 J

D

126 J

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NTA JEE Main 7th May 2012 Online - Question 6

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A circular hole of diameter $$R$$ is cut from a disc of mass $$M$$ and radius $$R$$; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is

A

$$\left(\tfrac{15}{32}\right) MR^2$$

B

$$\left(\tfrac{1}{8}\right) MR^2$$

C

$$\left(\tfrac{3}{8}\right) MR^2$$

D

$$\left(\tfrac{13}{32}\right) MR^2$$

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NTA JEE Main 7th May 2012 Online - Question 7

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A solid sphere having mass $$m$$ and radius $$r$$ rolls down an inclined plane. Then its kinetic energy is

A

$$\tfrac{5}{7}$$ rotational and $$\tfrac{2}{7}$$ translational

B

$$\tfrac{2}{7}$$ rotational and $$\tfrac{5}{7}$$ translational

C

$$\tfrac{2}{5}$$ rotational and $$\tfrac{3}{5}$$ translational

D

$$\tfrac{1}{2}$$ rotational and $$\tfrac{1}{2}$$ translational

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NTA JEE Main 7th May 2012 Online - Question 8

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Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth = $$R_E$$)?

A

B

C

D

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NTA JEE Main 7th May 2012 Online - Question 9

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A structural steel rod has a radius of 10 mm and length of 1.0 m. A 100 kN force stretches it along its length. Young's modulus of structural steel is $$2 \times 10^{11}\ \text{Nm}^{-2}$$. The percentage strain is about

A

0.16%

B

0.32%

C

0.08%

D

0.24%

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NTA JEE Main 7th May 2012 Online - Question 10

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The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line

A

$$OA$$

B

$$OC$$

C

$$OD$$

D

$$OB$$

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NTA JEE Main 7th May 2012 Online - Question 11

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A square hole of side length $$\ell$$ is made at a depth of $$h$$ and a circular hole of radius $$r$$ is made at a depth of $$4h$$ from the surface of water in a water tank kept on a horizontal surface. If $$\ell << h, r << h$$ and the rate of water flow from the holes is the same, then $$r$$ is equal to

A

$$\dfrac{\ell}{\sqrt{2\pi}}$$

B

$$\dfrac{\ell}{\sqrt{3\pi}}$$

C

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

D

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

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NTA JEE Main 7th May 2012 Online - Question 12

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The heat radiated per unit area in 1 hour by a furnace whose temperature is 3000 K is ($$\sigma = 5.7 \times 10^{-8}\ \text{W m}^{-2}\text{K}^{-4}$$)

A

$$1.7 \times 10^{10}$$ J

B

$$1.1 \times 10^{12}$$ J

C

$$2.8 \times 10^{8}$$ J

D

$$4.6 \times 10^{6}$$ J

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NTA JEE Main 7th May 2012 Online - Question 13

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A perfect gas at $$27^\circ$$C is heated at constant pressure so as to double its volume. The final temperature of the gas will be, close to

A

$$327^\circ$$C

B

$$200^\circ$$C

C

$$54^\circ$$C

D

$$300^\circ$$C

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NTA JEE Main 7th May 2012 Online - Question 14

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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: In an adiabatic process, change in internal energy of a gas is equal to work done on/by the gas in the process. Statement 2: The temperature of a gas remains constant in an adiabatic process.

A

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

B

Statement 1 is true, Statement 2 is false.

C

Statement 1 is false, Statement 2 is true.

D

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

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NTA JEE Main 7th May 2012 Online - Question 15

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Following are expressions for four plane simple harmonic waves (i) $$y_1 = A \cos 2\pi \left(n_1 t + \dfrac{x}{\lambda_1}\right)$$ (ii) $$y_2 = A \cos 2\pi \left(n_1 t + \dfrac{x}{\lambda_1} + 0.5\right)$$ (iii) $$y_3 = A \cos 2\pi \left(n_2 t + \dfrac{x}{\lambda_2}\right)$$ (iv) $$y_4 = A \cos 2\pi \left(n_2 t - \dfrac{x}{\lambda_2}\right)$$. The pairs of waves which will produce destructive interference and stationary waves respectively in a medium, are

A

(iii, iv), (i, ii)

B

(i, iii), (ii, iv)

C

(i, iv), (ii, iii)

D

(i, ii), (iii, iv)

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NTA JEE Main 7th May 2012 Online - Question 16

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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: In the resonance tube experiment, if the tuning fork is replaced by another identical turning fork but with its arm having been filled, the length of the air column should be increased to obtain resonance again. Statement 2: On filling the arms, the frequency of a tuning fork increases.

