NTA JEE Main 27th June 2022 Shift 1

NTA JEE Main 27th June 2022 Shift 1 - Question 1

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A silver wire has a mass $$(0.6 \pm 0.006)$$ g, radius $$(0.5 \pm 0.005)$$ mm and length $$(4 \pm 0.04)$$ cm. The maximum percentage error in the measurement of its density will be

A

$$7\%$$

B

$$3\%$$

C

$$4\%$$

D

$$6\%$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 2

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A projectile is launched at an angle $$\alpha$$ with the horizontal with a velocity $$20$$ m s$$^{-1}$$. After $$10$$ s, its inclination with horizontal is $$\beta$$. The value of $$\tan\beta$$ will be : $$(g = 10$$ m s$$^{-2})$$.

A

$$\tan\alpha + 5\sec\alpha$$

B

$$\tan\alpha - 5\sec\alpha$$

C

$$2\tan\alpha - 5\sec\alpha$$

D

$$2\tan\alpha + 5\sec\alpha$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 3

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A girl standing on road holds her umbrella at $$45°$$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $$15\sqrt{2}$$ km h$$^{-1}$$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is

A

$$30$$ km h$$^{-1}$$

B

$$\frac{25}{\sqrt{2}}$$ km h$$^{-1}$$

C

$$\frac{30}{\sqrt{2}}$$ km h$$^{-1}$$

D

$$25$$ km h$$^{-1}$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 4

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A system of two blocks of masses $$m = 2$$ kg and $$M = 8$$ kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $$0.5$$. The maximum horizontal force $$F$$ that can be applied to the block of mass $$M$$ so that the blocks move together will be $$(g = 9.8$$ m s$$^{-2})$$

A

$$9.8$$ N

B

$$39.2$$ N

C

$$49$$ N

D

$$78.4$$ N

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NTA JEE Main 27th June 2022 Shift 1 - Question 5

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Two blocks of masses $$10$$ kg and $$30$$ kg are placed on the same straight line with coordinates $$(0, 0)$$ cm and $$(x, 0)$$ cm respectively. The block of $$10$$ kg is moved on the same line through a distance of $$6$$ cm towards the other block. The distance through which the block of $$30$$ kg must be moved to keep the position of centre of mass of the system unchanged is

A

$$4$$ cm towards the $$10$$ kg block

B

$$2$$ cm away from the $$10$$ kg block

C

$$2$$ cm towards the $$10$$ kg block

D

$$4$$ cm away from the $$10$$ kg block

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NTA JEE Main 27th June 2022 Shift 1 - Question 6

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What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of $$5$$ times its mass?
(Assume the collision to be head-on elastic collision)

A

$$50.0\%$$

B

$$66.6\%$$

C

$$55.6\%$$

D

$$33.3\%$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 7

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Statement I : The law of gravitation holds good for any pair of bodies in the universe.
Statement II : The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the above statements, choose the correct answer from the options given below.

A

Statement 1 and statement 2 both are true.

B

Statement 1 is true and statement 2 is false.

C

Statement 1 and statement 2 both are false.

D

Statement 1 is false and statement 2 is true.

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NTA JEE Main 27th June 2022 Shift 1 - Question 8

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The velocity of a small ball of mass $$m$$ and density $$d_1$$, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $$d_2$$, then the viscous force acting on the ball will be

A

$$mg\left(1 - \frac{d_1}{d_2}\right)$$

B

$$mg\left(1 - \frac{d_2}{d_1}\right)$$

C

$$mg\left(\frac{d_1}{d_2} - 1\right)$$

D

$$mg\left(\frac{d_2}{d_1} - 1\right)$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 9

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A mixture of hydrogen and oxygen has volume $$2000$$ cm$$^3$$, temperature $$300$$ K, pressure $$100$$ kPa and mass $$0.76$$ g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be
[Take gas constant $$R = 8.3$$ J K$$^{-1}$$ mol$$^{-1}$$]

A

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

B

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

C

$$\frac{1}{16}$$

D

$$\frac{16}{1}$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 10

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The displacement of simple harmonic oscillator after $$3$$ seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is

A

$$12$$ s

B

$$8$$ s

C

$$36$$ s

D

$$6$$ s

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NTA JEE Main 27th June 2022 Shift 1 - Question 11

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An observer moves towards a stationary source of sound with a velocity one-fifth of the velocity of sound. The percentage change in the apparent frequency is

A

zero

B

$$5\%$$

C

$$10\%$$

D

$$20\%$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 12

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A force of $$10$$ N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.

