JEE Main 31 January 2024 Shift 1 Question Paper

Question 1

For $0<c<b<a$, let $(a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0$ and $\alpha
e 1$ be one of its root. Then, among the two statements (I) If $\alpha\in(-1,0)$, then b cannot be the geometric mean of a and c (II) If $\alpha\in(0,1)$, then b may be the geometric mean of a and c

Accepted Answer

(A) Both (I) and (II) are true

Answer

(B) Neither (I) nor (II) is true

Answer

(C) Only (II) is true

Answer

(D) Only (I) is true

Question 2

Let a be the sum of all coefficients in the expansion of $\left(1-2x+2x^2ight)^{2023}\left(3-4x^2+2x^3ight)^{2024}$ and $b=\displaystyle\lim_{x	o 0}\left(\dfrac{\int_0^x \frac{\log(1+t)}{t^{2024}+1}dt}{x^2}ight)$. If the equations $cx^2+dx+e=0$ and $2bx^2+ax+4=0$ have a common root, where $c,d,e\in R$, then $d:c:e$ equals

Accepted Answer

(D) $1:1:4$

Answer

(A) $2:1:4$

Answer

(B) $4:1:4$

Answer

(C) $1:2:4$

Question 3

If the foci of a hyperbola are same as that of the ellipse $\dfrac{x^2}{9}+\dfrac{y^2}{25}=1$ and the eccentricity of the hyperbola is $\dfrac{15}{8}$ times the eccentricity of the ellipse, then the smaller focal distance of the point $\left(\sqrt{2},\dfrac{14}{3}\sqrt{\dfrac{2}{5}}\right)$ on the hyperbola, is equal to

Accepted Answer

(A) $7\sqrt{\dfrac{2}{5}}-\dfrac{8}{3}$

Answer

(B) $14\sqrt{\dfrac{2}{5}}-\dfrac{4}{3}$

Answer

(C) $14\sqrt{\dfrac{2}{5}}-\dfrac{16}{3}$

Answer

(D) $7\sqrt{\dfrac{2}{5}}+\dfrac{8}{3}$

Question 4

If one of the diameters of the circle $x^2+y^2-10x+4y+13=0$ is a chord of another circle C, whose center is the point of intersection of the lines $2x+3y=12$ and $3x-2y=5$, then the radius of the circle C is

Accepted Answer

(C) $6$

Answer

(A) $\sqrt{20}$

Answer

(B) $4$

Answer

(D) $3\sqrt{2}$

Question 5

The area of the region $\left\{(x,y): y^2\le 4x,\ x<4,\ \dfrac{xy(x-1)(x-2)}{(x-3)(x-4)}>0,\ x
e 3ight\}$ is

Accepted Answer

(D) $\dfrac{32}{3}$

Answer

(A) $\dfrac{16}{3}$

Answer

(B) $\dfrac{64}{3}$

Answer

(C) $\dfrac{8}{3}$

Question 6

If $f(x)=\dfrac{4x+3}{6x-4}$, $x
e\dfrac{2}{3}$ and $(f\circ f)(x)=g(x)$, where $g:R-\left\{\dfrac{2}{3}ight\}	o R-\left\{\dfrac{2}{3}ight\}$, then $(g\circ g\circ g)(4)$ is equal to

Accepted Answer

(D) $4$

Answer

(A) $-\dfrac{19}{20}$

Answer

(B) $\dfrac{19}{20}$

Answer

(C) $-4$

Question 7

$\displaystyle\lim_{x	o 0}\dfrac{e^{2|\sin x|}-2|\sin x|-1}{x^2}$

Accepted Answer

(D) is equal to $2$

Answer

(A) is equal to $-1$

Answer

(B) does not exist

Answer

(C) is equal to $1$

Question 8

If the system of linear equations $x-2y+z=-4$; $2x+\alpha y+3z=5$; $3x-y+\beta z=3$ has infinitely many solutions, then $12\alpha+13\beta$ is equal to

Accepted Answer

(D) $58$

Answer

(A) $60$

Answer

(B) $64$

Answer

(C) $54$

Question 9

The solution curve of the differential equation $y\dfrac{dx}{dy}=x\left(\log_e x-\log_e y+1\right)$, $x>0,\ y>0$ passing through the point $(e,1)$ is

