NTA JEE Main 12th April 2019 Shift 1

NTA JEE Main 12th April 2019 Shift 1 - Question 1

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Which of the following combinations has the dimension of electrical resistance ($$\varepsilon_0$$ is the permittivity of vacuum and $$\mu_0$$ is the permeability of vacuum)?

A

$$\frac{\varepsilon_0}{\mu_0}$$

B

$$\sqrt{\frac{\varepsilon_0}{\mu_0}}$$

C

$$\frac{\mu_0}{\varepsilon_0}$$

D

$$\sqrt{\frac{\mu_0}{\varepsilon_0}}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 2

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The trajectory of a projectile near the surface of the earth is given as $$y = 2x - 9x^2$$. If it were launched at an angle $$\theta_0$$ with speed $$v_0$$ then g = 10 m s$$^{-2}$$:

A

$$\theta_0 = \cos^{-1}\frac{1}{\sqrt{5}}$$ and $$v_0 = \frac{5}{3}$$ ms$$^{-1}$$

B

$$\theta_0 = \cos^{-1}\frac{2}{\sqrt{5}}$$ and $$v_0 = \frac{3}{5}$$ ms$$^{-1}$$

C

$$\theta_0 = \sin^{-1}\frac{1}{\sqrt{5}}$$ and $$v_0 = \frac{5}{3}$$ ms$$^{-1}$$

D

$$\theta_0 = \sin^{-1}\frac{2}{\sqrt{5}}$$ and $$v_0 = \frac{3}{5}$$ ms$$^{-1}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 3

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A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t$$_1$$ and t$$_2$$ are the values of the time taken by it to hit the target in two possible ways, the product t$$_1$$t$$_2$$ is:

A

R/2g

B

R/g

C

2R/g

D

R/4g

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NTA JEE Main 12th April 2019 Shift 1 - Question 4

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A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 m s$$^{-1}$$ with respect to the man. The speed of the man with respect to the surface is:

A

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

B

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

C

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

D

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

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NTA JEE Main 12th April 2019 Shift 1 - Question 5

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A person of mass M is sitting on a swing of length L and swinging with an angular amplitude $$\theta_0$$. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance $$l$$ ($$l << L$$), is close to:

A

$$Mgl(1 - \theta_0^2)$$

B

$$Mgl\left(1 + \frac{\theta_0^2}{2}\right)$$

C

$$Mgl$$

D

$$Mgl(1 + \theta_0^2)$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 6

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A uniform rod of length $$l$$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely?

A

B

C

D

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NTA JEE Main 12th April 2019 Shift 1 - Question 7

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A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as $$\frac{\sigma_0}{r}$$, then the radius of gyration of the disc about its axis passing through the center is

A

$$\frac{a+b}{3}$$

B

$$\sqrt{\frac{a^2 + b^2 + ab}{3}}$$

C

$$\frac{a+b}{2}$$

D

$$\sqrt{\frac{a^2 + b^2 + ab}{2}}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 8

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At 40°C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40°C to 20°C it regains its original length of 0.2 m. The value of M is close to:
(Coefficient of linear expansion of brass are $$10^{-5}$$/°C and Young's modulus of brass is $$10^{11}$$ N/m$$^2$$, respectively; g = 10 m s$$^{-2}$$)

A

0.9 kg

B

0.5 kg

C

1.5 kg

D

9 kg

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NTA JEE Main 12th April 2019 Shift 1 - Question 9

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When M$$_1$$ gram of ice at -10°C (specific heat = 0.5 cal g$$^{-1}$$ °C$$^{-1}$$) is added to M$$_2$$ gram of water at 50°C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g$$^{-1}$$ is:

A

$$\frac{50M_2}{M_1}$$

B

$$\frac{5M_1}{M_2} - 50$$

C

$$\frac{5M_2}{M_1} - 5$$

D

$$\frac{50M_2}{M_1} - 5$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 10

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A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is -180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is:

A

130 J

B

100 J

C

120 J

D

140 J

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NTA JEE Main 12th April 2019 Shift 1 - Question 11

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Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? R = 8.3 J/mol K

A

17.4 J/mol K

B

19.7 J/mol K

C

15.7 J/mol K

D

21.6 J/mol K

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NTA JEE Main 12th April 2019 Shift 1 - Question 12

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A submarine A travelling at 18 km hr$$^{-1}$$ is being chased along the line of its velocity by another submarine B travelling at 27 km hr$$^{-1}$$. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency v. The value of v is close to (Speed of sound in water 1500 m s$$^{-1}$$)

A

504 Hz

B

499 Hz

C

502 Hz

D

507 Hz

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NTA JEE Main 12th April 2019 Shift 1 - Question 13

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A progressive wave travelling along the positive x-direction is represented by $$y(x, t) = A\sin(kx - \omega t + \phi)$$. Its snapshot at t = 0 is given in the figure.

