NTA JEE Main 25th June 2022 Shift 2

NTA JEE Main 25th June 2022 Shift 2 - Question 1

Report

Two buses $$P$$ and $$Q$$ start from a point at the same time and move in a straight line and their positions are represented by $$x_P(t) = \alpha t + \beta t^2$$ and $$x_Q(t) = ft - t^2$$. At what time, both the buses have same velocity?

A

$$\frac{\alpha - f}{1 + \beta}$$

B

$$\frac{\alpha + f}{2\beta - 1}$$

C

$$\frac{\alpha + f}{2(1 + \beta)}$$

D

$$\frac{f - \alpha}{2(1 + \beta)}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 2

Report

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. If A and B reached the maximum height $$h_1$$ and $$h_2$$ respectively, then $$R = 4\sqrt{h_1 h_2}$$
Reason R: Product of said heights. $$h_1 h_2 = \frac{u^2\sin^2\theta}{2g} \cdot \frac{u^2\cos^2\theta}{2g}$$

A

Both A and R are true and R is the correct explanation of A.

B

Both A and R are true but R is NOT the correct explanation of A.

C

A is true but R is false.

D

A is false but R is true.

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 3

Report

A disc with a flat small bottom beaker placed on it at a distance $$R$$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $$\omega$$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $$\mu$$. The beaker will revolve with the disc if :

A

$$R \leq \frac{\mu g}{2\omega^2}$$

B

$$R \leq \frac{\mu g}{\omega^2}$$

C

$$R \geq \frac{\mu g}{2\omega^2}$$

D

$$R \geq \frac{\mu g}{\omega^2}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 4

Report

For a particle in uniform circular motion, the acceleration $$\vec{a}$$ at any point $$P(R, \theta)$$ on the circular path of radius $$R$$ is (when $$\theta$$ is measured from the positive $$x$$-axis and $$v$$ is uniform speed):

A

$$-\dfrac{v^2}{R}\sin\theta\hat{i} + \dfrac{v^2}{R}\cos\theta\hat{j}$$

B

$$-\dfrac{v^2}{R}\cos\theta\hat{i} + \dfrac{v^2}{R}\sin\theta\hat{j}$$

C

$$-\dfrac{v^2}{R}\cos\theta\hat{i} - \dfrac{v^2}{R}\sin\theta\hat{j}$$

D

$$-\dfrac{v^2}{R}\hat{i} + \dfrac{v^2}{R}\hat{j}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 5

Report

A solid metallic cube having total surface area $$24$$ m$$^2$$ is uniformly heated. If its temperature is increased by $$10°$$C, calculate the increase in volume of the cube. (Given $$\alpha = 5.0 \times 10^{-4}$$ °C$$^{-1}$$).

A

$$2.4 \times 10^6$$ cm$$^3$$

B

$$1.2 \times 10^5$$ cm$$^3$$

C

$$6 \times 10^4$$ cm$$^3$$

D

$$4.8 \times 10^5$$ cm$$^3$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 6

Report

A copper block of mass $$5.0$$ kg is heated to a temperature of $$500°$$C and is placed on a large ice block. What is the maximum amount of ice that can melt?
[Specific heat of copper : $$0.39$$ J g$$^{-1}$$ °C$$^{-1}$$ and latent heat of fusion of water : $$335$$ J g$$^{-1}$$]

A

1.5 kg

B

5.8 kg

C

2.9 kg

D

3.8 kg

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 7

Report

The ratio of specific heats $$\frac{C_p}{C_v}$$ in terms of degree of freedom $$f$$ is given by :

A

$$1 + \frac{f}{3}$$

B

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

C

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

D

$$1 + \frac{1}{f}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 8

Report

Two metallic plates form a parallel plate capacitor. The distance between the plate is '$$d$$'. A metal sheet of thickness $$\frac{d}{2}$$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