A

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

B

Statement 1 is true, Statement 2 is false.

C

Statement 1 is false, Statement 2 is true.

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 7th May 2012 Online - Question 17

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The electric potential $$V(x)$$ in a region around the origin is given by $$V(x) = 4x^2$$ volts. The electric charge enclosed in a cube of 1 m side with its centre at the origin is (in coulomb)

A

$$8\varepsilon_0$$

B

$$-4\varepsilon_0$$

C

0

D

$$-8\varepsilon_0$$

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NTA JEE Main 7th May 2012 Online - Question 18

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Two circuits (a) and (b) have charged capacitors of capacitance C, 2C and 3C with open switches. Charges on each of the capacitor are as shown in the figures. On closing the switches

Circuit (a)    Circuit (b)

A

No charge flows in (a) but charge flows from $$R$$ to $$L$$ in (b)

B

Charges flow from $$L$$ to $$R$$ in both (a) and (b)

C

Charges flow from $$R$$ to $$L$$ in (a) and from $$L$$ to $$R$$ in (b)

D

No charge flows in (a) but charge flows from $$L$$ to $$R$$ in (b)

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NTA JEE Main 7th May 2012 Online - Question 19

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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: The possibility of an electric bulb fusing is higher at the time of switching ON. Statement 2: Resistance of an electric bulb when it is not lit up is much smaller than when it is lit up.

A

Statement 1 is true, Statement 2 is false

B

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

C

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

D

Statement 1 is false, Statement 2 is true.

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NTA JEE Main 7th May 2012 Online - Question 20

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A bar magnet of length 6 cm has a magnetic moment of $$4\ \text{J T}^{-1}$$. Find the strength of magnetic field at a distance of 200 cm from the centre of the magnet along its equatorial line.

A

$$4 \times 10^{-8}$$ tesla

B

$$3.5 \times 10^{-8}$$ tesla

C

$$5 \times 10^{-8}$$ tesla

D

$$3 \times 10^{-8}$$ tesla

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NTA JEE Main 7th May 2012 Online - Question 21

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The velocity of certain ions that pass undeflected through crossed electric field $$E = 7.7\ \text{kV/m}$$ and magnetic field $$B = 0.14\ \text{T}$$ is

A

18 km/s

B

77 km/s

C

55 km/s

D

1078 km/s

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NTA JEE Main 7th May 2012 Online - Question 22

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In an $$LCR$$ circuit shown in the following figure, what will be the readings of the voltmeter across the resistor and ammeter if an a.c. source of 220 V and 100 Hz is connected to it as shown?

A

800 V, 8 A

B

110 V, 1.1 A

C

300 V, 3 A

D

220 V, 2.2 A

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NTA JEE Main 7th May 2012 Online - Question 23

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Which of the following processes play a part in the formation of a rainbow? (i) Refraction (ii) Total internal reflection (iii) Dispersion (iv) Interference

A

(i), (ii) and (iii)

B

(i) and (ii)

C

(i), (ii) and (iv)

D

(iii) and (iv)

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NTA JEE Main 7th May 2012 Online - Question 24

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In a Young's double slit experiment with light of wavelength $$\lambda$$, fringe pattern on the screen has fringe width $$\beta$$. When two thin transparent glass (refractive index $$\mu$$) plates of thickness $$t_1$$ and $$t_2$$ ($$t_1 > t_2$$) are placed in the path of the two beams respectively, the fringe pattern will shift by a distance

A

$$\dfrac{\beta(\mu-1)}{\lambda}\left(\dfrac{t_1}{t_2}\right)$$

B

$$\dfrac{\mu \beta}{\lambda}\dfrac{t_1}{t_2}$$

C

$$\dfrac{\beta(\mu-1)}{\lambda}(t_1 - t_2)$$

D

$$\left(\mu - 1\dfrac{\lambda}{\beta}\right)(t_1 + t_2)$$

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NTA JEE Main 7th May 2012 Online - Question 25

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Two polaroids have their polarizing directions parallel so that the intensity of a transmitted light is maximum. The angle through which either polaroid must be turned if the intensity is to drop by one-half is

A

$$135^\circ$$

B

$$90^\circ$$

C

$$120^\circ$$

D

$$180^\circ$$

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NTA JEE Main 7th May 2012 Online - Question 26

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The electron of a hydrogen atom makes a transition from the $$(n+1)^{\text{th}}$$ orbit to the $$n^{\text{th}}$$ orbit. For large $$n$$ the wavelength of the emitted radiation is proportional to

A

$$n$$

B

$$n^3$$

C

$$n^4$$

D

$$n^2$$

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NTA JEE Main 7th May 2012 Online - Question 27

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In the Rutherford experiment, $$\alpha$$-particles are scattered from a nucleus as shown. Out of the four paths, which path is not possible?

A

$$D$$

B

$$B$$

C

$$C$$

D

$$A$$

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NTA JEE Main 7th May 2012 Online - Question 28

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A sample originally contained $$10^{20}$$ radioactive atoms, which emit $$\alpha$$-particles. The ratio of $$\alpha$$ particles emitted in the third year to that emitted during the second year is 0.3. How many $$\alpha$$ particles were emitted in the first year?

A

$$3 \times 10^{18}$$

B

$$3 \times 10^{19}$$

C

$$5 \times 10^{18}$$

D

$$7 \times 10^{19}$$

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NTA JEE Main 7th May 2012 Online - Question 29

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Which logic gate with inputs $$A$$ and $$B$$ performs the same operation as that performed by the following circuit?

A

NAND gate

B

OR gate

C

NOR gate

D

AND gate

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NTA JEE Main 7th May 2012 Online - Question 30

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Broadcasting antennas are generally

A

vertical type

B

both vertical and horizontal type

C

omni directional type

D

horizontal type

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NTA JEE Main 7th May 2012 Online - Question 31

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The concentrated sulphuric acid that is peddled commercial is 95% $$\text{H}_2\text{SO}_4$$ by weight. If the density of this commercial acid is $$1.834\ \text{g cm}^{-3}$$, the molarity of this solution is

A

17.8 M

B

12.0 M

C

10.5 M

D

15.7 M

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NTA JEE Main 7th May 2012 Online - Question 32

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The ratio of number of oxygen atoms (O) in 16.0 g ozone ($$\text{O}_3$$), 28.0 g carbon monoxide (CO) and 16.0 g oxygen ($$\text{O}_2$$) is (Atomic mass : C = 12, O = 16 and Avogadro's constant $$N_A = 6.0 \times 10^{23}\ \text{mol}^{-1}$$)

A

3 : 2 : 2

B

1 : 1 : 2

C

3 : 1 : 1

D

1 : 1 : 1

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NTA JEE Main 7th May 2012 Online - Question 33

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The limiting line in Balmer series will have a frequency of (Rydberg constant, $$R_\infty = 3.29 \times 10^{15}\ \text{cycles/s}$$)

A

$$8.22 \times 10^{14}\ \text{s}^{-1}$$

B

$$3.29 \times 10^{15}\ \text{s}^{-1}$$

C

$$3.65 \times 10^{14}\ \text{s}^{-1}$$

D

$$5.26 \times 10^{13}\ \text{s}^{-1}$$

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NTA JEE Main 7th May 2012 Online - Question 34

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In which of the following arrangements, the sequence is not strictly according to the property written against it?

A

$$\text{CO}_2 < \text{SiO}_2 < \text{SnO}_2 < \text{PbO}_2$$ : increasing oxidising power

B

$$\text{NH}_3 < \text{PH}_3 < \text{AsH}_3 < \text{SbH}_3$$ : increasing basic strength

C

$$\text{HF} < \text{HCl} < \text{HBr} < \text{HI}$$ : increasing acid strength

D

$$\text{B} < \text{C} < \text{O} < \text{N}$$ : increasing first ionisation enthalpy.

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NTA JEE Main 7th May 2012 Online - Question 35

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Among the following, the species having the smallest bond is

A

$$\text{NO}^-$$

B

$$\text{NO}^+$$

C

$$\text{O}_2$$

D

NO

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NTA JEE Main 7th May 2012 Online - Question 36

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Based on lattice energy and other considerations, which one of the following alkali metal chloride is expected to have the highest melting point?

A

NaCl

B

KCl

C

LiCl

D

RbCl

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NTA JEE Main 7th May 2012 Online - Question 37

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For 1 mol of an ideal gas at a constant temperature $$T$$, the plot of $$(\log P)$$ against $$(\log V)$$ is a ($$P$$ : Pressure, $$V$$ : Volume)

A

Straight line parallel to $$x$$-axis.

B

Straight line with a negative slope.

C

Curve starting at origin.

D

Straight line passing through origin.

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NTA JEE Main 7th May 2012 Online - Question 38

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The entropy of a sample of a certain substance increases by $$0.836\ \text{J K}^{-1}$$ on adding reversibly $$0.3344\ \text{J}$$ of heat at constant temperature. The temperature of the sample is:

A

2.5 K

B

0.3 K

C

0.016 K

D

0.4 K

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NTA JEE Main 7th May 2012 Online - Question 39

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The electron affinity of chlorine is 3.7 eV. 1 gram of chlorine is completely converted to $$\text{Cl}^-$$ ion in a gaseous state. ($$1\ \text{eV} = 23.06\ \text{kcal mol}^{-1}$$). Energy released in the process is

A

4.8 kcal

B

7.2 kcal

C

8.2 kcal

D

2.4 kcal

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NTA JEE Main 7th May 2012 Online - Question 40

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The solubility (in mol $$\text{L}^{-1}$$) of AgCl ($$K_{sp} = 1.0 \times 10^{-10}$$) in a 0.1 M KCl solution will be

A

$$1.0 \times 10^{-9}$$

B

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

C

$$1.0 \times 10^{-5}$$

D

$$1.0 \times 10^{-11}$$

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NTA JEE Main 7th May 2012 Online - Question 41

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Which of the oxide groups among the following cannot be reduced by carbon?

A

$$\text{Cu}_2\text{O}, \text{SnO}_2$$

B

CaO, $$\text{K}_2\text{O}$$

C

PbO, $$\text{Fe}_2\text{O}_4$$

D

$$\text{Fe}_2\text{O}_3$$, ZnO

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NTA JEE Main 7th May 2012 Online - Question 42

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Which of the following cannot be represented by resonance structures?

A

Dimethyl ether

B

Nitrate anion

C

Carboxylate anion

D

Toluene

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NTA JEE Main 7th May 2012 Online - Question 43

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Copper wire test for halogens is known as

A

Duma's Test

B

Beilstein's Test

C

Liebig's Test

D

Lassigne's Test

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NTA JEE Main 7th May 2012 Online - Question 44

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The IUPAC name of the compound

is

A

1, 2-Propoxide

B

Propylene oxide

C

1,2-Oxo propane

D

1, 2-Epoxy propane

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NTA JEE Main 7th May 2012 Online - Question 45

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Among the following the order of reactivity towards nucleophilic addition is

A

$$\text{CH}_3\text{CHO} > \text{CH}_3\text{COCH}_3 > \text{HCHO}$$

B

$$\text{HCHO} > \text{CH}_3\text{CHO} > \text{CH}_3\text{COCH}_3$$

C

$$\text{CH}_3\text{CHO} > \text{HCHO} > \text{CH}_3\text{COCH}_3$$

D

$$\text{CH}_3\text{COCH}_3 > \text{CH}_3\text{CHO} > \text{HCHO}$$

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NTA JEE Main 7th May 2012 Online - Question 46

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Green house gases can be arranged in 'Global Warming Potential' sequence as

A

$$\text{N}_2\text{O} > \text{CFC} > \text{CH}_4 > \text{CO}_2$$

B

$$\text{CFC} > \text{N}_2\text{O} > \text{CH}_4 > \text{CO}_2$$

C

$$\text{CFC} > \text{CO}_2 > \text{N}_2\text{O} > \text{CH}_4$$

D

$$\text{CO}_2 > \text{CFC} > \text{N}_2\text{O} > \text{CH}_4$$

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NTA JEE Main 7th May 2012 Online - Question 47

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Among the following which is the best description of water in the solid phase?