A

$$5$$ N

B

$$10$$ N

C

$$20$$ N

D

Zero

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NTA JEE Main 27th June 2022 Shift 1 - Question 13

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A $$72$$ $$\Omega$$ galvanometer is shunted by a resistance of $$8$$ $$\Omega$$. The percentage of the total current which passes through the galvanometer is

A

$$0.1\%$$

B

$$10\%$$

C

$$25\%$$

D

$$0.25\%$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 14

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The susceptibility of a paramagnetic material is $$99$$. The permeability of the material in Wb/A - m, is
[Permeability of free space $$\mu_0 = 4\pi \times 10^{-7}$$ Wb/A - m]

A

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

B

$$4\pi \times 10^{-6}$$

C

$$4\pi \times 10^{-7}$$

D

$$4\pi \times 10^{-4}$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 15

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The current flowing through an ac circuit is given by $$I = 5\sin(120\pi t)$$ A. How long will the current take to reach the peak value starting from zero?

A

$$\frac{1}{60}$$ s

B

$$60$$ s

C

$$\frac{1}{120}$$ s

D

$$\frac{1}{240}$$ s

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NTA JEE Main 27th June 2022 Shift 1 - Question 16

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Match List - I with List - II

List-I	List-II
(a) Ultraviolet rays	(i) Study crystal structure
(b) Microwaves	(ii) Greenhouse effect
(c) Infrared waves	(iii) Sterilizing surgical instrument
(d) X-rays	(iv) Radar system

A

(a)-(iii), (b)(iv), (c)-(ii), (d)-(i)

B

(a)-(iii), (b)(i), (c)-(ii), (d)-(iv)

C

(a)-(iv), (b)(iii), (c)-(ii), (d)-(i)

D

(a)-(iii), (b)(iv), (c)-(i), (d)-(ii)

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NTA JEE Main 27th June 2022 Shift 1 - Question 17

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Consider a light ray travelling in air is incident into a medium of refractive index $$\sqrt{2n}$$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be

A

$$\sin^{-1}(\sqrt{n})$$

B

$$\cos^{-1}\left(\frac{n}{\sqrt{2}}\right)$$

C

$$\sin^{-1}(\sqrt{2n})$$

D

$$2\cos^{-1}\left(\sqrt{\frac{n}{2}}\right)$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 18

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An $$\alpha$$ particle and a carbon 12 atom has same kinetic energy $$K$$. The ratio of their de-Broglie wavelengths $$(\lambda_\alpha : \lambda_{C12})$$ is

A

$$\sqrt{3} : 1$$

B

$$1 : \sqrt{3}$$

C

$$2 : \sqrt{3}$$

D

$$3 : 1$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 19

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A hydrogen atom in its ground state absorbs $$10.2$$ eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of (Given, Planck's constant $$= 6.6 \times 10^{-34}$$ Js).

A

$$2.10 \times 10^{-34}$$ Js

B

$$1.05 \times 10^{-34}$$ Js

C

$$3.15 \times 10^{-34}$$ Js

D

$$4.2 \times 10^{-34}$$ Js

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NTA JEE Main 27th June 2022 Shift 1 - Question 20

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Identify the correct Logic Gate for the following output ($$Y$$) of two inputs $$A$$ and $$B$$.

A

B

C

D

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NTA JEE Main 27th June 2022 Shift 1 - Question 21

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A pendulum of length $$2$$ m consists of a wooden bob of mass $$50$$ g. A bullet of mass $$75$$ g is fired towards the stationary bob with a speed $$v$$. The bullet emerges out of the bob with a speed $$\frac{v}{3}$$ and the bob just completes the vertical circle. The value of $$v$$ is ______ m s$$^{-1}$$
(if $$g = 10$$ m s$$^{-2}$$).

