JEE Main 25 July 2022 Shift 1 Question Paper

Question 1

The total number of functions,
f : $\{1, 2, 3, 4\} 	o \{1, 2, 3, 4, 5, 6\}$
such that f(1) + f(2) = f(3), is equal to :

Accepted Answer

(B) 90

Answer

(A) 60

Answer

(C) 108

Answer

(D) 126

Question 2

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^{4} + x^{3} + x^{2} + x + 1 = 0$, then $\alpha^{2021} + \beta^{2021} + \gamma^{2021} + \delta^{2021}$ is equal to .

Accepted Answer

(B) $-1$

Answer

(A) $-4$

Answer

(C) $1$

Answer

(D) $4$

Question 3

The number of $	heta \in (0, 4\pi)$ for which the system of linear equations
$3 (\sin 3	heta) x - y + z = 2$
$3 (\cos 2	heta) x + 4y + 3z = 3$
$6x + 7y + 7z = 9$
has no solution is :

Accepted Answer

(B) 7

Answer

(A) 6

Answer

(C) 8

Answer

(D) 9

Question 4

If $\lim_{n 	o \infty} \left( \sqrt{n^{2} - n - 1} + n\alpha + \beta ight) = 0$ then $8(\alpha + \beta)$ is equal to :

Accepted Answer

(C) $-4$

Answer

(A) $4$

Answer

(B) $-8$

Answer

(D) $8$

Question 5

If the absolute maximum value of the function $f(x) = (x^{2} - 2x + 7)\, e^{(4x^{3} - 12x^{2} - 180x + 31)}$ in the interval $[-3, 0]$ is $f(\alpha)$, then :

Accepted Answer

(B) $\alpha = -3$

Answer

(A) $\alpha = 0$

Answer

(C) $\alpha \in (-1, 0)$

Answer

(D) $\alpha \in (-3, -1)$

Question 6

The curve $y(x) = ax^{3} + bx^{2} + cx + 5$ touches the x-axis at the point P$(-2, 0)$ and cuts the y-axis at the point Q, where y' is equal to 3. Then the local maximum value of y(x) is :

Accepted Answer

(A) $\frac{27}{4}$

Answer

(B) $\frac{29}{4}$

Answer

(C) $\frac{37}{4}$

Answer

(D) $\frac{9}{2}$

Question 7

The area of the region given by $A = \{(x, y) : x^{2} \le y \le \min \{x + 2, 4 - 3x\}\}$ is :

Accepted Answer

(B) $\frac{17}{6}$

Answer

(A) $\frac{31}{8}$

Answer

(C) $\frac{19}{6}$

Answer

(D) $\frac{27}{8}$

Question 8

For any real number x, let [x] denote the largest integer less than equal to x. Let f be a real valued function defined on the interval $[-10, 10]$ by $f(x) = \begin{cases} x - [x], & 	ext{if}(x) 	ext{ is odd} \ 1 + [x] - x & 	ext{if}(x) 	ext{ is even} \end{cases}$
Then the value of $\frac{\pi^{2}}{10} \int_{-10}^{10} f(x) \cos \pi x\, dx$ is :

Accepted Answer

(A) 4

Answer

(B) 2

Answer

(C) 1

Answer

(D) 0

Question 9

The slope of the tangent to a curve C : y = y(x) at any point $[x, y)$ on it is $\frac{2e^{2x} - 6e^{-x} + 9}{2 + 9e^{-2x}}$. If C passes through the points $\left( 0, \frac{1}{2} + \frac{\pi}{2\sqrt{2}} \right)$ and $\left( \alpha, \frac{1}{2} e^{2\alpha} \right)$ then $e^{\alpha}$ is equal to :

Accepted Answer

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

Answer

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

Answer

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

Answer

(D) $\frac{\sqrt{2} + 1}{\sqrt{2} - 1}$

Question 10

The general solution of the differential equation $(x - y^{2})dx + y(5x + y^{2})dy = 0$ is :

