NTA JEE Main 15th April 2018 Shift 1

NTA JEE Main 15th April 2018 Shift 1 - Question 1

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The relative error in the determination of the surface area of a sphere is $$\alpha$$. Then the relative error in the determination of its volume is:

A

$$\frac{2}{3} \cdot \alpha$$

B

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

C

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

D

$$\alpha$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 2

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An automobile, travelling at 40 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is (assume no skidding):

A

75 m

B

160 m

C

100 m

D

150 m

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NTA JEE Main 15th April 2018 Shift 1 - Question 3

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The velocity-time graphs of a car and a scooter are shown in the figure. (i) the difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively.

A

337.5 m and 25 s

B

225.5 m and 10 s

C

112.5 m and 22.5 s

D

112.5 m and 15 s

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NTA JEE Main 15th April 2018 Shift 1 - Question 4

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A given object takes n times more time to slide down a 45$$^\circ$$ rough inclined plane as it takes to slide down a perfectly smooth 45$$^\circ$$ incline. The coefficient of kinetic friction between the object and the incline is:

A

$$\sqrt{1 - \frac{1}{n^2}}$$

B

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

C

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

D

$$\sqrt{\frac{1}{1-n^2}}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 5

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A uniform rod AB is suspended from a point X, at a variable distance x from A, as shown. To make the rod horizontal, a mass m is suspended from its end A. A set of (m, x) values is recorded. The appropriate variable that give a straight line, when plotted, are:

A

$$m, \frac{1}{x}$$

B

$$m, \frac{1}{x^2}$$

C

$$m, x$$

D

$$m, x^2$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 6

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A force of 40 N acts on a point B at the end of an L-shaped object, as shown in the figure. The angle $$\theta$$ that will produce maximum moment of the force about point A is given by:

A

$$\tan \theta = \frac{1}{4}$$

B

$$\tan \theta = 2$$

C

$$\tan \theta = \frac{1}{2}$$

D

$$\tan \theta = 4$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 7

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A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius $$\frac{R}{2}$$, and the other mass, in a circular orbit of radius $$\frac{3R}{2}$$. The difference between the final and initial total energies is:

A

$$-\frac{GMm}{2R}$$

B

$$+\frac{GMm}{6R}$$

C

$$-\frac{GMm}{6R}$$

D

$$\frac{GMm}{2R}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 8

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Take the mean distance of the moon and the sun from the earth to be $$0.4 \times 10^6$$ km and $$150 \times 10^6$$ km respectively. Their masses are $$8 \times 10^{22}$$ kg and $$2 \times 10^{30}$$ kg respectively. The radius of the earth is 6400 km. Let $$\Delta F_1$$ be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and $$\Delta F_2$$ be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to $$\frac{\Delta F_1}{\Delta F_2}$$ is:

A

2

B

6

C

$$10^{-2}$$

D

0.6

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NTA JEE Main 15th April 2018 Shift 1 - Question 9

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A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, whose densities are $$\rho_1$$ and $$\rho_2$$ ($$\rho_1 > \rho_2$$) fill half the circle. The angle $$\theta$$ between the radius vector passing through the common interface and the vertical is:

A

$$\theta = \tan^{-1}\left[\frac{\pi}{2}\left(\frac{\rho_1 - \rho_2}{\rho_1 + \rho_2}\right)\right]$$

B

$$\theta = \tan^{-1}\frac{\pi}{2}\left(\frac{\rho_1 + \rho_2}{\rho_1 - \rho_2}\right)$$

C

$$\theta = \tan^{-1}\pi\left(\frac{\rho_1}{\rho_2}\right)$$

D

$$\theta = \tan^{-1}\frac{\pi}{2}\left(\frac{\rho_2}{\rho_1}\right)$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 10

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A Carnot's engine works as a refrigerator between 250 K and 300 K. It receives 500 cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is:

A

420 J

B

2100 J

C

772 J

D

2520 J

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NTA JEE Main 15th April 2018 Shift 1 - Question 11

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One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, 27$$^\circ$$C. The work done on the gas will be:

A

300R ln 6

B

300R

C

300R ln 7

D

300R ln 2

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NTA JEE Main 15th April 2018 Shift 1 - Question 12

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A tuning fork vibrates with frequency 256 Hz and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe? (Speed of sound in air is 340 ms$$^{-1}$$)

A

190 cm

B

180 cm

C

220 cm

D

200 cm

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NTA JEE Main 15th April 2018 Shift 1 - Question 13

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A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along x-direction about its equilibrium position, taken to be at x = 0, with an amplitude A. An electric field E is applied along the x-direction. Which of the following statements is correct?

