JEE Main 27 July 2022 Shift 2 Question Paper

Question 1

The domain of the function $f(x) = \sin^{-1}[2x^{2}-3] + \log_{2}\left(\log_{\frac{1}{2}}\left(x^{2}-5x+5\right)\right)$, where $[t]$ is the greatest integer function, is :

Accepted Answer

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

Answer

(A) $\left(-\sqrt{\frac{5}{2}}, \frac{5-\sqrt{5}}{2}\right)$

Answer

(B) $\left(\frac{5-\sqrt{5}}{2}, \frac{5+\sqrt{5}}{2}\right)$

Answer

(D) $\left[1, \frac{5+\sqrt{5}}{2}\right)$

Question 2

Let S be the set of all $(\alpha, \beta)$, $\pi < \alpha, \beta < 2\pi$, for which the complex number $\frac{1-i\sin\alpha}{1+2i\sin\alpha}$ is purely imaginary and $\frac{1+i\cos\beta}{1-2i\cos\beta}$ is purely real. Let $Z_{\alpha\beta} = \sin 2\alpha + i\cos 2\beta, (\alpha,\beta) \in S$. Then $\sum_{(\alpha,\beta)\in S}\left(i Z_{\alpha\beta} + \frac{1}{i\,\overline{Z}_{\alpha\beta}}\right)$ is equal to :

Accepted Answer

(C) $1$

Answer

(A) $3$

Answer

(B) $3i$

Answer

(D) $2-i$

Question 3

If $\alpha, \beta$ are the roots of the equation $x^{2}-\left(5+3^{\sqrt{\log_{3}5}}-5^{\sqrt{\log_{5}3}}\right)+3\left(3^{(\log_{3}5)^{\frac{1}{3}}}-5^{(\log_{5}3)^{\frac{2}{3}}}-1\right)=0$ then the equation, whose roots are $\alpha+\frac{1}{\beta}$ and $\beta+\frac{1}{\alpha}$,

Accepted Answer

(B) $3x^{2}-10x-4=0$

Answer

(A) $3x^{2}-20x-12=0$

Answer

(C) $3x^{2}-10x+2=0$

Answer

(D) $3x^{2}-20x+16=0$

Question 4

Let $A = \begin{pmatrix} 4 & -2 \ \alpha & \beta \end{pmatrix}$. If $A^{2}+\gamma A + 18I = O$, then det (A) is equal to ______.

Accepted Answer

(B) $18$

Answer

(A) $-18$

Answer

(C) $-50$

Answer

(D) $50$

Question 5

If for $p 
eq q 
eq 0$, then function $f(x) = \frac{\sqrt[7]{p(729+x)}-3}{\sqrt[3]{729+qx}-9}$ is continuous at $x = 0$, then:

Accepted Answer

(B) $63q\,f(0)-p^{2}=0$

Answer

(A) $7pq\,f(0)-1=0$

Answer

(C) $21q\,f(0)-p^{2}=0$

Answer

(D) $7pq\,f(0)-9=0$

Question 6

Let $f(x) = 2 + |x| - |x-1| + |x+1|$, $x \in \mathbf{R}$. Consider
$(S1) : f'\left(-\frac{3}{2}\right) + f'\left(-\frac{1}{2}\right) + f'\left(\frac{1}{2}\right) + f'\left(\frac{3}{2}\right) = 2$
$(S2) : \int_{-2}^{2} f(x)dx = 12$
Then,

Accepted Answer

(D) only (S2) is correct

Answer

(A) both (S1) and (S2) are correct

Answer

(B) both (S1) and (S2) are wrong

Answer

(C) only (S1) is correct

Question 7

Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be $\frac{98}{25}$. Then the sum of the first 21 terms of an AP, whose first term is $10ar$, $n^{th}$ term is $a_{n}$ and the common difference is $10ar^{2}$, is equal to :

Accepted Answer

(A) $21\,a_{11}$

Answer

(B) $22\,a_{11}$

Answer

(C) $15\,a_{16}$

Answer

(D) $14\,a_{16}$

Question 8

The area of the region enclosed by $y \le 4x^{2}, x^{2} \le 9y$ and $y \le 4$, is equal to :

Accepted Answer

(D) $\frac{80}{3}$

Answer

(A) $\frac{40}{3}$

Answer

(B) $\frac{56}{3}$

Answer

(C) $\frac{112}{3}$

Question 9

$\int_{0}^{2}\left(\left|2x^{2}-3x\right|+\left[x-\frac{1}{2}\right]\right)dx$, where $[t]$ is the greatest integer function, is equal to:

Accepted Answer

(B) $\frac{19}{12}$

Answer

(A) $\frac{7}{6}$

Answer

(C) $\frac{31}{12}$

Answer

(D) $\frac{3}{2}$

Question 10

Consider a curve $y = y(x)$ in the first quadrant as shown in the figure. Let the area $A_{1}$ is twice the area $A_{2}$. Then the normal to the curve perpendicular to the line $2x - 12y = 15$ does NOT pass through the point.