Accepted Answer

(A) $(y^{2} + x)^{4} = C|(y^{2} + 2x)^{3}|$

Answer

(B) $(y^{2} + 2x)^{4} = C|(y^{2} + x)^{3}|$

Answer

(C) $|(y^{2} + x)^{3}| = C(2y^{2} + x)^{4}$

Answer

(D) $|(y^{2} + 2x)^{3}| = C(2y^{2} + x)^{4}$

Question 11

A line, with the slope greater than one, passes through the point A(4, 3) and intersects the line $x - y - 2 = 0$ at the point B. If the length of the line segment AB is $\frac{\sqrt{29}}{3}$, then B also lies on the line :

Accepted Answer

(C) $x + 2y = 6$

Answer

(A) $2x + y = 9$

Answer

(B) $3x - 2y = 7$

Answer

(D) $2x - 3y = 3$

Question 12

Let the locus of the centre $(\alpha, \beta)$, $\beta > 0$, of the circle which touches the circle $x^{2} + (y - 1)^{2} = 1$ externally and also touches the x-axis be L. Then the area bounded by L and the line $y = 4$ is :

Accepted Answer

(C) $\frac{64}{3}$

Answer

(A) $\frac{32\sqrt{2}}{3}$

Answer

(B) $\frac{40\sqrt{2}}{3}$

Answer

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

Question 13

Let P be the plane containing the straight line $\frac{x - 3}{9} = \frac{y + 4}{-1} = \frac{z - 7}{-5}$ and perpendicular to the plane containing the straight lines $\frac{x}{2} = \frac{y}{3} = \frac{z}{5}$ and $\frac{x}{3} = \frac{y}{7} = \frac{z}{8}$. If d is the distance of P from the point $(2, -5, 11)$, then $d^{2}$ is equal to :

Accepted Answer

(C) $\frac{32}{3}$

Answer

(A) $\frac{147}{2}$

Answer

(B) $96$

Answer

(D) $54$

Question 14

Let ABC be a triangle such that $\overrightarrow{BC} = \vec{a}$, $\overrightarrow{CA} = \vec{b}$, $\overrightarrow{AB} = \vec{c}$, $|\vec{a}| = 6\sqrt{2}$, $|\vec{b}| = 2\sqrt{3}$ and $\vec{b} \cdot \vec{c} = 12$. Consider the statements :
(S1) : $|(\vec{a} 	imes \vec{b}) + (\vec{c} 	imes \vec{b})| - |\vec{c}| = 6(2\sqrt{2} - 1)$
(S2) : $\angle ABC = \cos^{-1}\left( \sqrt{\frac{2}{3}} ight)$. Then

Accepted Answer

(D) both (S1) and (S2) are false

Answer

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

Answer

(B) only (S1) is true

Answer

(C) only (S2) is true

Question 15

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is :

Accepted Answer

(C) $\frac{33}{2^{28}}$

Answer

(A) $\frac{33}{2^{32}}$

Answer

(B) $\frac{33}{2^{29}}$

Answer

(D) $\frac{33}{2^{27}}$

Question 16

If the numbers appeared on the two throws of a fair six faced die are $\alpha$ and $\beta$, then the probability that $x^{2} + \alpha x + \beta > 0$, for all $x \in R$, is :

Accepted Answer

(A) $\frac{17}{36}$

Answer

(B) $\frac{4}{9}$

Answer

(C) $\frac{1}{2}$

Answer

(D) $\frac{19}{36}$

Question 17

The number of solutions of $|\cos x| = \sin x$, such that $-4\pi \le x \le 4\pi$ is :

Accepted Answer

(C) 8

Answer

(A) 4

Answer

(B) 6

Answer

(D) 12

Question 18

A tower PQ stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that QR = 15 m. If from a point A on the ground the angle of elevation of R is $60^\circ$ and the part PR of the tower subtends an angle of $15^\circ$ at A, then the height of the tower is :

Accepted Answer

(A) $5(2\sqrt{3}+3)$ m

Answer

(B) $5(\sqrt{3}+3)$ m

Answer

(C) $10(\sqrt{3}+1)$ m

Answer

(D) $10(2\sqrt{3}+1)$ m

Question 19

Which of the following statements is a tautology ?

Accepted Answer

(D) $q \Rightarrow ((\sim p) \vee q)$

Answer

(A) $((\sim p) \vee q) \Rightarrow p$

Answer

(B) $p \Rightarrow ((\sim p) \vee q)$

Answer

(C) $((\sim p) \vee q) \Rightarrow q$

Question 20

Let $A = \begin{bmatrix} 2 & -1 & -1 \ 1 & 0 & -1 \ 1 & -1 & 0 \end{bmatrix}$ and $B = A - I$. If $\omega = \frac{\sqrt{3}i - 1}{2}$, then the number of elements in the set $\{n \in \{1, 2, \ldots, 100\} : A^{n} + (\omega B)^{n} = A + B\}$ is equal to ________.

Accepted Answer

17

Question 21

The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is ________.

Accepted Answer

1492

Question 22

If the maximum value of the term independent of t in the expansion of $\left( t^{2}x^{\frac{1}{5}} + \frac{(1-x)^{\frac{1}{10}}}{t} \right)^{15}$, $x \ge 0$, is K, then 8K is equal to ________.

Accepted Answer

6006

Question 23

Let a, b be two non-zero real numbers. If p and r are the roots of the equation $x^{2} - 8ax + 2a = 0$ and q and s are the roots of the equation $x^{2} + 12bx + 6b = 0$, such that $\frac{1}{p}, \frac{1}{q}, \frac{1}{r}, \frac{1}{s}$ are in A.P., then $a^{-1} - b^{-1}$ is equal to ________.

Accepted Answer

38

Question 24

Let $a_{1} = b_{1} = 1$, $a_{n} = a_{n-1} + 2$ and $b_{n} = a_{n} + b_{n-1}$ for every natural number $n \ge 2$. Then $\sum_{n=1}^{15} a_{n} \cdot b_{n}$ is equal to ________.

Accepted Answer

27560

Question 25

Let $f(x) = \begin{cases} |4x^{2} - 8x + 5|, & 	ext{if } 8x^{2} - 6x + 1 \ge 0 \ [4x^{2} - 8x + 5], & 	ext{if } 8x^{2} - 6x + 1 < 0 \end{cases}$, where $[\alpha]$ denotes the greatest integer less than or equal to $\alpha$. Then the number of points in R where f is not differentiable is ________.

Accepted Answer

3

Question 26

If $\lim_{n	o\infty} \frac{(n+1)^{k-1}}{n^{k+1}} [(nk + 1) + (nk + 2) + \ldots + (nk + n)] = 33. \lim_{n	o\infty} \frac{1}{n^{k+1}} \cdot [1^{k} + 2^{k} + 3^{k} + \ldots + n^{k}]$, then the integral value of k is equal to ________.

Accepted Answer

5

Question 27

Let the equation of two diameters of a circle $x^{2} + y^{2} - 2x + 2fy + 1 = 0$ be $2px - y = 1$ and $2x + py = 4p$. Then the slope $m \in (0, \infty)$ of the tangent to the hyperbola $3x^{2} - y^{2} = 3$ passing through the centre of the circle is equal to ________.

Accepted Answer

2

Question 28

The sum of diameters of the circles that touch (i) the parabola $75x^{2} = 64(5y - 3)$ at the point $\left( \frac{8}{5}, \frac{6}{5} \right)$ and (ii) the y-axis, is equal to ________.

Accepted Answer

10

Question 29

The line of shortest distance between the lines $\frac{x-2}{0} = \frac{y-1}{1} = \frac{z}{1}$ and $\frac{x-3}{2} = \frac{y-5}{2} = \frac{z-1}{1}$ makes an angle of $\cos^{-1}\left( \sqrt{\frac{2}{27}} \right)$ with the plane $P : ax - y - z = 0$, $(a > 0)$. If the image of the point $(1, 1, -5)$ in the plane P is $(\alpha, \beta, \gamma)$, then $\alpha + \beta - \gamma$ is equal to ________.

Accepted Answer

3

Question 30

If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :

Accepted Answer

(A) $[P\ A^{-1}\ T^{0}]$

Answer

(B) $[P\ A\ T^{-1}]$

Answer

(C) $[P\ A^{-1}\ T]$

Answer

(D) $[P\ A^{-1}\ T^{-1}]$

Question 31

Which of the following physical quantities have the same dimensions ?

Accepted Answer

(A) Electric displacement $(\vec{D})$ and surface charge density

Answer

(B) Displacement current and electric field

Answer

(C) Current density and surface charge density

Answer

(D) Electric potential and energy

Question 32

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be : (Given $\cos 135^\circ = -\,0.7$)

Accepted Answer

(B) 47 m

Answer

(A) 42 m

Answer

(C) 19 m

Answer

(D) 40 m

Question 33

A body of mass 0.5 kg travels on straight line path with velocity $v = (3x^{2} + 4)$ m/s. The net workdone by the force during its displacement from $x = 0$ to $x = 2$ m is :

Accepted Answer

(B) 60 J

Answer

(A) 64 J

Answer

(C) 120 J

Answer

(D) 128 J

Question 34

A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :

Accepted Answer

(D) $\sqrt{\frac{14}{15}}$

Answer

(A) $\sqrt{\frac{5}{3}}$

Answer

(B) $\sqrt{\frac{4}{5}}$

Answer

(C) $\sqrt{\frac{3}{5}}$

Question 35

Three identical particle A, B and C of mass 100 kg each are placed in a straight line with AB = BC = 13 m. The gravitational force on a fourth particle P of the same mass is F, when placed at a distance 13 m from the particle B on the perpendicular bisector of the line AC. The value of F will be approximately :

Accepted Answer

(B) 100 G

Answer

(A) 21 G

Answer

(C) 59 G

Answer

(D) 42 G

Question 36

A certain amount of gas of volume V at $27^\circ$C temperature and pressure $2 	imes 10^{7}$ Nm$^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma = 1.5$)

Accepted Answer

(B) $3.536 	imes 10^{6}$ Pa

Answer

(A) $3.536 	imes 10^{5}$ Pa

Answer

(C) $1.25 	imes 10^{6}$ Pa

Answer

(D) $1.25 	imes 10^{5}$ Pa

Question 37

Following statements are given :
(1) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
(2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
(3) The average kinetic energy of a gas molecule decreases with increases in volume.
(4) Pressure of a gas increases with increase in temperature at constant pressure.
(5) The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below :

Accepted Answer

(A) (1) and (4) only

Answer

(B) (1), (2) and (4) only

Answer

(C) (2) and (4) only

Answer

(D) (1), (2) and (5) only

Question 38

In figure (A), mass '2 m' is fixed on mass 'm' which is attached to two springs of spring constant k. In figure (B), mass 'm' is attached to two spring of spring constant 'k' and '2k'. If mass 'm' in (A) and (B) are displaced by distance 'x' horizontally and then released, then time period $T_1$ and $T_2$ corresponding to (A) and (B) respectively follow the relation.

Accepted Answer

(A) $\frac{T_1}{T_2} = \frac{3}{\sqrt{2}}$

Answer

(B) $\frac{T_1}{T_2} = \sqrt{\frac{3}{2}}$

Answer

(C) $\frac{T_1}{T_2} = \sqrt{\frac{2}{3}}$

Answer

(D) $\frac{T_1}{T_2} = \frac{\sqrt{2}}{3}$

Question 39

A condenser of 2 $\mu$F capacitance is charged steadily from 0 to 5C. Which of the following graph represents correctly the variation of potential difference (V) across it's plates with respect to the charge (Q) on the condenser ?

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 40

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6 : 5 and their respective masses ratio is 9 : 4. Then, the ratio of their charges will be :

Accepted Answer

(B) 5 : 4

Answer

(A) 8 : 5

Answer

(C) 5 : 3

Answer

(D) 8 : 7

Question 41

To increase the resonant frequency in series LCR circuit,

Accepted Answer

(C) Another capacitor should be added in series with the first capacitor

Answer

(A) Source frequency should be increased

Answer

(B) Another resistance should be added in series with the first resistance.