A

$$1 : 2$$

B

$$2 : 1$$

C

$$1 : 4$$

D

$$4 : 1$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 9

Report

Two cells of the same EMF $$E$$ but different internal resistances, $$r_1$$ and $$r_2$$ are connected in series with an external resistance $$R$$ as shown in the figure. The terminal potential difference across the second cell is found to be zero. The external resistance $$R$$ must then be:

A

$$r_1 r_2$$

B

$$r_1 - r_2$$

C

$$r_2 - r_1$$

D

$$r_1 + r_2$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 10

Report

If $$n$$ represents the actual number of deflections in a converted galvanometer of resistance $$G$$ and shunt resistance $$S$$. Then the total current $$I$$ when its figure of merit is $$K$$ will be

A

$$\frac{KS}{S + G}$$

B

$$\frac{G + S}{nKS}$$

C

$$\frac{nKS}{G + S}$$

D

$$\frac{nK(G + S)}{S}$$

View Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 11

Report

Given below are two statements :
Statement - I : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature.
Statement - II : Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field.
Choose the correct answer from the options given below

A

Both Statement - I and Statement - II are true.

B

Both Statement - I and Statement - II are false.

C

Statement - I is true but Statement - II is false.

D

Statement- I is false but Statement - II is true.

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 12

Report

A long solenoid carrying a current produces a magnetic field $$B$$ along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to

A

$$2B$$

B

$$4B$$

C

$$\frac{B}{2}$$

D

$$B$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 13

Report

A sinusoidal voltage $$V(t) = 210\sin 3000t$$ volt is applied to a series LCR circuit in which $$L = 10$$ mH, $$C = 25$$ $$\mu$$F and $$R = 100\Omega$$. The phase difference $$\Phi$$ between the applied voltage and resultant current will be

A

$$\tan^{-1}(0.17)$$

B

$$\tan^{-1}(9.46)$$

C

$$\tan^{-1}(0.30)$$

D

$$\tan^{-1}(13.33)$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 14

Report

The electromagnetic waves travel in a medium at a speed of $$2.0 \times 10^8$$ m s$$^{-1}$$. The relative permeability of the medium is $$1.0$$. The relative permittivity of the medium will be

A

2.25

B

4.25

C

6.25

D

8.25

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 15

Report

The interference pattern is obtained with two coherent light sources of intensity ratio $$4:1$$. And the ratio $$\frac{I_{max} + I_{min}}{I_{max} - I_{min}}$$ is $$\frac{5}{x}$$. Then, the value of $$x$$ will be equal to :

A

3

B

4

C

2

D

1

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 16

Report

A light whose electric field vectors are completely removed by using a good polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

A

Reflected and refracted rays will be perpendicular to each other.

B

Wave will propagate along the surface of prism.

C

No refraction, and there will be total reflection of light.

D

No reflection. and there will be total transmission of light.

View Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 17

Report

A proton, a neutron, an electron and an $$\alpha$$-particle have same energy. If $$\lambda_p, \lambda_n, \lambda_e$$ and $$\lambda_\alpha$$ are the de Broglie's wavelengths of proton, neutron, electron and $$\alpha$$ particle respectively, then choose the correct relation from the following

A

$$\lambda_p = \lambda_n > \lambda_e > \lambda_\alpha$$

B

$$\lambda_\alpha < \lambda_n < \lambda_p < \lambda_e$$

C

$$\lambda_e < \lambda_p = \lambda_n > \lambda_\alpha$$

D

$$\lambda_e = \lambda_p = \lambda_n = \lambda_\alpha$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 18

Report

Which of the following figure represents the variation of $$\ln\frac{R}{R_0}$$ with $$\ln A$$ (if $$R$$ = radius of a nucleus and $$A$$ = its mass number)?