Accepted Answer

(C) $\left|\log_e\dfrac{x}{y}\right|=y$

Answer

(A) $\left|\log_e\dfrac{y}{x}\right|=x$

Answer

(B) $\left|\log_e\dfrac{y}{x}\right|=y^2$

Answer

(D) $2\left|\log_e\dfrac{x}{y}\right|=y+1$

Question 10

Let $\alpha,\beta,\gamma,\delta\in Z$ and let $A(\alpha,\beta)$, $B(1,0)$, $C(\gamma,\delta)$ and $D(1,2)$ be the vertices of a parallelogram ABCD. If $AB=\sqrt{10}$ and the points A and C lie on the line $3y=2x+1$, then $2(\alpha+\beta+\gamma+\delta)$ is equal to

Accepted Answer

(D) $8$

Answer

(A) $10$

Answer

(B) $5$

Answer

(C) $12$

Question 11

Let $y=y(x)$ be the solution of the differential equation $\dfrac{dy}{dx}=\dfrac{	an x+y}{\sin x(\sec x-\sin x	an x)}$, $x\in\left(0,\dfrac{\pi}{2}ight)$ satisfying the condition $y\left(\dfrac{\pi}{4}ight)=2$. Then, $y\left(\dfrac{\pi}{3}ight)$ is

Accepted Answer

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

Answer

(B) $\dfrac{\sqrt{3}}{2}\left(2+\log_e 3\right)$

Answer

(C) $\sqrt{3}\left(1+2\log_e 3\right)$

Answer

(D) $\sqrt{3}\left(2+\log_e 3\right)$

Question 12

Let $\vec{a}=3\hat{i}+\hat{j}-2\hat{k}$, $\vec{b}=4\hat{i}+\hat{j}+7\hat{k}$ and $\vec{c}=\hat{i}-3\hat{j}+4\hat{k}$ be three vectors. If a vector $\vec{p}$ satisfies $\vec{p}	imes\vec{b}=\vec{c}	imes\vec{b}$ and $\vec{p}\cdot\vec{a}=0$, then $\vec{p}\cdot\left(\hat{i}-\hat{j}-\hat{k}ight)$ is equal to

Accepted Answer

(D) $32$

Answer

(A) $24$

Answer

(B) $36$

Answer

(C) $28$

Question 13

The sum of the series $\dfrac{1}{1-3\cdot 1^2+1^4}+\dfrac{2}{1-3\cdot 2^2+2^4}+\dfrac{3}{1-3\cdot 3^2+3^4}+\cdots$ up to 10 terms is

Accepted Answer

(D) $-\dfrac{55}{109}$

Answer

(A) $\dfrac{45}{109}$

Answer

(B) $-\dfrac{45}{109}$

Answer

(C) $\dfrac{55}{109}$

Question 14

The distance of the point $Q(0,2,-2)$ from the line passing through the point $P(5,-4,3)$ and perpendicular to the lines $\vec{r}=\left(-3\hat{i}+2\hat{k}\right)+\lambda\left(2\hat{i}+3\hat{j}+5\hat{k}\right)$, $\lambda\in R$ and $\vec{r}=\left(\hat{i}-2\hat{j}+\hat{k}\right)+\mu\left(-\hat{i}+3\hat{j}+2\hat{k}\right)$, $\mu\in R$ is

Accepted Answer

(D) $\sqrt{74}$

Answer

(A) $\sqrt{86}$

Answer

(B) $\sqrt{20}$

Answer

(C) $\sqrt{54}$

Question 15

For $\alpha,\beta,\gamma
e 0$. If $\sin^{-1}\alpha+\sin^{-1}\beta+\sin^{-1}\gamma=\pi$ and $(\alpha+\beta+\gamma)(\alpha-\gamma+\beta)=3\alpha\beta$, then $\gamma$ equal to

Accepted Answer

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

Answer

(B) $\dfrac{1}{\sqrt{2}}$

Answer

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

Answer

(D) $\sqrt{3}$

Question 16

Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is

Accepted Answer

(D) $\dfrac{4}{75}$

Answer

(A) $\dfrac{2}{25}$

Answer

(B) $\dfrac{4}{25}$

Answer

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

Question 17

Let $g(x)$ be a linear function and $f(x)=\begin{cases}g(x), & x\le 0\ \left(\dfrac{1+x}{2+x}ight)^{\frac{1}{x}}, & x>0\end{cases}$, is continuous at $x=0$. If $f'(1)=f(-1)$, then the value of $g(3)$ is