For this wave, the phase $$\phi$$ is:

A

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

B

0

C

$$\pi$$

D

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

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NTA JEE Main 12th April 2019 Shift 1 - Question 14

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Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre a dipole $$\vec{p}$$ is placed as shown then:

A

Surface charge density on the inner surface of the shell is zero everywhere.

B

Electric field outside the shell is the same as that of a point charge at the centre of the shell.

C

Surface charge density on the inner surface is uniform and equal to $$\frac{(Q/2)}{4\pi a^2}$$.

D

Surface charge density on the outer surface depends on $$\vec{p}$$.

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NTA JEE Main 12th April 2019 Shift 1 - Question 15

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A Point dipole $$\vec{p} = -p_0\hat{x}$$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Taken V = 0 at infinity)

A

$$\frac{|\vec{p}|}{4\pi\varepsilon_0 d^2}$$, $$\frac{-\vec{p}}{4\pi\varepsilon_0 d^3}$$

B

$$0$$, $$\frac{|\vec{p}|}{4\pi\varepsilon_0 d^3}$$

C

$$\frac{|\vec{p}|}{4\pi\varepsilon_0 d^3}$$, $$\frac{\vec{p}}{4\pi\varepsilon_0 d^3}$$

D

$$0$$, $$\frac{-\vec{p}}{4\pi\varepsilon_0 d^3}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 16

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Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants K$$_1$$, K$$_2$$ and K$$_3$$. The first capacitor is filled as shown in figure I, and the second one is filled as shown in figure II.

If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (E$$_1$$ refers to capacitor I and E$$_2$$ to capacitor II):

A

$$\frac{E_1}{E_2} = \frac{9K_1K_2K_3}{(K_1K_2K_3)(K_2K_3 + K_3K_1K_1 + K_1K_2)}$$

B

$$\frac{E_1}{E_2} = \frac{(K_1K_2K_3)(K_2K_3 + K_3K_1K_1 + K_1K_2)}{K_1K_2K_3}$$

C

$$\frac{E_1}{E_2} = \frac{(K_1K_2K_3)(K_2K_3 + K_3K_1K_1 + K_1K_2)}{9K_1K_2K_3}$$

D

$$\frac{E_1}{E_2} = \frac{K_1K_2K_3}{(K_1K_2K_3)(K_2K_3 + K_3K_1K_1 + K_1K_2)}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 17

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To verify Ohm's law, a student connects the voltmeter across the battery as shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained.

If V$$_0$$ is almost zero, identify the correct statement:

A

The emf of the battery is 1.5 V and its internal resistance is 1.5 Ω

B

The value of the resistance R is 1.5 Ω

C

The potential difference across the battery is 1.5 V when it sends a current of 1000 mA

D

The emf of the battery is 1.5 V and the value of R is 1.5 Ω

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NTA JEE Main 12th April 2019 Shift 1 - Question 18

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A galvanometer of resistance 100 Ω has 50 divisions on its scale and has sensitivity of 20 μA/division. It is to be converted to voltmeter with three ranges, of 0 - 2 V, 0 - 10 V and 0 - 20 V. The appropriate circuit to do so is:

A

B

C

D

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NTA JEE Main 12th April 2019 Shift 1 - Question 19

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The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is:

A

16 Ω

B

8 Ω

C

6 Ω

D

1 Ω

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NTA JEE Main 12th April 2019 Shift 1 - Question 20

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A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45° and 40 times per minute where the dip is 30°. If B$$_1$$ and B$$_2$$ are the net magnetic fields due to the earth at the two places respectively, then the ratio B$$_1$$/B$$_2$$ is approximately equal to

A

3.6

B

1.8

C

1.2

D

0.7

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NTA JEE Main 12th April 2019 Shift 1 - Question 21

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A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $$40\pi$$ rad s$$^{-1}$$ about its axis, perpendicular to its plane. If the magnetic field at its centre is $$3.8 \times 10^{-9}$$ T, then the charge carried by the ring is close to $$\mu_0 = 4\pi \times 10^{-7}$$ N/A$$^2$$.