A

B

C

D

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 19

Report

Identify the logic operation performed by the given circuit

A

AND gate

B

OR gate

C

NOR gate

D

NAND gate

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 20

Report

Match List I with List II

List I	List II
(A) Facsimile	(I) Static Document Image
(B) Guided media Channel	(II) Local Broadcast Radio
(C) Frequency Modulation	(III) Rectangular wave
(D) Digital Signal	(IV) Optical Fiber

A

A - IV, B - III, C - II, D - I

B

A - I, B - IV, C - II, D - III

C

A - IV, B - II, C - III, D - I

D

A - I, B - II, C - III, D - IV

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 21

Report

For $$z = a^2 x^3 y^{\frac{1}{2}}$$, where '$$a$$' is a constant. If percentage error in measurement of '$$x$$' and '$$y$$' are $$4\%$$ and $$12\%$$, respectively, then the percentage error for '$$z$$' will be ______ %.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 22

Report

A curved in a level road has a radius $$75$$ m. The maximum speed of a car turning this curved road can be $$30$$ m s$$^{-1}$$ without skidding. If radius of curved road is changed to $$48$$ m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ______ m s$$^{-1}$$.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 23

Report

A block of mass $$200$$ g is kept stationary on a smooth inclined plane by applying a minimum horizontal force $$F = \sqrt{x}$$ N as shown in figure. The value of $$x$$ = ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 24

Report

Moment of Inertia (M.I.) of four bodies having same mass $$M$$ and radius $$2R$$ are as follows
$$I_1$$ = M.I. of solid sphere about its diameter
$$I_2$$ = M.I. of solid cylinder about its axis
$$I_3$$ = M.I. of solid circular disc about its diameter
$$I_4$$ = M.I. of thin circular ring about its diameter
If $$2(I_2 + I_3) + I_4 = xI_1$$ then the value of $$x$$ will be ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 25

Report

Two satellites $$S_1$$ and $$S_2$$ are revolving in circular orbits around a planet with radius $$R_1 = 3200$$ km and $$R_2 = 800$$ km respectively. The ratio of speed of satellite $$S_1$$ to the speed of satellite $$S_2$$ in their respective orbits would be $$\frac{1}{x}$$ where $$x =$$ ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 26

Report

When a gas filled in a closed vessel is heated by raising the temperature by $$1°$$C, its pressure increases by $$0.4\%$$. The initial temperature of the gas is ______ K.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 27

Report

$$27$$ identical drops are charged at $$22$$ V each. They combine to form a bigger drop. The potential of the bigger drop will be ______ V.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 28

Report

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______ %.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 29

Report

In a series LCR circuit, the inductance, capacitance and resistance are $$L = 100$$ mH, $$C = 100$$ $$\mu$$F and $$R = 10$$ $$\Omega$$ respectively. They are connected to an AC source of voltage $$220$$ V and frequency of $$50$$ Hz. The approximate value of current in the circuit will be ______ A.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 30

Report

In an experiment of CE configuration of $$n-p-n$$ transistor, the transfer characteristics are observed as given in figure. If the input resistance is $$200\Omega$$ and output resistance is $$60\Omega$$, the voltage gain in this experiment will be ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 31

Report

The minimum energy that must be possessed by photons in order to produce the photoelectric effect with platinum metal is:
[Given: The threshold frequency of platinum is $$1.3 \times 10^{15}$$ s$$^{-1}$$ and $$h = 6.6 \times 10^{-34}$$ Js]

A

$$8.58 \times 10^{-19}$$ J

B

$$9.76 \times 10^{-20}$$ J

C

$$3.21 \times 10^{-14}$$ J

D

$$6.24 \times 10^{-16}$$ J

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 32

Report

What is the correct order of electron gain enthalpy of Cl, F, Te, Po

A

$$F > Cl > Te > Po$$

B

$$Cl > F > Te > Po$$

C

$$Te > Po > Cl > F$$

D

$$Po > Te > F > Cl$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 33

Report

At $$25°$$C and $$1$$ atm pressure, the enthalpy of combustion of benzene $$1$$ and acetylene $$g$$ are $$-3268$$ kJ mol$$^{-1}$$ and $$-1300$$ kJ mol$$^{-1}$$, respectively. The change in enthalpy for the reaction
$$3C_2H_2(g) \to C_6H_6(l)$$, is