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NTA JEE Main 27th June 2022 Shift 1 - Question 22

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The area of cross-section of a large tank is $$0.5$$ m$$^2$$. It has a narrow opening near the bottom having area of cross-section $$1$$ cm$$^2$$. A load of $$25$$ kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is $$40$$ cm above the bottom, will be ______ cm s$$^{-1}$$.
[Take $$g = 10$$ m s$$^{-2}$$]

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NTA JEE Main 27th June 2022 Shift 1 - Question 23

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In a carnot engine, the temperature of reservoir is $$527°$$C and that of sink is $$200$$ K. If the work done by the engine when it transfers heat from reservoir to sink is $$12000$$ kJ, the quantity of heat absorbed by the engine from reservoir is ______ $$\times 10^6$$ J.

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NTA JEE Main 27th June 2022 Shift 1 - Question 24

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A capacitor of capacitance $$50$$ pF is charged by $$100$$ V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ______ nJ.

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NTA JEE Main 27th June 2022 Shift 1 - Question 25

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A $$220$$ V, $$50$$ Hz AC source is connected to a $$25$$ V, $$5$$ W lamp and an additional resistance $$R$$ in series (as shown in figure) to run the lamp at its peak brightness, then the value of $$R$$ (in ohm) will be

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NTA JEE Main 27th June 2022 Shift 1 - Question 26

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A cell, shunted by a $$8$$ $$\Omega$$ resistance, is balanced across a potentiometer wire of length $$3$$ m. The balancing length is $$2$$ m when the cell is shunted by $$4$$ $$\Omega$$ resistance. The value of internal resistance of the cell will be ______ $$\Omega$$.

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NTA JEE Main 27th June 2022 Shift 1 - Question 27

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The current density in a cylindrical wire of radius $$4$$ mm is $$4 \times 10^6$$ A m$$^{-2}$$. The current through the outer portion of the wire between radial distances $$\frac{R}{2}$$ and $$R$$ is ______ $$\pi$$ A.

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NTA JEE Main 27th June 2022 Shift 1 - Question 28

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In Young's double slit experiment the two slits are $$0.6$$ mm distance apart. Interference pattern is observed on a screen at a distance $$80$$ cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be ______ nm.

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NTA JEE Main 27th June 2022 Shift 1 - Question 29

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A beam of monochromatic light is used to excite the electron in $$Li^{++}$$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $$x \times 10^{-10}$$ m. The value of $$x$$ is ______.
[Given $$hc = 1242$$ eV nm]

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NTA JEE Main 27th June 2022 Shift 1 - Question 30

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The height of a transmitting antenna at the top of a tower is $$25$$ m and that of receiving antenna is, $$49$$ m. The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is $$K\sqrt{5} \times 10^2$$ m. The value of $$K$$ is ______.
(Assume radius of Earth is $$64 \times 10^5$$ m) [Calculate upto nearest integer value]

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NTA JEE Main 27th June 2022 Shift 1 - Question 31

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Given below are two statements : one is labelled as Assertion and the other is labelled as Reason.
Assertion: The ionic radii of $$O^{2-}$$ and $$Mg^{2+}$$ are same.
Reason: Both $$O^{2-}$$ and $$Mg^{2+}$$ are isoelectronic species.

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.

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NTA JEE Main 27th June 2022 Shift 1 - Question 32

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Based upon VSEPR theory, match the shape (geometry) of the molecules in List-I with the molecules in List-II

List-I (Shape)	List-II (Molecules)
A T-shaped	I. $$XeF_4$$
B Trigonal planar	II. $$SF_4$$
C Square planar	III. $$ClF_3$$
D See-saw	IV. $$BF_3$$

A

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

B

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

C

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

D

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

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NTA JEE Main 27th June 2022 Shift 1 - Question 33

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Match List - I with List - II.