A

$$4 \times 10^{-5}$$ C

B

$$3 \times 10^{-5}$$ C

C

$$2 \times 10^{-6}$$ C

D

$$7 \times 10^{-6}$$ C

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NTA JEE Main 12th April 2019 Shift 1 - Question 22

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The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole setup is moving towards the right with a constant speed of 1 cm s$$^{-1}$$. At some instant, a part of L is in a uniform magnetic field of 1T perpendicular to the plane of the loop. If the resistance of L is 1.7 Ω, the current in the loop at that instant will be close to:

A

115 μA

B

60 μA

C

150 μA

D

170 μA

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NTA JEE Main 12th April 2019 Shift 1 - Question 23

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An electromagnetic wave is represented by the electric field $$\vec{E} = E_0\hat{n}\sin(\omega t + 6y - 8z)$$. Taking unit vectors in x, y and z directions to be $$\hat{i}, \hat{j}, \hat{k}$$, the direction of propagation $$\hat{s}$$, is:

A

$$\hat{s} = \frac{3\hat{i} - 4\hat{j}}{5}$$

B

$$\hat{s} = \frac{-3\hat{j} + 4\hat{k}}{5}$$

C

$$\hat{s} = \frac{4\hat{i} - 3\hat{k}}{5}$$

D

$$\hat{s} = \frac{-4\hat{i} - 3\hat{k}}{5}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 24

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A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to: (Refractive index of water = 1.33)

A

13.4 cm

B

8.8 cm

C

6.7 cm

D

11.7 cm

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NTA JEE Main 12th April 2019 Shift 1 - Question 25

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The value of numerical aperture of the objective lens of a microscope is 1.25. If light of wavelength 5000 Å is used, the minimum separation between two points, to be seen as distinct, will be:

A

0.48 μm

B

0.24 μm

C

0.38 μm

D

0.12 μm

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NTA JEE Main 12th April 2019 Shift 1 - Question 26

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In a double slit experiment, when a thin film of thickness t having refractive index μ is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is ($$\lambda$$ is the wavelength of the light used):

A

$$\frac{\lambda}{2(\mu - 1)}$$

B

$$\frac{\lambda}{(2\mu - 1)}$$

C

$$\frac{2\lambda}{(\mu - 1)}$$

D

$$\frac{\lambda}{(\mu - 1)}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 27

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The stopping potential V$$_0$$ (in volt) as a function of frequency ($$\nu$$) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be:
(Given: Planck's constant h = $$6.63 \times 10^{-34}$$ J s, electron charge (e) = $$1.6 \times 10^{-19}$$ C)

A

2.12 eV

B

1.82 eV

C

1.95 eV

D

1.66 eV

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NTA JEE Main 12th April 2019 Shift 1 - Question 28

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An excited He$$^+$$ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm in making a transition to the ground state. The quantum number n, corresponding to its initial excited state is
(for a photon of wavelength $$\lambda$$, energy E = $$\frac{1240 \text{ eV}}{\lambda(\text{in nm})}$$)

A

n = 6

B

n = 5

C

n = 7

D

n = 4

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NTA JEE Main 12th April 2019 Shift 1 - Question 29

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The truth table for the circuit given in the figure is:

A

B

C

D

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NTA JEE Main 12th April 2019 Shift 1 - Question 30

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The transfer characteristic curve of a transistor, having input and output resistance 100 Ω and 100 kΩ respectively, is shown in the figure. The voltage and power gain, are respectively:

A

$$5 \times 10^4$$, $$2.5 \times 10^6$$

B

$$2.5 \times 10^4$$, $$2.5 \times 10^6$$

C

$$5 \times 10^4$$, $$5 \times 10^6$$

D

$$5 \times 10^4$$, $$5 \times 10^5$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 31

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5 moles of AB$$_2$$ weigh $$125 \times 10^{-3}$$ kg and 10 moles of A$$_2$$B$$_2$$ weigh $$300 \times 10^{-3}$$ kg. The molar mass of A (M$$_A$$) in kg mol$$^{-1}$$ are:

A

M$$_A$$ = $$5 \times 10^{-3}$$ and M$$_B$$ = $$10 \times 10^{-3}$$

B

M$$_A$$ = $$25 \times 10^{-3}$$ and M$$_B$$ = $$50 \times 10^{-3}$$

C

M$$_A$$ = $$50 \times 10^{-3}$$ and M$$_B$$ = $$25 \times 10^{-3}$$

D

M$$_A$$ = $$10 \times 10^{-3}$$ and M$$_B$$ = $$5 \times 10^{-3}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 32

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The electrons are more likely to be found:

A

Only in the region a

B

In the region a and b

C

In the region a and c

D

Only in the region c

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NTA JEE Main 12th April 2019 Shift 1 - Question 33

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The group number, number of valence electrons, and valency of an element with atomic number 15, respectively, are:

A

15, 6 and 2

B

16, 6 and 3

C

16, 5 and 2

D

15, 5 and 3

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NTA JEE Main 12th April 2019 Shift 1 - Question 34

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The correct statement among the following is:

A

$$(SiH_3)_3N$$ is planar and less basic than $$(CH_3)_3N$$

B

$$(SiH_3)_3N$$ is pyramidal and more basic than $$(CH_3)_3N$$

C

$$(SiH_3)_3N$$ is pyramidal and less basic than $$(CH_3)_3N$$

D

$$(SiH_3)_3N$$ is planar and more basic than $$(CH_3)_3N$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 35

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An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1 bar. The work done in kJ is:

A

+10.0

B

-2.0

C

-0.9

D

-9.0

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NTA JEE Main 12th April 2019 Shift 1 - Question 36

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Enthalpy of sublimation of iodine is 24 cal g$$^{-1}$$ at 200°C. If specific heat of I$$_2$$(s) and I$$_2$$(vap) are 0.055 and 0.031 cal g$$^{-1}$$ K$$^{-1}$$ respectively, then enthalpy of sublimation of iodine at 250°C in cal g$$^{-1}$$ is:

A

11.4

B

2.85

C

22.8

D

5.7

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NTA JEE Main 12th April 2019 Shift 1 - Question 37

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What is the molar solubility of Al(OH)$$_3$$ in 0.2 M NaOH solution? Given that, solubility product of Al(OH)$$_3$$ = $$2.4 \times 10^{-24}$$:

A

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

B

$$12 \times 10^{-21}$$

C

$$12 \times 10^{-23}$$

D

$$3 \times 10^{-22}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 38

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An example of a disproportionation reaction is

A

$$2KMnO_4 \to K_2MnO_4 + MnO_2 + O_2$$

B

$$2MnO_4^- + 10I^- + 16H^+ \to 2Mn^{2+} + 5I_2 + 8H_2O$$

C

2 CuBr $$\to$$ CuBr$$_2$$ + Cu

D

2 NaBr + Cl$$_2$$ $$\to$$ 2NaCl + Br$$_2$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 39

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Given:
Co$$^{3+}$$ + e$$^-$$ $$\to$$ Co$$^{2+}$$; E° = +1.81V
Pb$$^{3+}$$ + 2e$$^-$$ $$\to$$ Pb$$^{2+}$$; E° = +1.67V
Ce$$^{4+}$$ + e$$^-$$ $$\to$$ Ce$$^{3+}$$; E° = +1.61V
Bi$$^{3+}$$ + 3e$$^-$$ $$\to$$ Bi; E° = +0.20V
Oxidizing power of the species will increase in the order:

A

Co$$^{3+}$$ < Ce$$^{4+}$$ < Bi$$^{3+}$$ < Pb$$^{4+}$$

B

Bi$$^{3+}$$ < Ce$$^{4+}$$ < Pb$$^{4+}$$ < Co$$^{3+}$$

C

Co$$^{3+}$$ < Pb$$^{4+}$$ < Ce$$^{3+}$$ < Bi$$^{4+}$$

D

Ce$$^{4+}$$ < Pb$$^{4+}$$ < Bi$$^{3+}$$ < Co$$^{3+}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 40

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The correct sequence of thermal stability of the following carbonates is:

A

BaCO$$_3$$ < CaCO$$_3$$ < SrCO$$_3$$ < MgCO$$_3$$

B

MgCO$$_3$$ < CaCO$$_3$$ < SrCO$$_3$$ < BaCO$$_3$$

C

BaCO$$_3$$ < SrCO$$_3$$ < CaCO$$_3$$ < MgCO$$_3$$

D

MgCO$$_3$$ < SrCO$$_3$$ < CaCO$$_3$$ < BaCO$$_3$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 41

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The basic structural unit of feldspar, zeolites, mica, and asbestos is:

A

SiO$$_4^{4-}$$

B

C

SiO$$_3^{2-}$$

D

SiO$$_2$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 42

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The increasing order of the pK$$_b$$ of the following compound is:

A

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

B

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

C

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

D

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

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NTA JEE Main 12th April 2019 Shift 1 - Question 43

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The major product(s) obtained in the following reaction is/are:

A

B

C

CHO and OHC-CHO

D

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NTA JEE Main 12th April 2019 Shift 1 - Question 44

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The major product of the following addition reaction is

A

B

C

D

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NTA JEE Main 12th April 2019 Shift 1 - Question 45

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But-2-ene on reaction with alkaline KMnO$$_4$$ at elevated temperature followed by acidification will give:

A

2 molecules of CH$$_3$$COOH

B

C

2 Molecules of CH$$_3$$CHO

D

One molecule of CH$$_3$$CHO and one molecule of CH$$_3$$COOH

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NTA JEE Main 12th April 2019 Shift 1 - Question 46

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The correct set of species responsible for the photochemical smog is:

A

CO$$_2$$, NO$$_2$$, SO$$_2$$ and hydrocarbons

B

NO$$_2$$, O$$_2$$, O$$_3$$ and hydrocarbons

C

NO$$_2$$, NO$$_2$$ and hydrocarbons

D

NO, NO$$_2$$, O$$_3$$ and hydrocarbons

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NTA JEE Main 12th April 2019 Shift 1 - Question 47

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An element has a face-centered cubic fcc structure with a cell edge of a. The distance between the centres of two nearest tetrahedral voids in the lattice is

A

$$\frac{a}{2}$$

B

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

C

a

D

$$\sqrt{2}a$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 48

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The mole fraction of a solvent in aqueous solution of a solute is 0.8. The molality (in mol kg$$^{-1}$$) of the aqueous solution is:

A

$$13.88 \times 10^{-3}$$

B

$$13.88 \times 10^{-1}$$

C

13.88

D

$$13.88 \times 10^{-2}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 49

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In the following reaction; xA $$\to$$ yB
$$\log_{10}\left(-\frac{dA}{dt}\right) = \log_{10}\left(-\frac{dB}{dt}\right) + 0.3010$$
'A' and 'B' respectively can be:

A

C$$_2$$H$$_4$$ and C$$_4$$H$$_8$$

B

C$$_2$$H$$_2$$ and C$$_6$$H$$_6$$

C

n-Butane and Iso-butane

D

N$$_2$$O$$_4$$ and NO$$_2$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 50

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Peptization is a:

A

Process of converting a colloidal solution into precipitate

B

Process of converting soluble particles to form colloidal solution

C

Process of bringing colloidal molecule into solution

D

Process of converting precipitate into colloidal solution

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NTA JEE Main 12th April 2019 Shift 1 - Question 51

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The idea of froth flotation method came from a person X and this method is related to the process Y of ores. X and Y, respectively, are:

A

Washer man and reduction

B

Fisher women and concentration

C

Fisher man and reduction

D

Washer woman and concentration

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NTA JEE Main 12th April 2019 Shift 1 - Question 52

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The metal that gives hydrogen gas upon treatment with both the acid as well as the base is

A

Zinc

B

Magnesium

C

Iron

D

Mercury

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NTA JEE Main 12th April 2019 Shift 1 - Question 53

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The complex ion that will lose its crystal field stabilization energy upon oxidation of metal to +3 state is:

(Phen = phenanthroline, ignore pairing energy)

A

[Ni(phen)$$_3$$]$$^{2+}$$

B

[Fe(phen)$$_3$$]$$^{2+}$$

C

[Co(phen)$$_3$$]$$^{2+}$$

D

[Zn(phen)$$_3$$]$$^{2+}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 54

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Complete removal of both the axial ligands (along the z-axis) from an octahedral complex leads to which of the following splitting patterns? (relative orbital energies not on scale).

A

B

C

D

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NTA JEE Main 12th April 2019 Shift 1 - Question 55

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The major products of the following reaction are:

A

B

C

D

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NTA JEE Main 12th April 2019 Shift 1 - Question 56

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The major product of the following reaction:

A

B

C

D

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NTA JEE Main 12th April 2019 Shift 1 - Question 57

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Which of the following is a thermosetting polymer?

A

Bakelite

B

PVC

C

Nylon 6

D

Buna-N

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NTA JEE Main 12th April 2019 Shift 1 - Question 58

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An organic compound 'A' is oxidized with Na$$_2$$O$$_2$$ followed by boiling with HNO$$_3$$. The resultant solution is then treated with ammonium molybdate to yield a yellow precipitate. Based on above observation, the element present in the given compound is:

A

Fluorine

B

Phosphorus

C

Nitrogen

D

Sulphur

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NTA JEE Main 12th April 2019 Shift 1 - Question 59

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Glucose and Galactose are having identical configuration in all the positions except position.

A

C - 3

B

C - 4

C

C - 5

D

C - 2

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NTA JEE Main 12th April 2019 Shift 1 - Question 60

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Which of the following statements is not true about RNA?

A

It controls the synthesis of protein

B

It usually does not replicate

C

It has always double standard α-helix structure

D

It is present in the nucleus of the cell

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NTA JEE Main 12th April 2019 Shift 1 - Question 61

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If $$\alpha$$ and $$\beta$$ are the roots of the equation $$375x^2 - 25x - 2 = 0$$, then $$\lim_{n \to \infty} \sum_{r=1}^{n} \alpha^r + \lim_{n \to \infty} \sum_{r=1}^{n} \beta^r$$ is equal to:

A

$$\frac{1}{12}$$

B

$$\frac{21}{346}$$

C

$$\frac{7}{116}$$

D

$$\frac{29}{358}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 62

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The equation $$|z - i| = |z - 1|$$, $$i = \sqrt{-1}$$, represents:

A

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

B

a circle of radius 1

C

the line through the origin with slope 1

D

the line through the origin with slope -1

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NTA JEE Main 12th April 2019 Shift 1 - Question 63

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The Number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:

A

$$2^{20}$$

B

$$2^{21}$$

C

$$2^{20} + 1$$

D

$$2^{20} - 1$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 64

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If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is:

A

$$\frac{1}{10}$$

B

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

C

$$\frac{1}{5}$$

D

$$\frac{3}{20}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 65

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Let S$$_n$$ denote the sum of the first n terms of an A.P. If S$$_4$$ = 16 and S$$_6$$ = -48, then S$$_{10}$$ is equal to:

A

-320

B

-380

C

-260

D

-410

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NTA JEE Main 12th April 2019 Shift 1 - Question 66

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The coefficient of $$x^{18}$$ in the product $$(1 + x)(1 - x)^{10}(1 + x + x^2)^9$$ is

A

84

B

-84

C

-126

D

126

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NTA JEE Main 12th April 2019 Shift 1 - Question 67

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The equation $$y=\sin x\sin\left(x+2\right)-\sin^2(x+1)$$ represents a straight line lying in:

A

first, third and fourth quadrants

B

second and third quadrants only

C

first, second and fourth quadrants

D

third and fourth quadrants only

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NTA JEE Main 12th April 2019 Shift 1 - Question 68

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The number of solutions of the equation $$1 + \sin^4 x = \cos^2 3x$$, $$x \in \left[-\frac{5\pi}{2}, \frac{5\pi}{2}\right]$$ is:

A

5

B

7

C

3

D

4

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NTA JEE Main 12th April 2019 Shift 1 - Question 69

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If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm) of their common chord is:

A

$$\frac{120}{13}$$

B

$$\frac{60}{13}$$

C

$$\frac{13}{5}$$

D

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

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NTA JEE Main 12th April 2019 Shift 1 - Question 70

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If the normal to the ellipse $$3x^2 + 4y^2 = 12$$ at a point P on it is parallel to the line, $$2x + y = 4$$ and the tangent to the ellipse at P passes through Q(4, 4) then PQ is equal to:

A

$$\frac{\sqrt{61}}{2}$$

B

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

C

$$\frac{\sqrt{157}}{2}$$

D

$$\frac{\sqrt{221}}{2}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 71

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Let P be the point of intersection of the common tangents to the parabola $$y^2 = 12x$$ and the hyperbola $$8x^2 - y^2 = 8$$. If S and S' denote the foci of the hyperbola where S lies on the positive x-axis then P divides SS' in a ratio:

A

5:4

B

2:1

C

13:11

D

14:13

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NTA JEE Main 12th April 2019 Shift 1 - Question 72

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If the truth value of the statement $$p \to (\sim q \vee r)$$ is false F, then the truth values of the statements p, q, r are respectively

A

T, F, T

B

T, F, F

C

T, T, F

D

F, T, T

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NTA JEE Main 12th April 2019 Shift 1 - Question 73

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If the data $$x_1, x_2, \ldots, x_{10}$$ is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2000, then the standard deviation of this data is:

A

$$2\sqrt{2}$$

B

4

C

2

D

$$\sqrt{2}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 74

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If $$B = \begin{pmatrix} 5 & 2\alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1 \end{pmatrix}$$ is the inverse of a 3$$\times$$3 matrix A, then the sum of all values of $$\alpha$$ for which det(A) + 1 = 0, is:

A

2

B

1

C

0

D

-1

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NTA JEE Main 12th April 2019 Shift 1 - Question 75

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If A is a symmetric matrix and B is skew-symmetric matrix such that $$A + B = \begin{pmatrix} 2 & 3 \\ 5 & -1 \end{pmatrix}$$, then AB is equal to:

A

$$\begin{pmatrix} -4 & 2 \\ 1 & 4 \end{pmatrix}$$

B

$$\begin{pmatrix} 4 & -2 \\ 1 & -4 \end{pmatrix}$$

C

$$\begin{pmatrix} 4 & -2 \\ -1 & -4 \end{pmatrix}$$

D

$$\begin{pmatrix} -4 & -2 \\ -1 & 4 \end{pmatrix}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 76

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The value of $$\sin^{-1}\frac{12}{13} - \sin^{-1}\frac{3}{5}$$ is equal to:

A

$$\pi - \cos^{-1}\frac{33}{65}$$

B

$$\frac{\pi}{2} - \cos^{-1}\frac{9}{65}$$

C

$$\pi - \sin^{-1}\frac{63}{65}$$

D

$$\frac{\pi}{2} - \sin^{-1}\frac{56}{65}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 77

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For $$x \in R$$, Let [x] denotes the greatest integer $$\leq x$$, then the sum of the series $$\left[-\frac{1}{3}\right] + \left[-\frac{1}{3} - \frac{1}{100}\right] + \left[-\frac{1}{3} - \frac{2}{100}\right] + \ldots + \left[-\frac{1}{3} - \frac{99}{100}\right]$$ is

A

-131

B

-153

C

-135

D

-133

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NTA JEE Main 12th April 2019 Shift 1 - Question 78

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For $$x \in \left(0, \frac{3}{2}\right)$$, let $$f(x) = \sqrt{x}$$, $$g(x) = \tan x$$ and $$h(x) = \frac{1 - x^2}{1 + x^2}$$. If $$\phi(x) = ((h \circ f) \circ g)(x)$$, then $$\phi\left(\frac{\pi}{3}\right)$$ is equal to:

A

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

B

$$\tan\frac{5\pi}{12}$$

C

$$\tan\frac{7\pi}{12}$$

D

$$\tan\frac{11\pi}{12}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 79

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If $$e^y + xy = e$$, the ordered pair $$\left(\frac{dy}{dx}, \frac{d^2y}{dx^2}\right)$$ at x = 0 is equal to

A

$$\left(-\frac{1}{e}, -\frac{1}{e^2}\right)$$

B

$$\left(-\frac{1}{e}, \frac{1}{e^2}\right)$$

C

$$\left(\frac{1}{e}, -\frac{1}{e^2}\right)$$

D

$$\left(\frac{1}{e}, \frac{1}{e^2}\right)$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 80

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A 2m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/sec, then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is:

A

25

B

$$25\sqrt{3}$$

C

$$\frac{25}{3}$$

D

$$\frac{25}{\sqrt{3}}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 81

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If m is the minimum value of k for which the function $$f(x) = x\sqrt{kx - x^2}$$ is increasing in the interval [0, 3] and M is the maximum value of f in [0, 3] when k = m, then the ordered pair (m, M) is equal to:

A

$$\left(4, 3\sqrt{3}\right)$$

B

$$\left(5, 3\sqrt{6}\right)$$

C

$$\left(3, 3\sqrt{3}\right)$$

D

$$\left(4, 3\sqrt{2}\right)$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 82

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The integral $$\int \frac{2x^3 - 1}{x^4 + x} dx$$, is equal to

A

$$\frac{1}{2}\log_e\frac{(x^3 + 1)^2}{|x^3|} + C$$

B

$$\log_e\frac{|x^3 + 1|}{x^2} + C$$

C

$$\log_e\frac{x^3 + 1}{x} + C$$

D

$$\frac{1}{2}\log_e\frac{|x^3 + 1|}{x^2} + C$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 83

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Let $$f: R \to R$$ be a continuous and differentiable function such that $$f(2) = 6$$ and $$f'(2) = \frac{1}{48}$$. If $$\int_6^{f(x)}4t^3dt=\left(x-2\right)g(x)$$, then $$\lim_{x \to 2} g(x)$$ is equal to

A

24

B

18

C

12

D

36

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NTA JEE Main 12th April 2019 Shift 1 - Question 84

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If $$\int_0^{\pi/2} \frac{\cot x}{\cot x + \text{cosec} x} dx = m(\pi + n)$$, then mn is equal to

A

1

B

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

C

-1

D

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

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NTA JEE Main 12th April 2019 Shift 1 - Question 85

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If the area (in sq. units) of the region $$\{(x, y): y^2 \leq 4x, x + y \leq 1, x \geq 0, y \geq 0\}$$ is $$a\sqrt{2} + b$$, then a - b is

A

6

B

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

C

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

D

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

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NTA JEE Main 12th April 2019 Shift 1 - Question 86

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Consider the differential equation, $$y^2 dx + \left(x - \frac{1}{y}\right) dy = 0$$. If value of y is 1 when x = 1, then the value of x for which y = 2, is

A

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

B

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

C

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

D

$$\frac{5}{2} + \frac{1}{\sqrt{e}}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 87

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If the volume of parallelepiped formed by the vectors $$\hat{i} + \lambda\hat{j} + \hat{k}$$, $$\hat{j} + \lambda\hat{k}$$ and $$\lambda\hat{i} + \hat{k}$$ is minimum, then $$\lambda$$ is

A

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

B

$$-\sqrt{3}$$

C

$$\sqrt{3}$$

D

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

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NTA JEE Main 12th April 2019 Shift 1 - Question 88

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Let $$\vec{a} = 3\hat{i} + 2\hat{j} + 2\hat{k}$$ and $$\vec{b} = \hat{i} + 2\hat{j} - 2\hat{k}$$ be two vectors. If a vector perpendicular to both the vectors $$\vec{a} + \vec{b}$$ and $$\vec{a} - \vec{b}$$ has the magnitude 12 then one such vector is:

A

$$4(2\hat{i} + 2\hat{j} + \hat{k})$$

B

$$4(2\hat{i} - 2\hat{j} - \hat{k})$$

C

$$4(-2\hat{i} - 2\hat{j} + \hat{k})$$

D

$$4(2\hat{i} + 2\hat{j} - \hat{k})$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 89

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If the line $$\frac{x-2}{3} = \frac{y+1}{2} = \frac{z-1}{-1}$$ intersects the plane $$2x + 3y - z + 13 = 0$$ at a point P and the plane $$3x + y + 4z = 16$$ at a point Q, then PQ is equal to

A

$$2\sqrt{7}$$

B

14

C

$$2\sqrt{14}$$

D

$$\sqrt{14}$$

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NTA JEE Main 12th April 2019 Shift 1 - Question 90

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Let a random variable X has a binomial distribution with mean 8 and variance 4. If $$P(X \leq 2) = \frac{k}{2^{16}}$$, then the value of k is equal to

A

121

B

1

C

17

D

137

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