JEE Main 27 January 2024 Shift 2 Question Paper

Question 1

Considering only the principal values of inverse trigonometric functions, the number of positive real values of $x$ satisfying $	an^{-1}(x)+	an^{-1}(2x)=\dfrac{\pi}{4}$ is :

Accepted Answer

(B) 1

Answer

(A) More than 2

Answer

(C) 2

Answer

(D) 0

Question 2

Consider the function $f:(0,2)	o\mathbb{R}$ defined by $f(x)=\dfrac{x}{2}+\dfrac{2}{x}$ and the function $g(x)$ defined by $g(x)=\begin{cases}\min\{f(t)\},\ 0<t\le x	ext{ and }0<x\le 1 \ \dfrac{3}{2}+x,\ 1<x<2\end{cases}$. Then

Accepted Answer

(A) $g$ is continuous but not differentiable at $x=1$

Answer

(B) $g$ is not continuous for all $x\in(0,2)$

Answer

(C) $g$ is neither continuous nor differentiable at $x=1$

Answer

(D) $g$ is continuous and differentiable for all $x\in(0,2)$

Question 3

Let the image of the point $(1,0,7)$ in the line $\dfrac{x}{1}=\dfrac{y-1}{2}=\dfrac{z-2}{3}$ be the point $(\alpha,\beta,\gamma)$. Then which one of the following points lies on the line passing through $(\alpha,\beta,\gamma)$ and making angles $\dfrac{2\pi}{3}$ and $\dfrac{3\pi}{4}$ with y-axis and z-axis respectively and an acute angle with x-axis ?

Accepted Answer

(C) $\left(3,4,3-2\sqrt2\right)$

Answer

(A) $\left(1,-2,1+\sqrt2\right)$

Answer

(B) $\left(1,2,1-\sqrt2\right)$

Answer

(D) $\left(3,-4,3+2\sqrt2\right)$

Question 4

Let R be the interior region between the lines $3x-y+1=0$ and $x+2y-5=0$ containing the origin. The set of all values of $a$, for which the points $(a^2,a+1)$ lie in R, is :

Accepted Answer

(B) $(-3,0)\cup\left(\dfrac13,1\right)$

Answer

(A) $(-3,-1)\cup\left(-\dfrac13,1\right)$

Answer

(C) $(-3,0)\cup\left(\dfrac23,1\right)$

Answer

(D) $(-3,-1)\cup\left(\dfrac13,1\right)$

Question 5

The $20^{	ext{th}}$ term from the end of the progression $20,19\dfrac14,18\dfrac12,17\dfrac34,\ldots,-129\dfrac14$ is :

Accepted Answer

(C) $-115$

Answer

(A) $-118$

Answer

(B) $-110$

Answer

(D) $-100$

Question 6

Let $f:\mathbb{R}-\left\{-\dfrac12ight\}	o\mathbb{R}$ and $g:\mathbb{R}-\left\{-\dfrac52ight\}	o\mathbb{R}$ be defined as $f(x)=\dfrac{2x+3}{2x+1}$ and $g(x)=\dfrac{|x|+1}{2x+5}$. Then the domain of the function $f\circ g$ is :

Accepted Answer

(A) $\mathbb{R}-\left\{-\dfrac52\right\}$

Answer

(B) $\mathbb{R}$

Answer

(C) $\mathbb{R}-\left\{-\dfrac74\right\}$

Answer

(D) $\mathbb{R}-\left\{-\dfrac52,-\dfrac74\right\}$

Question 7

For $0<a<1$, the value of the integral $\displaystyle\int_{0}^{\pi}\dfrac{dx}{1-2a\cos x+a^2}$ is :

Accepted Answer

(C) $\dfrac{\pi}{1-a^2}$

Answer

(A) $\dfrac{\pi^2}{\pi+a^2}$

Answer

(B) $\dfrac{\pi^2}{\pi-a^2}$

Answer

(D) $\dfrac{\pi}{1+a^2}$

Question 8

Let $g(x)=3f\left(\dfrac{x}{3}\right)+f(3-x)$ and $f''(x)>0$ for all $x\in(0,3)$. If $g$ is decreasing in $(0,\alpha)$ and increasing in $(\alpha,3)$, then $8\alpha$ is