Accepted Answer

(C) $(10, -4)$

Answer

(A) $(6, 21)$

Answer

(B) $(8, 9)$

Answer

(D) $(12, -15)$

Question 11

The equations of the sides AB, BC and CA of a triangle ABC are $2x + y = 0$, $x + py = 39$ and $x - y = 3$ respectively and $P(2, 3)$ is its circumcentre. Then which of the following is NOT true :

Accepted Answer

(D) $34 < 	ext{area } (\Delta ABC) < 38$

Answer

(A) $(AC)^{2} = 9p$

Answer

(B) $(AC)^{2} + p^{2} = 136$

Answer

(C) $32 < 	ext{area } (\Delta ABC) < 36$

Question 12

A circle $C_{1}$ passes through the origin O and has diameter 4 on the positive x-axis. The line $y = 2x$ gives a chord OA of a circle $C_{1}$. Let $C_{2}$ be the circle with OA as a diameter. If the tangent to $C_{2}$ at the point A meets the x-axis at P and y-axis at Q, then QA : AP is equal to :

Accepted Answer

(A) $1 : 4$

Answer

(B) $1 : 5$

Answer

(C) $2 : 5$

Answer

(D) $1 : 3$

Question 13

If the length of the latus rectum of a parabola, whose focus is $(a, a)$ and the tangent at its vertex is $x + y = a$, is 16, then $|a|$ is equal to :

Accepted Answer

(C) $4\sqrt{2}$

Answer

(A) $2\sqrt{2}$

Answer

(B) $2\sqrt{3}$

Answer

(D) $4$

Question 14

If the length of the perpendicular drawn from the point $P(a, 4, 2)$, $a > 0$ on the line $\frac{x+1}{2} = \frac{y-3}{3} = \frac{z-1}{-1}$ is $2\sqrt{6}$ units and $Q(\alpha_{1}, \alpha_{2}, \alpha_{3})$ is the image of the point P in this line, then $a + \sum_{i=1}^{3}\alpha_{i}$ is equal to :

Accepted Answer

(B) $8$

Answer

(A) $7$

Answer

(C) $12$

Answer

(D) $14$

Question 15

If the line of intersection of the planes $ax + by = 3$ and $ax + by + cz = 0$, $a > 0$ makes an angle $30^{\circ}$ with the plane $y - z + 2 = 0$, then the direction cosines of the line are :

Accepted Answer

(B) $\frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}}, 0$

Answer

(A) $\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0$

Answer

(C) $\frac{1}{\sqrt{5}}, -\frac{2}{\sqrt{5}}, 0$

Answer

(D) $\frac{1}{2}, -\frac{\sqrt{3}}{2}, 0$

Question 16

Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If $P(X > n - 3) = \frac{k}{2^{n}}$, then k is equal to

Accepted Answer

(B) 529

Answer

(A) 528

Answer

(C) 629

Answer

(D) 630

Question 17

A six faced die is biased such that $3 	imes P(	ext{a prime number}) = 6 	imes P(	ext{a composite number}) = 2 	imes P(1)$. Let X be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of X is :

Accepted Answer

(D) $\frac{8}{11}$

Answer

(A) $\frac{3}{11}$

Answer

(B) $\frac{5}{11}$

Answer

(C) $\frac{7}{11}$

Question 18

The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is $45^\circ$. Let R be a point on AQ and from a point B, vertically above R, the angle of elevation of P is $60^\circ$. If $\angle BAQ = 30^\circ$, $AB = d$ and the area of the trapezium PQRB is $\alpha$, then the ordered pair $(d, \alpha)$ is :