A

$$+324$$ kJ mol$$^{-1}$$

B

$$+632$$ kJ mol$$^{-1}$$

C

$$-632$$ kJ mol$$^{-1}$$

D

$$-732$$ kJ mol$$^{-1}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 34

Report

The $$K_{sp}$$ for bismuth sulphide $$Bi_2S_3$$ is $$1.08 \times 10^{-73}$$. The solubility of $$Bi_2S_3$$ in mol L$$^{-1}$$ at $$298$$ K is

A

$$1.0 \times 10^{-15}$$

B

$$2.7 \times 10^{-12}$$

C

$$3.2 \times 10^{-10}$$

D

$$4.2 \times 10^{-8}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 35

Report

Assertion: The amphoteric behaviour of water is explained by Lewis acid base theory
Reason: water acts as acid with $$NH_3$$ and base with $$H_2S$$

A

Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

B

Both Assertion and Reason are true but Reason is NOT the correct explanation of Assertion.

C

Assertion is true but Reason is false.

D

Assertion is false but Reason is true.

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 36

Report

The number of bridged oxygen atoms present in compound B formed from the following reactions is
$$PbNO_{3_2} \xrightarrow{673 K} A + PbO + O_2$$
$$A \xrightarrow{Dimerise} B$$

A

0

B

1

C

2

D

3

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 37

Report

Given below are two statements: one is labelled as Assertion and the other is labelled as Reason.
Assertion: A mixture contains benzoic acid and naphthalene. The pure benzoic acid can be separated out by the use of benzene.
Reason: Benzoic acid is soluble in hot water.
In the light of the above statements, choose the most appropriate answer from the options given below.

A

Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

B

Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

C

Assertion is true but Reason is false.

D

Assertion is false but Reason is true.

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 38

Report

Given below are two statements: one is labelled as Assertion and the other is labelled as Reason.
Assertion: Polluted water may have a value of BOD of the order of 17ppm.
Reason: BOD is a measure of oxygen required to oxidise both the biodegradable and non-biodegradable organic material in water.
In the light of the above statements, choose the most appropriate answer from the options given below.

A

Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

B

Both Assertion and Reason are true but Reason is NOT the correct explanation of Assertion.

C

Assertion is true but Reason is false.

D

Assertion is false but Reason is true.

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 39

Report

Solute A associates in water. When $$0.7$$ g of solute A is dissolved in $$42.0$$ g of water, it depresses the freezing point by $$0.2°$$C. The percentage association of solute A in water, is
[Given: Molar mass of A $$= 93$$ g mol$$^{-1}$$. Molal depression constant of water is $$1.86$$ K kg mol$$^{-1}$$]

A

50%

B

60%

C

70%

D

80%

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 40

Report

The correct order of reduction potentials of the following pairs is
A. $$Cl_2/Cl^-$$
B. $$I_2/I^-$$
C. $$Ag^+/Ag$$
D. $$Na^+/Na$$
E. $$Li^+/Li$$
Choose the correct answer from the options given below.

A

$$A > B > C > E > D$$

B

$$A > C > B > E > D$$

C

$$A > B > C > D > E$$

D

$$A > C > B > D > E$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 41

Report

Given below are two statements.
Statement I: During electrolytic refining, blister copper deposits precious metals.
Statement II: In the process of obtaining pure copper by electrolysis method, copper blister is used to make the anode.
In the light of the above statements, choose the correct answer from the options given below.

A

Both Statement I and Statement II are true.

B

Both Statement I and Statement II are false.

C

Statement I is true but Statement II is false.

D

Statement I is false but Statement II is true.