List-I	List-II
(A) Spontaneous process	(I) $$\Delta H < 0$$
(B) Process with $$\Delta P = 0, \Delta T = 0$$	(II) $$\Delta G_{T,P} < 0$$
(C) $$\Delta H_{reaction}$$	(III) Isothermal and isobaric process
(D) Exothermic Process	(IV) [Bond energies in reactants] - [Bond energies in products]

Choose the correct answer from the options given below

A

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

B

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

C

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

D

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

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NTA JEE Main 27th June 2022 Shift 1 - Question 34

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Addition of $$H_2SO_4$$ to $$BaO_2$$ produces

A

BaO, $$SO_2$$ and $$H_2O$$

B

$$BaHSO_4$$ and $$O_2$$

C

$$BaSO_4, H_2$$ and $$O_2$$

D

$$BaSO_4$$ and $$H_2O_2$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 35

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$$BeCl_2$$ reacts with $$LiAlH_4$$ to give

A

$$Be + Li[AlCl_4] + H_2$$

B

$$Be + AlH_3 + LiCl + HCl$$

C

$$BeH_2 + LiCl + AlCl_3$$

D

$$BeH_2 + Li[AlCl_4]$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 36

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Match List - I with List - II.

List-I (Si-Compounds)	List-II (Si-Polymeric/Other Products)
A $$(CH_3)_4Si$$	I Chain Silicone
B $$(CH_3)Si(OH)_3$$	II Dimeric Silicone
C $$(CH_3)_2Si(OH)_2$$	III Silane
D $$(CH_3)_3Si(OH)$$	IV 2D-Silicone

Choose the correct answer from the options given below

A

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

B

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

C

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

D

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

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NTA JEE Main 27th June 2022 Shift 1 - Question 37

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L-isomer of a compound 'A'($$C_4H_8O_4$$) gives a positive test with $$[Ag(NH_3)_2]^+$$. Treatment of 'A' with acetic anhydride yields triacetate derivative. Compound 'A' produces an optically active compound (B) and an optically inactive compound (C) on treatment with bromine water and $$HNO_3$$ respectively. Compound (A) is :

A

B

C

D

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NTA JEE Main 27th June 2022 Shift 1 - Question 38

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Given below are two Statements :
Statement I : Classical smog occurs in cool humid climate. It is a reducing mixture of smoke, fog and sulphur dioxide.
Statement II : Photochemical smog has components, ozone, nitric oxide, acrolein, formaldehyde, PAN etc.
In the light of the above statements, choose the most appropriate answer from the options given below.

A

Both Statement I and Statement II are correct.

B

Both Statement I and Statement II are incorrect.

C

Statement I is incorrect but Statement II is correct.

D

Statement I is correct but Statement II is incorrect.

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NTA JEE Main 27th June 2022 Shift 1 - Question 39

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Given below are two statements : one is labelled as Assertion and the other is labelled as Reason.
Assertion: At $$10°$$C, the density of a $$5$$ M solution of KCl [atomic masses of K & Cl are $$39$$ & $$35.5$$ g mol$$^{-1}$$ respectively], is 'x' g mL$$^{-1}$$. The solution is cooled to $$-21°$$C. The molality of the solution will remain unchanged.
Reason: The molality of a solution does not change with temperature as mass remains unaffected with temperature.
In the light of the above statements, choose the most appropriate answer from the options given below.

A

Assertion is true but Reason is false.

B

Assertion is false but Reason is true.

C

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

D

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

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NTA JEE Main 27th June 2022 Shift 1 - Question 40

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Match List - I with List - II.

List-I	List-II
A Lyophilic colloid	I Liquid-liquid colloid
B Emulsion	II Protective colloid
C Positively charged colloid	III $$FeCl_3 + NaOH$$
D Negatively charged colloid	IV $$FeCl_3$$ + hot water

Choose the correct answer from the options given below

A

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

B

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

C

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

D

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

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NTA JEE Main 27th June 2022 Shift 1 - Question 41

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Match List - I with List - II.

List-I	List-II
A Concentration of gold ore	I Aniline
B Leaching of alumina	II NaOH
C Froth stabiliser	III $$SO_2$$
D Blister copper	IV NaCN

Choose the correct answer from the options given below

A

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

B

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

C

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

D

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

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NTA JEE Main 27th June 2022 Shift 1 - Question 42

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Heating white phosphorus with conc. NaOH solution gives mainly

A

$$Na_3P$$ and $$H_2O$$

B

$$H_3PO$$ and NaH

C

$$P(OH)_3$$ and $$NaH_2PO_4$$

D

$$PH_3$$ and $$NaH_2PO_2$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 43

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Which of the following will have maximum stabilization due to crystal field?

