NTA JEE Main 10th April 2019 Shift 1

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

Report

A particle of mass m is moving along a trajectory given by
$$x = x_0 + a\cos\omega_1 t$$
$$y = y_0 + b\sin\omega_2 t$$
The torque, acting on the particle about the origin, at t = 0 is:

A

$$+my_0 a\omega_1^2 \hat{k}$$

B

$$-m(x_0 b\omega_2^2 - y_0 a\omega_1^2)\hat{k}$$

C

Zero

D

$$m(-x_0 b + y_0 a)\omega_1^2 \hat{k}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 2

Report

A ball is thrown upward with an initial velocity $$V_0$$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $$m\gamma v^2$$ (where m is the mass of the ball, $$v$$ is its instantaneous velocity and $$\gamma$$ is a constant). Time taken by the ball to rise to its zenith is:

A

$$\frac{1}{\sqrt{\gamma g}}\ln\left(1 + \sqrt{\frac{\gamma}{g}}V_0\right)$$

B

$$\frac{1}{\sqrt{\gamma g}}\tan^{-1}\left(\sqrt{\frac{\gamma}{g}}V_0\right)$$

C

$$\frac{1}{\sqrt{\gamma g}}\sin^{-1}\left(\sqrt{\frac{\gamma}{g}}V_0\right)$$

D

$$\frac{1}{\sqrt{2\gamma g}}\tan^{-1}\left(\sqrt{\frac{2\gamma}{g}}V_0\right)$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 3

Report

Two particles, of masses $$M$$ and $$2M$$, moving, as shown, with speeds of $$10m/s$$ and $$5m/s$$, collide elastically at the origin. After the collision, they move along the indicated directions with speeds $$υ_1$$  and $$υ_2$$​, respectively. The values of $$υ_1$$ and $$υ_2$$ are nearly : 

A

6.5 m s$$^{-1}$$ and 6.3 m s$$^{-1}$$

B

3.2 m s$$^{-1}$$ and 12.6 m s$$^{-1}$$

C

13.02 m s$$^{-1}$$ and 19.7 m s$$^{-1}$$

D

3.2 m s$$^{-1}$$ and 6.3 m s$$^{-1}$$

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 4

Report

A thin disc of mass M and radius R has mass per unit area $$\sigma(r) = kr^2$$ where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is:

A

$$\frac{MR^2}{3}$$

B

$$\frac{MR^2}{2}$$

C

$$\frac{MR^2}{6}$$

D

$$\frac{2MR^2}{3}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 5

Report

Two coaxial discs, having moments of inertia $$I_1$$ and $$\frac{I_1}{2}$$, are rotating with respective angular velocities $$\omega_1$$ and $$\frac{\omega_1}{2}$$, about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If $$E_f$$ and $$E_i$$ are the final and initial total energies, then $$(E_f - E_i)$$ is:

A

$$\frac{I_1\omega_1^2}{6}$$

B

$$\frac{3}{8}I_1\omega_1^2$$

C

$$-\frac{I_1\omega_1^2}{12}$$

D

$$-\frac{I_1\omega_1^2}{24}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 6

Report

The value of acceleration due to gravity at Earth's surface is 9.8 m s$$^{-2}$$. The altitude above its surface at which the acceleration due to gravity decreases to 4.9 m s$$^{-2}$$, is close to: (Radius of earth = $$6.4 \times 10^6$$ m)

A

$$1.6 \times 10^6$$ m

B

$$2.6 \times 10^6$$ m

C

$$6.4 \times 10^6$$ m

D

$$9.0 \times 10^6$$ m

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 7

Report

The ratio of surface tensions of mercury and water is given to be 7.5, while the ratio of their densities is 13.6. Their contact angles, with glass, are close to 135° and 0°, respectively. If it is observed that mercury gets depressed by an amount $$h$$ in a capillary tube of radius $$r_1$$, while water rises by the same amount $$h$$ in a capillary tube of radius $$r_2$$, then the ratio $$\frac{r_1}{r_2}$$ is close to

A

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

B

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

C

$$\frac{4}{5}$$

D

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

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 8

Report

n moles of an ideal gas with constant volume heat capacity $$C_V$$ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is:

A

$$\dfrac{4nR}{C_V + nR}$$

B

$$\dfrac{4nR}{C_V - nR}$$

C

$$\dfrac{nR}{C_V + nR}$$

D

$$\dfrac{nR}{C_V - nR}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 9

Report

A cylinder with fixed capacity of 67.2 litre contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is:
[Given that R = 8.31 J mol$$^{-1}$$ K$$^{-1}$$]

A

748 J

B

700 J

C

350 J

D

374 J

View Solution Video Solution

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

Report

A $$25 \times 10^{-3}$$ m$$^3$$ volume cylinder is filled with 1 mol of O$$_2$$ gas at room temperature (300 K). The molecular diameter of O$$_2$$, and its root mean square speed, are found to be 0.3 nm and 200 m/s, respectively. What is the average collision rate (per second) for an O$$_2$$ molecule?

A

~10$$^{11}$$

B

~10$$^{12}$$

C

~10$$^{10}$$

D

~10$$^{13}$$

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 11

Report

The displacement of a damped harmonic oscillator is given by $$x(t) = e^{-0.1t}\cos(10\pi t + \varphi)$$. Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to:

A

27 s

B

4 s

C

13 s

D

7 s

View Solution Video Solution

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

Report

A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds are, in m s$$^{-1}$$,
(Given speed of sound = 300 m/s)

A

16, 14

B

12, 16

C

12, 18

D

8, 18

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 13

Report

A uniformly charged ring of radius 3a and total charge q is placed in x-y plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed v at z = 4a. The minimum value of v such that it crosses the origin is:

A

$$\sqrt{\frac{2}{m}}\left(\frac{1}{15}\cdot\frac{q^2}{4\pi\varepsilon_0 a}\right)^{1/2}$$

B

$$\sqrt{\frac{2}{m}}\left(\frac{4}{15}\cdot\frac{q^2}{4\pi\varepsilon_0 a}\right)^{1/2}$$

C

$$\sqrt{\frac{2}{m}}\left(\frac{1}{5}\cdot\frac{q^2}{4\pi\varepsilon_0 a}\right)^{1/2}$$

D

$$\sqrt{\frac{2}{m}}\left(\frac{2}{15}\cdot\frac{q^2}{4\pi\varepsilon_0 a}\right)^{1/2}$$

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 14

Report

Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are:

A

60 μF and 40 μF

B

50 μF and 30 μF

C

20 μF and 30 μF

D

40 μF and 10 μF

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 15

Report

A current of 5 A passes through a copper conductor (resistivity = $$1.7 \times 10^{-8}$$ Ω m) of radius of cross-section 5 mm. Find the mobility of the charges if their drift velocity is $$1.1 \times 10^{-3}$$ ms$$^{-1}$$.

A

1.5 m$$^2$$ V$$^{-1}$$ s$$^{-1}$$

B

1.8 m$$^2$$ V$$^{-1}$$ s$$^{-1}$$

C

1.0 m$$^2$$ V$$^{-1}$$ s$$^{-1}$$

D

1.3 m$$^2$$ V$$^{-1}$$ s$$^{-1}$$

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 16

Report

In the given circuit, an ideal voltmeter connected across the 10 Ω resistance reads 2 V. The internal resistance r, of each cell is:

A

0 Ω

B

1.5 Ω

C

0.5 Ω

D

1 Ω

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 17

Report

A moving coil galvanometer allows a full scale current of $$10^{-4}$$ A. A series resistance of $$2 \times 10^4$$ Ω is required to convert the galvanometer into a voltmeter of range 0 - 5 V. Therefore, the value of shunt resistance required to convert the above galvanometer into an ammeter of range 0 - 10 mA is:

A

100 Ω

B

200 Ω

C

300 Ω

D

10 Ω

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 18

Report

In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line.

One may conclude that

A

$$R(T) = R_0 e^{T^2/T_0^2}$$

B

$$R(T) = \frac{R_0}{T^2}$$

C

$$R(T) = R_0 e^{-T^2/T_0^2}$$

D

$$R(T) = R_0 e^{-T_0^2/T^2}$$

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 19

Report

Two wires A & B are carrying currents I$$_1$$ and I$$_2$$ as shown in the figure. The separation between them is d. A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are:

A

$$x = \pm\frac{I_1 d}{(I_1 - I_2)}$$

B

$$x = \left(\frac{I_1}{I_1 + I_2}\right)d$$ and $$x = \frac{I_2}{(I_1 - I_2)}d$$

C

$$x = \left(\frac{I_2}{I_1 + I_2}\right)d$$ and $$x = \left(\frac{I_2}{I_1 - I_2}\right)d$$

