NTA JEE Main 26th June 2022 Shift 2

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

In the arrangement shown in figure $$a_1, a_2, a_3$$ and $$a_4$$ are the accelerations of masses $$m_1, m_2, m_3$$ and $$m_4$$ respectively. Which of the following relation is true for this arrangement?

NTA JEE Main 26th June 2022 Shift 2 - Question 3

Arrange the four graphs in descending order of total work done; where $$W_1, W_2, W_3$$ and $$W_4$$ are the work done corresponding to figure a, b, c and d respectively.

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NTA JEE Main 26th June 2022 Shift 2 - Question 4

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is

NTA JEE Main 26th June 2022 Shift 2 - Question 5

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.
Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below

NTA JEE Main 26th June 2022 Shift 2 - Question 6

If $$p$$ is the density and $$\eta$$ is coefficient of viscosity of fluid which flows with a speed $$v$$ in the pipe of diameter $$d$$, the correct formula for Reynolds number $$R_e$$ is

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NTA JEE Main 26th June 2022 Shift 2 - Question 8

For a specific wavelength $$670$$ nm of light coming from a galaxy moving with velocity $$v$$, the observed wavelength is $$670.7$$ nm. The value of $$v$$ is

NTA JEE Main 26th June 2022 Shift 2 - Question 9

Sixty four conducting drops each of radius $$0.02$$ m and each carrying a charge of $$5$$ $$\mu$$C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be

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NTA JEE Main 26th June 2022 Shift 2 - Question 11

A parallel plate capacitor with plate area $$A$$ and plate separation $$d = 2$$ m has a capacitance of $$4$$ $$\mu$$F. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant $$K = 3$$ (as shown in figure) will be

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NTA JEE Main 26th June 2022 Shift 2 - Question 13

A bar magnet having a magnetic moment of $$2.0 \times 10^5$$ J T$$^{-1}$$, is placed along the direction of uniform magnetic field of magnitude $$B = 14 \times 10^{-5}$$ T. The work done in rotating the magnet slowly through $$60°$$ from the direction of field is

NTA JEE Main 26th June 2022 Shift 2 - Question 14

A metal surface is illuminated by a radiation of wavelength $$4500$$ Å. The ejected photo-electron enters a constant magnetic field of $$2$$ mT making an angle of $$90°$$ with the magnetic field. If it starts revolving in a circular path of radius $$2$$ mm, the work function of the metal is approximately

NTA JEE Main 26th June 2022 Shift 2 - Question 15

Two coils of self inductance $$L_1$$ and $$L_2$$ are connected in series combination having mutual inductance of the coils as $$M$$. The equivalent self inductance of the combination will be

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NTA JEE Main 26th June 2022 Shift 2 - Question 16

A metallic conductor of length $$1$$ m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity $$5$$ rad s$$^{-1}$$. If the horizontal component of earth's magnetic field is $$0.2 \times 10^{-4}$$ T, then emf induced between the two ends of the conductor is

NTA JEE Main 26th June 2022 Shift 2 - Question 17

Which is the correct ascending order of wavelengths?

NTA JEE Main 26th June 2022 Shift 2 - Question 18

A radioactive nucleus can decay by two different processes. Half-life for the first process is $$3.0$$ hours while it is $$4.5$$ hours for the second process. The effective halflife of the nucleus will be

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NTA JEE Main 26th June 2022 Shift 2 - Question 19

The positive feedback is required by an amplifier to act as an oscillator. The feedback here means

NTA JEE Main 26th June 2022 Shift 2 - Question 21

A ball is projected vertically upward with an initial velocity of $$50$$ m s$$^{-1}$$ at $$t = 0$$ s. At $$t = 2$$ s, another ball is projected vertically upward with same velocity. At $$t =$$ ______ s, second ball will meet the first ball.
$$(g = 10$$ m s$$^{-2})$$

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NTA JEE Main 26th June 2022 Shift 2 - Question 22

A system to 10 balls each of mass $$2$$ kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $$7^{th}$$ and $$8^{th}$$ ball is ______ N when $$6^{th}$$ ball just leaves the table.

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NTA JEE Main 26th June 2022 Shift 2 - Question 24

A geyser heats water flowing at a rate of $$2.0$$ kg per minute from $$30°$$C to $$70°$$C. If geyser operates on a gas burner, the rate of combustion of fuel will be ______ g min$$^{-1}$$.
[Heat of combustion $$= 8 \times 10^3$$ J g$$^{-1}$$, Specific heat of water $$= 4.2$$ J g$$^{-1}$$ °C$$^{-1}$$]

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

A heat engine operates with the cold reservoir at temperature $$324$$ K. The minimum temperature of the hot reservoir, if the heat engine takes $$300$$ J heat from the hot reservoir and delivers $$180$$ J heat to the cold reservoir per cycle, is ______ K.

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

A set of $$20$$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $$4$$ beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is ______ Hz.

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NTA JEE Main 26th June 2022 Shift 2 - Question 28

A small bulb is placed at the bottom of a tank containing water to a depth of $$\sqrt{7}$$ m. The refractive index of water is $$\frac{4}{3}$$. The area of the surface of water through which light from the bulb can emerge out is $$x\pi$$ m$$^2$$. The value of $$x$$ is ______

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

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength $$6630$$ Å is $$0.42$$ V. If the threshold frequency is $$x \times 10^{13}$$ s, where $$x$$ is (nearest integer): (Given, speed light $$= 3 \times 10^8$$ m s$$^{-1}$$, Planck's constant $$= 6.63 \times 10^{-34}$$ J s)

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NTA JEE Main 26th June 2022 Shift 2 - Question 30

A travelling microscope is used to determine the refractive index of a glass slab. If $$40$$ divisions are there in $$1$$ cm on main scale and $$50$$ Vernier scale divisions are equal to $$49$$ main scale divisions, then least count of the travelling microscope is ______ $$\times 10^{-6}$$ m.

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NTA JEE Main 26th June 2022 Shift 2 - Question 34

Which one of the following is an example of disproportionation reaction?

NTA JEE Main 26th June 2022 Shift 2 - Question 35

Boiling of hard water is helpful in removing the temporary hardness by converting calcium hydrogen carbonate and magnesium hydrogen carbonate to

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NTA JEE Main 26th June 2022 Shift 2 - Question 41

The role of depressants in 'Froth Floation method' is to

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NTA JEE Main 26th June 2022 Shift 2 - Question 46

Which statement is NOT correct for p-toluenesulphonyl chloride?

NTA JEE Main 26th June 2022 Shift 2 - Question 48

Match List I with List II.

List-I (Enzyme)List-II (Conversion of)
A. InvertaseI. Starch into maltose
B. ZymaseII. Maltose into glucose
C. DiastaseIII. Glucose into ethanol
D. MaltaseIV. Cane sugar into glucose

Choose the most appropriate answer from the options given below

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NTA JEE Main 26th June 2022 Shift 2 - Question 51

CNG is an important transportation fuel. When $$100$$ g CNG is mixed with $$208$$ g oxygen in vehicles, it leads to the formation of $$CO_2$$ and $$H_2O$$ and produces large quantity of heat during this combustion, then the amount of carbon dioxide, produced in grams is ______ [nearest integer] [Assume CNG to be methane]

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NTA JEE Main 26th June 2022 Shift 2 - Question 54

A fish swimming in water body when taken out from the water body is covered with a film of water of weight $$36$$ g. When it is subjected to cooking at $$100°$$C, then the internal energy for vaporization in kJ mol$$^{-1}$$ is ______ [integer]
[Assume steam to be an ideal gas. Given $$\Delta_{vap}H^\circ$$ for water at $$373$$ K and $$1$$ bar is $$41.1$$ kJ mol$$^{-1}$$ : $$R = 8.31$$ J K$$^{-1}$$ mol$$^{-1}$$]

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NTA JEE Main 26th June 2022 Shift 2 - Question 55

$$40\%$$ of HI undergoes decomposition to $$H_2$$ and $$I_2$$ at $$300$$ K. $$\Delta G^\circ$$ for this decomposition reaction at one atmosphere pressure is ______ J mol$$^{-1}$$ [nearest integer]
(Use $$R = 8.31$$ J K$$^{-1}$$ mol$$^{-1}$$; $$\log 2 = 0.3010$$, $$\ln 10 = 2.3$$, $$\log 3 = 0.477$$)

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NTA JEE Main 26th June 2022 Shift 2 - Question 56

In a solid AB, A atoms are in ccp arrangement and B atoms occupy all the octahedral sites. If two atoms from the opposite faces are removed, then the resultant stoichiometry of the compound is $$A_xB_y$$. The value of $$x$$ is ______ [nearest integer]

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NTA JEE Main 26th June 2022 Shift 2 - Question 57

The osmotic pressure exerted by a solution prepared by dissolving $$2.0$$ g of protein of molar mass $$60$$ kg mol$$^{-1}$$ in $$200$$ mL of water at $$27°$$C is ______ Pa. [integer value] (use $$R = 0.083$$ L bar mol$$^{-1}$$ K$$^{-1}$$)

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NTA JEE Main 26th June 2022 Shift 2 - Question 58

$$Cu(s) + Sn^{2+}(0.001M) \to Cu^{2+}(0.01M) + Sn(s)$$
The Gibbs free energy change for the above reaction at $$298$$ K is $$x \times 10^{-1}$$ kJ mol$$^{-1}$$. The value of $$x$$ is ______ [nearest integer]
[Given : $$E^\circ_{Cu^{2+}/Cu} = 0.34$$ V; $$E^\circ_{Sn^{2+}/Sn} = -0.14$$ V; $$F = 96500$$ C mol$$^{-1}$$]

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NTA JEE Main 26th June 2022 Shift 2 - Question 59

Catalyst A reduces the activation energy for a reaction by $$10$$ kJ mol$$^{-1}$$ at $$300$$ K. The ratio of rate constants, $$\frac{k_T \text{ Catalysed}}{k_T \text{ Uncatalysed}}$$ is $$e^x$$. The value of $$x$$ is ______ [nearest integer] [Assume that the pre-exponential factor is same in both the cases. Given $$R = 8.31$$ J K$$^{-1}$$ mol$$^{-1}$$]

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NTA JEE Main 26th June 2022 Shift 2 - Question 64

The locus of the mid-point of the line segment joining the point $$(4, 3)$$ and the points on the ellipse $$x^2 + 2y^2 = 4$$ is an ellipse with eccentricity

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NTA JEE Main 26th June 2022 Shift 2 - Question 67

Let $$r \in (P, q, \sim p, \sim q)$$ be such that the logical statement $$r \vee (\sim p) \Rightarrow (p \wedge q) \vee r$$ is a tautology. Then $$r$$ is equal to

NTA JEE Main 26th June 2022 Shift 2 - Question 68

Let the mean of 50 observations is 15 and the standard deviation is 2. However, one observation was wrongly recorded. The sum of the correct and incorrect observations is 70. If the mean of the correct set of observations is 16, then the variance of the correct set is equal to

NTA JEE Main 26th June 2022 Shift 2 - Question 69

If the system of equations $$\alpha x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = \beta$$. Has infinitely many solutions, then the ordered pair $$(\alpha, \beta)$$ is equal to

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NTA JEE Main 26th June 2022 Shift 2 - Question 70

If the inverse trigonometric functions take principal values, then
$$\cos^{-1}\left(\frac{3}{10}\cos\left(\tan^{-1}\left(\frac{4}{3}\right)\right) + \frac{2}{5}\sin\left(\tan^{-1}\left(\frac{4}{3}\right)\right)\right)$$ is equal to

NTA JEE Main 26th June 2022 Shift 2 - Question 71

Let $$f : \mathbb{R} \to \mathbb{R}$$ be defined as $$f(x) = x - 1$$ and $$g : R \to \{1, -1\} \to \mathbb{R}$$ be defined as $$g(x) = \frac{x^2}{x^2 - 1}$$. Then the function $$fog$$ is:

NTA JEE Main 26th June 2022 Shift 2 - Question 72

Let $$f(x) = \min\{1, 1 + x\sin x\}, 0 \leq x \leq 2\pi$$. If $$m$$ is the number of points, where $$f$$ is not differentiable and $$n$$ is the number of points, where $$f$$ is not continuous, then the ordered pair $$(m, n)$$ is equal to

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NTA JEE Main 26th June 2022 Shift 2 - Question 73

Consider a cuboid of sides $$2x, 4x$$ and $$5x$$ and a closed hemisphere of radius $$r$$. If the sum of their surface areas is constant $$k$$, then the ratio $$x : r$$, for which the sum of their volumes is maximum, is

NTA JEE Main 26th June 2022 Shift 2 - Question 74

If $$\int \frac{1}{x}\sqrt{\frac{1-x}{1+x}} dx = g(x) + c, g(1) = 0$$, then $$g\left(\frac{1}{2}\right)$$ is equal to

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NTA JEE Main 26th June 2022 Shift 2 - Question 78

Let $$\vec{a} = \hat{i} + \hat{j} + 2\hat{k}, \vec{b} = 2\hat{i} - 3\hat{j} + \hat{k}$$ and $$\vec{c} = \hat{i} - \hat{j} + \hat{k}$$ be the three given vectors. Let $$\vec{v}$$ be a vector in the plane of $$\vec{a}$$ and $$\vec{b}$$ whose projection on $$\vec{c}$$ is $$\frac{2}{\sqrt{3}}$$. If $$\vec{v} \cdot \hat{j} = 7$$, then $$\vec{v} \cdot (\hat{i} + \hat{k})$$ is equal to

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NTA JEE Main 26th June 2022 Shift 2 - Question 79

If the plane $$2x + y - 5z = 0$$ is rotated about its line of intersection with the plane $$3x - y + 4z - 7 = 0$$ by an angle of $$\frac{\pi}{2}$$, then the plane after the rotation passes through the point

NTA JEE Main 26th June 2022 Shift 2 - Question 80

If the lines $$\vec{r} = (\hat{i} - \hat{j} + \hat{k}) + \lambda(3\hat{j} - \hat{k})$$ and $$\vec{r} = (\alpha\hat{i} - \hat{j}) + \mu(2\hat{i} - 3\hat{k})$$ are co-planar, then the distance of the plane containing these two lines from the point $$(\alpha, 0, 0)$$ is

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NTA JEE Main 26th June 2022 Shift 2 - Question 86

Let a line $$L_1$$ be tangent to the hyperbola $$\frac{x^2}{16} - \frac{y^2}{4} = 1$$ and let $$L_2$$ be the line passing through the origin and perpendicular to $$L_1$$. If the locus of the point of intersection of $$L_1$$ and $$L_2$$ is $$(x^2 + y^2)^2 = \alpha x^2 + \beta y^2$$, then $$\alpha + \beta$$ is equal to ______

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NTA JEE Main 26th June 2022 Shift 2 - Question 87

Let $$X = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{bmatrix}$$, $$Y = \alpha I + \beta X + \gamma X^2$$ and $$Z = \alpha^2 I - \alpha\beta X + (\beta^2 - \alpha\gamma)X^2, \alpha, \beta, \gamma \in \mathbb{R}$$.
If $$Y^{-1} = \begin{bmatrix} \frac{1}{5} & \frac{-2}{5} & \frac{1}{5} \\ 0 & \frac{1}{5} & \frac{-2}{5} \\ 0 & 0 & \frac{1}{5} \end{bmatrix}$$, then $$(\alpha - \beta + \gamma)^2$$ is equal to ______

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NTA JEE Main 26th June 2022 Shift 2 - Question 90

If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is $$p$$, then $$96p$$ is equal to ______

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