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 42

Report

The metal ion (in gaseous state) with lowest spin-only magnetic moment value is

A

$$V^{2+}$$

B

$$Ni^{2+}$$

C

$$Cr^{2+}$$

D

$$Fe^{2+}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 43

Report

In the given reaction

'A' can be

A

benzyl bromide

B

bromobenzene

C

cyclohexyl bromide

D

methyl bromide

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 44

Report

Amongst the following, the major product of the given chemical reaction is

A

B

C

D

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 45

Report

The major product formed in the following reaction, is

A

B

C

D

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 46

Report

Which of the following conditions or reaction sequence will NOT give acetophenone as the major product?

A

B

C

D

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 47

Report

During halogen test, sodium fusion extract is boiled with concentrated $$HNO_3$$ to

A

remove unreacted sodium

B

decompose cyanide or sulphide of sodium

C

extract halogen from organic compound

D

maintain the pH of extract.

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 48

Report

Which of the following ketone will NOT give enamine on treatment with secondary amines? [where t-Bu is $$-C(CH_3)_3$$]

A

B

C

D

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 49

Report

Match the following correctly
(i) Zymase - (a) Stomach
(ii) Urease - (b) Yeast
(iii) Diastase - (c) Malt
(iv) Pepsin - (d) Soyabean

A

(i)-B; (ii) D(iii)-C; (iv)-A

B

(i)-B; (ii)-A; (iii)-C; (iv)-D

C

(i)-A; (ii)-B; (iii)-C; (iv)-D

D

(i)-D; (ii)-C; (iii)-B; (iv)-A

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 50

Report

An antiseptic dettol is a mixture of two compounds 'A' and 'B' where A has $$6\pi$$ electrons and B has $$2\pi$$ electrons. What is B?

A

Bithional

B

Terpineol

C

Chlorophenol

D

Chloroxyenol

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 51

Report

A protein 'A' contains $$0.30\%$$ of glycine (molecular weight $$75$$). The minimum molar mass of the protein 'A' is ______ $$\times 10^3$$ g mol$$^{-1}$$ [nearest integer]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 52

Report

How many of the following molecules are with non-zero net dipole moment,
$$NH_3$$, HCl, $$H_2O$$, $$BeF_2$$, $$BH_3$$, $$CCl_4$$

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 53

Report

A rigid nitrogen tank stored inside a laboratory has a pressure of $$30$$ atm at $$06:00$$ am when the temperature is $$27°$$C. At $$03:00$$ pm, when the temperature is $$45°$$C, the pressure in the tank will be ______ atm. [nearest integer]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 54

Report

The neutralization occurs when $$10$$ mL of $$0.1$$ M acid 'A' is allowed to react with $$30$$ mL of $$0.05$$ M base $$MOH_2$$. The basicity of the acid 'A' is ______
[M is a metal]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 55

Report

A solution of $$Fe_2(SO_4)_3$$ is electrolyzed for '$$x$$' min with a current of $$1.5$$ A to deposit $$0.3482$$ g of Fe. The value of $$x$$ is ______ [nearest integer]
Given : $$1 F = 96500$$ C mol$$^{-1}$$. Atomic mass of Fe $$= 56$$ g mol$$^{-1}$$

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 56

Report

At $$345$$ K, the half life for the decomposition of a sample of a gaseous compound initially at $$55.5$$ kPa was $$340$$ s. When the pressure was $$27.8$$ kPa, the half life was found to be $$170$$ s. The order of the reaction is ______ [integer answer]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 57

Report

$$PCl_5 + H_2O \to A + HCl$$
$$A + H_2O \to B + HCl$$
Find number of ionisable hydrogen in B

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 58

Report

Amongst $$FeCl_3 \cdot 3H_2O$$, $$K_3[Fe(CN)_6]$$ and $$[Co(NH_3)_6]Cl_3$$, the spin-only magnetic moment value of the inner-orbital complex that absorbs light at shortest wavelength is ______ B.M. [nearest integer]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 59

Report

The Novolac polymer has mass of $$963$$ g. The number of monomer units present in it are ______

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 60

Report

How many of the given compounds will give a positive Biuret test? ______
Glycine, Glycylalanine, Tripeptide, Biuret

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 61

Report

Let $$A = \{x \in R : |x + 1| < 2\}$$ and $$B = \{x \in R : |x - 1| \geq 2\}$$. Then which one the following statements is NOT true?