Accepted Answer

(C) 18

Answer

(A) 24

Answer

(B) 0

Answer

(D) 20

Question 9

If $\displaystyle\lim_{x	o 0}\dfrac{3+\alpha\sin x+\beta\cos x+\log_e(1-x)}{3	an^2 x}=\dfrac13$, then $2\alpha-\beta$ is equal to :

Accepted Answer

(C) 5

Answer

(A) 2

Answer

(B) 7

Answer

(D) 1

Question 10

If $\alpha,\beta$ are the roots of the equation $x^2-x-1=0$ and $S_n=2023\alpha^n+2024\beta^n$, then

Accepted Answer

(B) $S_{12}=S_{11}+S_{10}$

Answer

(A) $2S_{12}=S_{11}+S_{10}$

Answer

(C) $2S_{11}=S_{12}+S_{10}$

Answer

(D) $S_{11}=S_{10}+S_{12}$

Question 11

Let A and B be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of the set A is 56 more than the total number of subsets of B. Then the distance of the point $P(m,n)$ from the point $Q(-2,-3)$ is

Accepted Answer

(A) 10

Answer

(B) 6

Answer

(C) 4

Answer

(D) 8

Question 12

The values of $\alpha$, for which $\begin{vmatrix} 1 & \dfrac32 & \alpha+\dfrac32 \ 1 & \dfrac13 & \alpha+\dfrac13 \ 2\alpha+3 & 3\alpha+1 & 0\end{vmatrix}=0$, lie in the interval

Accepted Answer

(B) $(-3,0)$

Answer

(A) $(-2,1)$

Answer

(C) $\left(-\dfrac32,\dfrac32\right)$

Answer

(D) $(0,3)$

Question 13

An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is :

Accepted Answer

(C) $\dfrac{3}{715}$

Answer

(A) $\dfrac{5}{256}$

Answer

(B) $\dfrac{5}{715}$

Answer

(D) $\dfrac{3}{256}$

Question 14

The integral $\displaystyle\int\dfrac{(x^8-x^2)\,dx}{(x^{12}+3x^6+1)	an^{-1}\left(x^3+\dfrac{1}{x^3}ight)}$ is equal to :

Accepted Answer

(A) $\log_e\left(\left|	an^{-1}\left(x^3+\dfrac{1}{x^3}ight)ight|^{1/3}ight)+C$

Answer

(B) $\log_e\left(\left|	an^{-1}\left(x^3+\dfrac{1}{x^3}ight)ight|^{1/2}ight)+C$

Answer

(C) $\log_e\left(\left|	an^{-1}\left(x^3+\dfrac{1}{x^3}ight)ight|ight)+C$

Answer

(D) $\log_e\left(\left|	an^{-1}\left(x^3+\dfrac{1}{x^3}ight)ight|^{3}ight)+C$

Question 15

If $2	an^2	heta-5\sec	heta=1$ has exactly 7 solutions in the interval $\left[0,\dfrac{n\pi}{2}ight]$, for the least value of $n\in\mathbb{N}$, then $\displaystyle\sum_{k=1}^{n}\dfrac{k}{2^k}$ is equal to :

Accepted Answer

(D) $\dfrac{1}{2^{13}}(2^{14}-15)$

Answer

(A) $\dfrac{1}{2^{15}}(2^{14}-14)$

Answer

(B) $\dfrac{1}{2^{14}}(2^{15}-15)$

Answer

(C) $1-\dfrac{15}{2^{13}}$

Question 16

The position vectors of the vertices A, B and C of a triangle are $2\hat i-3\hat j+3\hat k$, $2\hat i+2\hat j+3\hat k$ and $-\hat i+\hat j+3\hat k$ respectively. Let $l$ denotes the length of the angle bisector AD of $\angle BAC$ where D is on the line segment BC, then $2l^2$ equals :

Accepted Answer

(D) 45

Answer

(A) 49

Answer

(B) 42

Answer

(C) 50

Question 17

If $y=y(x)$ is the solution curve of the differential equation $(x^2-4)\,dy-(y^2-3y)\,dx=0$, $x>2$, $y(4)=\dfrac32$ and the slope of the curve is never zero, then the value of $y(10)$ equals :