A

Covalent solid

B

Molecular solid

C

Ionic solid

D

Network solid

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NTA JEE Main 7th May 2012 Online - Question 48

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A solid has a '$$bcc$$' structure. If the distance of nearest approach between two atoms is $$1.73\ \text{Å}$$, the edge length of the cell is

A

314.20 pm

B

1.41 pm

C

200 pm

D

216 pm

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NTA JEE Main 7th May 2012 Online - Question 49

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A battery is constructed of Cr and $$\text{Na}_2\text{Cr}_2\text{O}_7$$. The unbalanced chemical equation when such a battery discharges is following: $$$\text{Na}_2\text{Cr}_2\text{O}_7 + \text{Cr} + \text{H}^+ \rightarrow \text{Cr}^{3+} + \text{H}_2\text{O} + \text{Na}^+$$$ If one Faraday of electricity is passed through the battery during the charging, the number of moles of $$\text{Cr}^{3+}$$ removed from the solution is

A

$$\dfrac{4}{3}$$

B

$$\dfrac{1}{3}$$

C

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

D

$$\dfrac{2}{3}$$

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NTA JEE Main 7th May 2012 Online - Question 50

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$$K_1, K_2$$ and $$K_3$$ are the equilibrium constants of the following reactions (I), (II) and (III) respectively: (I) $$\text{N}_2 + 2\text{O}_2 \rightleftharpoons 2\text{NO}_2$$ (II) $$2\text{NO}_2 \rightleftharpoons \text{N}_2 + 2\text{O}_2$$ (III) $$\text{NO}_2 \rightleftharpoons \tfrac{1}{2}\text{N}_2 + \text{O}_2$$. The correct relation from the following is

A

$$K_1 = \dfrac{1}{K_2} = \dfrac{1}{K_3}$$

B

$$K_1 = \dfrac{1}{K_2} = \dfrac{1}{(K_3)^2}$$

C

$$K_1 = \sqrt{K_2} = K_3$$

D

$$K_1 = \dfrac{1}{K_2} = K_3$$

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NTA JEE Main 7th May 2012 Online - Question 51

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Reaction rate between two substance $$A$$ and $$B$$ is expressed as following: $$\text{rate} = k[A]^n[B]^m$$. If the concentration of $$A$$ is doubled and concentration of $$B$$ is made half of initial concentration, the ratio of the new rate to the earlier rate will be:

A

$$m + n$$

B

$$n - m$$

C

$$\dfrac{1}{2^{(m+n)}}$$

D

$$2^{(n-m)}$$

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NTA JEE Main 7th May 2012 Online - Question 52

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If $$x$$ is the mass of the gas adsorbed on mass $$m$$ of the adsorbent at pressure $$p$$, Freundlich adsorption isotherm gives a straight line on plotting

A

$$x/m$$ vs $$p$$

B

$$x/m$$ vs $$1/p$$

C

$$\log x/m$$ vs $$\log p$$

D

$$\log x/m$$ vs $$p$$

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NTA JEE Main 7th May 2012 Online - Question 53

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The $$d$$-electron configurations of $$\text{Cr}^{2+}, \text{Mn}^{2+}, \text{Fe}^{2+}$$ and $$\text{Co}^{2+}$$ are $$d^4, d^5, d^6$$ and $$d^7$$ respectively. Which one of the following will exhibit the lowest paramagnetic behaviour? (Atomic no. Cr = 24, Mn = 25, Fe = 26, Co = 27).

A

$$[\text{Co}(\text{H}_2\text{O})_6]^{2+}$$

B

$$[\text{Cr}(\text{H}_2\text{O})_6]^{2+}$$

C

$$[\text{Mn}(\text{H}_2\text{O})_6]^{2+}$$

D

$$[\text{Fe}(\text{H}_2\text{O})_6]^{2+}$$

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NTA JEE Main 7th May 2012 Online - Question 54

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Which is not the correct Statement? (At. nos. Ce = 58, Lu = 71, La = 57, Yb = 70)

A

Colour of $$\text{Yb}^{3+}$$ ion is pink.

B

$$\text{La}^{3+}$$ is diamagnetic.

C

$$\text{Ce}^{4+}$$ has $$f^0$$ configuration.

D

$$\text{Lu}^{3+}$$ had $$f^{14}$$ configuration.

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NTA JEE Main 7th May 2012 Online - Question 55

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How many cyclic structures are possible for $$\text{C}_4\text{H}_6$$?

