NTA JEE Main 29th June 2022 Shift 2

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NTA JEE Main 29th June 2022 Shift 2 - Question 3

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below. The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of block is: (Given $$g = 10$$ m s$$^{-2}$$.)

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NTA JEE Main 29th June 2022 Shift 2 - Question 4

A block of mass $$M$$ placed inside a box descends vertically with acceleration $$a$$. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of '$$a$$' will be

NTA JEE Main 29th June 2022 Shift 2 - Question 6

The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be

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NTA JEE Main 29th June 2022 Shift 2 - Question 7

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both the diameters have been measured at room temperature (27°C).
(Given: coefficient of linear thermal expansion of gold $$\alpha_L = 1.4 \times 10^{-5}$$ K$$^{-1}$$)

NTA JEE Main 29th June 2022 Shift 2 - Question 8

Starting with the same initial conditions, an ideal gas expands from volume $$V_1$$ to $$V_2$$ in three different ways. The work done by the gas is $$W_1$$ if the process is purely isothermal, $$W_2$$, if the process is purely adiabatic and $$W_3$$ if the process is purely isobaric. Then, choose the correct option

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NTA JEE Main 29th June 2022 Shift 2 - Question 11

Two point charges $$Q$$ each are placed at a distance $$d$$ apart. A third point charge $$q$$ is placed at a distance $$x$$ from mid-point on the perpendicular bisector. The value of $$x$$ at which charge $$q$$ will experience the maximum Coulomb's force is:

NTA JEE Main 29th June 2022 Shift 2 - Question 12

If the electric potential at any point $$(x, y, z)$$ m in space is given by $$V = 3x^2$$ volt. The electric field at the point $$(1, 0, 3)$$ m will be:

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NTA JEE Main 29th June 2022 Shift 2 - Question 13

A capacitor is discharging through a resistor $$R$$. Consider in time $$t_1$$, the energy stored in the capacitor reduces to half of its initial value and in time $$t_2$$, the charge stored reduces to one eighth of its initial value. The ratio $$\frac{t_1}{t_2}$$ will be

NTA JEE Main 29th June 2022 Shift 2 - Question 14

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of 2 $$\Omega$$. The value of internal resistance of each cell is

NTA JEE Main 29th June 2022 Shift 2 - Question 15

Two long current carrying conductors are placed parallel to each other at a distance of 8 cm between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is 300 $$\mu$$T. The equal current flowing in the two conductors is:

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NTA JEE Main 29th June 2022 Shift 2 - Question 16

Given below are two statements:
Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.
Statement II: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.
In the light of the above statements, choose the most appropriate answer from the options below:

NTA JEE Main 29th June 2022 Shift 2 - Question 17

The speed of light in media 'A' and 'B' are $$2.0 \times 10^{10}$$ cm s$$^{-1}$$ and $$1.5 \times 10^{10}$$ cm s$$^{-1}$$ respectively. A ray of light enters from the medium $$B$$ to $$A$$ at an incident angle $$\theta$$. If the ray suffers total internal reflection, then

NTA JEE Main 29th June 2022 Shift 2 - Question 18

The electric field at a point associated with a light wave is given by
$$E = 200\left[\sin(6 \times 10^{15})t + \sin(9 \times 10^{15})t\right]$$ Vm$$^{-1}$$
Given: $$h = 4.14 \times 10^{-15}$$ eVs
If this light falls on a metal surface having a work function of 2.50 eV, the maximum kinetic energy of the photoelectrons will be

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NTA JEE Main 29th June 2022 Shift 2 - Question 19

In the following nuclear reaction,
$$D \xrightarrow{\alpha} D_1 \xrightarrow{\beta} D_2 \xrightarrow{\alpha} D_3 \xrightarrow{\gamma} D_4$$
Mass number of $$D$$ is 182 and atomic number is 74. Mass number and atomic number of $$D_4$$ respectively will be

NTA JEE Main 29th June 2022 Shift 2 - Question 21

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is $$I_1$$. The same rod is bent into a ring and its moment of inertia about a diameter is $$I_2$$. If $$\frac{I_1}{I_2}$$ is $$\frac{x\pi^2}{3}$$, then the value of $$x$$ will be ______.