A

The total energy of the system is $$\frac{1}{2}m\omega^2A^2 + \frac{1}{2}\frac{q^2E^2}{k}$$

B

The new equilibrium position is at a distance $$\frac{2qE}{k}$$ from x = 0

C

The new equilibrium position is at a distance $$\frac{qE}{2k}$$ from x = 0

D

The total energy of the system is $$\frac{1}{2}m\omega^2A^2 - \frac{1}{2}\frac{q^2E^2}{k}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 14

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A charge Q is placed at a distance a/2 above the centre of the square surface of edge a as shown in the figure. The electric flux through the square surface is:

A

$$\frac{Q}{3\varepsilon_0}$$

B

$$\frac{Q}{6\varepsilon_0}$$

C

$$\frac{Q}{2\varepsilon_0}$$

D

$$\frac{Q}{\varepsilon_0}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 15

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The equivalent capacitance between A and B in the circuit given below is:

A

4.9 $$\mu$$F

B

3.6 $$\mu$$F

C

5.4 $$\mu$$F

D

2.4 $$\mu$$F

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NTA JEE Main 15th April 2018 Shift 1 - Question 16

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In the given circuit all resistances are of value R ohm each. The equivalent resistance between A and B is:

A

2R

B

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

C

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

D

3R

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NTA JEE Main 15th April 2018 Shift 1 - Question 17

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In a meter bridge, as shown in the figure, it is given that resistance Y = 12.5 $$\Omega$$ and that the balance is obtained at a distance 39.5 cm from end A (by jockey J). After interchanging the resistances X and Y a new balance point is found at a distance $$l_2$$ from end A. What are the values of X and $$l_2$$?

A

19.15 $$\Omega$$ and 39.5 cm

B

8.16 $$\Omega$$ and 60.5 cm

C

19.15 $$\Omega$$ and 60.5 cm

D

8.16 $$\Omega$$ and 39.5 cm

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NTA JEE Main 15th April 2018 Shift 1 - Question 18

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The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with 1000 turns/cm. The current that should be passed in the solenoid to demagnetize the ferromagnet completely is:

A

2 mA

B

1 mA

C

40 $$\mu$$A

D

20 $$\mu$$A

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NTA JEE Main 15th April 2018 Shift 1 - Question 19

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A Helmholtz coil has pair of loops, each with N turns and radius R. They are placed coaxially at distance R and the same current I flows through the loops in the same direction. The magnitude of magnetic field at P, midway between the centres A and C, is given by (Refer to figure):

A

$$\frac{4N\mu_0 I}{5^{3/2}R}$$

B

$$\frac{8N\mu_0 I}{5^{3/2}R}$$

C

$$\frac{4N\mu_0 I}{5^{1/2}R}$$

D

$$\frac{8N\mu_0 I}{5^{1/2}R}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 20

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An ideal capacitor of capacitance 0.2 $$\mu$$F is charged to a potential difference of 10 V. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance 0.5 mH. The current at a time when the potential difference across the capacitor is 5 V, is:

A

0.17 A

B

0.15 A

C

0.34 A

D

0.25 A

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NTA JEE Main 15th April 2018 Shift 1 - Question 21

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A monochromatic beam of light has a frequency $$\nu = \frac{3}{2\pi} \times 10^{12}$$ Hz and is propagating along the direction $$\frac{\hat{i}+\hat{j}}{\sqrt{2}}$$. It is polarized along the $$\hat{k}$$ direction. The acceptable form for the magnetic field is:

A

$$\frac{E_0}{C}\left(\frac{\hat{i}-\hat{j}}{\sqrt{2}}\right) \cos\left[10^4\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right) \cdot \vec{r} - (3 \times 10^{12})t\right]$$

B

$$\frac{E_0}{C}\left(\frac{\hat{i}-\hat{j}}{\sqrt{2}}\right) \cos\left[10^4\left(\frac{\hat{i}-\hat{j}}{\sqrt{2}}\right) \cdot \vec{r} - (3 \times 10^{12})t\right]$$

C

$$\frac{E_0}{C}\hat{k} \cos\left[10^4\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)\cdot\vec{r} + (3 \times 10^{12})t\right]$$

D

$$\frac{E_0}{C}\frac{(\hat{i}+\hat{j}+\hat{k})}{\sqrt{3}} \cos\left[10^4\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)\cdot\vec{r} + (3 \times 10^{12})t\right]$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 22