A

3

B

5

C

6

D

4

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NTA JEE Main 7th May 2012 Online - Question 56

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The most basic compound among the following is

A

Acetanilide

B

Benzylamine

C

$$p$$-Nitro aniline

D

Aniline

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NTA JEE Main 7th May 2012 Online - Question 57

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$$\text{C}_2\text{H}_5\text{Br} \xrightarrow{\text{AgCN}} X \xrightarrow[\text{Zn-Hg/HCl}]{\text{Reduction}} Y$$. Here Y is

A

Ethyl methyl amine

B

n-propylamine

C

Isopropylamine

D

Ethylamine

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NTA JEE Main 7th May 2012 Online - Question 58

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Which one of the following is a chain growth polymerisation?

A

Nucleic acid

B

Polystyrene

C

Protein

D

Starch

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NTA JEE Main 7th May 2012 Online - Question 59

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Which one of the following compounds is an antifertility drug?

A

Aspirin

B

Chloromycetin

C

Saheli

D

Penicillin

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NTA JEE Main 7th May 2012 Online - Question 60

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All of the following statements apply to proteins except

A

Proteins generally have no definite melting point

B

Proteins contain the grouping -CONH-

C

Proteins have high molecular weight

D

Proteins can only contain the elements C, H, O and N.

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NTA JEE Main 7th May 2012 Online - Question 61

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The value of $$k$$ for which the equation $$(K-2)x^2 + 8x + K + 4 = 0$$ has both roots real, distinct and negative can be:

A

6

B

3

C

4

D

1

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NTA JEE Main 7th May 2012 Online - Question 62

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Let $$Z_1$$ and $$Z_2$$ be any two complex number. Statement 1: $$|Z_1 - Z_2| \geq |Z_1| - |Z_2|$$ Statement 2: $$|Z_1 + Z_2| \leq |Z_1| + |Z_2|$$

A

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

B

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

C

Statement 1 is true, Statement 2 is false.

D

Statement 1 is false, Statement 2 is true.

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NTA JEE Main 7th May 2012 Online - Question 63

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If the number of 5-element subsets of the set $$A = \{a_1, a_2, \ldots, a_{20}\}$$ of 20 distinct elements is $$k$$ times the number of 5-element subsets containing $$a_4$$, then $$k$$ is

A

5

B

$$\dfrac{20}{7}$$

C

4

D

$$\dfrac{10}{3}$$

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NTA JEE Main 7th May 2012 Online - Question 64

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The difference between the fourth term and the first term of a Geometrical Progression is 52. If the sum of its first three terms is 26, then the sum of the first six terms of the progression is

A

63

B

189

C

728

D

364

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NTA JEE Main 7th May 2012 Online - Question 65

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The sum of the series $$1^2 + 2 \cdot 2^2 + 3^2 + 2 \cdot 4^2 + 5^2 + 2 \cdot 6^2 + \ldots + 2(2m)^2$$ is

A

$$m(2m+1)^2$$

B

$$m^2(m+2)$$

C

$$m^2(2m+1)$$

D

$$m(m+2)^2$$

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NTA JEE Main 7th May 2012 Online - Question 66

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If $$f(y) = 1 - (y-1) + (y-1)^2 - (y-1)^3 + \ldots - (y-1)^{17}$$ then the coefficient of $$y^2$$ in it is

A

$${}^{17}C_2$$

B

$${}^{17}C_3$$

C

$${}^{18}C_2$$

D

$${}^{18}C_3$$

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NTA JEE Main 7th May 2012 Online - Question 67

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If the straight lines $$x + 3y = 4, 3x + y = 4$$ and $$x + y = 0$$ form a triangle, then the triangle is

A

scalene

B

equilateral triangle

C

isosceles

D

right angled isosceles

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NTA JEE Main 7th May 2012 Online - Question 68

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The point of intersection of the lines $$(a^3 + 3)x + ay + a - 3 = 0$$ and $$(a^5 + 2)x + (a+2)y + 2a + 3 = 0$$ ($$a$$ real) lies on the $$y$$-axis for

A

no value of $$a$$

B

more than two values of $$a$$

C

exactly one value of $$a$$

D

exactly two values of $$a$$

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NTA JEE Main 7th May 2012 Online - Question 69

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The equation of the circle passing through the point $$(1, 2)$$ and through the points of intersection of $$x^2 + y^2 - 4x - 6y - 21 = 0$$ and $$3x + 4y + 5 = 0$$ is given by

A

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

B

$$x^2 + y^2 - 2x + 2y - 7 = 0$$

C

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

D

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

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NTA JEE Main 7th May 2012 Online - Question 70

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Statement 1: $$y = mx - \dfrac{1}{m}$$ is always a tangent to the parabola, $$y^2 = -4x$$ for all non-zero values of $$m$$. Statement 2: Every tangent to the parabola, $$y^2 = -4x$$ will meet its axis at a point whose abscissa is non-negative.