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NTA JEE Main 29th June 2022 Shift 2 - Question 22

A small spherical ball of radius 0.1 mm and density $$10^4$$ kg m$$^{-3}$$ falls freely under gravity through a distance $$h$$ before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of $$h$$ will be ______ m. (Given $$g = 10$$ m s$$^{-2}$$, viscosity of water $$= 1.0 \times 10^{-5}$$ N-s m$$^{-2}$$).

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NTA JEE Main 29th June 2022 Shift 2 - Question 23

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 m s$$^{-1}$$. The third resonance is observed when the air column has a length of ______ cm.

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NTA JEE Main 29th June 2022 Shift 2 - Question 24

The displacement current of 4.425 $$\mu$$A is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of $$10^6$$ V s$$^{-1}$$. The area of each plate of the capacitor is 40 cm$$^2$$. The distance between each plate of the capacitor is $$x \times 10^{-3}$$ m. The value of $$x$$ is,
(Permittivity of free space, $$\varepsilon_0 = 8.85 \times 10^{-12}$$ C$$^2$$ N$$^{-1}$$ m$$^{-2}$$)

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

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 $$\Omega$$ is used to measure the potential difference across 500 $$\Omega$$ resister, the reading of the voltmeter will be ______ V.

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NTA JEE Main 29th June 2022 Shift 2 - Question 26

An inductor of 0.5 mH, a capacitor of 200 $$\mu$$F and a resistor of 2 $$\Omega$$ are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______ $$\times 10^2$$ Hz.

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NTA JEE Main 29th June 2022 Shift 2 - Question 27

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by $$5 \times 10^{-2}$$ m towards the slits, the change in fringe width is $$3 \times 10^{-3}$$ cm. If the distance between the slits is 1 mm, then the wavelength of the light will be ______ nm.

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

A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the $$n$$-side with a speed of $$6.0 \times 10^5$$ m s$$^{-1}$$. The speed with which electron enters the $$p$$ side will be $$\frac{x}{3} \times 10^5$$ m s$$^{-1}$$, then the value of $$x$$ is ______.: (Given mass of electron $$= 9 \times 10^{-31}$$ kg, charge on electron $$= 1.6 \times 10^{-19}$$ C.)

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NTA JEE Main 29th June 2022 Shift 2 - Question 30

The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of ($$-$$0.05 cm). While measuring diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The corrected diameter will be ______ $$\times 10^{-2}$$ cm.

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NTA JEE Main 29th June 2022 Shift 2 - Question 33

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The first ionization enthalpy for oxygen is lower than that of nitrogen.
Reason R: The four electrons in 2p orbitals of oxygen experience more electron-electron repulsion.
In the light of the above statements, choose the correct answer from the options given below.

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NTA JEE Main 29th June 2022 Shift 2 - Question 34

Consider the species CH$$_4$$, NH$$_4^+$$ and BH$$_4^-$$. Choose the correct option with respect to the three species:

NTA JEE Main 29th June 2022 Shift 2 - Question 36

4.0 moles of argon and 5.0 moles of PCl$$_5$$ are introduced into an evacuated flask of 100 litre capacity at 610 K. The system is allowed to equilibrate. At equilibrium, the total pressure of mixture was found to be 6.0 atm. The K$$_p$$ for the reaction is [Given: R = 0.082 L atm K$$^{-1}$$ mol$$^{-1}$$]

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NTA JEE Main 29th June 2022 Shift 2 - Question 40

Sulphur dioxide is one of the components of polluted air. SO$$_2$$ is also a major contributor to acid rain. The correct and complete reaction to represent acid rain caused by SO$$_2$$ is:

NTA JEE Main 29th June 2022 Shift 2 - Question 41

42.12% (w/v) solution of NaCl causes precipitation of a certain sol in 10 hours. The coagulating value of NaCl for the sol is
[Given: Molar mass: Na = 23.0 g mol$$^{-1}$$; Cl = 35.5 g mol$$^{-1}$$]