Accepted Answer

(D) $\log_e\left(\dfrac{4}{9e^{1/3}}\right)$

Answer

(A) $\dfrac{1}{3}\log_e\left(\dfrac{4}{9e^{1/3}}\right)$

Answer

(B) $\dfrac{1}{3}\log_e\left(\dfrac{4}{9}\right)+1$

Answer

(C) $\log_e\left(\dfrac{4}{9}\right)-1$

Question 18

If $f(x)=\begin{vmatrix}x^3 & 2x^2+1 & 1+3x\ 3x^2+2 & 2x & x^3+6\ x^3-x & 4 & x^2-2\end{vmatrix}$ for all $x\in R$, then $2f(0)+f'(0)$ is equal to

Accepted Answer

(C) $42$

Answer

(A) $48$

Answer

(B) $24$

Answer

(D) $18$

Question 19

Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable x to be the number of rotten apples in a draw of two apples, the variance of x is

Accepted Answer

(D) $\dfrac{40}{153}$

Answer

(A) $\dfrac{37}{153}$

Answer

(B) $\dfrac{57}{153}$

Answer

(C) $\dfrac{47}{153}$

Question 20

Let S be the set of positive integral values of a for which $\dfrac{ax^2+2(a+1)x+9a+4}{x^2-8x+32}<0$, $\forall x\in R$. Then, the number of elements in S is

Accepted Answer

(B) $0$

Answer

(A) $1$

Answer

(C) $\infty$

Answer

(D) $3$

Question 21

If the integral $525\displaystyle\int_0^{\pi/2}\sin 2x\cos^{11/2}x\left(1+\cos^{5/2}x\right)^{1/2}dx$ is equal to $\left(n\sqrt{2}-64\right)$, then n is equal to ______.

Accepted Answer

176

Question 22

Let $S=(-1,\infty)$ and $f:S	o R$ be defined as $f(x)=\displaystyle\int_{-1}^x \left(e^t-1ight)^{11}(2t-1)^5(t-2)^7(t-3)^{12}(2t-10)^{61}dt$. Let p = Sum of square of the values of x, where $f(x)$ attains local maxima on S, and q = Sum of the values of x, where $f(x)$ attains local minima on S. Then, the value of $p^2+2q$ is ______.

Accepted Answer

27

Question 23

The total number of words (with or without meaning) that can be formed out of the letters of the word "DISTRIBUTION" taken four at a time, is equal to ______.

Accepted Answer

3734

Question 24

Let Q and R be the feet of perpendiculars from the point $P(a,a,a)$ on the lines $x=y$, $z=1$ and $x=-y$, $z=-1$ respectively. If $\angle QPR$ is a right angle, then $12a^2$ is equal to ______.

Accepted Answer

12

Question 25

In the expansion of $(1+x)\left(1-x^2ight)\left(1+\dfrac{3}{x}+\dfrac{3}{x^2}+\dfrac{1}{x^3}ight)^5$, $x
e 0$, the sum of the coefficient of $x^3$ and $x^{-13}$ is equal to ______.

Accepted Answer

118

Question 26

If $\alpha$ denotes the number of solutions of $|1-i|^x=2^x$ and $\beta=\dfrac{|z|}{\arg(z)}$, where $z=\dfrac{\pi}{4}(1+i)^4\left[\dfrac{1-\sqrt{\pi}i}{\sqrt{\pi}+i}+\dfrac{\sqrt{\pi}-i}{1+\sqrt{\pi}i}\right]$, $i=\sqrt{-1}$, then the distance of the point $(\alpha,\beta)$ from the line $4x-3y=7$ is ______.

Accepted Answer

3

Question 27

Let the foci and length of the latus rectum of an ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, $a>b$ be $(\pm 5,0)$ and $\sqrt{50}$ respectively. Then, the square of the eccentricity of the hyperbola $\dfrac{x^2}{b^2}-\dfrac{y^2}{a^2 b^2}=1$ equals ______.