Answer

(D) The source frequency should be decreased

Question 42

A small square loop of wire of side $l$ is placed inside a large square loop of wire L (L >> $l$). Both loops are coplanar and their centres coincide at point O as shown in figure. The mutual inductance of the system is :

Accepted Answer

(C) $\frac{2\sqrt{2}\mu_0 \ell^{2}}{\pi L}$

Answer

(A) $\frac{2\sqrt{2}\mu_0 L^{2}}{\pi \ell}$

Answer

(B) $\frac{\mu_0 \ell^{2}}{2\sqrt{2}\pi L}$

Answer

(D) $\frac{\mu_0 L^{2}}{2\sqrt{2}\pi \ell}$

Question 43

The rms value of conduction current in a parallel plate capacitor is 6.9 $\mu$A. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of 600 rad/s, will be :

Accepted Answer

(B) 50 pF

Answer

(A) 5 pF

Answer

(C) 100 pF

Answer

(D) 200 pF

Question 44

Which of the following statement is correct ?

Accepted Answer

(A) In primary rainbow, observer sees red colour on the top and violet on the bottom

Answer

(B) In primary rainbow, observer sees violet colour on the top and red on the bottom

Answer

(C) In primary rainbow, light wave suffers total internal reflection twice before coming out of water drops

Answer

(D) Primary rainbow is less bright than secondary rainbow.

Question 45

Time taken by light to travel in two different materials A and B of refractive indices $\mu_A$ and $\mu_B$ of same thickness is $t_1$ and $t_2$ respectively. If $t_2 - t_1 = 5 	imes 10^{-10}$ s and the ratio of $\mu_A$ to $\mu_B$ is 1 : 2. Then the thickness of material, in meter is : (Given $v_A$ and $v_B$ are velocities of light in A and B materials respectively).

Accepted Answer

(A) $5 	imes 10^{-10} v_a$ m

Answer

(B) $5 	imes 10^{-10}$ m

Answer

(C) $1.5 	imes 10^{-10}$ m

Answer

(D) $5 	imes 10^{-10} v_B$ m

Question 46

A metal exposed to light of wavelength 800 nm and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength 500 nm is used. The work function of the metal is (Take hc = 1230 eV-nm).

Accepted Answer

(C) 0.615 eV

Answer

(A) 1.537 eV

Answer

(B) 2.46 eV

Answer

(D) 1.23 eV

Question 47

The momentum of an electron revolving in $n^{th}$ orbit is given by : (Symbols have their usual meanings)

Accepted Answer

(A) $\frac{nh}{2\pi r}$

Answer

(B) $\frac{nh}{2r}$

Answer

(C) $\frac{nh}{2\pi}$

Answer

(D) $\frac{2\pi r}{nh}$

Question 48

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by :

Accepted Answer

(B) $\vec{\mu}_L = -\frac{e\vec{L}}{2m}$

Answer

(A) $\vec{\mu}_L = \frac{e\vec{L}}{2m}$

Answer

(C) $\vec{\mu}_l = -\frac{e\vec{L}}{m}$

Answer

(D) $\vec{\mu}_l = \frac{2e\vec{L}}{m}$

Question 49

In the circuit, the logical value of A = 1 or B = 1 when potential at A or B is 5V and the logical value of A = 0 or B = 0 when potential at A or B is 0 V.
The truth table of the given circuit will be :

Accepted Answer

(A) A  B  Y
0  0  0
1  0  0
0  1  0
1  1  1

Answer

(B) A  B  Y
0  0  0
1  0  1
0  1  1
1  1  1

Answer

(C) A  B  Y
0  0  0
1  0  0
0  1  0
1  1  0

Answer

(D) A  B  Y
0  0  1
1  0  1
0  1  1
1  1  0

Question 50

A car is moving with speed of 150 km/h and after applying the brake it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling _______ m distance.

Accepted Answer

3

Question 51

Four forces are acting at a point P in equilibrium as shown in figure. The ratio of force $F_1$ to $F_2$ is 1 : x where x = _______ .

Accepted Answer

3

Question 52

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5 cm. Another wire of the same material of length 4L and radius 4r is pulled by a force 4F under same conditions. The increase in length of this wire is _______ cm.

Accepted Answer

5

Question 53

A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is 40 cm and length of iron will be _______ cm.
($\alpha_{iron} = 1.2 	imes 10^{-5}$ $K^{-1}$ and $\alpha_{brass} = 1.8 	imes 10^{-5}$ $K^{-1}$).