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A planoconvex lens becomes an optical system of 28 cm focal length when its plane surface is silvered and illuminated from left to right as shown in Fig. A. If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig. B, it acts like an optical system of focal length 10 cm. The refractive index of the material of lens is:

A

1.50

B

1.55

C

1.75

D

1.51

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NTA JEE Main 15th April 2018 Shift 1 - Question 23

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A particle is oscillating on the X-axis with an amplitude 2 cm about the point $$x_0 = 10$$ cm with a frequency $$\omega$$. A concave mirror of focal length 5 cm is placed at the origin (see figure). Identify the correct statements: (A) The image executes periodic motion (B) The image executes non-periodic motion (C) The turning points of the image are asymmetric w.r.t the image of the point at x = 10 cm (D) The distance between the turning points of the oscillation of the image is $$\frac{100}{21}$$ cm.

A

(B), (D)

B

(B), (C)

C

(A), (C), (D)

D

(A), (D)

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NTA JEE Main 15th April 2018 Shift 1 - Question 24

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Light of wavelength 550 nm falls normally on a slit of width $$22.0 \times 10^{-5}$$ cm. The angular position of the second minima from the central maximum will be (in radians):

A

$$\frac{\pi}{8}$$

B

$$\frac{\pi}{12}$$

C

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

D

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

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NTA JEE Main 15th April 2018 Shift 1 - Question 25

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Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are $$\lambda_1$$ and $$\lambda_2$$, their de Broglie wavelength in the frame of reference attached to their centre of mass is:

A

$$\lambda_{CM} = \lambda_1 = \lambda_2$$

B

$$\frac{1}{\lambda_{CM}} = \frac{1}{\lambda_1} + \frac{1}{\lambda_2}$$

C

$$\lambda_{CM} = \frac{2\lambda_1\lambda_2}{\sqrt{\lambda_1^2 + \lambda_2^2}}$$

D

$$\lambda_{CM} = \frac{\lambda_1 + \lambda_2}{2}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 26

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The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is:

A

20 eV

B

79 eV

C

109 eV

D

34 eV

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NTA JEE Main 15th April 2018 Shift 1 - Question 27

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A solution containing active cobalt $$^{60}_{27}$$Co having activity of 0.8 $$\mu$$Ci and decay constant $$\lambda$$ is injected in an animal's body. If 1 cm$$^3$$ of blood is drawn from the animal's body after 10 hrs of injection, the activity found was 300 decays per minute. What is the volume of blood that is flowing in the body? (1 Ci = $$3.7 \times 10^{10}$$ decay per second and at t = 10 hrs the value of $$e^{-\lambda t}$$ = 0.84)

A

6 litres

B

7 litres

C

4 litres

D

5 litres

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NTA JEE Main 15th April 2018 Shift 1 - Question 28

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In a common emitter configuration with suitable bias, it is given than $$R_L$$ is the load resistance and $$R_{BE}$$ is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by: [$$\beta$$ is current gain, $$I_B$$, $$I_C$$, $$I_E$$ are respectively base, collector and emitter currents]

A

$$\beta \frac{R_L}{R_{BE}}, \frac{\Delta I_E}{\Delta I_B}, \beta^2 \frac{R_L}{R_{BE}}$$

B

$$\beta^2 \frac{R_L}{R_{BE}}, \frac{\Delta I_C}{\Delta I_B}, \beta \frac{R_L}{R_{BE}}$$

C

$$\beta^2 \frac{R_L}{R_{BE}}, \frac{\Delta I_C}{\Delta I_E}, \beta^2 \frac{R_L}{R_{BE}}$$

D

$$\beta \frac{R_L}{R_{BE}}, \frac{\Delta I_C}{\Delta I_B}, \beta^2 \frac{R_L}{R_{BE}}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 29

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The number of amplitude modulated broadcast stations that can be accommodated in a 300 kHz band width for the highest modulating frequency 15 kHz will be:

A

20

B

10

C

8

D

15

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NTA JEE Main 15th April 2018 Shift 1 - Question 30

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In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25 cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is:

A

0.0430 cm

B

0.3150 cm

C

0.4300 cm

D

0.2150 cm

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NTA JEE Main 15th April 2018 Shift 1 - Question 31

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A sample of NaClO$$_3$$ is converted by heat to NaCl with a loss of 0.16 g of oxygen. The residue is dissolved in water and precipitated as AgCl. The mass of AgCl (in g) obtained will be: (Given: Molar mass of AgCl = 143.5 g mol$$^{-1}$$)