NTA JEE Main 29th June 2022 Shift 2 - Question 42

Match List I with List II.
List I With Ore       List II Composition
(A) Siderite             (I) FeCO$$_3$$
(B) Malachite         (II) CuCO$$_3$$ · Cu(OH)$$_2$$
(C) Sphalerite         (III) ZnS
(D) Calamine          (IV) ZnCO$$_3$$
Choose the correct answer from the options given below:

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NTA JEE Main 29th June 2022 Shift 2 - Question 43

Given below are two statements.
Statement I: In CuSO$$_4$$ · 5H$$_2$$O, Cu - O bonds are present.
Statement II: In CuSO$$_4$$ · 5H$$_2$$O, ligands coordinating with Cu (II) ion are O-and S-based ligands.
In the light of the above statements, choose the correct answer from the options given below

NTA JEE Main 29th June 2022 Shift 2 - Question 45

Two isomers (A) and (B) with Molar mass 184 g/mol and elemental composition C, 52.2%; H, 49% and Br 42.9% gave benzoic acid and p-bromobenzoic acid, respectively on oxidation with KMnO$$_4$$. Isomer 'A' is optically active and gives a pale yellow precipitate when warmed with alcoholic AgNO$$_3$$. Isomer 'A' and 'B' are, respectively:

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NTA JEE Main 29th June 2022 Shift 2 - Question 47

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Dacron is an example of polyester polymer.
Reason R: Dacron is made up of ethylene glycol and terephthalic acid monomers.
In the light of the above statements, choose the most appropriate answer from the options given below.

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NTA JEE Main 29th June 2022 Shift 2 - Question 49

A white precipitate was formed when BaCl$$_2$$ was added to water extract of an inorganic salt. Further, a gas 'X' with characteristic odour was released when the formed white precipitate was dissolved in dilute HCI. The anion present in the inorganic salt is:

NTA JEE Main 29th June 2022 Shift 2 - Question 51

A box contains 0.90 g of liquid water in equilibrium with water vapour at 27°C. The equilibrium vapour pressure of water at 27°C 32.0 Torr. When the volume of the box is increased, some of the liquid water evaporates to maintain the equilibrium pressure. If all the liquid water evaporates, then the volume of the box must be ______ litre. [nearest integer]
(Given: R = 0.082 L atm K$$^{-1}$$ mol$$^{-1}$$)
(Ignore the volume of the liquid water and assume water vapours behave as an ideal gas.)

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NTA JEE Main 29th June 2022 Shift 2 - Question 52

2.2 g of nitrous oxide (N$$_2$$O) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression of the gas from 217.1 mL to 167.75 mL. The change in internal energy of the process, $$\Delta$$U is '-x'J. The value of 'x' is ______.
[nearest integer]
(Given: atomic mass of N = 14 g mol$$^{-1}$$ and of O = 16 g mol$$^{-1}$$. Molar heat capacity of N$$_2$$O is 100 JK$$^{-1}$$ mol$$^{-1}$$)

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NTA JEE Main 29th June 2022 Shift 2 - Question 55

Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The depression in freezing point for 4.5 molal solution of glucose in water is 4 K. The ratio of molal elevation constant to molal depression constant (K$$_b$$/K$$_f$$) is

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NTA JEE Main 29th June 2022 Shift 2 - Question 56

The cell potential for the given cell at 298 K Pt|H$$_2$$(g, 1 bar)|H$$^+$$(aq)||Cu$$^{2+}$$(aq)|Cu(s) is 0.31 V. The pH of the acidic solution is found to be 3, whereas the concentration of Cu$$^{2+}$$ is $$10^x$$ M. The value of x is ______.
(Given: $$E^\ominus_{Cu^{2+}/Cu} = 0.34$$ V and $$\frac{2.303RT}{F} = 0.06$$ V)

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NTA JEE Main 29th June 2022 Shift 2 - Question 57

The equation $$k = (6.5 \times 10^{12} s^{-1})e^{-26000 K/T}$$ is followed for the decomposition of compound A. The activation energy for the reaction is ______ KJ mol$$^{-1}$$. [nearest integer]
(Given: R = 8.314 J K$$^{-1}$$ mol$$^{-1}$$)

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NTA JEE Main 29th June 2022 Shift 2 - Question 62