Accepted Answer

(A) $\dfrac{3}{1+(8)^{1/4}}$

Answer

(B) $\dfrac{3}{1+2\sqrt2}$

Answer

(C) $\dfrac{3}{1-2\sqrt2}$

Answer

(D) $\dfrac{3}{1-(8)^{1/4}}$

Question 18

Let $e_1$ be the eccentricity of the hyperbola $\dfrac{x^2}{16}-\dfrac{y^2}{9}=1$ and $e_2$ be the eccentricity of the ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, $a>b$, which passes through the foci of the hyperbola. If $e_1 e_2=1$, then the length of the chord of the ellipse parallel to the x-axis and passing through $(0,2)$ is :

Accepted Answer

(C) $\dfrac{10\sqrt5}{3}$

Answer

(A) $4\sqrt5$

Answer

(B) $\dfrac{8\sqrt5}{3}$

Answer

(D) $3\sqrt5$

Question 19

Let $\alpha=\dfrac{(4!)!}{(4!)^{3!}}$ and $\beta=\dfrac{(5!)!}{(5!)^{4!}}$. Then :

Accepted Answer

(C) $\alpha\in\mathbb{N}$ and $\beta\in\mathbb{N}$

Answer

(A) $\alpha\in\mathbb{N}$ and $\beta
otin\mathbb{N}$

Answer

(B) $\alpha
otin\mathbb{N}$ and $\beta\in\mathbb{N}$

Answer

(D) $\alpha
otin\mathbb{N}$ and $\beta
otin\mathbb{N}$

Question 20

Let the position vectors of the vertices A, B and C of a triangle be $2\hat i+2\hat j+\hat k$, $\hat i+2\hat j+2\hat k$ and $2\hat i+\hat j+2\hat k$ respectively. Let $l_1$, $l_2$ and $l_3$ be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides AB, BC and CA respectively, then $l_1^2+l_2^2+l_3^2$ equals :

Accepted Answer

(B) $\dfrac12$

Answer

(A) $\dfrac15$

Answer

(C) $\dfrac14$

Answer

(D) $\dfrac13$

Question 21

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12. If $\mu$ and $\sigma^2$ denote the mean and variance of the correct observations respectively, then $15(\mu+\mu^2+\sigma^2)$ is equal to __________.

Accepted Answer

2521

Question 22

If the area of the region $\{(x,y):0\le y\le\min\{2x,6x-x^2\}\}$ is A, then $12A$ is equal to __________.

Accepted Answer

304

Question 23

Let A be a $2	imes 2$ real matrix and I be the identity matrix of order 2. If the roots of the equation $|A-xI|=0$ be $-1$ and $3$, then the sum of the diagonal elements of the matrix $A^2$ is __________.

Accepted Answer

10

Question 24

If the sum of squares of all real values of $\alpha$, for which the lines $2x-y+3=0$, $6x+3y+1=0$ and $\alpha x+2y-2=0$ do not form a triangle is $p$, then the greatest integer less than or equal to $p$ is __________.

Accepted Answer

32

Question 25

The coefficient of $x^{2012}$ in the expansion of $(1-x)^{2008}(1+x+x^2)^{2007}$ is equal to __________.

Accepted Answer

0

Question 26

If the solution curve, of the differential equation $\dfrac{dy}{dx}=\dfrac{x+y-2}{x-y}$ passing through the point $(2,1)$ is $	an^{-1}\left(\dfrac{y-1}{x-1}ight)-\dfrac{1}{\beta}\log_e\left(\alpha+\left(\dfrac{y-1}{x-1}ight)^2ight)=\log_e|x-1|$, then $5\beta+\alpha$ is equal to __________.

Accepted Answer

11

Question 27

Let $f(x)=\displaystyle\int_{0}^{x} g(t)\log_e\left(\dfrac{1-t}{1+t}\right)dt$, where $g$ is a continuous odd function. If $\displaystyle\int_{-\pi/2}^{\pi/2}\left(f(x)+\dfrac{x^2\cos x}{1+e^x}\right)dx=\left(\dfrac{\pi}{\alpha}\right)^2-\alpha$, then $\alpha$ is equal to __________.