Accepted Answer

(A) $\left(10\left(\sqrt{3}-1\right), 25\right)$

Answer

(B) $\left(10\left(\sqrt{3}-1\right), \frac{25}{2}\right)$

Answer

(C) $\left(10\left(\sqrt{3}+1\right), 25\right)$

Answer

(D) $\left(10\left(\sqrt{3}+1\right), \frac{25}{2}\right)$

Question 19

Let $S = \left\{	heta \in \left(0, \frac{\pi}{2}ight) : \sum_{m=1}^{9} \sec\left(	heta + (m-1)\frac{\pi}{6}ight)\sec\left(	heta + \frac{m\pi}{6}ight) = -\frac{8}{\sqrt{3}}ight\}$ Then

Accepted Answer

(C) $\sum_{	heta \in S} 	heta = \frac{\pi}{2}$

Answer

(A) $S = \left\{\frac{\pi}{12}\right\}$

Answer

(B) $S = \left\{\frac{2\pi}{3}\right\}$

Answer

(D) $\sum_{	heta \in S} 	heta = \frac{3\pi}{4}$

Question 20

If the truth value of the statement $\left(P \wedge (\sim R)\right) \rightarrow \left((\sim R) \wedge Q\right)$ is F, then the truth value of which of the following is F ?

Accepted Answer

(D) $\sim\left(R \vee Q\right) \rightarrow \sim P$

Answer

(A) $P \vee Q \rightarrow \sim R$

Answer

(B) $R \vee Q \rightarrow \sim P$

Answer

(C) $\sim\left(P \vee Q\right) \rightarrow \sim R$

Question 21

Consider a matrix $A = \begin{bmatrix} \alpha & \beta & \gamma \ \alpha^{2} & \beta^{2} & \gamma^{2} \ \beta+\gamma & \gamma+\alpha & \alpha+\beta \end{bmatrix}$, where $\alpha, \beta, \gamma$ are three distinct natural numbers. If $\frac{\det\left(\operatorname{adj}\left(\operatorname{adj}\left(\operatorname{adj}\left(\operatorname{adj}Aight)ight)ight)ight)}{\left(\alpha-\betaight)^{16}\left(\beta-\gammaight)^{16}\left(\gamma-\alphaight)^{16}} = 2^{32} 	imes 3^{16}$, then the number of such 3 – tuples $(\alpha, \beta, \gamma)$ is ________.

Accepted Answer

42

Question 22

The number of functions f, from the set $A = \left\{x \in N : x^{2} - 10x + 9 \le 0\right\}$ to the set $B = \left\{n^{2} : n \in N\right\}$ such that $f(x) \le (x-3)^{2} + 1$, for every $x \in A$, is __________.

Accepted Answer

1440

Question 23

Let for the $9^{	ext{th}}$ term in the binomial expansion of $(3 + 6x)^{n}$, in the increasing powers of $6x$, to be the greatest for $x = \frac{3}{2}$, the least value of n is $n_0$. If k is the ratio of the coefficient of $x^{6}$ to the coefficient of $x^{3}$, then $k + n_0$ is equal to:

Accepted Answer

24

Question 24

$\frac{2^{3}-1^{3}}{1 	imes 7} + \frac{4^{3}-3^{3}+2^{3}-1^{3}}{2 	imes 11} + \frac{6^{3}-5^{3}+4^{3}-3^{3}+2^{3}-1^{3}}{3 	imes 15} + ..... + \frac{30^{3}-29^{3}+28^{3}-27^{3}+...+2^{3}-1^{3}}{15 	imes 63}$ is equal to _____.

Accepted Answer

120

Question 25

A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is $	an^{-1}\frac{3}{4}$. Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is ________.

Accepted Answer

5

Question 26

For the curve $C : (x^{2} + y^{2} - 3) + (x^{2} - y^{2} - 1)^{5} = 0$, the value of $3y' - y^{3}y''$, at the point $(\alpha, \alpha)$, $\alpha > 0$, on C, is equal to ________.

Accepted Answer

16

Question 27

Let $f(x) = \min\{[x-1], [x-2], ..., [x-10]\}$ where $[t]$ denotes the greatest integer $\le t$. Then $\int_{0}^{10} f(x)dx + \int_{0}^{10} (f(x))^{2}dx + \int_{0}^{10} |f(x)|dx$ is equal to ___.

Accepted Answer

385

Question 28

Let f be a differentiable function satisfying $f(x) = \frac{2}{\sqrt{3}}\int_{0}^{\sqrt{3}} f\left(\frac{\lambda^{2}x}{3}\right)d\lambda$, $x > 0$ and $f(1) = \sqrt{3}$. If $y = f(x)$ passes through the point $(\alpha, 6)$, then $\alpha$ is equal to _______.