A

$$[Ti(H_2O)_6]^{3+}$$

B

$$[Co(H_2O)_6]^{2+}$$

C

$$[Co(CN)_6]^{3-}$$

D

$$[Cu(NH_3)_4]^{2+}$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 44

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The major product of the following reaction is

A

B

C

D

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NTA JEE Main 27th June 2022 Shift 1 - Question 45

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Which of the following reactions will yield benzaldehyde as a product?

A

B & C

B

C & D

C

A & D

D

A & C

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NTA JEE Main 27th June 2022 Shift 1 - Question 46

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'A' and 'B' respectively are
A $$\xrightarrow[(2) Zn-H_2O]{(1) O_3 \atop}$$ Ethane-1,2-dicarbaldehyde + Glyoxal/Oxaldehyde
B $$\xrightarrow[(2) Zn-H_2O]{(1) O_3 \atop}$$ 5-oxohexanal

A

1-methylcyclohex-1,3-diene & cyclopentene

B

Cyclohex-1,3-diene & cyclopentene

C

Cyclohex-1,3-diene & 1-methylcyclopent-1-ene

D

1-methylcyclohex-1,4-diene & 1-methylcyclopent-1-ene

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NTA JEE Main 27th June 2022 Shift 1 - Question 47

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Given below are two statements :
Statement - I : In Hofmann degradation reaction, the migration of only an alkyl group takes place from carbonyl carbon of the amide to the nitrogen atom.
Statement - II : The group is migrated in Hofmann degradation reaction to electron deficient atom.
In the light of the above statements, choose the most appropriate answer from the options given below

A

Both Statement I and Statement II are correct.

B

Both Statement I and Statement II are incorrect.

C

Statement I is correct but Statement II is incorrect.

D

Statement I is incorrect but Statement II is correct.

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NTA JEE Main 27th June 2022 Shift 1 - Question 48

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Match List - I with List - II.

List-I (Polymer)	List-II (Used in)
A Bakelite	I Radio and television cabinets
B Glyptal	II Electrical switches
C PVC	III Paints and Lacquers
D Polystyrene	IV Water pipes

A

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

B

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

C

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

D

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

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NTA JEE Main 27th June 2022 Shift 1 - Question 49

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Match List - I with List - II.

Choose the correct answer from the options given below

A

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

B

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

C

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

D

A-(II), B-(IV), C-(I), D-(II)

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NTA JEE Main 27th June 2022 Shift 1 - Question 50

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Which of the following is structure of a separating funnel?

A

B

C

D

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NTA JEE Main 27th June 2022 Shift 1 - Question 51

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If the uncertainty in velocity and position of a minute particle in space are, $$2.4 \times 10^{-26}$$ (ms$$^{-1}$$) and $$10^{-7}$$ (m) respectively. The mass of the particle in g is ______ (Nearest integer)
(Given : $$h = 6.626 \times 10^{-34}$$ Js)

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NTA JEE Main 27th June 2022 Shift 1 - Question 52

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$$2NOCl(g) \rightleftharpoons 2NO(g) + Cl_2(g)$$
In an experiment, $$2.0$$ moles of NOCl was placed in a one-litre flask and the concentration of NO after equilibrium established, was found to be $$0.4$$ mol/L. The equilibrium constant at $$30°$$C is ______ $$\times 10^{-4}$$.

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NTA JEE Main 27th June 2022 Shift 1 - Question 53

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Total number of possible stereoisomers of dimethyl cyclopentane is ______

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NTA JEE Main 27th June 2022 Shift 1 - Question 54

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Metal deficiency defect is shown by $$Fe_{0.93}O$$. In the crystal, some $$Fe^{2+}$$ cations are missing and loss of positive charge is compensated by the presence of $$Fe^{3+}$$ ions. The percentage of $$Fe^{2+}$$ ions in the $$Fe_{0.93}O$$ crystals is ______ (Nearest integer)

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NTA JEE Main 27th June 2022 Shift 1 - Question 55

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Two elements A and B which form $$0.15$$ moles of $$A_2B$$ and $$AB_3$$ type compounds. If both $$A_2B$$ and $$AB_3$$ weigh equally, then the atomic weight of A is ______ times of atomic weight of B.