Let $$(z)$$ represent the principal argument of the complex number $$z$$. The, $$|z| = 3$$ and $$\arg(z-1) - \arg(z+1) = \frac{\pi}{4}$$ intersect:

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NTA JEE Main 29th June 2022 Shift 2 - Question 64

Let $$n \geq 5$$ be an integer. If $$9^n - 8n - 1 = 64\alpha$$ and $$6^n - 5n - 1 = 25\beta$$, then $$\alpha - \beta$$ is equal to:

NTA JEE Main 29th June 2022 Shift 2 - Question 65

The distance of the origin from the centroid of the triangle whose two sides have the equations $$x - 2y + 1 = 0$$ and $$2x - y - 1 = 0$$ and whose orthocenter is $$\left(\frac{7}{3}, \frac{7}{3}\right)$$ is:

NTA JEE Main 29th June 2022 Shift 2 - Question 66

Let a triangle $$ABC$$ be inscribed in the circle $$x^2 - \sqrt{2}(x+y) + y^2 = 0$$ such that $$\angle BAC = \frac{\pi}{2}$$. If the length of side $$AB$$ is $$\sqrt{2}$$, then the area of the $$\triangle ABC$$ is equal to:

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NTA JEE Main 29th June 2022 Shift 2 - Question 67

Let $$P : y^2 = 4ax$$, $$a > 0$$ be a parabola with focus $$S$$. Let the tangents to the parabola $$P$$ make an angle of $$\frac{\pi}{4}$$ with the line $$y = 3x + 5$$ touch the parabola $$P$$ at $$A$$ and $$B$$. Then the value of $$a$$ for which $$A$$, $$B$$ and $$S$$ are collinear is:

NTA JEE Main 29th June 2022 Shift 2 - Question 69

Negation of the Boolean statement $$(p \vee q) \Rightarrow ((\sim r) \vee p)$$ is equivalent to:

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NTA JEE Main 29th June 2022 Shift 2 - Question 71

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is:

NTA JEE Main 29th June 2022 Shift 2 - Question 72

Let $$A = \begin{pmatrix} 2 & -1 \\ 0 & 2 \end{pmatrix}$$. If $$B = I - {}^5C_1(\text{adj } A) + {}^5C_2(\text{adj } A)^2 - \ldots - {}^5C_5(\text{adj } A)^5$$, then the sum of all elements of the matrix $$B$$ is:

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NTA JEE Main 29th June 2022 Shift 2 - Question 73

Let $$f : R \to R$$ be a function defined by $$f(x) = (x-3)^{n_1}(x-5)^{n_2}$$, $$n_1, n_2 \in N$$. The, which of the following is NOT true?

NTA JEE Main 29th June 2022 Shift 2 - Question 74

Let $$f$$ be a real valued continuous function on $$[0, 1]$$ and $$f(x) = x + \int_0^1 (x-t)f(t)dt$$. Then which of the following points $$(x, y)$$ lies on the curve $$y = f(x)$$?

NTA JEE Main 29th June 2022 Shift 2 - Question 75

If $$\int_0^2 \left(\sqrt{2x} - \sqrt{2x - x^2}\right)dx = \int_0^1 \left(1 - \sqrt{1-y^2}-\frac{y^2}{2}\right)dy + \int_1^2 \left(2 - \frac{y^2}{2}\right)dy + I$$, then $$I$$ equal to

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NTA JEE Main 29th June 2022 Shift 2 - Question 76

If $$y = y(x)$$ is the solution of the differential equation $$(1+e^{2x})\frac{dy}{dx} + 2(1+y^2)e^x = 0$$ and $$y(0) = 0$$, then $$6\left(y'(0) + \left(y\left(\log_e \sqrt{3}\right)\right)^2\right)$$ is equal to:

NTA JEE Main 29th June 2022 Shift 2 - Question 77

Let $$A$$, $$B$$, $$C$$ be three points whose position vectors respectively are:
$$\vec{a} = \hat{i} + 4\hat{j} + 3\hat{k}$$
$$\vec{b} = 2\hat{i} + \alpha\hat{j} + 4\hat{k}$$, $$\alpha \in R$$
$$\vec{c} = 3\hat{i} - 2\hat{j} + 5\hat{k}$$
If $$\alpha$$ is the smallest positive integer for which $$\vec{a}$$, $$\vec{b}$$, $$\vec{c}$$ are non-collinear, then the length of the median, through $$A$$, of $$\triangle ABC$$ is:

NTA JEE Main 29th June 2022 Shift 2 - Question 78

Let $$\frac{x-2}{3} = \frac{y+1}{-2} = \frac{z+3}{-1}$$ lie on the plane $$px - qy + z = 5$$, for some $$p, q \in R$$. The shortest distance of the plane from the origin is:

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NTA JEE Main 29th June 2022 Shift 2 - Question 79

Let $$Q$$ be the mirror image of the point $$P(1, 2, 1)$$ with respect to the plane $$x + 2y + 2z = 16$$. Let $$T$$ be a plane passing through the point $$Q$$ and contains the line $$\vec{r} = -\hat{k} + \lambda(\hat{i} + \hat{j} + 2\hat{k})$$, $$\lambda \in R$$. Then, which of the following points lies on $$T$$?

NTA JEE Main 29th June 2022 Shift 2 - Question 80

The probability that a relation $$R$$ from $$\{x, y\}$$ to $$\{x, y\}$$ is both symmetric and transitive, is equal to:

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NTA JEE Main 29th June 2022 Shift 2 - Question 83

Let the coefficients of $$x^{-1}$$ and $$x^{-3}$$ in the expansion of $$\left(2x^{1/5} - \frac{1}{x^{1/5}}\right)^{15}$$, $$x > 0$$, be $$m$$ and $$n$$ respectively. If $$r$$ is a positive integer such $$mn^2 = {}^{15}C_r \cdot 2^r$$, then the value of $$r$$ is equal to ______.

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NTA JEE Main 29th June 2022 Shift 2 - Question 85

Let $$M = \begin{bmatrix} 0 & -\alpha \\ \alpha & 0 \end{bmatrix}$$, where $$\alpha$$ is a non-zero real number and $$N = \sum_{k=1}^{49} M^{2k}$$. If $$(I - M^2)N = -2I$$, then the positive integral value of $$\alpha$$ is ______.

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NTA JEE Main 29th June 2022 Shift 2 - Question 87

Let $$f$$ and $$g$$ be twice differentiable even functions on $$(-2, 2)$$ such that $$f\left(\frac{1}{4}\right) = 0$$, $$f\left(\frac{1}{2}\right) = 0$$, $$f(1) = 1$$ and $$g\left(\frac{3}{4}\right) = 0$$, $$g(1) = 2$$. Then, the minimum number of solutions of $$f(x)g''(x) + f'(x)g'(x) = 0$$ in $$(-2, 2)$$ is equal to ______.

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NTA JEE Main 29th June 2022 Shift 2 - Question 88

For real numbers $$a$$, $$b$$ ($$a > b > 0$$), let
Area $$\{(x, y) : x^2 + y^2 \leq a^2$$ and $$\frac{x^2}{a^2} + \frac{y^2}{b^2} \geq 1\} = 30\pi$$
and
Area $$\{(x, y) : x^2 + y^2 \geq b^2$$ and $$\frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1\} = 18\pi$$
Then the value of $$(a-b)^2$$ is equal to ______.

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NTA JEE Main 29th June 2022 Shift 2 - Question 89

Let $$y = y(x)$$, $$x > 1$$, be the solution of the differential equation $$(x-1)\frac{dy}{dx} + 2xy = \frac{1}{x-1}$$, with $$y(2) = \frac{1+e^4}{2e^4}$$. If $$y(3) = \frac{e^{\alpha}+1}{\beta e^{\alpha}}$$, then the value of $$\alpha + \beta$$ is equal to ______.

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NTA JEE Main 29th June 2022 Shift 2 - Question 90

Let $$\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}$$, $$\vec{b} = \hat{i} + \hat{j} + \hat{k}$$ and $$\vec{c}$$ be a vector such that $$\vec{a}  \times (\vec{b}+ \vec{c}) = \vec{0}$$, then the value of $$3(\vec{c} \cdot \vec{a})$$ is equal to ______.

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