Accepted Answer

51

Question 28

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=1$, $|\vec{b}|=4$ and $\vec{a}\cdot\vec{b}=2$. If $\vec{c}=(2\vec{a}	imes\vec{b})-3\vec{b}$ and the angle between $\vec{b}$ and $\vec{c}$ is $\alpha$, then $192\sin^2\alpha$ is equal to ______.

Accepted Answer

48

Question 29

Let $A=\{1,2,3,4\}$ and $R=\{(1,2),(2,3),(1,4)\}$ be a relation on A. Let S be the equivalence relation on A such that $R\subset S$ and the number of elements in S is n. Then, the minimum value of n is ______.

Accepted Answer

16

Question 30

Let $f:R	o R$ be a function defined by $f(x)=\dfrac{4^x}{4^x+2}$ and $M=\displaystyle\int_{f(a)}^{f(1-a)} x\sin^4\left(x(1-x)ight)dx$, $N=\displaystyle\int_{f(a)}^{f(1-a)}\sin^4\left(x(1-x)ight)dx$; $a
e\dfrac{1}{2}$. If $\alpha M=\beta N$, $\alpha,\beta\in N$, then the least value of $\alpha^2+\beta^2$ is equal to ______.

Accepted Answer

5

Question 31

The parameter that remains the same for molecules of all gases at a given temperature is :

Accepted Answer

(A) kinetic energy

Answer

(B) momentum

Answer

(C) mass

Answer

(D) speed

Question 32

Identify the logic operation performed by the given circuit.

Accepted Answer

(C) OR

Answer

(A) NAND

Answer

(B) NOR

Answer

(D) AND

Question 33

The relation between time 't' and distance 'x' is $t=\alpha x^2+\beta x$, where $\alpha$ and $\beta$ are constants. The relation between acceleration (a) and velocity (v) is :

Accepted Answer

(A) $a=-2\alpha v^3$

Answer

(B) $a=-5\alpha v^5$

Answer

(C) $a=-3\alpha v^2$

Answer

(D) $a=-4\alpha v^4$

Question 34

The refractive index of a prism with apex angle A is $\cot\dfrac{A}{2}$. The angle of minimum deviation is :

Accepted Answer

(D) $\delta_m=180^\circ-2A$

Answer

(A) $\delta_m=180^\circ-A$

Answer

(B) $\delta_m=180^\circ-3A$

Answer

(C) $\delta_m=180^\circ-4A$

Question 35

A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field $B=B_0\hat{j}$ as shown in figure. The magnetic force on the wire if it has a current i is :

Accepted Answer

(D) $-2iBR\hat{j}$

Answer

(A) $-iBR\hat{j}$

Answer

(B) $2iBR\hat{j}$

Answer

(C) $iBR\hat{j}$

Question 36

If the wavelength of the first member of Lyman series of hydrogen is $\lambda$. The wavelength of the second member will be :

Accepted Answer

(A) $\dfrac{27}{32}\lambda$

Answer

(B) $\dfrac{32}{27}\lambda$

Answer

(C) $\dfrac{27}{5}\lambda$

Answer

(D) $\dfrac{5}{27}\lambda$

Question 37

Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is $\left(\dfrac{2\sqrt{2}+1}{32}\right)\dfrac{Gm^2}{L^2}$, the length of the sides of the square is :

Accepted Answer

(B) $4L$

Answer

(A) $\dfrac{L}{2}$

Answer

(C) $3L$

Answer

(D) $2L$

Question 38

The given figure represents two isobaric processes for the same mass of an ideal gas, then

Accepted Answer

(D) $P_1>P_2$

Answer

(A) $P_2\ge P_1$

Answer

(B) $P_2>P_1$

Answer

(C) $P_1=P_2$

Question 39

If the percentage errors in measuring the length and the diameter of a wire are 0.1% each. The percentage error in measuring its resistance will be :

Accepted Answer

(B) $0.3\%$

Answer

(A) $0.2\%$

Answer

(C) $0.1\%$

Answer

(D) $0.144\%$

Question 40

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5	imes10^{10}$ Hz and an amplitude of 50 Vm$^{-1}$. The total average energy density of the electromagnetic field of the wave is : [Use $\epsilon_0=8.85	imes10^{-12}$ C$^2$/Nm$^2$]