Accepted Answer

12

Question 29

A common tangent T to the curves $C_{1} : \frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$ and $C_{2} : \frac{x^{2}}{42} - \frac{y^{2}}{143} = 1$ does not pass through the fourth quadrant. If T touches $C_{1}$ at $(x_{1}, y_{1})$ and $C_{2}$ at $(x_{2}, y_{2})$, then $|2x_{1} + x_{2}|$ is equal to ________.

Accepted Answer

20

Question 30

An expression of energy density is given by $u = \frac{\alpha}{\beta}\sin\left(\frac{\alpha x}{kt}\right)$, where α, β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of β will be :

Accepted Answer

(D) $[M^{0}L^{2}T^{0}]$

Answer

(A) $[ML^{2}T^{-2}	heta^{-1}]$

Answer

(B) $[M^{0}L^{2}T^{-2}]$

Answer

(C) $[M^{0}L^{0}T^{0}]$

Question 31

A body of mass 10 kg is projected at an angle of 45° with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time $t = \frac{T}{\sqrt{2}}$, is ________
[Take g = 10 m/s$^{2}$]

Accepted Answer

(D) $100\sqrt{2}\,\hat{i} + (100\sqrt{2} - 200)\hat{j}$

Answer

(A) $100\hat{i} + (100\sqrt{2} - 200)\hat{j}$

Answer

(B) $100\sqrt{2}\,\hat{i} + (100 - 200\sqrt{2})\hat{j}$

Answer

(C) $100\,\hat{i} + (100 - 200\sqrt{2})\hat{j}$

Question 32

A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is θ. The magnitude of the contact force will be :

Accepted Answer

(A) Mg

Answer

(B) Mg cos θ

Answer

(C) $\sqrt{Mg\sin	heta + Mg\cos	heta}$

Answer

(D) $Mg\sin	heta\sqrt{1 + \mu}$

Question 33

A block 'A' takes 2 s to slide down a frictionless incline of 30° and length '$l$', kept inside a lift going up with uniform velocity '$v$'. If the incline is changed to 45°, the time taken by the block, to slide down the incline, will be approximately:

Accepted Answer

(C) 1.68 s

Answer

(A) 2.66 s

Answer

(B) 0.83 s

Answer

(D) 0.70 s

Question 34

The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:

Accepted Answer

(C) 0. 5

Answer

(A) 2.0

Answer

(B) 1.0

Answer

(D) 1.5

Question 35

A body of mass m is projected with velocity $\lambda v_e$ in vertically upward direction from the surface of the earth into space. It is given that $v_e$ is escape velocity and λ < 1. If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be (R : radius of earth)

Accepted Answer

(B) $\frac{R}{1 - \lambda^{2}}$

Answer

(A) $\frac{R}{1 + \lambda^{2}}$

Answer

(C) $\frac{R}{1 - \lambda}$

Answer

(D) $\frac{\lambda^{2}R}{1 - \lambda^{2}}$

Question 36

A steel wire of length 3.2 m ($Y_S$ = 2.0 × 10$^{11}$ Nm$^{-2}$) and a copper wire of length 4.4 M ($Y_C$ = 1.1 × 10$^{11}$ Nm$^{-2}$), both of radius 1.4 mm are connected end to end. When stretched by a load, the net elongation is found to be 1.4 mm. The load applied, in Newton, will be: (Given $\pi = \frac{22}{7}$ )

Accepted Answer

(D) 154

Answer

(A) 360

Answer

(B) 180

Answer

(C) 1080

Question 37

In 1$^{st}$ case, Carnot engine operates between temperatures 300 K and 100 K. In 2$^{nd}$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2$^{nd}$ case) will be :

Accepted Answer

(A) same as the 1$^{st}$ case

Answer

(B) always greater than the 1$^{st}$ case

Answer

(C) always less than the 1$^{st}$ case

Answer

(D) may increase or decrease with respect to the 1$^{st}$ case

Question 38

Which statements are correct about degrees of freedom?
A. A molecule with n degrees of freedom has n$^{2}$ different ways of storing energy.
B. Each degree of freedom is associated with $\frac{1}{2}RT$ average energy per mole.
C. A monoatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom
D. CH$_4$ has a total to 6 degrees of freedom
Choose the correct answer from the option given below:

Accepted Answer

(B) B and D only

Answer

(A) B and C only

Answer

(C) A and B only

Answer

(D) C and D only

Question 39

A charge of 4 μC is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be:

Accepted Answer

(B) 2 μC and 2 μC

Answer

(A) 1 μC and 3 μC

Answer

(C) 0 and 4 μC

Answer

(D) 1.5 μC and 2.5 μC

Question 40

A. The drift velocity of electrons decreases with the increase in the temperature of conductor.
B. The drift velocity is inversely proportional to the area of cross-section of given conductor.
C. The drift velocity does not depend on the applied potential difference to the conductor.
D. The drift velocity of electron is inversely proportional to the length of the conductor.
E. The drift velocity increases with the increase in the temperature of conductor.
Choose the correct answer from the options given below:

Accepted Answer

(B) A and D only

Answer

(A) A and B only

Answer

(C) B and E only

Answer

(D) B and C only

Question 41

A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30°. The number of oscillations per minute become 10 at another place Q of 60° dip. The ratio of the total magnetic field at the two places ($B_Q$ : $B_P$) is:

Accepted Answer

(A) $\sqrt{3} : 4$

Answer

(B) $4 : \sqrt{3}$

Answer

(C) $\sqrt{3} : 2$

Answer

(D) $2 : \sqrt{3}$

Question 42

A cyclotron is used to accelerate protons. If the operating magnetic field is 1.0 T and the radius of the cyclotron 'dees' is 60 cm, the kinetic energy of the accelerated protons in MeV will be :
[use $m_p$ = 1.6 × 10$^{-27}$ kg, e = 1.6 × 10$^{-19}$ C]

Accepted Answer

(B) 18

Answer

(A) 12

Answer

(C) 16

Answer

(D) 32

Question 43

A series LCR circuit has L = 0.01 H, R = 10 Ω and C = 1 μF and it is connected to ac voltage of amplitude ($V_m$) 50 V. At frequency 60% lower than resonant frequency, the amplitude of current will be approximately :

Accepted Answer

(C) 238 mA

Answer

(A) 466 mA

Answer

(B) 312 mA

Answer

(D) 196 mA

Question 44

Identify the correct statements from the following descriptions of various properties of electromagnetic waves.
A. In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field.
B. The energy in electromagnetic wave is divided equally between electric and magnetic fields.
C. Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave.
D. The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other.
E. The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light.
Choose the most appropriate answer from the options given below:

Accepted Answer

(B) B and D only

Answer

(A) D only

Answer

(C) B, C and E only

Answer

(D) A, B and E only

Question 45

Two coherent sources of light interfere. The intensity ratio of two sources is 1 : 4. For this interference pattern if the value of $\frac{I_{max} + I_{min}}{I_{max} - I_{min}}$ is equal to $\frac{2\alpha + 1}{\beta + 3}$, then $\frac{\alpha}{\beta}$ will be :

Accepted Answer

(B) 2

Answer

(A) 1.5

Answer

(C) 0.5

Answer

(D) 1

Question 46

With reference to the observations in photo-electric effect, identify the correct statements from below:
A. The square of maximum velocity of photoelectrons varies linearly with frequency of incident light.
B. The value of saturation current increases on moving the source of light away from the metal surface.
C. The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light.
D. The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves.
E. Existence of threshold wavelength can not be explained by wave nature of light/electromagnetic waves.
Choose the correct answer from the options given below:

Accepted Answer

(B) A and E only

Answer

(A) A and B only

Answer

(C) C and E only

Answer

(D) D and E only

Question 47

The activity of a radioactive material is $6.4 	imes 10^{-4}$ curie. Its half life is 5 days. The activity will become $5 	imes 10^{-6}$ curie after :

Accepted Answer

(D) 35 days

Answer

(A) 7 days

Answer

(B) 15 days

Answer

(C) 25 days

Question 48

For a constant collector-emitter voltage of 8V, the collector current of a transistor reached to the value of 6 mA from 4 mA, whereas base current changed from 20 μA to 25 μA value. If transistor is in active state, small signal current gain (current amplification factor) will be :

Accepted Answer

(B) 400

Answer

(A) 240

Answer

(C) 0.0025

Answer

(D) 200

Question 49

A square wave of the modulating signal is shown in the figure. The carrier wave is given by C(t) = 5 sin (8 πt) Volt. The modulation index is :

Accepted Answer

(A) 0.2

Answer

(B) 0.1

Answer

(C) 0.3

Answer

(D) 0.4

Question 50

In an experiment to determine the Young's modulus, steel wires of five different lengths (1, 2, 3, 4 and 5 m) but of same cross section (2 mm$^{2}$) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is x × $10^{11}$ Nm$^{-2}$, then the value of x is __________ .

Accepted Answer

2

Question 51

In the given figure of meter bridge experiment, the balancing length AC corresponding to null deflection of the galvanometer is 40 cm. The balancing length, if the radius of the wire AB is doubled, will be……….cm.

Accepted Answer

40

Question 52

A thin prism of angle 6° and refractive index for yellow light (n$_Y$)1.5 is combined with another prism of angle 5° and n$_Y$ = 1.55. The combination produces no dispersion. The net average deviation (δ) produced by the combination is $\left(\frac{1}{x}\right)^{\circ}$. The value of x is…….

Accepted Answer

4

Question 53

A conducting circular loop is placed in X − Y plane in presence of magnetic field $\vec{B} = \left(3t^{3}\hat{j} + 3t^{2}\hat{k}\right)$ in SI unit. If the radius of the loop is 1m, the induced emf in the loop, at time, t = 2s is nπV. The value of n is……..

Accepted Answer

12

Question 54

As show in the figure, in steady state, the charge stored in the capacitor is……. × $10^{-6}$C.

Accepted Answer

10

Question 55

A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4mm is connected to a battery of 20 V. A dielectric slab of dielectric constant 5 having length 1cm, width 4 cm and thickness 4 mm is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be………∈$_0$ J. (Where ∈$_0$ is the permittivity of free space)

Accepted Answer

240

Question 56

A wire of length 30 cm, stretched between rigid supports, has it's n$^{th}$ and (n + 1)$^{th}$ harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, it's linear mass density is……..kg/m.

Accepted Answer

3

Question 57

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is…….

Accepted Answer

2

Question 58

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should by unbinding the strings to achieve a speed of 4 ms$^{-1}$, is…….cm.
(take g = 10 ms$^{-2}$)

Accepted Answer

120

Question 59

Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. Time it takes to reach to the point C from point A is $t\left(\sqrt{2} + 1\right)$s. The value of t is……..(use g = 10 m/s$^{2}$)

Accepted Answer

2

Question 60

The correct decreasing order of energy, for the orbitals having, following set of quantum numbers:
(A) n = 3, l = 0, m = 0
(B) n = 4, l = 0, m = 0
(C) n = 3, l = 1, m = 0
(D) n = 3, l = 2, m = 1

Accepted Answer

(A) (D) > (B) > (C) > (A)

Answer

(B) (B) > (D) > (C) > (A)

Answer

(C) (C) > (B) > (D) > (A)

Answer

(D) (B) > (C) > (D) > (A)

Question 61

Match List-I with List-II
List-I
(A) $\Psi_{MO} = \Psi_{A} - \Psi_{B}$
(B) $\mu = Q 	imes r$
(C) $\frac{N_{b} - N_{a}}{2}$
(D) $\Psi_{MO} = \Psi_{A} + \Psi_{B}$
List-II
(I) Dipole moment
(II) Bonding molecular orbital
(III) Anti-bonding molecualr orbital
(IV) Bond order

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 62

The Plot of pH-metric titration of weak base NH$_{4}$OH vs strong acid HCl looks like:

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 63

Given below are two statements:
Statement I: For KI, molar conductivity increases steeply with dilution.
Statement II: For carbonic acid, molar conductivity increases slowly with dilution.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(B) Both Statement I and Statement II are false

Answer

(A) Both Statement I and Statement II are true

Answer

(C) Statement I is true but Statement II is false

Answer

(D) Statement I is false but Statement II is true

Question 64

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A) : Dissolved substances can be removed from a colloidal solution by diffusion through a parchment paper.
Reason (R) : Particles in a true solution cannot pass through parchment paper but the collodial particles can pass through the parchment paper.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(C) (A) is correct but (R) is not correct

Answer

(A) Both (A) and (R) are correct and (R) is the correct explanation of (A)

Answer

(B) Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Answer

(D) (A) is not correct but (R) is correct

JEE Main 27 July 2022 Shift 2 Question Paper with Answers

Physics — JEE Main 27 July 2022 Shift 2

Chemistry — JEE Main 27 July 2022 Shift 2

Mathematics — JEE Main 27 July 2022 Shift 2

Chapters tested in this paper

Attempt this paper under exam timing.