A

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

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NTA JEE Main 7th May 2012 Online - Question 71

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If the eccentricity of a hyperbola $$\dfrac{x^2}{9} - \dfrac{y^2}{b^2} = 1$$, which passes through $$(K, 2)$$, is $$\dfrac{\sqrt{13}}{3}$$, then the value of $$K^2$$ is

A

18

B

8

C

1

D

2

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NTA JEE Main 7th May 2012 Online - Question 72

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$$\lim_{x \to 0} \left(\dfrac{x - \sin x}{x}\right) \sin\left(\dfrac{1}{x}\right)$$

A

equals 1

B

equals 0

C

does not exist

D

equals $$-1$$

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NTA JEE Main 7th May 2012 Online - Question 73

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The Statement that is TRUE among the following is

A

The contrapositive of $$3x + 2 = 8 \Rightarrow x = 2$$ is $$x \neq 2 \Rightarrow 3x + 2 \neq 8$$.

B

The converse of $$\tan x = 0 \Rightarrow x = 0$$ is $$x \neq 0 \Rightarrow \tan x = 0$$.

C

$$p \Rightarrow q$$ is equivalent to $$p \vee \sim q$$.

D

$$p \vee q$$ and $$p \wedge q$$ have the same truth table.

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NTA JEE Main 7th May 2012 Online - Question 74

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The frequency distribution of daily working expenditure of families in a locality is as follows:

If the mode of the distribution is Rs. 140, then the value of $$b$$ is

A

34

B

31

C

26

D

36

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NTA JEE Main 7th May 2012 Online - Question 75

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If two vertical poles 20 m and 80 m high stand apart on a horizontal plane, then the height (in m) of the point of intersection of the lines joining the top of each pole to the foot of other is

A

16

B

18

C

50

D

15

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NTA JEE Main 7th May 2012 Online - Question 76

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Let $$X$$ and $$Y$$ are two events such that $$P(X \cup Y) = P(X \cap Y)$$. Statement 1: $$P(X \cap Y') = P(X' \cap Y) = 0$$ Statement 2: $$P(X) + P(Y) = 2 P(X \cap Y)$$

A

Statement 1 is false, Statement 2 is true.

B

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

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 7th May 2012 Online - Question 77

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If $$A = \begin{pmatrix} \alpha - 1 \\ 0 \\ 0 \end{pmatrix}, B = \begin{pmatrix} \alpha + 1 \\ 0 \\ 0 \end{pmatrix}$$ be two matrices, then $$AB^T$$ is a non-zero matrix for $$|\alpha|$$ not equal to

A

2

B

0

C

1

D

3

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NTA JEE Main 7th May 2012 Online - Question 78

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If the system of equations $$\begin{aligned} x + y + z &= 6 \\ x + 2y + 3z &= 10 \\ x + 2y + \lambda z &= 0 \end{aligned}$$ has a unique solution, then $$\lambda$$ is not equal to

A

1

B

0

C

2

D

3

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NTA JEE Main 7th May 2012 Online - Question 79

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The range of the function $$f(x) = \dfrac{x}{1+|x|}, x \in R$$, is

A

$$R$$

B

$$(-1, 1)$$

C

$$R - \{0\}$$

D

$$[-1, 1]$$

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NTA JEE Main 7th May 2012 Online - Question 80

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Let $$f(x) = \sin x, g(x) = x$$. Statement 1: $$f(x) \leq g(x)$$ for $$x$$ in $$(0, \infty)$$ Statement 2: $$f(x) \leq 1$$ for $$x$$ in $$(0, \infty)$$ but $$g(x) \to \infty$$ as $$x \to \infty$$.

A

Statement 1 is true, Statement 2 is false.

B

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

C

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

D

Statement 1 is false, Statement 2 is true.