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NTA JEE Main 27th June 2022 Shift 1 - Question 56

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$$2$$ g of a non-volatile non-electrolyte solute is dissolved in $$200$$ g of two different solvents A and B whose ebullioscopic constants are in the ratio of $$1 : 8$$. The elevation in boiling points of A and B are in the ratio $$\frac{x}{y}$$ ($$x : y$$). The value of $$y$$ is ______ (Nearest Integer)

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NTA JEE Main 27th June 2022 Shift 1 - Question 57

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The limiting molar conductivities of NaI, $$NaNO_3$$ and $$AgNO_3$$ are $$12.7, 12.0$$ and $$13.3$$ mS m$$^2$$ mol$$^{-1}$$, respectively (all at $$25°$$C). The limiting molar conductivity of AgI at this temperature is ______ mS m$$^2$$ mol$$^{-1}$$.

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NTA JEE Main 27th June 2022 Shift 1 - Question 58

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The rate constant for a first order reaction is given by the following equation :
$$\ln k = 33.24 - \frac{2.0 \times 10^4 K}{T}$$
The Activation energy for the reaction is given by ______ kJ mol$$^{-1}$$. (In Nearest integer) (Given : $$R = 8.3$$ J K$$^{-1}$$ mol$$^{-1}$$)

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NTA JEE Main 27th June 2022 Shift 1 - Question 59

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The number of statement(s) correct from the following for Copper is/are
(A) Cu(II) complexes are always paramagnetic
(B) Cu(I) complexes are generally colourless
(C) Cu(I) is easily oxidized
(D) In Fehling solution, the active reagent has Cu(I)

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NTA JEE Main 27th June 2022 Shift 1 - Question 60

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Acidified potassium permanganate solution oxidises oxalic acid. The spin-only magnetic moment of the mangenese product formed from the above reaction is ______ B.M. (Nearest Integer)

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NTA JEE Main 27th June 2022 Shift 1 - Question 61

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The area of the polygon, whose vertices are the non-real roots of the equation $$\bar{z} = iz^2$$ is

A

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

B

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

C

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

D

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

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NTA JEE Main 27th June 2022 Shift 1 - Question 62

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If $$x = \sum_{n=0}^{\infty} a^n, y = \sum_{n=0}^{\infty} b^n, z = \sum_{n=0}^{\infty} c^n$$, where $$a, b, c$$ are in A.P. and $$|a| < 1, |b| < 1, |c| < 1, abc \neq 0$$, then

A

$$x, y, z$$ are in A.P.

B

$$\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$$ are in A.P.

C

$$x, y, z$$ are in G.P.

D

$$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 1 - (a+b+c)$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 63

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The value of $$\cos\left(\frac{2\pi}{7}\right) + \cos\left(\frac{4\pi}{7}\right) + \cos\left(\frac{6\pi}{7}\right)$$ is equal to

A

$$-1$$

B

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

C

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

D

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

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NTA JEE Main 27th June 2022 Shift 1 - Question 64

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In an isosceles triangle $$ABC$$, the vertex $$A$$ is $$(6, 1)$$ and the equation of the base $$BC$$ is $$2x + y = 4$$. Let the point $$B$$ lie on the line $$x + 3y = 7$$. If $$(\alpha, \beta)$$ is the centroid of $$\triangle ABC$$, then $$15(\alpha + \beta)$$ is equal to

A

$$51$$

B

$$39$$

C

$$41$$

D

$$49$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 65

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Let the eccentricity of an ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, a > b$$, be $$\frac{1}{4}$$. If this ellipse passes through the point $$\left(-4\sqrt{\frac{2}{5}}, 3\right)$$, then $$a^2 + b^2$$ is equal to

A

$$29$$

B

$$31$$

C

$$32$$

D

$$34$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 66

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Let $$a$$ be an integer such that $$\lim_{x \to 7} \frac{18 - [1-x]}{[x-3a]}$$ exists, where $$[t]$$ is greatest integer $$\leq t$$. Then $$a$$ is equal to