A

$$A - B = (-1, 1)$$

B

$$B - A = R - (-3, 1)$$

C

$$A \cap B = (-3, -1]$$

D

$$A \cup B = R - [1, 3)$$

View Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 62

Report

Let $$a, b \in R$$ be such that the equation $$ax^2 - 2bx + 15 = 0$$ has repeated root $$\alpha$$ and if $$\alpha$$ and $$\beta$$ are the roots of the equation $$x^2 - 2bx + 21 = 0$$, then $$\alpha^2 + \beta^2$$ is equal to:

A

37

B

58

C

68

D

92

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 63

Report

Let $$z_1$$ and $$z_2$$ be two complex numbers such that $$\bar{z}_1 = iz_2$$ and $$\arg\frac{z_1}{z_2} = \pi$$, then the argument of $$z_1$$ is

A

$$\arg z_2 = \frac{\pi}{4}$$

B

$$\arg z_2 = -\frac{3\pi}{4}$$

C

$$\arg z_1 = \frac{\pi}{4}$$

D

$$\arg z_1 = -\frac{3\pi}{4}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 64

Report

The sum $$1 + 2 \cdot 3 + 3 \cdot 3^2 + \ldots + 10 \cdot 3^9$$ is equal to

A

$$\frac{2 \cdot 3^{12} + 10}{4}$$

B

$$\frac{19 \cdot 3^{10} + 1}{4}$$

C

$$5 \cdot 3^{10} - 2$$

D

$$\frac{9 \cdot 3^{10} + 1}{2}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 65

Report

The coefficient of $$x^{101}$$ in the expression
$$5 + x^{500} + x(5 + x)^{499} + x^2(5 + x)^{498} + \ldots + x^{500}, x > 0$$ is

A

$$^{501}C_{101} \times 5^{399}$$

B

$$^{501}C_{101} \times 5^{400}$$

C

$$^{501}C_{100} \times 5^{400}$$

D

$$^{500}C_{101} \times 5^{399}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 66

Report

The value of $$2\sin 12° - \sin 72°$$ is

A

$$\frac{\sqrt{5}(1-\sqrt{3})}{4}$$

B

$$\frac{1-\sqrt{5}}{8}$$

C

$$\frac{\sqrt{3}(1-\sqrt{5})}{2}$$

D

$$\frac{\sqrt{3}(1-\sqrt{5})}{4}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 67

Report

A circle touches both the $$y$$-axis and the line $$x + y = 0$$. Then the locus of its center is

A

$$y = \sqrt{2}x$$

B

$$x = \sqrt{2}y$$

C

$$y^2 - x^2 = 2xy$$

D

$$x^2 - y^2 = 2xy$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 68

Report

The line $$y = x + 1$$ meets the ellipse $$\frac{x^2}{4} + \frac{y^2}{2} = 1$$ at two points $$P$$ and $$Q$$. If $$r$$ is the radius of the circle with $$PQ$$ as diameter then $$(3r)^2$$ is equal to

A

20

B

12

C

11

D

8

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 69

Report

$$\lim_{x \to \frac{\pi}{2}} {\tan^2 x(2\sin^2 x + 3\sin x + 4)^{\frac{1}{2}} - (\sin^2 x + 6\sin x + 2)^{\frac{1}{2}}}$$ is equal to

A

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

B

$$-\frac{1}{18}$$

C

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

D

$$\frac{1}{6}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 70

Report

The negation of the Boolean expression $$\sim q \wedge p \Rightarrow \sim p \vee q$$ is logically equivalent to