D

$$x = \left(\frac{I_1}{I_1 - I_2}\right)d$$ and $$x = \frac{I_2}{(I_1 + I_2)}d$$

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 20

Report

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let $$r_p$$, $$r_e$$ and $$r_{He}$$ be their respective radii, then,

A

$$r_e > r_p = r_{He}$$

B

$$r_e < r_p = r_{He}$$

C

$$r_e < r_p < r_{He}$$

D

$$r_e > r_p > r_{He}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 21

Report

A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coil is 10 A, then the input voltage and current in the primary coil are:

A

440 V and 20 A

B

220 V and 20 A

C

440 V and 5 A

D

220 V and 10 A

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 22

Report

Given below in the left column are different modes of communication using the kinds of waves given in the right column.
(1) Optical Fibre Communication    (P) Ultrasound
(2) Radar                                          (Q) Infrared Light
(3) Sonar                                           (R) Microwaves
(4) Mobile Phones                            (S) Radio Waves
From the options given below, find the most appropriate match between entries in the left and the right column.

A

1 - Q, 2 - S, 3 - P, 4 - R

B

1 - S, 2 - Q, 3 - R, 4 - P

C

1 - Q, 2 - S, 3 - R, 4 - P

D

1 - R, 2 - P, 3 - S, 4 - Q

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 23

Report

The electric field of a plane electromagnetic wave is given by
$$\vec{E} = E_0 \hat{i}\cos(kz)\cos(\omega t)$$
The corresponding magnetic field $$\vec{B}$$ is then given by:

A

$$\vec{B} = \frac{E_0}{C}\hat{j}\cos(kz)\sin(\omega t)$$

B

$$\vec{B} = \frac{E_0}{C}\hat{k}\sin(kz)\cos(\omega t)$$

C

$$\vec{B} = \frac{E_0}{C}\hat{j}\sin(kz)\sin(\omega t)$$

D

$$\vec{B} = \frac{E_0}{C}\hat{j}\sin(kz)\cos(\omega t)$$

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 24

Report

A ray of light AO in vacuum is incident on a glass slab at angle 60° and refracted at angle 30° along OB as shown in the figure. The optical path length of light ray from A to B is:

A

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

B

$$2a + 2b$$

C

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

D

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

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 25

Report

One plano-convex and one plano-concave lens of the same radius of curvature R but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is $$\mu_1$$ and that of 2 is $$\mu_2$$, then the focal length of the combination is:

A

$$\dfrac{R}{2 - (\mu_1 - \mu_2)}$$

B

$$\dfrac{R}{2(\mu_1 - \mu_2)}$$

C

$$\dfrac{2R}{\mu_1 - \mu_2}$$

D

$$\dfrac{R}{\mu_1 - \mu_2}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 26

Report

In a photoelectric effect experiment, the threshold wavelength of light is 380 nm. If the wavelength of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be
Given E (in eV) = $$\frac{1237}{\lambda(\text{in nm})}$$

A

4.5 eV

B

3.0 eV

C

1.5 eV

D

15.1 eV

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 27

Report

Two radioactive materials A and B have decay constants $$10\lambda$$ and $$\lambda$$, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time:

A

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

B

$$\frac{1}{9\lambda}$$

C

$$\frac{1}{11\lambda}$$

D

$$\frac{11}{10\lambda}$$

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 28

Report

An NPN transistor operates as a common emitter amplifier, with a power gain of 60 dB. The input circuit resistance is 100 Ω and the output load resistance is 10 kΩ. The common emitter current gain β is:

A

$$6 \times 10^2$$

B

$$10^2$$

C

$$10^4$$

D

60

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 29

Report

A message signal of frequency 100 MHz and peak voltage 100 V is used to execute amplitude modulation on a carrier wave of frequency 300 GHz and peak voltage 400 V. The modulation index and difference between the two side band frequencies are:

A

4; $$2 \times 10^8$$ Hz

B

0.25; $$2 \times 10^8$$ Hz

C

4; $$1 \times 10^8$$ Hz

D

0.25; $$1 \times 10^8$$ Hz

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 30

Report

In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure.

S. No.   R(Ω)       l(cm)
1.        1000         60
2.        100          13
3.        10            1.5
4.        1              1.0

Which of the reading is inconsistent?