Accepted Answer

(A) $1.106	imes10^{-8}$ Jm$^{-3}$

Answer

(B) $4.425	imes10^{-8}$ Jm$^{-3}$

Answer

(C) $2.212	imes10^{-8}$ Jm$^{-3}$

Answer

(D) $2.212	imes10^{-10}$ Jm$^{-3}$

Question 41

A force is represented by $F=ax^2+bt^{1/2}$ where x = distance and t = time. The dimensions of $\dfrac{b^2}{a}$ are :

Accepted Answer

(A) $[ML^3T^{-3}]$

Answer

(B) $[MLT^{-2}]$

Answer

(C) $[ML^{-1}T^{-1}]$

Answer

(D) $[ML^2T^{-3}]$

Question 42

Two charges q and 3q are separated by a distance 'r' in air. At a distance x from charge q, the resultant electric field is zero. The value of x is :

Accepted Answer

(C) $\dfrac{r}{(1+\sqrt{3})}$

Answer

(A) $\dfrac{(1+\sqrt{3})}{r}$

Answer

(B) $\dfrac{r}{3(1+\sqrt{3})}$

Answer

(D) $r(1+\sqrt{3})$

Question 43

In the given arrangement of a doubly inclined plane two blocks of masses M and m are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of m, for which M = 10 kg will move down with an acceleration of 2 m/s$^2$, is : (take $g=10$ m/s$^2$ and $	an 37^\circ=3/4$)

Accepted Answer

(B) 4.5 kg

Answer

(A) 9 kg

Answer

(C) 6.5 kg

Answer

(D) 2.25 kg

Question 44

A coil is placed perpendicular to a magnetic field of 5000 T. When the field is changed to 3000 T in 2s, an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m, then the number of turns in the coil is :

Accepted Answer

(B) 70

Answer

(A) 7

Answer

(C) 35

Answer

(D) 140

Question 45

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is 60 cm, the length of the closed pipe will be :

Accepted Answer

(D) 15 cm

Answer

(A) 60 cm

Answer

(B) 45 cm

Answer

(C) 30 cm

Question 46

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 47

A coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is r, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :

Accepted Answer

(C) $\sqrt{\dfrac{\mu g}{r}}$

Answer

(A) $\dfrac{\mu g}{r}$

Answer

(B) $\sqrt{\dfrac{r}{\mu g}}$

Answer

(D) $\dfrac{\mu}{\sqrt{rg}}$

Question 48

Two conductors have the same resistances at 0$^\circ$C but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficients for their series and parallel combinations are :

Accepted Answer

(B) $\dfrac{\alpha_1+\alpha_2}{2},\ \dfrac{\alpha_1+\alpha_2}{2}$

Answer

(A) $\alpha_1+\alpha_2,\ \dfrac{\alpha_1+\alpha_2}{2}$

Answer

(C) $\alpha_1+\alpha_2,\ \dfrac{\alpha_1\alpha_2}{\alpha_1+\alpha_2}$

Answer

(D) $\dfrac{\alpha_1+\alpha_2}{2},\ \alpha_1+\alpha_2$

Question 49

An artillery piece of mass $M_1$ fires a shell of mass $M_2$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is :

Accepted Answer

(B) $\dfrac{M_2}{M_1}$

Answer

(A) $\dfrac{M_1}{(M_1+M_2)}$

Answer

(C) $\dfrac{M_2}{(M_1+M_2)}$

Answer

(D) $\dfrac{M_1}{M_2}$

Question 50

When a metal surface is illuminated by light of wavelength $\lambda$, the stopping potential is 8V. When the same surface is illuminated by light of wavelength $3\lambda$, stopping potential is 2V. The threshold wavelength for this surface is :

Accepted Answer

(C) $9\lambda$

Answer

(A) $5\lambda$

Answer

(B) $3\lambda$

Answer

(D) $4.5\lambda$

Question 51

An electron moves through a uniform magnetic field $\vec{B}=B_0\hat{i}+2B_0\hat{j}$ T. At a particular instant of time, the velocity of electron is $\vec{u}=3\hat{i}+5\hat{j}$ m/s. If the magnetic force acting on electron is $\vec{F}=5e\hat{k}$ N, where e is the charge of electron, then the value of $B_0$ is ______ T.

Accepted Answer

5

Question 52

A parallel plate capacitor with plate separation 5 mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25% more charge from the battery than before. The dielectric constant of the sheet is ______.

Accepted Answer

2

Question 53

Equivalent resistance of the following network is ______ $\Omega$.