Accepted Answer

2

Question 28

Consider a circle $(x-\alpha)^2+(y-\beta)^2=50$, where $\alpha,\beta>0$. If the circle touches the line $y+x=0$ at the point P, whose distance from the origin is $4\sqrt2$, then $(\alpha+\beta)^2$ is equal to __________.

Accepted Answer

100

Question 29

The lines $\dfrac{x-2}{1}=\dfrac{y}{-2}=\dfrac{z-7}{8}$ and $\dfrac{x+3}{4}=\dfrac{y+2}{3}=\dfrac{z+2}{1}$ intersect at the point P. If the distance of P from the line $\dfrac{x+1}{2}=\dfrac{y-1}{3}=\dfrac{z-1}{1}$ is $l$, then $14l^2$ is equal to __________.

Accepted Answer

108

Question 30

Let the complex numbers $\alpha$ and $\dfrac{1}{\bar\alpha}$ lie on the circles $|z-z_0|^2=4$ and $|z-z_0|^2=16$ respectively, where $z_0=1+i$. Then, the value of $100|\alpha|^2$ is __________.

Accepted Answer

20

Question 31

The equation of state of a real gas is given by $\left(P+\dfrac{a}{V^2}\right)(V-b)=RT$, where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of $\dfrac{a}{b^2}$ is similar to that of :

Accepted Answer

(B) P

Answer

(A) PV

Answer

(C) RT

Answer

(D) R

Question 32

Wheatstone bridge principle is used to measure the specific resistance $(S_l)$ of given wire, having length L, radius r. If X is the resistance of wire, then specific resistance is $S_l=X\left(\dfrac{\pi r^2}{L}\right)$. If the length of the wire gets doubled then the value of specific resistance will be :

Accepted Answer

(D) $S_l$

Answer

(A) $\dfrac{S_l}{4}$

Answer

(B) $2S_l$

Answer

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

Question 33

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
Reason (R) : The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements, choose the most appropriate answer from the options given below : (1) (A) is correct but (R) is not correct (2) Both (A) and (R) are correct and (R) is the correct explanation of (A) (3) (A) is not correct but (R) is correct (4) (A) is correct but (R) is not the correct explanation of (A)

Accepted Answer

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

Answer

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

Answer

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

Answer

(D) (A) is correct but (R) is not the correct explanation of (A)

Question 34

Given below are two statements : Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials. Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials. In the light of the above statements, choose the most appropriate answer from the options given below :

Accepted Answer

(B) Statement I is incorrect but Statement II is correct

Answer

(A) Statement I is correct but Statement II is incorrect

Answer

(C) Both Statement I and Statement II are incorrect

Answer

(D) Both Statement I and Statement II are correct

Question 35

The truth table of the given circuit diagram is :

Accepted Answer

(B) $\begin{array}{ccc} A&B&Y\ 0&0&0\ 0&1&1\ 1&0&1\ 1&1&0\end{array}$

Answer

(A) $\begin{array}{ccc} A&B&Y\ 0&0&0\ 0&1&0\ 1&0&0\ 1&1&1\end{array}$

Answer

(C) $\begin{array}{ccc} A&B&Y\ 0&0&0\ 0&1&1\ 1&0&1\ 1&1&1\end{array}$

Answer

(D) $\begin{array}{ccc} A&B&Y\ 0&0&1\ 0&1&1\ 1&0&1\ 1&1&0\end{array}$

Question 36

A current of 200 $\mu$A deflects the coil of a moving coil galvanometer through $60^\circ$. The current to cause deflection through $\dfrac{\pi}{10}$ radian is :

Accepted Answer

(A) $60\,\mu$A

Answer

(B) $120\,\mu$A

Answer

(C) $30\,\mu$A

Answer

(D) $180\,\mu$A

Question 37

The atomic mass of $_6	ext{C}^{12}$ is 12.000000 u and that of $_6	ext{C}^{13}$ is 13.003354 u. The required energy to remove a neutron from $_6	ext{C}^{13}$, if mass of neutron is 1.008665 u, will be :