A

1

B

3

C

2

D

4

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 31

Report

At 300 K and 1 atmospheric pressure, 10 mL of a hydrocarbon required 55 mL of O$$_2$$ for complete combustion, and 40 mL of CO$$_2$$ is formed. The formula of the hydrocarbon is:

A

C$$_4$$H$$_8$$

B

C$$_4$$H$$_{10}$$

C

C$$_4$$H$$_6$$

D

C$$_4$$H$$_7$$Cl

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 32

Report

The graph between $$|\psi|^2$$ and r (radical distance) is shown below. This represents:

A

3s orbital

B

2p orbital

C

2s orbital

D

1s orbital

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 33

Report

The isoelectronic set of ions is:

A

F$$^-$$, Li$$^+$$, Na$$^+$$ and Mg$$^{2+}$$

B

N$$^{3-}$$, Li$$^+$$, Mg$$^{2+}$$ and O$$^{2-}$$

C

N$$^{3-}$$, O$$^{2-}$$, F$$^-$$ and Na$$^+$$

D

Li$$^+$$, Na$$^+$$, O$$^{2-}$$ and F$$^-$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 34

Report

During the change of O$$_2$$ to O$$_2^-$$, the incoming electron goes to the orbital:

A

$$\pi$$ 2p$$_x$$

B

$$\pi^*$$ 2p$$_x$$

C

$$\pi$$ 2p$$_y$$

D

$$\sigma^*$$ 2p$$_z$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 35

Report

Consider the following table:

Gas    a/(kPa dm$$^6$$ mol$$^{-1}$$)    b/(dm$$^3$$ mol$$^{-1}$$)
A              642.32                    0.05196
B              155.21                    0.04136
C              431.91                    0.05196
D              155.21                    0.4382

a and b are van der Waals constants. The correct statement about the gases is:

A

Gas C will occupy more volume than gas A; gas B will be lesser compressible than gas D

B

Gas C will occupy lesser volume than gas A; gas B will be lesser compressible than gas D

C

Gas C will occupy more volume than gas A; gas B will be more compressible than gas D

D

Gas C will occupy lesser volume than gas A; gas B will be more compressible than gas D

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 36

Report

A process will be spontaneous at all temperatures if:

A

$$\Delta H < 0$$ and $$\Delta S < 0$$

B

$$\Delta H < 0$$ and $$\Delta S > 0$$

C

$$\Delta H > 0$$ and $$\Delta S > 0$$

D

$$\Delta H > 0$$ and $$\Delta S < 0$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 37

Report

Consider the following statements
(a) The pH of a mixture containing 400 mL of 0.1 M H$$_2$$SO$$_4$$ and 400 mL of 0.1 M NaOH will be approximately 1.3.
(b) Ionic product of water is temperature dependent.
(c) A monobasic acid with K$$_a$$ = 10$$^{-5}$$ has a pH = 5. The degree of dissociation of this acid is 50%.
(d) The Le Chatelier's principle is not applicable to common-ion effect.
The correct statements are:

A

(b) and (c)

B

(a), (b) and (d)

C

(a) and (b)

D

(a), (b) and (c)

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 38

Report

The synonym for water gas when used in the production of methanol is:

A

syn gas

B

laughing gas

C

natural gas

D

fuel gas

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 39

Report

The alloy used in the construction of aircrafts is:

A

Mg - Al

B

Mg - Mn

C

Mg - Sn

D

Mg - Zn

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 40

Report

The correct order of catenation is:

A

Ge > Sn > Si > C

B

C > Sn > Si ≈ Ge

C

C > Si > Ge ≈ Sn

D

Si > Sn > C > Ge

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 41

Report

The principle of column chromatography is:

A

Differential adsorption of the substances on the solid phase.

B

Differential absorption of the substances on the solid phase.

C

Gravitational force.

D

Capillary action

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 42

Report

The increasing order of the reactivity of the following compounds towards electrophilic aromatic substitution reactions is:

A

II < I < III

B

III < II < I

C

III < I < II

D

I < III < II

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 43

Report

The regions of the atmosphere, where clouds form and where we live, respectively, are:

A

Troposphere and Troposphere

B

Stratosphere and Stratosphere

C

Stratosphere and Troposphere

D

Troposphere and Stratosphere

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 44

Report

At room temperature, a dilute solution of urea is prepared by dissolving 0.60 g of urea in 360 g of water. If the vapour pressure of pure water at this temperature is 35 mm Hg, lowering of vapour pressure will be:
(molar mass of urea = 60 g mol$$^{-1}$$)

A

0.028 mm Hg

B

0.027 mm Hg

C

0.031 mm Hg

D

0.017 mm Hg

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 45

Report

Consider the statements S1 and S2:
S1: Conductivity always increases with decreases in the concentration of electrolyte.
S2: Molar conductivity always increases with decreases in the concentration of electrolyte.
The correct option among the following

A

S1 is wrong and S2 is correct

B

S1 is correct and S2 is wrong

C

Both S1 and S2 are correct

D

Both S1 and S2 are wrong

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 46

Report

A bacterial infection in an internal wound grows as N'(t) = N$$_0$$exp(t), where the time t is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as $$\frac{dN}{dt} = -5N^2$$. What will be the plot of $$\frac{N_0}{N}$$ vs t after 1 hour?

A

B

C

D

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 47

Report

A gas undergoes physical adsorption on a surface and follows the given Freundlich adsorption isotherm equation
$$\frac{x}{m} = kp^{0.5}$$
Adsorption of the gas increases with:

A

Decrease in p and increase in T

B

Increase in p and decrease in T

C

Increase in p and increase in T

D

Decrease in p and decrease in T

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 48

Report

Match the refining methods (Column I) with metals (Column II).
      Column I                       Column II
(Refining methods)              (Metals)
(I)   Liquation                      (a) Zr
(II)  Zone Refining                (b) Ni
(III) Mond Process                (c) Sn
(IV) Van Arkel Method          (d) Ga

A

(I) - (b); (II) - (c); (III) - (d); (IV) - (a)

B

(I) - (b); (II) - (d); (III) - (a); (IV) - (c)

C

(I) - (c); (II) - (d); (III) - (b); (IV) - (a)

D

(I) - (c); (II) - (a); (III) - (b); (IV) - (d)

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 49

Report

The oxoacid of sulphur that does not contain bond between sulphur atom is:

A

H$$_2$$S$$_2$$O$$_7$$

B

H$$_2$$S$$_2$$O$$_4$$

C

H$$_2$$S$$_4$$O$$_6$$

D

H$$_2$$S$$_2$$O$$_3$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 50

Report

Consider the hydrated ions of Ti$$^{2+}$$, V$$^{2+}$$, Ti$$^{3+}$$ and Sc$$^{3+}$$. The correct order of their spin-only magnetic moments is:

A

Sc$$^{3+}$$ < Ti$$^{3+}$$ < V$$^{2+}$$ < Ti$$^{2+}$$

B

Ti$$^{3+}$$ < Ti$$^{2+}$$ < Sc$$^{3+}$$ < V$$^{2+}$$

C

Sc$$^{3+}$$ < Ti$$^{3+}$$ < Ti$$^{2+}$$ < V$$^{2+}$$

D

V$$^{2+}$$ < Ti$$^{2+}$$ < Ti$$^{3+}$$ < Sc$$^{3+}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 51

Report

The species that can have a trans-isomer is:
(en = ethane-1, 2-diamine, ox = oxalate)

A

[Cr(en)$$_2$$(ox)]$$^+$$

B

[Pt(en)Cl$$_2$$]

C

[Zn(en)Cl$$_2$$]

D

[Pt(en)$$_2$$Cl$$_2$$]$$^{2+}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 52

Report

Three complexes,
[CoCl(NH$$_3$$)$$_5$$]$$^{2+}$$(I), [Co(NH$$_3$$)$$_5$$H$$_2$$O]$$^{3+}$$(II) and [Co(NH$$_3$$)$$_6$$]$$^{3+}$$(III)
absorb light in the visible region. The correct order of the wavelength of light absorbed by them is:

A

(II) > (I) > (III)

B

(III) > (II) > (I)

C

(I) > (II) > (III)

D

(III) > (I) > (II)

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 53

Report

Increasing rate of S$$_N$$1 reaction in the following compounds is:

A

(I) < (II) < (III) < (IV)

B

(II) < (I) < (III) < (IV)

C

(II) < (I) < (IV) < (III)

D

(I) < (II) < (IV) < (III)

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 54

Report

The major product of the following reaction is:

A

B

C

D

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 55

Report

The major product of the following reaction is:

A

B

C

D

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 56

Report

Major products of the following reaction are:

A

CH$$_3$$OH and HCO$$_2$$H

B

C

D

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 57

Report

The major product of the following reaction is:

A

B

C

D

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 58

Report

Ethylamine (C$$_2$$H$$_5$$NH$$_2$$) can be obtained from N-ethylphthalimide on treatment with:

A

CaH$$_2$$

B

NH$$_2$$NH$$_2$$

C

H$$_2$$O

D

NaBH$$_4$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 59

Report

Which of the following is a condensation polymer?

A

Nylon 6, 6

B

Neoprene

C

Buna-S

D

Teflon

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 60

Report

Amylopectin is composed of:

A

β - D - glucose, C$$_1$$ - C$$_4$$ and C$$_1$$ - C$$_6$$ linkages

B

α - D - glucose, C$$_1$$ - C$$_4$$ and C$$_2$$ - C$$_6$$ linkages

C

α - D - glucose, C$$_1$$ - C$$_4$$ and C$$_1$$ - C$$_6$$ linkages

D

β - D - glucose, C$$_1$$ - C$$_4$$ and C$$_2$$ - C$$_6$$ linkages

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 61

Report

If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$x^2 + x\sin\theta - 2\sin\theta = 0$$, $$\theta \in \left(0, \frac{\pi}{2}\right)$$, then $$\frac{\alpha^{12} + \beta^{12}}{(\alpha^{-12} + \beta^{-12})\cdot(\alpha - \beta)^{24}}$$ is equal to:

A

$$\frac{2^6}{(\sin\theta + 8)^{12}}$$

B

$$\frac{2^{12}}{(\sin\theta - 4)^{12}}$$

C

$$\frac{2^{12}}{(\sin\theta + 8)^{12}}$$

D

$$\frac{2^{12}}{(\sin\theta - 8)^6}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 62

Report

If $$a > 0$$ and $$z = \frac{(1+i)^2}{a-i}$$, has magnitude $$\sqrt{\frac{2}{5}}$$, then $$\bar{z}$$ is equal to:

A

$$-\frac{1}{5} - \frac{3}{5}i$$

B

$$-\frac{3}{5} - \frac{1}{5}i$$

C

$$\frac{1}{5} - \frac{3}{5}i$$

D

$$-\frac{1}{5} + \frac{3}{5}i$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 63

Report

The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is:

A

36

B

60

C

72

D

48

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 64

Report

If $$a_1, a_2, a_3, \ldots, a_n$$ are in A.P. and $$a_1 + a_4 + a_7 + \ldots + a_{16} = 114$$, then $$a_1 + a_6 + a_{11} + a_{16}$$ is equal to:

A

64

B

98

C

38

D

76

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 65

Report

The sum $$\frac{3 \times 1^3}{1^2} + \frac{5 \times (1^3 + 2^3)}{1^2 + 2^2} + \frac{7 \times (1^3 + 2^3 + 3^3)}{1^2 + 2^2 + 3^2} + \ldots$$ upto 10$$^{th}$$ term is

A

660

B

600

C

620

D

680

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 66

Report

If the coefficients of $$x^2$$ and $$x^3$$ are both zero, in the expansion of the expression $$(1 + ax + bx^2)(1 - 3x)^{15}$$, in powers of x, then the ordered pair (a, b) is equal to

A

(28, 315)

B

(-21, 714)

C

(28, 861)

D

(-54, 315)

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 67

Report

All the pairs (x, y), that satisfy the inequality $$2^{\sqrt{\sin^2 x - 2\sin x + 5}} \cdot \frac{1}{4^{\sin^2 y}} \leq 1$$ also satisfy the equation:

A

$$2\sin x = \sin y$$

B

$$\sin x = 2\sin y$$

C

$$|\sin x| = |\sin y|$$

D

$$2|\sin x| = 3\sin y$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 68

Report

The line $$x = y$$ touches a circle at the point (1, 1). If the circle also passes through the point (1, -3), then its radius is

A

$$3\sqrt{2}$$

B

3

C

2

D

$$2\sqrt{2}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 69

Report

If the circles $$x^2 + y^2 + 5Kx + 2y + K = 0$$ and $$2(x^2 + y^2) + 2Kx + 3y - 1 = 0$$, (K ∈ R), intersect at the points P and Q, then the line $$4x + 5y - K = 0$$, passes through P and Q, for:

A

exactly two values of K

B

no value of K

C

exactly one value of K

D

infinitely many values of K

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 70

Report

If the line $$x - 2y = 12$$ is a tangent to the ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ at the point $$\left(3, -\frac{9}{2}\right)$$, then the length of the latus rectum of the ellipse is

A

5 units

B

$$12\sqrt{2}$$ units

C

9 units

D

$$8\sqrt{3}$$ units

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 71

Report

If a directrix of a hyperbola centered at the origin and passing through the point $$(4, -2\sqrt{3})$$ is $$5x = 4\sqrt{5}$$ and its eccentricity is e, then:

A

$$4e^4 + 8e^2 - 35 = 0$$

B

$$4e^4 - 24e^2 + 35 = 0$$

C

$$4e^4 - 24e^2 + 27 = 0$$

D

$$4e^4 - 12e^2 - 27 = 0$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 72

Report

If $$\lim_{x \to 1}\frac{x^4 - 1}{x - 1} = \lim_{x \to k}\frac{x^3 - k^3}{x^2 - k^2}$$, then k is

A

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

B

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

C

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

D

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

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 73

Report

Which one of the following Boolean expression is a tautology?

A

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

B

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

C

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

D

$$(p \vee q) \vee (\sim p \vee \sim q)$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 74

Report

If for some $$x \in$$ R, the frequency distribution of the marks obtained by 20 students in a test is:

Then the mean of the marks is:

A

3.0

B

2.5

C

3.2

D

2.8

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 75

Report

ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are $$\cot^{-1}(3\sqrt{2})$$ and $$\text{cosec}^{-1}(2\sqrt{2})$$ respectively, then the height of the tower (in metres) is

A

$$\frac{100}{3\sqrt{3}}$$

B

20

C

25

D

$$10\sqrt{5}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 76

Report

If the system of linear equations $$x + y + z = 5$$, $$x + 2y + 2z = 6$$, $$x + 3y + \lambda z = \mu$$, ($$\lambda, \mu \in$$ R), has infinitely many solutions, then the value of $$\lambda + \mu$$ is:

A

7

B

10

C

12

D

9

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 77

Report

If $$\Delta_1 = \begin{vmatrix} x & \sin\theta & \cos\theta \\ -\sin\theta & -x & 1 \\ \cos\theta & 1 & x \end{vmatrix}$$ and $$\Delta_2 = \begin{vmatrix} x & \sin 2\theta & \cos 2\theta \\ -\sin 2\theta & -x & 1 \\ \cos 2\theta & 1 & x \end{vmatrix}$$, $$x \neq 0$$; then for all $$\theta \in \left(0, \frac{\pi}{2}\right)$$:

A

$$\Delta_1 + \Delta_2 = -2(x^3 + x - 1)$$

B

$$\Delta_1 - \Delta_2 = x(\cos 2\theta - \cos 4\theta)$$

C

$$\Delta_1 + \Delta_2 = -2x^3$$

D

$$\Delta_1 - \Delta_2 = -2x^3$$

View Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 78

Report

Let $$f(x) = x^2$$, $$x \in R$$. For any $$A \subseteq R$$, define $$g(A) = \{x \in R : f(x) \in A\}$$. If $$S = [0, 4]$$, then which one of the following statements is not true?

A

$$g(f(S)) \neq S$$

B

$$f(g(S)) \neq f(S)$$

C

$$f(g(S)) = S$$

D

$$g(f(S)) = g(S)$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 79

Report

Let $$f : R \to R$$ be differentiable at $$c \in R$$ and $$f(c) = 0$$. If $$g(x) = |f(x)|$$, then at $$x = c$$, g is:

A

not differentiable

B

not differentiable if $$f'(c) = 0$$

C

differentiable if $$f'(c) = 0$$

D

differentiable if $$f'(c) \neq 0$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 80

Report

If $$f(x) = \begin{cases} \frac{\sin(p+1)x + \sin x}{x}, & x < 0 \\ q, & x = 0 \\ \frac{\sqrt{x + x^2} - \sqrt{x}}{x^{3/2}}, & x > 0 \end{cases}$$ is continuous at $$x = 0$$, then the ordered pair (p, q) is equal to:

A

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

B

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

C

$$\left(\frac{5}{2}, \frac{1}{2}\right)$$

D

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

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 81

Report

Let $$f(x) = e^x - x$$ and $$g(x) = x^2 - x$$, $$\forall$$ x ∈ R. Then the set of all x ∈ R, where the function $$h(x) = (f \circ g)(x)$$ is increasing, is:

A

$$\left[-1, -\frac{1}{2}\right] \cup \left[\frac{1}{2}, \infty\right)$$

B

$$[0, \infty)$$

C

$$\left[0, \frac{1}{2}\right] \cup [1, \infty)$$

D

$$\left[-\frac{1}{2}, 0\right] \cup [1, \infty)$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 82

Report

If $$\int \frac{dx}{(x^2 - 2x + 10)^2} = A\left(\tan^{-1}\left(\frac{x-1}{3}\right) + \frac{f(x)}{x^2 - 2x + 10}\right) + C$$, then (where C is a constant of integration)

A

$$A = \frac{1}{27}$$ and $$f(x) = 9(x - 1)$$

B

$$A = \frac{1}{81}$$ and $$f(x) = 3(x - 1)$$

C

$$A = \frac{1}{54}$$ and $$f(x) = 9(x - 1)^2$$

D

$$A = \frac{1}{54}$$ and $$f(x) = 3(x - 1)$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 83

Report

The value of $$\int_0^{2\pi} [\sin 2x(1 + \cos 3x)]dx$$, where [t] denotes the greatest integer function is

A

$$\pi$$

B

$$2\pi$$

C

$$-\pi$$

D

$$-2\pi$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 84

Report

$$\lim_{n \to \infty}\left(\frac{(n+1)^{1/3}}{n^{4/3}} + \frac{(n+2)^{1/3}}{n^{4/3}} + \ldots + \frac{(2n)^{1/3}}{n^{4/3}}\right)$$ is equal to

A

$$\frac{3}{4}(2)^{4/3} - \frac{3}{4}$$

B

$$\frac{4}{3}(2)^{3/4}$$

C

$$\frac{4}{3}(2)^{4/3}$$

D

$$\frac{3}{4}(2)^{4/3} - \frac{4}{3}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 85

Report

The region represented by $$|x - y| \leq 2$$ and $$|x + y| \leq 2$$ is bounded by a

A

rhombus of area $$8\sqrt{2}$$ sq. units

B

rhombus of side length 2 units

C

square of area 16 sq. units

D

square of side length $$2\sqrt{2}$$ units

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 86

Report

If $$y = y(x)$$ is the solution of the differential equation $$\frac{dy}{dx} = (\tan x - y)\sec^2 x$$, $$x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$, such that $$y(0) = 0$$, then $$y\left(-\frac{\pi}{4}\right)$$ is equal to:

A

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

B

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

C

$$e - 2$$

D

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

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 87

Report

Let A(3, 0, -1), B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the mid-point of AC. If G divides BM in the ratio, 2 : 1, then $$\cos(\angle GOA)$$ (O being the origin) is equal to

A

$$\frac{1}{\sqrt{30}}$$

B

$$\frac{1}{6\sqrt{10}}$$

C

$$\frac{1}{\sqrt{15}}$$

D

$$\frac{1}{2\sqrt{15}}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 88

Report

If the length of the perpendicular from the point $$(\beta, 0, \beta)$$, ($$\beta \neq 0$$) to the line, $$\frac{x}{1} = \frac{y-1}{0} = \frac{z+1}{-1}$$ is $$\sqrt{\frac{3}{2}}$$, then $$\beta$$ is equal to

A

2

B

-1

C

-2

D

1

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 89

Report

If Q(0, -1, -3) is the image of the point P in the plane $$3x - y + 4z = 2$$ and R is the point (3, -1, -2), then the area (in sq. units) of $$\triangle PQR$$ is

A

$$\frac{\sqrt{91}}{4}$$

B

$$\frac{\sqrt{91}}{2}$$

C

$$2\sqrt{13}$$

D

$$\frac{\sqrt{65}}{2}$$

View Solution Video Solution

NTA JEE Main 10th April 2019 Shift 1 - Question 90

Report

Assume that each born child is equally likely to be a boy or girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is:

A

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

B

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

C

$$\frac{1}{11}$$

D

$$\frac{1}{17}$$

View Solution Video Solution