Accepted Answer

60

Question 54

An observer is riding on a bicycle and moving towards a hill at 18 $kmh^{-1}$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and velocity of the sound in air is 320 m/s, the beat frequency between the two sounds heard by observer will be _______ Hz.

Accepted Answer

20

Question 55

The volume charge density of a sphere of radius 6 m is 2 $\mu C$ $cm^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is _______ $	imes 10^{10}$ $NC^{-1}$.
[Given : Permittivity of vacuum $\in_0 = 8.85 	imes 10^{-12}$ $C^2$ $N^{-1} - m^{-2}$ ]

Accepted Answer

45

Question 56

In the given figure, the value of $V_0$ will be _______ V.

Accepted Answer

4

Question 57

Eight copper wire of length $l$ and diameter d are joined in parallel to form a single composite conductor of resistance R. If a single copper wire of length $2l$ have the same resistance (R) then its diameter will be _______ d.

Accepted Answer

4

Question 58

The energy band gap of semiconducting material to produce violet (wavelength = 4000 Å) LED is _______ eV. (Round off to the nearest integer).

Accepted Answer

3

Question 59

The required height of a TV tower which can cover the population of 6.03 lakh is h. If the average population density is 100 per square km and the radius of earth is 6400 km, then the value of h will be _______ m.

Accepted Answer

150

Question 60

$SO_{2}Cl_{2}$ on reaction with excess of water results into acidic mixture
$SO_{2}Cl_{2} + 2H_{2}O \rightarrow H_{2}SO_{4} + 2HCl$
16 moles of NaOH is required for the complete neutralisation of the resultant acidic mixture. The number of moles of $SO_{2}Cl_{2}$ used is :

Accepted Answer

(C) 4

Answer

(A) 16

Answer

(B) 8

Answer

(D) 2

Question 61

Which of the following sets of quantum numbers is not allowed ?

Accepted Answer

(C) $n = 3, l = 3, m_{l} = -3, s = -\frac{1}{2}$

Answer

(A) $n = 3, l = 2, m_{l} = 0, s = +\frac{1}{2}$

Answer

(B) $n = 3, l = 2, m_{l} = -2, s = +\frac{1}{2}$

Answer

(D) $n = 3, l = 0, m_{l} = 0, s = -\frac{1}{2}$

Question 62

The depression in freezing point observed for a formic acid solution of concentration 0.5 mL $L^{-1}$ is 0.0405°C. Density of formic acid is 1.05 g $mL^{-1}$. The Van't Hoff factor of the formic acid solution is nearly : (Given for water $k_{f}$= 1.86 K kg $mol^{-1}$)

Accepted Answer

(C) 1.9

Answer

(A) 0.8

Answer

(B) 1.1

Answer

(D) 2.4

Question 63

20 mL of 0.1 M $NH_{4}OH$ is mixed with 40 mL of 0.05 M HCl. The pH of the mixture is
nearest to:
(Given: $K_{b}(NH_{4}OH) = 1 	imes 10^{-5}$, log 2 = 0.30,
log 3 = 0.48, log 5 = 0.69, log 7 = 0.84,
log 11 =1.04)

Accepted Answer

(C) 5.2

Answer

(A) 3.2

Answer

(B) 4.2

Answer

(D) 6.2

Question 64

Match List - I with List - II
Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

List - I	List - II
A. $N_{2}(g) + 3H_{2}(g) \rightarrow 2NH_{3}(g)$	I.Cu
B. $CO(g) + 3H_{2}(g) \rightarrow CH_{4}(g) + H_{2}O(g)$	II. $Cu/ZnO - Cr_{2}O_{3}$
C. $CO(g) + H_{2}(g) \rightarrow HCHO(g)$	III. $Fe_{x}O_{y} + K_{2}O + Al_{2}O_{3}$
D. $CO(g) + 2H_{2}(g) \rightarrow CH_{3}OH(g)$	IV.Ni

JEE Main 25 July 2022 Shift 1 Question Paper with Answers

Physics — JEE Main 25 July 2022 Shift 1

Chemistry — JEE Main 25 July 2022 Shift 1

Mathematics — JEE Main 25 July 2022 Shift 1

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