Accepted Answer

(C) 4.95 MeV

Answer

(A) 62.5 MeV

Answer

(B) 6.25 MeV

Answer

(D) 49.5 MeV

Question 38

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $	heta$ of thread deflection in the extreme position will be :

Accepted Answer

(B) $2	an^{-1}\left(\dfrac12ight)$

Answer

(A) $	an^{-1}(\sqrt2)$

Answer

(C) $	an^{-1}\left(\dfrac12ight)$

Answer

(D) $2	an^{-1}\left(\dfrac{1}{\sqrt5}ight)$

Question 39

Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across A and B, their readings are $V_1$, $V_2$ and $V_3$. Choose the correct option.

Accepted Answer

(D) $V_1+V_2=V_3$

Answer

(A) $V_1=V_2$

Answer

(B) $V_1=V_3-V_2$

Answer

(C) $V_1+V_2>V_3$

Question 40

The total kinetic energy of 1 mole of oxygen at $27^\circ$C is : [Use universal gas constant (R) = 8.31 J/mole K]

Accepted Answer

(C) 6232.5 J

Answer

(A) 6845.5 J

Answer

(B) 5942.0 J

Answer

(D) 5670.5 J

Question 41

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading.
Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

(C) (A) is true but (R) is false

Answer

(D) (A) is false but (R) is true

Question 42

Primary side of a transformer is connected to 230 V, 50 Hz supply. Turns ratio of primary to secondary winding is $10:1$. Load resistance connected to secondary side is 46 $\Omega$. The power consumed in it is :

Accepted Answer

(C) 11.5 W

Answer

(A) 12.5 W

Answer

(B) 10.0 W

Answer

(D) 12.0 W

Question 43

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $\dfrac{C_P}{C_V}$ for the gas is :

Accepted Answer

(B) $\dfrac73$

Answer

(A) $\dfrac53$

Answer

(C) $\dfrac75$

Answer

(D) $\dfrac97$

Question 44

The threshold frequency of a metal with work function 6.63 eV is :

Accepted Answer

(D) $1.6	imes10^{15}$ Hz

Answer

(A) $16	imes10^{15}$ Hz

Answer

(B) $16	imes10^{12}$ Hz

Answer

(C) $1.6	imes10^{12}$ Hz

Question 45

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity.
Reason (R) : The restoring force depends on the bonded inter atomic and inter molecular force of solid.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

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

Answer

(A) (A) is true but (R) is false

Answer

(B) (A) is false but (R) is true

Answer

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

Question 46

When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of :

Accepted Answer

(D) $45^\circ$

Answer

(A) $60^\circ$

Answer

(B) $30^\circ$

Answer

(C) $90^\circ$

Question 47

An object is placed in a medium of refractive index 3. An electromagnetic wave of intensity $6	imes10^7$ W/m$^2$ falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space $=3	imes10^8$ m/s) :

Accepted Answer

(C) $6$ Nm$^{-2}$

Answer

(A) $36$ Nm$^{-2}$

Answer

(B) $18$ Nm$^{-2}$

Answer

(D) $2$ Nm$^{-2}$

Question 48

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero.
Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces.
In the light of the above statements, choose the most appropriate answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 49

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle $60^\circ$ with the horizontal, the weight experienced by the man is :

Accepted Answer

(C) 3 kg

Answer

(A) 6 kg

Answer

(B) 12 kg

Answer

(D) $6\sqrt3$ kg

Question 50

The magnetic field at the centre O of a wire loop formed by two semicircular wires of radii $R_1=2\pi$ m and $R_2=4\pi$ m carrying current $I=4$ A as that figure given below is $\alpha	imes10^{-7}$ T. The value of $\alpha$ is ________. (Centre O is common for all segments)

Accepted Answer

3.00

Question 51

Two charges of $-4\,\mu$C and $+4\,\mu$C are placed at the points A(1,0,4) m and B(2,-1,5) m located in an electric field $\vec E=0.20\,\hat i$ V/cm. The magnitude of the torque acting on the dipole is $8\sqrt\alpha	imes10^{-5}$ Nm. Where $\alpha$ is ________.

Accepted Answer

2.00

Question 52

A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is ________ m/s.