A

$$p \Rightarrow q$$

B

$$q \Rightarrow p$$

C

$$\sim(p\Rightarrow q)$$

D

$$\sim q \Rightarrow p$$

View Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 71

Report

The system of equations
$$-kx + 3y - 14z = 25$$
$$-15x + 4y - kz = 3$$
$$-4x + y + 3z = 4$$
is consistent for all $$k$$ in the set

A

$$R$$

B

$$R - \{-11, 13\}$$

C

$$R - \{-13\}$$

D

$$R - \{-11, 11\}$$

View Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 72

Report

The value of $$\tan^{-1}\left(\frac{\cos\frac{15\pi}{4} - 1}{\sin\frac{\pi}{4}}\right)$$ is equal to

A

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

B

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

C

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

D

$$-\frac{4\pi}{9}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 73

Report

Water is being filled at the rate of $$1$$ cm$$^3$$ sec$$^{-1}$$ in a right circular conical vessel (vertex downwards) of height $$35$$ cm and diameter $$14$$ cm. When the height of the water level is $$10$$ cm, the rate (in cm$$^2$$ sec$$^{-1}$$) at which the wet conical surface area of the vessel increases is

A

$$5$$

B

$$\frac{\sqrt{21}}{5}$$

C

$$\frac{\sqrt{26}}{5}$$

D

$$\frac{\sqrt{26}}{10}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 74

Report

If the line $$y = 4 + kx, k > 0$$, is the tangent to the parabola $$y = x - x^2$$ at the point $$P$$ and $$V$$ is the vertex of the parabola, then the slope of the line through $$P$$ and $$V$$ is

A

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

B

$$\frac{26}{9}$$

C

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

D

$$\frac{23}{6}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 75

Report

If the angle made by the tangent at the point $$(x_0, y_0)$$ on the curve $$x = 12(t + \sin t \cos t), y = 12(1 + \sin t)^2, 0 < t < \frac{\pi}{2}$$, with the positive $$x$$-axis is $$\frac{\pi}{3}$$, then $$y_0$$ is equal to

A

$$63 + 2\sqrt{2}$$

B

$$37 + 4\sqrt{3}$$

C

$$27$$

D

$$48$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 76

Report

If $$b_n = \int_0^{\pi/2} \frac{\cos^2(nx)}{\sin x} dx, n \in \mathbb{N}$$, then

A

$$b_3 - b_2, b_4 - b_3, b_5 - b_4$$ are in an A.P. with common difference $$-2$$

B

$$\frac{1}{b_3 - b_2}, \frac{1}{b_4 - b_3}, \frac{1}{b_5 - b_4}$$ are in an A.P. with common difference $$2$$

C

$$b_3 - b_2, b_4 - b_3, b_5 - b_4$$ are in a G.P.

D

$$\frac{1}{b_3 - b_2}, \frac{1}{b_4 - b_3}, \frac{1}{b_5 - b_4}$$ are in an A.P. with common difference $$-2$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 77

Report

The area of the region enclosed between the parabolas $$y^2 = 2x - 1$$ and $$y^2 = 4x - 3$$ is

A

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

B

$$\frac{1}{6}$$

C

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

D

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

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 78

Report

If $$y = yx$$ is the solution of the differential equation $$2x^2\frac{dy}{dx} - 2xy + 3y^2 = 0$$ such that $$y(e) = \frac{e}{3}$$, then $$y(1)$$ is equal to

A

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

B

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

C

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

D

$$3$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 79

Report

Let $$P$$ be the plane passing through the intersection of the planes $$\vec{r} \cdot (\hat{i} + 3\hat{j} - \hat{k}) = 5$$ and $$\vec{r} \cdot (2\hat{i} - \hat{j} + \hat{k}) = 3$$, and the point $$(2, 1, -2)$$. Let the position vectors of the points $$X$$ and $$Y$$ be $$\hat{i} - 2\hat{j} + 4\hat{k}$$ and $$5\hat{i} - \hat{j} + 2\hat{k}$$ respectively. Then the points