A

0.35

B

0.54

C

0.41

D

0.48

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NTA JEE Main 15th April 2018 Shift 1 - Question 32

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Ejection of the photoelectron from metal in the photoelectric effect experiment can be stopped by applying 0.5 V when the radiation of 250 nm is used. The work function of the metal is:

A

4 eV

B

5.5 eV

C

4.5 eV

D

5 eV

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NTA JEE Main 15th April 2018 Shift 1 - Question 33

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For Na$$^+$$, Mg$$^{2+}$$, F$$^-$$ and O$$^{2-}$$; the correct order of increasing ionic radii is:

A

O$$^{2-}$$ < F$$^-$$ < Na$$^+$$ < Mg$$^{2+}$$

B

Na$$^+$$ < Mg$$^{2+}$$ < F$$^-$$ < O$$^{2-}$$

C

Mg$$^{2+}$$ < Na$$^+$$ < F$$^-$$ < O$$^{2-}$$

D

Mg$$^{2+}$$ < O$$^{2-}$$ < Na$$^+$$ < F$$^-$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 34

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In the molecular orbital diagram for the molecular ion, N$$_2^+$$, the number of electrons in the $$\sigma_{2p}$$ molecular orbital is:

A

0

B

2

C

3

D

1

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NTA JEE Main 15th April 2018 Shift 1 - Question 35

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Identify the pair in which the geometry of the species is T-shape and square pyramidal, respectively:

A

ICl$$_2^-$$ and ICl$$_5$$

B

IO$$_3^-$$ and IO$$_2$$F$$_2^-$$

C

ClF$$_3$$ and IO$$_4^-$$

D

XeOF$$_2$$ and XeOF$$_4$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 36

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In hydrogen azide, the bond orders of bonds (I) and (II) are:

A

I < 2, II > 2

B

I > 2, II > 2

C

I > 2, II < 2

D

I < 2, II < 2

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NTA JEE Main 15th April 2018 Shift 1 - Question 37

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In graphite and diamond, the percentage of p characters of the hybrid orbitals in hybridization are respectively:

A

33 and 25

B

67 and 75

C

50 and 75

D

33 and 75

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NTA JEE Main 15th April 2018 Shift 1 - Question 38

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The decreasing order of bond angles in BF$$_3$$, NH$$_3$$, PF$$_3$$ and I$$_3^-$$ is:

A

I$$_3^-$$ > BF$$_3$$ > NH$$_3$$ > PF$$_3$$

B

BF$$_3$$ > I$$_3^-$$ > PF$$_3$$ > NH$$_3$$

C

BF$$_3$$ > NH$$_3$$ > PF$$_3$$ > I$$_3^-$$

D

I$$_3^-$$ > NH$$_3$$ > PF$$_3$$ > BF$$_3$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 39

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For which of the following reactions, $$\Delta H$$ is equal to $$\Delta U$$?

A

N$$_2$$(g) + 3H$$_2$$(g) $$\rightarrow$$ 2NH$$_3$$(g)

B

2HI(g) $$\rightarrow$$ H$$_2$$(g) + I$$_2$$(g)

C

2SO$$_2$$(g) + O$$_2$$(g) $$\rightarrow$$ 2SO$$_3$$(g)

D

2NO$$_2$$(g) $$\rightarrow$$ N$$_2$$O$$_4$$(g)

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NTA JEE Main 15th April 2018 Shift 1 - Question 40

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An ideal gas undergoes a cyclic process as shown in Figure.

$$\Delta U_{BC} = -5$$ kJ mol$$^{-1}$$, $$q_{AB} = 2$$ kJ mol$$^{-1}$$
$$W_{AB} = -5$$ kJ mol$$^{-1}$$, $$W_{CA} = 3$$ kJ mol$$^{-1}$$
Heat absorbed by the system during process CA is:

A

-5 kJ mol$$^{-1}$$

B

+5 kJ mol$$^{-1}$$

C

18 kJ mol$$^{-1}$$

D

-18 kJ mol$$^{-1}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 41

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In which of the following reactions, an increase in the volume of the container will favour the formation of products?

A

4NH$$_3$$(g) + 5O$$_2$$(g) $$\rightleftharpoons$$ 4NO(g) + 6H$$_2$$O(l)

B

2NO$$_2$$(g) $$\rightleftharpoons$$ 2NO(g) + O$$_2$$(g)

C

3O$$_2$$ $$\rightleftharpoons$$ 2O$$_3$$(g)

D

H$$_2$$(g) + I$$_2$$(g) $$\rightleftharpoons$$ 2HI(g)

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NTA JEE Main 15th April 2018 Shift 1 - Question 42

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Which of the following is a Lewis acid?

A

PH$$_3$$

B

NF$$_3$$

C

NaH

D

B(CH$$_3$$)$$_3$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 43

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The minimum volume of water required to dissolve 0.1 g lead (II) chloride to get a saturated solution ($$K_{SP}$$ of PbCl$$_2$$ = $$3.2 \times 10^{-8}$$; atomic mass of Pb = 207 u) is:

A

1.798 L

B

0.36 L

C

17.95 L

D

0.18 L

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NTA JEE Main 15th April 2018 Shift 1 - Question 44

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A white sodium salt dissolves readily in water to give a solution which is neutral to litmus. When silver nitrate solution is added to the aforementioned solution, a white precipitate is obtained which does not dissolve in dil. nitric acid. The anion is:

A

CO$$_3^{2-}$$

B

SO$$_4^{2-}$$

C

S$$^{2-}$$

D

Cl$$^-$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 45

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The correct match between items of List-I and List-II is:

A

(A)-(r), (B)-(s), (C)-(p), (D)-(q)

B

(A)-(p), (B)-(s), (C)-(r), (D)-(q)

C

(A)-(r), (B)-(p), (C)-(q), (D)-(s)

D

(A)-(r), (B)-(p), (C)-(s), (D)-(q)

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NTA JEE Main 15th April 2018 Shift 1 - Question 46

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The IUPAC name of the following compound is:

A

3-ethyl-4-methylhex-4-ene

B

4,4-diethyl-3-methylbut-2-ene

C

4-methyl-3-ethylhex-4-ene

D

4-ethyl-3-methylhex-2-ene

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NTA JEE Main 15th April 2018 Shift 1 - Question 47

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Which of the following will most readily give the dehydrohalogenation product?

A

B

C

D

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NTA JEE Main 15th April 2018 Shift 1 - Question 48

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The major product of the following reaction is:

A

B

C

D

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NTA JEE Main 15th April 2018 Shift 1 - Question 49

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The increasing order of nitration of the following compounds is:

(A) Aniline, (B) Chlorobenzene, (C) Anisole, (D) Toluene

A

< (B) < (D) < (C)

B

< (B) < (C) < (D)

C

< (A) < (C) < (D)

D

< (A) < (D) < (C)

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NTA JEE Main 15th April 2018 Shift 1 - Question 50

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Which of the following arrangements shows the schematic alignment of magnetic moments of antiferromagnetic substance?

A

B

C

D

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NTA JEE Main 15th April 2018 Shift 1 - Question 51

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When an electric current is passes through acidified water, 112 mL of hydrogen gas at N.T.P. was collected at the cathode in 965 seconds. The current passed, in ampere, is:

A

2.0

B

0.1

C

0.5

D

1.0

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NTA JEE Main 15th April 2018 Shift 1 - Question 52

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N$$_2$$O$$_5$$ decomposes to NO$$_2$$ and O$$_2$$ and follows first order kinetics. After 50 minutes, the pressure inside the vessel increases from 50 mm Hg to 87.5 mm Hg. The pressure of the gaseous mixture after 100 minutes at constant temperature will be:

A

136.25 mm Hg

B

106.25 mm Hg

C

175.0 mm Hg

D

116.25 mm Hg

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NTA JEE Main 15th April 2018 Shift 1 - Question 53

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Which of the following statements about colloids is false?

A

When silver nitrate solution is added to potassium iodide solution, a negatively charged colloidal solution is formed

B

Freezing point of colloidal solution is lower than true solution at same concentration of a solute

C

Colloidal particles can pass through ordinary filter paper

D

When excess of electrolyte is added to colloidal solution, colloidal particle will be precipitated

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NTA JEE Main 15th April 2018 Shift 1 - Question 54

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Xenon hexafluoride on partial hydrolysis produces compounds 'X' and 'Y'. Compounds 'X' and 'Y' and the oxidation state of Xe are respectively:

A

XeOF$$_4$$(+6) and XeO$$_3$$(+6)

B

XeO$$_2$$(+4) and XeO$$_3$$(+6)

C

XeOF$$_4$$(+6) and XeO$$_2$$F$$_2$$(+6)

D

XeO$$_2$$F$$_2$$(+6) and XeO$$_2$$(+4)

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NTA JEE Main 15th April 2018 Shift 1 - Question 55

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The correct combination is:

A

[NiCl$$_4$$]$$^{2-}$$ - square-planar; [Ni(CN)$$_4$$]$$^{2-}$$ - paramagnetic

B

[Ni(CN)$$_4$$]$$^{2-}$$ - tetrahedral; [Ni(CO)$$_4$$] - paramagnetic

C

[NiCl$$_4$$]$$^{2-}$$ - paramagnetic; [Ni(CO)$$_4$$] - tetrahedral

D

[NiCl$$_4$$]$$^{2-}$$ - diamagnetic; [Ni(CO)$$_4$$] - square-planar

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NTA JEE Main 15th April 2018 Shift 1 - Question 56

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The main reduction product of the following compound with NaBH$$_4$$ in methanol is:

A

B

C

D

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NTA JEE Main 15th April 2018 Shift 1 - Question 57

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The reagent(s) required for the following conversion are:

A

(i) NaBH$$_4$$, (ii) Raney Ni/H$$_2$$, (iii) H$$_3$$O$$^+$$

B

(i) LiAlH$$_4$$, (ii) H$$_3$$O$$^+$$

C

(i) B$$_2$$H$$_6$$, (ii) DIBAL-H, (iii) H$$_3$$O$$^+$$

D

(i) B$$_2$$H$$_6$$, (ii) SnCl$$_2$$/HCl, (iii) H$$_3$$O$$^+$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 58

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The copolymer formed by addition polymerization of styrene and acrylonitrile in the presence of peroxide is:

A

B

C

D

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NTA JEE Main 15th April 2018 Shift 1 - Question 59

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Which of the following will not exist in zwitter ionic form at pH = 7?

A

Amino acid with NH$$_2$$ and COOH

B

Cyclic amide with CO$$_2$$H

C

Aniline with SO$$_3$$H

D

Cyclohexylamine with SO$$_3$$H

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NTA JEE Main 15th April 2018 Shift 1 - Question 60

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Which of the following is the correct structure of adenosine?

A

B

C

D

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NTA JEE Main 15th April 2018 Shift 1 - Question 61

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If $$\lambda \in R$$ is such that the sum of the cubes of the roots of the equation, $$x^2 + (2 - \lambda)x + (10 - \lambda) = 0$$ is minimum, then the magnitude of the difference of the roots of this equation is:

A

20

B

$$2\sqrt{5}$$

C

$$2\sqrt{7}$$

D

$$4\sqrt{2}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 62

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The set of all $$\alpha \in R$$, for which $$w = \frac{1+(1-8\alpha)z}{1-z}$$ is a purely imaginary number, for all $$z \in C$$ satisfying $$|z| = 1$$ and Re(z) $$\neq$$ 1, is:

A

$$\{0\}$$

B

an empty set

C

$$\{0, \frac{1}{4}, -\frac{1}{4}\}$$

D

equal to R

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NTA JEE Main 15th April 2018 Shift 1 - Question 63

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n-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is:

A

6

B

8

C

9

D

7

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NTA JEE Main 15th April 2018 Shift 1 - Question 64

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If b is the first term of an infinite G.P whose sum is five, then b lies in the interval:

A

$$(-\infty, -10)$$

B

$$(10, \infty)$$

C

$$(0, 10)$$

D

$$(-10, 0)$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 65

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If $$x_1, x_2, \ldots, x_n$$ and $$\frac{1}{h_1}, \frac{1}{h_2}, \ldots, \frac{1}{h_n}$$ are two A.P.s such that $$x_3 = h_2 = 8$$ and $$x_8 = h_7 = 20$$, then $$x_5 \cdot h_{10}$$ equals:

A

2560

B

2650

C

3200

D

1600

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NTA JEE Main 15th April 2018 Shift 1 - Question 66

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If n is the degree of the polynomial, $$\left[\frac{1}{\sqrt{5x^3+1} - \sqrt{5x^3-1}}\right]^8 + \left[\frac{1}{\sqrt{5x^3+1} + \sqrt{5x^3-1}}\right]^8$$ and m is the coefficient of $$x^n$$ in it, then the ordered pair (n, m) is equal to:

A

$$(12, (20)^4)$$

B

$$(8, 5(10)^4)$$

C

$$(24, (10)^8)$$

D

$$(12, 8(10)^4)$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 67

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If $$\tan A$$ and $$\tan B$$ are the roots of the quadratic equation, $$3x^2 - 10x - 25 = 0$$ then the value of $$3\sin^2(A+B) - 10\sin(A+B) \cdot \cos(A+B) - 25\cos^2(A+B)$$ is:

A

25

B

-25

C

-10

D

10

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NTA JEE Main 15th April 2018 Shift 1 - Question 68

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In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are $$x + y = 5$$ and $$x = 4$$ respectively. Then area of $$\triangle ABC$$ (in sq. units) is:

A

5

B

9

C

12

D

4

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NTA JEE Main 15th April 2018 Shift 1 - Question 69

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A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, $$y - 4x + 3 = 0$$, then its radius is equal to:

A

$$\sqrt{5}$$

B

$$\sqrt{2}$$

C

1

D

2

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NTA JEE Main 15th April 2018 Shift 1 - Question 70

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Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is:

A

$$3(x + y) + 4 = 0$$

B

$$8(2x + y) + 3 = 0$$

C

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

D

$$4(x + y) + 3 = 0$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 71

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If $$\beta$$ is one of the angles between the normals to the ellipse, $$x^2 + 3y^2 = 9$$ at the points $$(3\cos\theta, \sqrt{3}\sin\theta)$$ and $$(-3\sin\theta, \sqrt{3}\cos\theta)$$; $$\theta \in (0, \frac{\pi}{2})$$; then $$\frac{2\cot\beta}{\sin 2\theta}$$ is equal to:

A

$$\sqrt{2}$$

B

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

C

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

D

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

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NTA JEE Main 15th April 2018 Shift 1 - Question 72

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If the tangents drawn to the hyperbola $$4y^2 = x^2 + 1$$ intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid point of AB is:

A

$$x^2 - 4y^2 + 16x^2y^2 = 0$$

B

$$4x^2 - y^2 + 16x^2y^2 = 0$$

C

$$4x^2 - y^2 - 16x^2y^2 = 0$$

D

$$x^2 - 4y^2 - 16x^2y^2 = 0$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 73

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If $$(p \wedge \sim q) \wedge (p \wedge r) \rightarrow \sim p \vee q$$ is false, then the truth values of p, q and r are respectively:

A

F, T, F

B

T, F, T

C

F, F, F

D

T, T, T

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NTA JEE Main 15th April 2018 Shift 1 - Question 74

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The mean of a set of 30 observations is 75. If each observation is multiplied by a nonzero number $$\lambda$$ and then each of them is decreased by 25, their mean remains the same. The $$\lambda$$ is equal to $$\{0\}$$:

A

$$\frac{10}{3}$$

B

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

C

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

D

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

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NTA JEE Main 15th April 2018 Shift 1 - Question 75

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An aeroplane flying at a constant speed, parallel to the horizontal ground, $$\sqrt{3}$$ km above it, is observed at an elevation of 60$$^\circ$$ from a point on the ground. If, after five seconds, its elevation from the same point is 30$$^\circ$$, then the speed (in km/hr) of the aeroplane is:

A

1500

B

750

C

720

D

1440

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NTA JEE Main 15th April 2018 Shift 1 - Question 76

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Consider the following two binary relations on the set $$A = \{a, b, c\}$$: $$R_1 = \{(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)\}$$ and $$R_2 = \{(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)\}$$. Then:

A

$$R_2$$ is symmetric but it is not transitive

B

Both $$R_1$$ and $$R_2$$ are not symmetric

C

Both $$R_1$$ and $$R_2$$ are transitive

D

$$R_1$$ is not symmetric but it is transitive

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NTA JEE Main 15th April 2018 Shift 1 - Question 77

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Let A be a matrix such that $$A \cdot \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}$$ is a scalar matrix and $$|3A| = 108$$. Then $$A^2$$ equals:

A

$$\begin{bmatrix} 4 & -32 \\ 0 & 36 \end{bmatrix}$$

B

$$\begin{bmatrix} 4 & 0 \\ -32 & 36 \end{bmatrix}$$

C

$$\begin{bmatrix} 36 & 0 \\ -32 & 4 \end{bmatrix}$$

D

$$\begin{bmatrix} 36 & -32 \\ 0 & 4 \end{bmatrix}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 78

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If $$f(x) = \begin{vmatrix} \cos x & x & 1 \\ 2\sin x & x^2 & 2x \\ \tan x & x & 1 \end{vmatrix}$$, then $$\lim_{x \to 0} \frac{f'(x)}{x}$$:

A

Exists and is equal to -2

B

Does not exist

C

Exist and is equal to 0

D

Exists and is equal to 2

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NTA JEE Main 15th April 2018 Shift 1 - Question 79

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Let S be the set of all real values of k for which the system of linear equations
$$x + y + z = 2$$
$$2x + y - z = 3$$
$$3x + 2y + kz = 4$$
has a unique solution. Then S is:

A

an empty set

B

equal to R $$-$$ $$\{0\}$$

C

equal to $$\{0\}$$

D

equal to R

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NTA JEE Main 15th April 2018 Shift 1 - Question 80

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Let $$S = \{(\lambda, \mu) \in R \times R : f(t) = (|\lambda|e^t - \mu) \cdot \sin(2|t|), t \in R$$, is a differentiable function$$\}$$. Then S is a subset of?

A

$$R \times [0, \infty)$$

B

$$(-\infty, 0) \times R$$

C

$$[0, \infty) \times R$$

D

$$R \times (-\infty, 0)$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 81

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If $$x^2 + y^2 + \sin y = 4$$, then the value of $$\frac{d^2y}{dx^2}$$ at the point (-2, 0) is:

A

-34

B

-32

C

-2

D

4

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NTA JEE Main 15th April 2018 Shift 1 - Question 82

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If a right circular cone having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm$$^2$$) of this cone is:

A

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

B

$$6\sqrt{2}\pi$$

C

$$6\sqrt{3}\pi$$

D

$$8\sqrt{2}\pi$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 83

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If $$f\left(\frac{x-4}{x+2}\right) = 2x + 1$$, $$(x \in R - \{1, -2\})$$, then $$\int f(x)dx$$ is equal to (where C is a constant of integration):

A

$$12 \log_e|1-x| - 3x + c$$

B

$$-12 \log_e|1-x| - 3x + c$$

C

$$-12 \log_e|1-x| + 3x + c$$

D

$$12 \log_e|1-x| + 3x + c$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 84

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The value of the integral $$\int_{-\pi/2}^{\pi/2} \sin^4 x\left(1 + \log\left(\frac{2+\sin x}{2-\sin x}\right)\right)dx$$ is:

A

$$\frac{3}{16}\pi$$

B

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

C

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

D

0

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NTA JEE Main 15th April 2018 Shift 1 - Question 85

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The area (in sq. units) of the region $$\{x \in R : x \geq 0, y \geq 0, y \geq x - 2$$ and $$y \leq \sqrt{x}\}$$, is:

A

$$\frac{13}{3}$$

B

$$\frac{10}{3}$$

C

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

D

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

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NTA JEE Main 15th April 2018 Shift 1 - Question 86

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Let $$y = y(x)$$ be the solution of the differential equation $$\frac{dy}{dx} + 2y = f(x)$$, where $$f(x) = \begin{cases} 1, & x \in [0, 1] \\ 0, & \text{otherwise} \end{cases}$$. If $$y(0) = 0$$, then $$y\left(\frac{3}{2}\right)$$ is:

A

$$\frac{e^2-1}{2e^3}$$

B

$$\frac{e^2-1}{e^3}$$

C

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

D

$$\frac{e^2+1}{2e^4}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 87

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If $$\vec{a}$$, $$\vec{b}$$, and $$\vec{c}$$ are unit vectors such that $$\vec{a} + 2\vec{b} + 2\vec{c} = \vec{0}$$, then $$|\vec{a} \times \vec{c}|$$ is equal to:

A

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

B

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

C

$$\frac{15}{16}$$

D

$$\frac{\sqrt{15}}{16}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 88

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A variable plane passes through a fixed point (3, 2, 1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz-plane through A, a second plane is drawn parallel zx plane through B and a third plane is drawn parallel to xy-plane through C. Then the locus of the point of intersection of these three planes, is:

A

$$(x + y + z = 6)$$

B

$$\frac{x}{3} + \frac{y}{2} + \frac{z}{1} = 1$$

C

$$\frac{3}{x} + \frac{2}{y} + \frac{1}{z} = 1$$

D

$$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{11}{6}$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 89

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An angle between the plane, $$x + y + z = 5$$ and the line of intersection of the planes, $$3x + 4y + z - 1 = 0$$ and $$5x + 8y + 2z + 14 = 0$$, is:

A

$$\cos^{-1}\left(\frac{3}{\sqrt{17}}\right)$$

B

$$\cos^{-1}\left(\sqrt{\frac{3}{17}}\right)$$

C

$$\sin^{-1}\left(\frac{3}{\sqrt{17}}\right)$$

D

$$\sin^{-1}\left(\sqrt{\frac{3}{17}}\right)$$

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NTA JEE Main 15th April 2018 Shift 1 - Question 90

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A box 'A' contains 2 white, 3 red and 2 black balls. Another box 'B' contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box 'B' is:

A

$$\frac{7}{16}$$

B

$$\frac{9}{32}$$

C

$$\frac{7}{8}$$

D

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

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