Accepted Answer

294.00

Question 53

A body falling under gravity covers two points A and B separated by 80 m in 2 s. The distance of upper point A from the starting point is ________ m. (use $g=10$ ms$^{-2}$)

Accepted Answer

45.00

Question 54

The reading of pressure metre attached with a closed pipe is $4.5	imes10^5$ N/m$^2$. On opening the valve, water starts flowing and the reading of pressure metre falls to $2.0	imes10^5$ N/m$^2$. The velocity of water is found to be $\sqrt V$ m/s. The value of V is ________.

Accepted Answer

50.00

Question 55

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is $\dfrac{7}{x}$ where x is ________.

Accepted Answer

7.00

Question 56

A parallel beam of monochromatic light of wavelength 5000 $\mathring{A}$ is incident normally on a single narrow slit of width 0.001 mm. The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of ________ (degree).

Accepted Answer

30.00

Question 57

The electric potential at the surface of an atomic nucleus $(Z=50)$ of radius $9	imes10^{-13}$ cm is ________ $	imes10^6$ V.

Accepted Answer

8.00

Question 58

If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be $\dfrac{\alpha}{7R}$, where $\alpha$ is ________.

Accepted Answer

144.00

Question 59

A series LCR circuit with $L=\dfrac{100}{\pi}$ mH, $C=\dfrac{10^{-3}}{\pi}$ F and $R=10\,\Omega$, is connected across an ac source of 220 V, 50 Hz supply. The power factor of the circuit would be ________.

Accepted Answer

1.00

Question 60

The order of relative stability of the contributing structures (I, II and III) is :

Accepted Answer

(A) I > II > III

Answer

(B) II > I > III

Answer

(C) I = II = III

Answer

(D) III > II > I

Question 61

Which among the following halide/s will not show $S_N1$ reaction ? Choose the most appropriate answer from the options given below :

Accepted Answer

(D) (B) only

Answer

(A) (A), (B) and (D) only

Answer

(B) (A) and (B) only

Answer

(C) (B) and (C) only

Question 62

Which of the following statements is not correct about rusting of iron ?

Accepted Answer

(A) Coating of iron surface by tin prevents rusting, even if the tin coating is peeling off.

Answer

(B) When pH lies above 9 or 10, rusting of iron does not take place.

Answer

(C) Dissolved acidic oxides $SO_2$, $NO_2$ in water act as catalyst in the process of rusting.

Answer

(D) Rusting of iron is envisaged as setting up of electrochemical cell on the surface of iron object.

Question 63

Given below are two statements : Statement (I) : In the Lanthanoids, the formation of $Ce^{+4}$ is favoured by its noble gas configuration. Statement (II) : $Ce^{+4}$ is a strong oxidant reverting to the common +3 state. In the light of the above statements, choose the most appropriate answer from the options given below :

Accepted Answer

(B) Both Statement I and Statement II are true

Answer

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

Answer

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

Answer

(D) Both Statement I and Statement II are false

Question 64

Choose the correct option having all the elements with $d^{10}$ electronic configuration from the following :

Accepted Answer

(B) $_{29}$Cu, $_{30}$Zn, $_{48}$Cd, $_{47}$Ag

Answer

(A) $_{27}$Co, $_{28}$Ni, $_{24}$Cr

Answer

(C) $_{46}$Pd, $_{28}$Ni, $_{26}$Fe, $_{24}$Cr

Answer

(D) $_{28}$Ni, $_{24}$Cr, $_{26}$Fe, $_{29}$Cu

List-I (Reaction)	List-II (Reagent)
A.see figure	I. $Na_2Cr_2O_7$ ; $H_2SO_4$
B.see figure	II.(i) NaOH (ii) $CH_3Cl$
C.see figure	III.(i) NaOH, $CHCl_3$ (ii) NaOH (iii) HCl
D.see figure	IV.(i) $CO_2$ (ii) HCl

JEE Main 27 January 2024 Shift 2 Question Paper with Answers

Physics — JEE Main 27 January 2024 Shift 2

Chemistry — JEE Main 27 January 2024 Shift 2

Mathematics — JEE Main 27 January 2024 Shift 2

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