A

$$X$$ and $$X + Y$$ are on the same side of $$P$$

B

$$Y$$ and $$Y - X$$ are on the opposite sides of $$P$$

C

$$X$$ and $$Y$$ are on the opposite sides of $$P$$

D

$$X + Y$$ and $$X - Y$$ are on the same side of $$P$$

View Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 80

Report

A biased die is marked with numbers $$2, 4, 8, 16, 32, 32$$ on its faces and the probability of getting a face with mark $$n$$ is $$\frac{1}{n}$$. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is $$48$$, is

A

$$\frac{7}{2^{11}}$$

B

$$\frac{7}{2^{12}}$$

C

$$\frac{3}{2^{10}}$$

D

$$\frac{13}{2^{12}}$$

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 81

Report

The total number of three-digit numbers, with one digit repeated exactly two times, is ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 82

Report

If the sum of the co-efficients of all the positive even powers of $$x$$ in the binomial expansion of $$\left(2x^3 + \frac{3}{x}\right)^{10}$$ is $$5^{10} - \beta \cdot 3^9$$, then $$\beta$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 83

Report

Let the eccentricity of the hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ be $$\frac{5}{4}$$. If the equation of the normal at the point $$\left(\frac{8}{\sqrt{5}}, \frac{12}{5}\right)$$ on the hyperbola is $$8\sqrt{5}x + \beta y = \lambda$$, then $$\lambda - \beta$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 84

Report

If the mean deviation about the mean of the numbers $$1, 2, 3, \ldots, n$$, where $$n$$ is odd, is $$\frac{5(n+1)}{n}$$, then $$n$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 85

Report

Let $$A = \begin{pmatrix} 2 & -2 \\ 1 & -1 \end{pmatrix}$$ and $$B = \begin{pmatrix} -1 & 2 \\ -1 & 2 \end{pmatrix}$$. Then the number of elements in the set $$\{(n, m) : n, m \in \{1, 2, \ldots, 10\}$$ and $$nA^n + mB^m = I\}$$ is ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 86

Report

Let $$f(x) = [2x^2 + 1]$$ and $$g(x) = \begin{cases} 2x - 3, & x < 0 \\ 2x + 3, & x \geq 0 \end{cases}$$, where $$[t]$$ is the greatest integer $$\leq t$$. Then, in the open interval $$(-1, 1)$$, the number of points where $$f \circ g$$ is discontinuous is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 87

Report

Let $$f(x) = x|x^2 - 1| - 2|x - 3| + x - 3, x \in \mathbb{R}$$. If $$m$$ and $$M$$ are respectively the number of points of local minimum and local maximum of $$f$$ in the interval $$(0, 4)$$, then $$m + M$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 88

Report

The value of $$b > 3$$ for which $$12\int_3^b \frac{1}{(x^2 - 1)(x^2 - 4)} dx = \log_e\frac{49}{40}$$, is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 89

Report

Let $$\vec{b} = \hat{i} + \hat{j} + \lambda\hat{k}, \lambda \in \mathbb{R}$$. If $$\vec{a}$$ is a vector such that $$\vec{a} \times \vec{b} = 13\hat{i} - \hat{j} - 4\hat{k}$$ and $$\vec{a} \cdot \vec{b} + 21 = 0$$, then
$$\vec{b} - \vec{a} \cdot \hat{k} - \hat{j} + \vec{b} + \vec{a} \cdot \hat{i} - \hat{k}$$ is equal to ______

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Main 25th June 2022 Shift 2 - Question 90

Report

Let $$l_1$$ be the line in $$xy$$-plane with $$x$$ and $$y$$ intercepts $$\frac{1}{8}$$ and $$\frac{1}{4\sqrt{2}}$$ respectively, and $$l_2$$ be the line in $$zx$$-plane with $$x$$ and $$z$$ intercepts $$-\frac{1}{8}$$ and $$-\frac{1}{6\sqrt{3}}$$ respectively. If $$d$$ is the shortest distance between the line $$l_1$$ and $$l_2$$, then $$d^{-2}$$ is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution