JEE Main 28 July 2022 Shift 2 Question Paper

Question 1

Let $S=\left\{x \in[-6,3]-\{-2,2\}: \frac{|x+3|-1}{|x|-2} \geq 0\right\}$ and $T=\left\{x \in Z: x^{2}-7|x|+9 \leq 0\right\}$. Then the number of elements in $S \cap T$ is

Accepted Answer

(D) 3

Answer

(A) 7

Answer

(B) 5

Answer

(C) 4

Question 2

Let $\alpha$, $\beta$ be the roots of the equation $x^{2}-\sqrt{2}x+\sqrt{6}=0$ and $\frac{1}{\alpha^{2}}+1, \frac{1}{\beta^{2}}+1$ be the roots of the equation $x^{2}+ax+b=0$. Then the roots of the equation $x^{2}-(a+b-2)x+(a+b+2)=0$ are :

Accepted Answer

(B) real and both negative

Answer

(A) non-real complex numbers

Answer

(C) real and both positive

Answer

(D) real and exactly one of them is positive

Question 3

Let A and B be any two $3 imes 3$ symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?

Accepted Answer

(C) $B^{5}-A^{5}$ is a skew-symmetric matrix

Answer

(A) $A^{4}-B^{4}$ is a symmetric matrix

Answer

(B) $AB-BA$ is a symmetric matrix

Answer

(D) $AB+BA$ is a skew-symmetric matrix

Question 4

Let $f(x)=ax^{2}+bx+c$ be such that $f(1)=3$, $f(-2)=\lambda$ and $f(3)=4$. If $f(0)+f(1)+f(-2)+f(3)=14$, then $\lambda$ is equal to

Accepted Answer

(D) 4

Answer

(A) $-4$

Answer

(B) $\frac{13}{2}$

Answer

(C) $\frac{23}{2}$

Question 5

The function $f: R \rightarrow R$ defined by $f(x)=\lim_{n \rightarrow \infty} \frac{\cos(2\pi x)-x^{2n}\sin(x-1)}{1+x^{2n+1}-x^{2n}}$ is continuous for all x in

Accepted Answer

(B) $R-\{-1,1\}$

Answer

(A) $R-\{-1\}$

Answer

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

Answer

(D) $R-\{0\}$

Question 6

The function $f(x)=xe^{x(1-x)}$, $x \in R$, is

Accepted Answer

(A) increasing in $\left(-\frac{1}{2},1\right)$

Answer

(B) decreasing in $\left(\frac{1}{2},2\right)$

Answer

(C) increasing in $\left(-1,-\frac{1}{2}\right)$

Answer

(D) decreasing in $\left(-\frac{1}{2},\frac{1}{2}\right)$

Question 7

The sum of the absolute maximum and absolute minimum values of the function $f(x)=	an^{-1}(\sin x-\cos x)$ in the interval $[0,\pi]$ is

Accepted Answer

(C) $\cos^{-1}\left(\frac{1}{\sqrt{3}}\right)-\frac{\pi}{4}$

Answer

(A) 0

Answer

(B) $	an^{-1}\left(\frac{1}{\sqrt{2}}ight)-\frac{\pi}{4}$

Answer

(D) $\frac{-\pi}{12}$

Question 8

Let $x(t)=2\sqrt{2}\cos t\sqrt{\sin 2t}$ and $y(t)=2\sqrt{2}\sin t\sqrt{\sin 2t}$, $t \in \left(0,\frac{\pi}{2}\right)$. Then $\frac{1+\left(\frac{dy}{dx}\right)^{2}}{\frac{d^{2}y}{dx^{2}}}$ at $t=\frac{\pi}{4}$ is equal to

Accepted Answer

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

Answer

(A) $\frac{-2\sqrt{2}}{3}$

Answer

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

Answer

(C) $\frac{1}{3}$

Question 9

Let $I_{n}(x)=\int_{0}^{x}\frac{1}{\left(t^{2}+5\right)^{n}}dt$, $n=1,2,3,\ldots.$ Then

Accepted Answer

(A) $50I_{6}-9I_{5}=xI_{5}'$

Answer

(B) $50I_{6}-11I_{5}=xI_{5}'$

Answer

(C) $50I_{6}-9I_{5}=I_{5}'$

Answer

(D) $50I_{6}-11I_{5}=I_{5}'$

Question 10

The area enclosed by the curves $y=\log_{e}\left(x+e^{2}\right)$, $x=\log_{e}\left(\frac{2}{y}\right)$ and $x=\log_{e}2$, above the line $y=1$ is

Accepted Answer

(B) $1+e-\log_{e}2$

Answer

(A) $2+e-\log_{e}2$

Answer

(C) $e-\log_{e}2$

Answer

(D) $1+\log_{e}2$

Question 11

Let $y=y(x)$ be the solution curve of the differential equation $\frac{dy}{dx}+\frac{1}{x^{2}-1}y=\left(\frac{x-1}{x+1}\right)^{\frac{1}{2}}$, $x>1$ passing through the point $\left(2,\sqrt{\frac{1}{3}}\right)$. Then $\sqrt{7}y(8)$ is equal to

Accepted Answer

(D) $19-6\log_{e}3$

Answer

(A) $11+6\log_{e}3$

Answer

(B) 19

Answer

(C) $12-2\log_{e}3$

Question 12

The differential equation of the family of circles passing through the points $(0,2)$ and $(0,-2)$ is

Accepted Answer

(A) $2xy\frac{dy}{dx}+\left(x^{2}-y^{2}+4\right)=0$

Answer

(B) $2xy\frac{dy}{dx}+\left(x^{2}+y^{2}-4\right)=0$

Answer

(C) $2xy\frac{dy}{dx}+\left(y^{2}-x^{2}+4\right)=0$

Answer

(D) $2xy\frac{dy}{dx}-\left(x^{2}-y^{2}+4\right)=0$

Question 13

Let the tangents at two points A and B on the circle $x^{2}+y^{2}-4x+3=0$ meet at origin $O(0,0)$. Then the area of the triangle of OAB is

Accepted Answer

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

Answer

(A) $\frac{3\sqrt{3}}{2}$

Answer

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

Answer

(D) $\frac{3}{4\sqrt{3}}$

Question 14

Let the hyperbola $H: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ pass through the point $\left(2\sqrt{2},-2\sqrt{2}\right)$. A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H. If the length of the latus rectum of the parabola is e times the length of the latus rectum of H, where e is the eccentricity of H, then which of the following points lies on the parabola?

Accepted Answer

(B) $\left(3\sqrt{3},-6\sqrt{2}\right)$

Answer

(A) $\left(2\sqrt{3},3\sqrt{2}\right)$

Answer

(C) $\left(\sqrt{3},-\sqrt{6}\right)$

Answer

(D) $\left(3\sqrt{6},6\sqrt{2}\right)$

Question 15

Let the lines $\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}$ and $\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}$ be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lies on P?

Accepted Answer

(D) $(0,4,5)$

Answer

(A) $(0,-2,-2)$

Answer

(B) $(-5,0,-1)$

Answer

(C) $(3,-1,0)$

Question 16

A plane P is parallel to two lines whose direction ratios are $-2, 1, -3$, and $-1, 2, -2$ and it contains the point $(2,2,-2)$. Let P intersect the co-ordinate axes at the points A, B, C making the intercepts $\alpha, \beta, \gamma$. If V is the volume of the tetrahedron OABC, where O is the origin and $p=\alpha+\beta+\gamma$, then the ordered pair $(V,p)$ is equal to

Accepted Answer

(B) $(24,-13)$

Answer

(A) $(48,-13)$

Answer

(C) $(48,11)$

Answer

(D) $(24,-5)$

Question 17

Let S be the set of all $a \in R$ for which the angle between the vectors $\vec{u}=a\left(\log_{e}b\right)\hat{i}-6\hat{j}+3\hat{k}$ and $\vec{v}=\left(\log_{e}b\right)\hat{i}+2\hat{j}+2a\left(\log_{e}b\right)\hat{k}, (b>1)$ is acute. Then S is equal to

Accepted Answer

(C) $\left(-\frac{4}{3},0\right)$

Answer

(A) $\left(-\infty,-\frac{4}{3}\right)$

Answer

(B) $\Phi$

Answer

(D) $\left(\frac{12}{7},\infty\right)$

Question 18

A horizontal park is in the shape of a triangle OAB with $AB=16$. A vertical lamp post OP is erected at the point O such that $\angle PAO = \angle PBO = 15^{\circ}$ and $\angle PCO = 45^{\circ}$, where C is the midpoint of AB. Then $(OP)^{2}$ is equal to

Accepted Answer

(B) $\frac{32}{\sqrt{3}}\left(2-\sqrt{3}\right)$

Answer

(A) $\frac{32}{\sqrt{3}}\left(\sqrt{3}-1\right)$

Answer

(C) $\frac{16}{\sqrt{3}}\left(\sqrt{3}-1\right)$

Answer

(D) $\frac{16}{\sqrt{3}}\left(2-\sqrt{3}\right)$

Question 19

Let A and B be two events such that $P(B|A)=\frac{2}{5}$, $P(A|B)=\frac{1}{7}$ and $P(A \cap B)=\frac{1}{9}$. Consider
(S1) $P(A' \cup B)=\frac{5}{6}$,
(S2) $P(A' \cap B')=\frac{1}{18}$. Then

Accepted Answer

(A) Both (S1) and (S2) are true

Answer

(B) Both (S1) and (S2) are false

Answer

(C) Only (S1) is true

Answer

(D) Only (S2) is true

Question 20

Let p : Ramesh listens to music. q : Ramesh is out of his village r : It is Sunday s : It is Saturday Then the statement “Ramesh listens to music only if he is in his village and it is Sunday or Saturday” can be expressed as

Accepted Answer

(D) $p \Rightarrow \left((\sim q)\wedge(r \vee s)\right)$

Answer

(A) $\left((\sim q)\wedge(r \vee s)\right) \Rightarrow p$

Answer

(B) $\left(q \wedge (r \vee s)\right) \Rightarrow p$

Answer

(C) $p \Rightarrow \left(q \wedge (r \vee s)\right)$

Question 21

Let the coefficients of the middle terms in the expansion of $\left(\frac{1}{\sqrt{6}}+\beta x\right)^{4}$, $\left(1-3\beta x\right)^{2}$ and $\left(1-\frac{\beta}{2}x\right)^{6}$, $\beta>0$, respectively form the first three terms of an A.P. If d is the common difference of this A.P., then $50-\frac{2d}{\beta^{2}}$ is equal to _____

Accepted Answer

57

Question 22

A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168, then $b + 3g$ is equal to

Accepted Answer

17

Question 23

Let the tangents at the points P and Q on the ellipse $\frac{x^{2}}{2}+\frac{y^{2}}{4}=1$ meet at the point $R\left(\sqrt{2},\,2\sqrt{2}-2\right)$. If S is the focus of the ellipse on its negative major axis, then $SP^{2} + SQ^{2}$ is equal to

Accepted Answer

13

Question 24

If $1+ \left(2 + {}^{49}C_{1} + {}^{49}C_{2} + \ldots + {}^{49}C_{49}\right)\left({}^{50}C_{2} + {}^{50}C_{4} + \ldots + {}^{50}C_{50}\right)$ is equal to $2^{n}.m$, where m is odd, then $n + m$ is equal to _____

Accepted Answer

99

Question 25

Two tangent lines $l_{1}$ and $l_{2}$ are drawn from the point (2, 0) to the parabola $2y^{2} = -x$. If the lines $l_{1}$ and $l_{2}$ are also tangent to the circle $(x - 5)^{2} + y^{2} = r$, then $17r$ is equal to

Accepted Answer

9

Question 26

If $\frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^{9}}+\ldots+\frac{10240}{3}=2^{n}\cdot m$, where m is odd, then $m.n$ is equal to _____

Accepted Answer

12

Question 27

Let $S=\left[-\pi,\frac{\pi}{2}ight)-\left\{-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3\pi}{4},\frac{\pi}{4}ight\}$. Then the number of elements in the set $A=\left\{	heta\in S:	an	heta\left(1+\sqrt{5}	an(2	heta)ight)=\sqrt{5}-	an(2	heta)ight\}$ is _____

Accepted Answer

5

Question 28

Let $z = a + ib$, $b 
eq 0$ be complex numbers satisfying $z^{2}=\bar{z}\cdot 2^{1-|z|}$. Then the least value of $n \in N$, such that $z^{n} = (z+1)^{n}$, is equal to _____

Accepted Answer

6

Question 29

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If $\sigma^{2}$ is the variance of X, then $100\,\sigma^{2}$ is equal to

Accepted Answer

56

Question 30

The value of the integral $\int_{0}^{\pi/2}60\frac{\sin(6x)}{\sin x}dx$ is equal to

Accepted Answer

104

Question 31

Consider the efficiency of Carnot's engine is given by $\eta = \dfrac{\alpha\beta}{\sin	heta}\log_e \dfrac{\beta x}{kT}$, where $\alpha$ and $\beta$ are constants. If T is temperature, k is Boltzman constant, $	heta$ is angular displacement and x has the dimensions of length. Then, choose the **incorrect** option.

Accepted Answer

(D) Dimensions of $\alpha$ is same as that of $\beta$

Answer

(A) Dimensions of $\beta$ is same as that of force.

Answer

(B) Dimensions of $\alpha^{-1}$ x is same as that of energy.

Answer

(C) Dimensions of $\eta^{-1}\sin	heta$ is same as that of $\alpha\beta$

Question 32

At time t = 0 a particle starts travelling from a height $7\hat{z}$ cm in a plane keeping z coordinate constant. At any instant of time it's position along the x and y directions are defined as 3t and $5t^3$ respectively. At t = 1s acceleration of the particle will be

Accepted Answer

(B) $30y$

Answer

(A) $-30y$

Answer

(C) $3x + 15y$

Answer

(D) $3x + 15y + 7\hat{z}$

Question 33

A pressure-pump has a horizontal tube of cross-sectional area 10 $cm^2$ for the outflow of water at a speed of 20 m/s. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is: [given : density of water = 1000 $kg/m^3$]

Accepted Answer

(D) 400 N

Answer

(A) 300 N

Answer

(B) 500 N

Answer

(C) 250 N

Question 34

A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length '$l$' is hanging on one side and rest of its length 'L $-$ $l$' is hanging on the other side of the pulley. At a certain point of time, when $l = \dfrac{L}{x}$, the acceleration of the chain is $\dfrac{g}{2}$. The value of x is ………

Accepted Answer

(D) 4

Answer

(A) 6

Answer

(B) 2

Answer

(C) 1.5

Question 35

A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 J within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is

Accepted Answer

(A) 45 m

Answer

(B) 90 m

Answer

(C) 125 m

Answer

(D) 25 m

Question 36

Assume there are two identical simple pendulum Clocks-1 is placed on the earth and Clock-2 is placed on a space station located at a height h above the earth surface. Clock-1 and Clock-2 operate at time periods 4s and 6s respectively. Then the value of h is $-$ (consider radius of earth $R_E$ = 6400 km and g on earth 10 $m/s^2$)

Accepted Answer

(C) 3200 km

Answer

(A) 1200 km

Answer

(B) 1600 km

Answer

(D) 4800 km

Question 37

A vessel contains 14 g of nitrogen gas at a temperature of 27$^\circ$C. The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be : (Take R = 8.32 J $mol^{-1}k^{-1}$)

Accepted Answer

(C) 9360 J

Answer

(A) 2229 J

Answer

(B) 5616 J

Answer

(D) 13,104 J

Question 38

A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $\dfrac{3}{4}d$, where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be : (Given $C_o$ = capacitance of capacitor with air as medium between plates.)

Accepted Answer

(A) $\dfrac{4KC_0}{3+K}$

Answer

(B) $\dfrac{3KC_0}{3+K}$

Answer

(C) $\dfrac{3+K}{4KC_0}$

Answer

(D) $\dfrac{K}{4+K}$

Question 39

A uniform electric field E = (8m/e) V/m is created between two parallel plates of length 1m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2m/s. The angle of the deviation ($	heta$) of the path of the electron as it comes out of the field will be ……….

Accepted Answer

(B) $	an^{-1}(2)$

Answer

(A) $	an^{-1}(4)$

Answer

(C) $	an^{-1}\left(\dfrac{1}{3}ight)$

Answer

(D) $	an^{-1}(3)$

Question 40

Given below are two statements :
Statement I : A uniform wire of resistance 80$\Omega$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be 5 $\Omega$.
Statement II : Two resistance 2R and 3R are connected in parallel in a electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio 3 : 2.
In the light of the above statements, choose the most appropriate answer from the options given below

Accepted Answer

(C) Statement I is correct but statement II is incorrect

Answer

(A) Both statement I and statement II are correct

Answer

(B) Both statement I and statement II are incorrect

Answer

(D) Statement I is incorrect but statement II is correct.

Question 41

A triangular shaped wire carrying 10A current is placed in a uniform magnetic field of 0.5T, as shown in figure. The magnetic force on segment CD is (Given BC = CD = BD = 5 cm).

Accepted Answer

(C) 0.216 N

Answer

(A) 0.126 N

Answer

(B) 0.312 N

Answer

(D) 0.245 N

Question 42

The magnetic field at the center of current carrying circular loop is $B_1$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $B_2$. The value of $B_1/B_2$ will be

Accepted Answer

(C) $8 : 1$

Answer

(A) $9 : 4$

Answer

(B) $12 : \sqrt{5}$

Answer

(D) $5 : \sqrt{3}$

Question 43

A transformer operating at primary voltage 8 kV and secondary voltage 160 V serves a load of 80 kW. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be

Accepted Answer

(C) 800 $\Omega$ and 0.32 $\Omega$

Answer

(A) 800 $\Omega$ and 1.06 $\Omega$

Answer

(B) 10 $\Omega$ and 500 $\Omega$

Answer

(D) 1.06 $\Omega$ and 500 $\Omega$

Question 44

Sun light falls normally on a surface of area 36 $cm^2$ and exerts an average force of $7.2	imes10^{-9}$ N within a time period of 20 minutes. Considering a case of complete absorption, the energy flux of incident light is

Accepted Answer

(D) 0.06 $W/cm^2$

Answer

(A) $25.92	imes10^{2}$ $W/cm^2$

Answer

(B) $8.64	imes10^{-6}$ $W/cm^2$

Answer

(C) 6.0 $W/cm^2$

Question 45

The power of a lens (biconvex) is 1.25 $m^{-1}$ in particular medium. Refractive index of the lens is 1.5 and radii of curvature are 20 cm and 40 cm respectively. The refractive index of surrounding medium :

Accepted Answer

(B) $\dfrac{9}{7}$

Answer

(A) 1.0

Answer

(C) $\dfrac{3}{2}$

Answer

(D) $\dfrac{4}{3}$

Question 46

Two streams of photons, possessing energies to five and ten times the work function of metal are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectron emitted, in the two cases respectively, will be

Accepted Answer

(C) $2 : 3$

Answer

(A) $1 : 2$

Answer

(B) $1 : 3$

Answer

(D) $3 : 2$

Question 47

An n.p.n transistor with current gain $\beta$ = 100 in common emitter configuration is shown in figure. The output voltage of the amplifier will be

Accepted Answer

(B) 1.0 V

Answer

(A) 0.1 V

Answer

(C) 10 V

Answer

(D) 100 V

Question 48

A FM Broad cast transmitter, using modulating signal of frequency 20 kHz has a deviation ratio of 10. The Bandwidth required for transmission is :

Accepted Answer

(D) 440 kHz

Answer

(A) 220 kHz

Answer

(B) 180 kHz

Answer

(C) 360 kHz

Question 49

A ball is thrown vertically upwards with a velocity of 19.6 $\mathrm{ms}^{-1}$ from the top of a tower. The ball strikes the ground after 6 s. The height from the ground up to which the ball can rise will be $\left(\dfrac{k}{5}\right)$ m. The value of k is ..... (use g = 9.8 m/s$^2$)

Accepted Answer

392

Question 50

The distance of centre of mass from end A of a one dimensional rod (AB) having mass density $\rho = \rho_0\left(1 - \dfrac{x^2}{L^2}\right)$ kg/m and length L (in meter) is $\dfrac{3L}{\alpha}$ m. The value of $\alpha$ is ......... (where x is the distance form end A)

Accepted Answer

8

Question 51

A string of area of cross-section 4 mm$^2$ and length 0.5 is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of 5 m/s at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is ...... $	imes 10^{-5}$. (Use Young's modulus $10^{11}$ N/m$^2$ and g = 10 m/s$^2$)

Accepted Answer

30

Question 52

At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be ........ J.