A

$$-2$$

B

$$6$$

C

$$-6$$

D

$$-7$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 67

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The boolean expression $$(\sim(p \wedge q)) \vee q$$ is equivalent to

A

$$q \to (p \wedge q)$$

B

$$p \to q$$

C

$$p \to (p \to q)$$

D

$$p \to (p \vee q)$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 68

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Let the system of linear equations $$x + 2y + z = 2, \alpha x + 3y - z = \alpha, -\alpha x + y + 2z = -\alpha$$ be inconsistent. Then $$\alpha$$ is equal to

A

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

B

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

C

$$\frac{7}{2}$$

D

$$-\frac{7}{2}$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 69

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$$\sin^{-1}\left(\sin\frac{2\pi}{3}\right) + \cos^{-1}\left(\cos\frac{7\pi}{6}\right) + \tan^{-1}\left(\tan\frac{3\pi}{4}\right)$$ is equal to

A

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

B

$$\frac{17\pi}{12}$$

C

$$\frac{31\pi}{12}$$

D

$$-\frac{3\pi}{4}$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 70

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If $$\cos^{-1}\left(\frac{y}{2}\right) = \log_e\left(\frac{x}{5}\right)^5, |y| < 2$$, then

A

$$x^2y'' + xy' - 25y = 0$$

B

$$x^2y'' - xy' - 25y = 0$$

C

$$x^2y'' - xy' + 25y = 0$$

D

$$x^2y'' + xy' + 25y = 0$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 71

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The number of distinct real roots of $$x^4 - 4x + 1 = 0$$ is

A

$$0$$

B

$$1$$

C

$$2$$

D

$$4$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 72

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The lengths of the sides of a triangle are $$10 + x^2, 10 + x^2$$ and $$20 - 2x^2$$. If for $$x = k$$, the area of the triangle is maximum, then $$3k^2$$ is equal to

A

$$5$$

B

$$12$$

C

$$10$$

D

$$20$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 73

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$$\int \frac{(x^2+1)e^x}{(x+1)^2} dx = f(x)e^x + C$$, where $$C$$ is a constant, then $$\frac{d^3f}{dx^3}$$ at $$x = 1$$ is equal to

A

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

B

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

C

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

D

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

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NTA JEE Main 27th June 2022 Shift 1 - Question 74

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The value of the integral $$\int_{-2}^{2} \frac{|x^3+x|}{(e^{x|x|}+1)} dx$$ is equal to

A

$$5e^2$$

B

$$3e^{-2}$$

C

$$4$$

D

$$6$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 75

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Let $$\frac{dy}{dx} = \frac{ax - by + a}{bx + cy + a}$$, where $$a, b, c$$ are constants, represent a circle passing through the point $$(2, 5)$$. Then the shortest distance of the point $$(11, 6)$$ from this circle is

A

$$10$$

B

$$8$$

C

$$7$$

D

$$5$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 76

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If $$\frac{dy}{dx} + \frac{2^{x-y}(2^y-1)}{2^x - 1} = 0, x, y > 0, y(1) = 1$$, then $$y(2)$$ is equal to

A

$$2 + \log_2 3$$

B

$$2 + \log_2 2$$

C

$$2 - \log_2 3$$

D

$$2 - \log_{-2} 3$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 77

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Let $$\vec{a} = \hat{i} + \hat{j} - \hat{k}$$ and $$\vec{c} = 2\hat{i} - 3\hat{j} + 2\hat{k}$$. Then the number of vectors $$\vec{b}$$ such that $$\vec{b} \times \vec{c} = \vec{a}$$ and $$|\vec{b}| \in \{1, 2, \ldots, 10\}$$ is

A

$$0$$

B

$$1$$

C

$$2$$

D

$$3$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 78

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If two straight lines whose direction cosines are given by the relations $$l + m - n = 0, 3l^2 + m^2 + cnl = 0$$ are parallel, then the positive value of $$c$$ is

A

$$6$$

B

$$4$$

C

$$3$$

D

$$2$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 79

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Five numbers $$x_1, x_2, x_3, x_4, x_5$$ are randomly selected from the numbers $$1, 2, 3, \ldots, 18$$ and are arranged in the increasing order $$(x_1 < x_2 < x_3 < x_4 < x_5)$$. The probability that $$x_2 = 7$$ and $$x_4 = 11$$ is

A

$$\frac{1}{136}$$

B

$$\frac{1}{68}$$

C

$$\frac{7}{68}$$

D

$$\frac{5}{68}$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 80

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Let $$X$$ be a random variable having binomial distribution $$B(7, p)$$. If $$P(X = 3) = 5P(X = 4)$$, then the sum of the mean and the variance of $$X$$ is

A

$$\frac{105}{16}$$

B

$$\frac{77}{36}$$

C

$$\frac{31}{36}$$

D

$$\frac{35}{36}$$

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NTA JEE Main 27th June 2022 Shift 1 - Question 81

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The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is ______

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NTA JEE Main 27th June 2022 Shift 1 - Question 82

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If the sum of the first ten terms of the series $$\frac{1}{5} + \frac{2}{65} + \frac{3}{325} + \frac{4}{1025} + \frac{5}{2501} + \ldots$$ is $$\frac{m}{n}$$, where $$m$$ and $$n$$ are co-prime numbers, then $$m + n$$ is equal to ______

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NTA JEE Main 27th June 2022 Shift 1 - Question 83

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If the coefficient of $$x^{10}$$ in the binomial expansion of $$\left(\frac{\sqrt{x}}{5^{1/4}} + \frac{\sqrt{5}}{x^{1/3}}\right)^{60}$$ is $$5^k l$$, where $$l, k \in N$$ and $$l$$ is coprime to $$5$$, then $$k$$ is equal to ______

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NTA JEE Main 27th June 2022 Shift 1 - Question 84

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A rectangle $$R$$ with end points of the one of its sides as $$(1, 2)$$ and $$(3, 6)$$ is inscribed in a circle. If the equation of a diameter of the circle is $$2x - y + 4 = 0$$, then the area of $$R$$ is ______

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NTA JEE Main 27th June 2022 Shift 1 - Question 85

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A circle of radius $$2$$ unit passes through the vertex and the focus of the parabola $$y^2 = 2x$$ and touches the parabola $$y = \left(x - \frac{1}{4}\right)^2 + \alpha$$, where $$\alpha > 0$$. Then $$(4\alpha - 8)^2$$ is equal to ______

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NTA JEE Main 27th June 2022 Shift 1 - Question 86

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The positive value of the determinant of the matrix $$A$$, whose $$Adj(Adj(A)) = \begin{bmatrix} 14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14 \end{bmatrix}$$, is ______

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NTA JEE Main 27th June 2022 Shift 1 - Question 87

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Let $$f : R \to R$$ be a function defined $$f(x) = \frac{2e^{2x}}{e^{2x}+e}$$. Then $$f\left(\frac{1}{100}\right) + f\left(\frac{2}{100}\right) + f\left(\frac{3}{100}\right) + \ldots + f\left(\frac{99}{100}\right)$$ is equal to ______

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NTA JEE Main 27th June 2022 Shift 1 - Question 88

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If the sum of all the roots of the equation $$e^{2x} - 11e^x - 45e^{-x} + \frac{81}{2} = 0$$ is $$\log_e P$$, then $$P$$ is equal to ______

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NTA JEE Main 27th June 2022 Shift 1 - Question 89

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Let $$A_1 = \{(x,y) : |x| \leq y^2, |x| + 2y \leq 8\}$$ and $$A_2 = \{(x,y) : |x| + |y| \leq k\}$$. If $$27$$ (Area $$A_1$$) $$= 5$$ (Area $$A_2$$), then $$k$$ is equal to ______

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NTA JEE Main 27th June 2022 Shift 1 - Question 90

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Let the mirror image of the point $$(a, b, c)$$ with respect to the plane $$3x - 4y + 12z + 19 = 0$$ be $$(a - 6, \beta, \gamma)$$. If $$a + b + c = 5$$, then $$7\beta - 9\gamma$$ is equal to ______

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