Accepted Answer

1

Question 54

A solid circular disc of mass 50 kg rolls along a horizontal floor so that its center of mass has a speed of 0.4 m/s. The absolute value of work done on the disc to stop it is ______ J.

Accepted Answer

6

Question 55

A body starts falling freely from height H hits an inclined plane in its path at height h. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $\dfrac{H}{h}$ for which the body will take the maximum time to reach the ground is ______.

Accepted Answer

2

Question 56

Two waves of intensity ratio 1 : 9 cross each other at a point. The resultant intensities at the point, when (a) Waves are incoherent is $I_1$ (b) Waves are coherent and differ in phase by $60^\circ$ is $I_2$. If $\dfrac{I_1}{I_2}=\dfrac{10}{x}$ then $x=$ ______.

Accepted Answer

13

Question 57

A small square loop of wire of side $\ell$ is placed inside a large square loop of wire of side L $(L=\ell^2)$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x}	imes10^{-7}$ H, where $x=$ ______.

Accepted Answer

128

Question 58

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0.02% is ______ m. (Take density of sea water = $10^3$ kgm$^{-3}$, Bulk modulus of rubber = $9	imes10^8$ Nm$^{-2}$, and $g=10$ ms$^{-2}$)

Accepted Answer

18

Question 59

A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is $\dfrac{2A}{3}$. The new amplitude of motion is $\dfrac{nA}{3}$. The value of n is ______.

Accepted Answer

7

Question 60

The mass defect in a particular reaction is 0.4 g. The amount of energy liberated is $n	imes10^7$ kWh, where $n=$ ______. (speed of light = $3	imes10^8$ m/s)

Accepted Answer

1

Question 61

Given below are two statements:
Statement-I : Noble gases have very high boiling points.
Statement-II : Noble gases are monoatomic gases. They are held together by strong dispersion forces. Because of this they are liquefied at very low temperature. Hence, they have very high boiling points.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(D) Both Statement I and Statement II are false.

Answer

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

Answer

(B) Both Statement I and Statement II are true.

Answer

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

Question 62

For the given reaction, choose the correct expression of $K_C$ from the following :- $Fe^{3+}_{(aq)}+SCN^-_{(aq)}\rightleftharpoons (FeSCN)^{2+}_{(aq)}$

Accepted Answer

(A) $K_C=\dfrac{[FeSCN^{2+}]}{[Fe^{3+}][SCN^-]}$

Answer

(B) $K_C=\dfrac{[Fe^{3+}][SCN^-]}{[FeSCN^{2+}]}$

Answer

(C) $K_C=\dfrac{[FeSCN^{2+}]}{[Fe^{3+}]^2[SCN^-]^2}$

Answer

(D) $K_C=\dfrac{[FeSCN^{2+}]^2}{[Fe^{3+}][SCN^-]}$

Question 63

Identify the mixture that shows positive deviations from Raoult's Law

Accepted Answer

(D) $(CH_3)_2CO+CS_2$

Answer

(A) $(CH_3)_2CO+C_6H_5NH_2$

Answer

(B) $CHCl_3+C_6H_6$

Answer

(C) $CHCl_3+(CH_3)_2CO$

Question 64

The compound that is white in color is

Accepted Answer

(B) lead sulphate

Answer

(A) ammonium sulphide

Answer

(C) lead iodide

Answer

(D) ammonium arsinomolybdate

List-I	List-II
A.Glucose/ $NaHCO_3/\Delta$	I.Gluconic acid
B.Glucose/ $HNO_3$	II.No reaction
C.Glucose/HI/ $\Delta$	III.n-hexane
D.Glucose/Bromine water	IV.Saccharic acid

List-I (Technique)	List-II (Application)
A.Distillation	I.Separation of glycerol from spent-lye
B.Fractional distillation	II.Aniline - Water mixture
C.Steam distillation	III.Separation of crude oil fractions
D.Distillation under reduced pressure	IV.Chloroform-Aniline

JEE Main 31 January 2024 Shift 1 Question Paper with Answers

Physics — JEE Main 31 January 2024 Shift 1

Chemistry — JEE Main 31 January 2024 Shift 1

Mathematics — JEE Main 31 January 2024 Shift 1

Chapters tested in this paper

Attempt this paper under exam timing.