Accepted Answer

750

Question 53

The potential energy of a particle of mass 4 kg in motion along the x-axis is given by $U = 4(1 - \cos 4x)$ J. The time period of the particle for small oscillation $(\sin	heta \simeq 	heta)$ is $\left(\dfrac{\pi}{K}ight)$ s. The value of K is ........

Accepted Answer

2

Question 54

An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about ......... W.

Accepted Answer

14

Question 55

For the given circuit the current through battery of 6 V just after closing the switch 'S' will be ......... A.

Accepted Answer

1

Question 56

An object 'o' is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm/s. The position of the image from the mirror after 10s will be at ....... cm.

Accepted Answer

400

Question 57

In an experiment with a convex lens. The plot of the image distance (v') against the object distance ($\mu$') measured from the focus gives a curve v' $\mu$' = 225. If all the distances are measured in cm. The magnitude of the focal length of the lens is .......... cm.

Accepted Answer

15

Question 58

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillation with a watch of 1s resolution. If measured value of length is 10 cm known to 1mm accuracy. The accuracy in the determination of g is found to be x %. The value of x is

Accepted Answer

5

Question 59

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Zero orbital overlap is an out of phase overlap.
Reason : It results due to different orientation/direction of approach of orbitals.
In the light of the above statements. Choose the correct answer from the options given below

Accepted Answer

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

Answer

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

Answer

(C) A is true but R is false

Answer

(D) A is false but R is true

Question 60

The correct decreasing order for metallic character is

Accepted Answer

(A) $\mathrm{Na > Mg > Be > Si > P}$

Answer

(B) $\mathrm{P > Si > Be > Mg > Na}$

Answer

(C) $\mathrm{Si > P > Be > Na > Mg}$

Answer

(D) $\mathrm{Be > Na > Mg > Si > P}$

Question 61

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The reduction of a metal oxide is easier if the metal formed is in liquid state than solid state.
Reason R : The value of $\Delta \mathrm{G}^{\ominus}$ becomes more on negative side as entropy is higher in liquid state than solid state.
In the light of the above statements. Choose the most appropriate answer from the options given below

Accepted 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

(C) A is correct but R is not correct

Answer

(D) A is not correct but R is correct

Question 62

The products obtained during treatment of hard water using Clark's method are:

Accepted Answer

(C) $\mathrm{CaCO_3}$ and $\mathrm{Mg(OH)_2}$

Answer

(A) $\mathrm{CaCO_3}$ and $\mathrm{MgCO_3}$

Answer

(B) $\mathrm{Ca(OH)_2}$ and $\mathrm{Mg(OH)_2}$

Answer

(D) $\mathrm{Ca(OH)_2}$ and $\mathrm{MgCO_3}$

Question 63

Statement I: An alloy of lithium and magnesium is used to make aircraft plates.
Statement II : The magnesium ions are important for cell-membrane integrity.
In the light 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

White phosphorus reacts with thionyl chloride to give

Accepted Answer

(B) $\mathrm{PCl_3}$. $\mathrm{SO_2}$ and $\mathrm{S_2Cl_2}$

Answer

(A) $\mathrm{PCl_5}$, $\mathrm{SO_2}$ and $\mathrm{S_2Cl_2}$

Answer

(C) $\mathrm{PCl_3}$, $\mathrm{SO_2}$ and $\mathrm{Cl_2}$

Answer

(D) $\mathrm{PCl_5}$, $\mathrm{SO_2}$ and $\mathrm{Cl_2}$

List I (Complex)	List II (Hybridization)
A. $\mathrm{Ni(CO)_4}$	I. $\mathrm{sp^3}$
B. $\mathrm{[Ni\,(CN)_4]^{2-}}$	II. $\mathrm{sp^3d^2}$
C. $\mathrm{[Co\,(CN)_6]^{3-}}$	III. $\mathrm{d^2sp^3}$
D. $\mathrm{[CoF_6]^{3-}}$	IV. $\mathrm{dsp^2}$

JEE Main 28 July 2022 Shift 2 Question Paper with Answers

Physics — JEE Main 28 July 2022 Shift 2

Chemistry — JEE Main 28 July 2022 Shift 2

Mathematics — JEE Main 28 July 2022 Shift 2

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