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NTA JEE Main 7th May 2012 Online - Question 81

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If $$x + |y| = 2y$$, then $$y$$ as a function of $$x$$, at $$x = 0$$ is

A

differentiable but not continuous

B

continuous but not differentiable

C

continuous as well as differentiable

D

neither continuous nor differentiable

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NTA JEE Main 7th May 2012 Online - Question 82

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If a circular iron sheet of radius 30 cm is heated such that its area increases at the uniform rate of $$6\pi\ \text{cm}^2/\text{hr}$$, then the rate (in mm/hr) at which the radius of the circular sheet increases is

A

1.0

B

0.1

C

1.1

D

2.0

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NTA JEE Main 7th May 2012 Online - Question 83

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Let $$f(x)$$ be an indefinite integral of $$\cos^3 x$$. Statement 1: $$f(x)$$ is a periodic function of period $$\pi$$. Statement 2: $$\cos^3 x$$ is a periodic function.

A

Statement 1 is true, Statement 2 is false.

B

Both the Statements are true, but Statement 2 is not the correct explanation of Statement 1.

C

Both the Statements are true, and Statement 2 is correct explanation of Statement 1.

D

Statement 1 is false, Statement 2 is true.

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NTA JEE Main 7th May 2012 Online - Question 84

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If $$\int_e^x t f(t)\, dt = \sin x - x \cos x - \dfrac{x^2}{2}$$, for all $$x \in R - \{0\}$$, then the value of $$f\left(\dfrac{\pi}{6}\right)$$ is

A

$$1/2$$

B

1

C

0

D

$$-1/2$$

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NTA JEE Main 7th May 2012 Online - Question 85

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The parabola $$y^2 = x$$ divides the circle $$x^2 + y^2 = 2$$ into two parts whose areas are in the ratio

A

$$9\pi + 2 : 3\pi - 2$$

B

$$9\pi - 2 : 3\pi + 2$$

C

$$7\pi - 2 : 2\pi - 3$$

D

$$7\pi + 2 : 3\pi + 2$$

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NTA JEE Main 7th May 2012 Online - Question 86

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Let $$y(x)$$ be a solution of $$\dfrac{(2+\sin x)}{(1+y)} \dfrac{dy}{dx} = \cos x$$. If $$y(0) = 2$$, then $$y\left(\dfrac{\pi}{2}\right)$$ equals

A

$$\dfrac{5}{2}$$

B

2

C

$$\dfrac{7}{2}$$

D

3

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NTA JEE Main 7th May 2012 Online - Question 87

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$$ABCD$$ is parallelogram. The position vectors of $$A$$ and $$C$$ are respectively, $$3\hat{i} + 3\hat{j} + 5\hat{k}$$ and $$\hat{i} - 5\hat{j} - 5\hat{k}$$. If $$M$$ is the midpoint of the diagonal $$DB$$, then the magnitude of the projection of $$\overrightarrow{OM}$$ on $$\overrightarrow{OC}$$, where $$O$$ is the origin, is

A

$$7\sqrt{51}$$

B

$$\dfrac{7}{\sqrt{50}}$$

C

$$7\sqrt{50}$$

D

$$\dfrac{7}{\sqrt{51}}$$

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NTA JEE Main 7th May 2012 Online - Question 88

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If $$\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}, \vec{b} = 2\hat{i} + 3\hat{j} - \hat{k}$$ and $$\vec{c} = \lambda\hat{i} + \hat{j} + (2\lambda - 1)\hat{k}$$ are coplanar vectors, then $$\lambda$$ is equal to

A

0

B

$$-1$$

C

2

D

1

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NTA JEE Main 7th May 2012 Online - Question 89

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The values of $$a$$ for which the two points $$(1, a, 1)$$ and $$(-3, 0, a)$$ lie on the opposite sides of the plane $$3x + 4y - 12z + 13 = 0$$, satisfy

A

$$0 < a < \dfrac{1}{3}$$

B

$$-1 < a < 0$$

C

$$a < -1$$ or $$a < \dfrac{1}{3}$$

D

$$a = 0$$

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NTA JEE Main 7th May 2012 Online - Question 90

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A line with positive direction cosines passes through the point $$P(2, -1, 2)$$ and makes equal angles with the coordinate axes. If the line meets the plane $$2x + y + z = 9$$ at point $$Q$$, then the length $$PQ$$ equals

A

$$\sqrt{2}$$

B

2

C

$$\sqrt{3}$$

D

1

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