JEE Main 29 July 2022 Shift 1 Question Paper

Question 1

Let R be a relation from the set $\{1, 2, 3\ldots\ldots\ldots,60\}$ to itself such that $R = \{(a, b) : b = pq,$ where $p, q \geq 3$ are prime numbers$\}$. Then, the number of elements in R is :

Accepted Answer

(B) 660

Answer

(A) 600

Answer

(C) 540

Answer

(D) 720

Question 2

If $z = 2 + 3i$, then $z^{5} + (\bar{z})^{5}$ is equal to :

Accepted Answer

(A) 244

Answer

(B) 224

Answer

(C) 245

Answer

(D) 265

Question 3

Let A and B be two $3 	imes 3$ non-zero real matrices such that AB is a zero matrix. Then

Accepted Answer

(B) The system of linear equations $AX = 0$ has infinitely many solutions

Answer

(A) The system of linear equations $AX = 0$ has a unique solution

Answer

(C) B is an invertible matrix

Answer

(D) adj (A) is an invertible matrix

Question 4

If $\frac{1}{(20 - a)\,(40 - a)} + \frac{1}{(40 - a)\,(60 - a)} + \ldots\ldots+ \frac{1}{(180 - a)\,(200 - a)} = \frac{1}{256}$, then the maximum value of a is :

Accepted Answer

(C) 212

Answer

(A) 198

Answer

(B) 202

Answer

(D) 218

Question 5

If $\lim_{x 	o 0} \frac{\alpha e^{x} + \beta e^{-x} + \gamma \sin x}{x \sin^{2} x} = \frac{2}{3}$, where $\alpha, \beta, \gamma \in R$, then which of the following is NOT correct ?

Accepted Answer

(C) $\alpha\beta^{2} + \beta\gamma^{2} + \gamma\alpha^{2} + 3 = 0$

Answer

(A) $\alpha^{2} + \beta^{2} + \gamma^{2} = 6$

Answer

(B) $\alpha\beta + \beta\gamma + \gamma\alpha + 1 = 0$

Answer

(D) $\alpha^{2} - \beta^{2} + \gamma^{2} = 4$

Question 6

The integral $\int_{0}^{\frac{\pi}{2}} \frac{1}{3 + 2\sin x + \cos x}\,dx$ is equal to:

Accepted Answer

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

Answer

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

Answer

(C) $\frac{1}{2}	an^{-1}(2) - \frac{\pi}{8}$

Answer

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

Question 7

Let the solution curve $y = y(x)$ of the differential equation $(1 + e^{2x})\left(\frac{dy}{dx} + yight) = 1$ pass through the point $\left(0, \frac{\pi}{2}ight)$. Then, $\lim_{x 	o \infty} e^{x} y(x)$ is equal to :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 8

Let a line L pass through the point of intersection of the lines $bx + 10y - 8 = 0$ and $2x - 3y = 0$, $b \in R - \left\{\frac{4}{3}\right\}$. If the line L also passes through the point $(1, 1)$ and touches the circle $17\,(x^{2} + y^{2}) = 16$, then the eccentricity of the ellipse $\frac{x^{2}}{5} + \frac{y^{2}}{b^{2}} = 1$ is :

Accepted Answer

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

Answer

(A) $\frac{2}{\sqrt{5}}$

Answer

(C) $\frac{1}{\sqrt{5}}$

Answer

(D) $\sqrt{\frac{2}{5}}$

Question 9

If the foot of the perpendicular from the point $A(-1, 4, 3)$ on the plane $P : 2x + my + nz = 4$, is $\left(-2, \frac{7}{2}, \frac{3}{2}\right)$, then the distance of the point A from the plane P, measured parallel to a line with direction ratios $3, -1, -4$, is equal to :

Accepted Answer

(B) $\sqrt{26}$

Answer

(A) 1

Answer

(C) $2\sqrt{2}$

Answer

(D) $\sqrt{14}$

Question 10

Let $\vec{a} = 3\hat{i} + \hat{j}$ and $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$. Let $\vec{c}$ be a vector satisfying $\vec{a} 	imes (\vec{b} 	imes \vec{c}) = \vec{b} + \lambda\vec{c}$. If $\vec{b}$ and $\vec{c}$ are non-parallel, then the value of $\lambda$ is :

Accepted Answer

(A) $-5$

Answer

(B) 5

Answer

(C) 1

Answer

(D) $-1$

Question 11

The angle of elevation of the top of a tower from a point A due north of it is $\alpha$ and from a point B at a distance of 9 units due west of A is $\cos^{-1}\left(\frac{3}{\sqrt{13}}\right)$. If the distance of the point B from the tower is 15 units, then $\cot \alpha$ is equal to :

Accepted Answer

(A) $\frac{6}{5}$

Answer

(B) $\frac{9}{5}$

Answer

(C) $\frac{4}{3}$

Answer

(D) $\frac{7}{3}$

Question 12

The statement $(p \wedge q) \Rightarrow (p \wedge r)$ is equivalent to :

Accepted Answer

(D) $(p \wedge q) \Rightarrow r$

Answer

(A) $q \Rightarrow (p \wedge r)$

Answer

(B) $p \Rightarrow (p \wedge r)$

Answer

(C) $(p \wedge r) \Rightarrow (p \wedge q)$

Question 13

Let the circumcentre of a triangle with vertices $A(a, 3)$, $B(b, 5)$ and $C(a, b)$, $ab > 0$ be $P(1, 1)$. If the line AP intersects the line BC at the point $Q(k_{1}, k_{2})$, then $k_{1} + k_{2}$ is equal to :

Accepted Answer

(B) $\frac{4}{7}$

Answer

(A) 2

Answer

(C) $\frac{2}{7}$

Answer

(D) 4

Question 14

Let $\hat{a}$ and $\hat{b}$ be two unit vectors such that the angle between them is $\frac{\pi}{4}$. If $	heta$ is the angle between the vectors $(\hat{a} + \hat{b})$ and $(\hat{a} + 2\hat{b} + 2(\hat{a} 	imes \hat{b}))$, then the value of $164 \cos^{2}	heta$ is equal to :

Accepted Answer

(A) $90 + 27\sqrt{2}$

Answer

(B) $45 + 18\sqrt{2}$

Answer

(C) $90 + 3\sqrt{2}$

Answer

(D) $54 + 90\sqrt{2}$

Question 15

If $f(\alpha) = \int_{1}^{\alpha} \frac{\log_{10} t}{1 + t}\,dt, \alpha > 0$, then $f(e^{3}) + f(e^{-3})$ is equal to :

Accepted Answer

(D) $\frac{9}{2\log_{e}(10)}$

Answer

(A) 9

Answer

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

Answer

(C) $\frac{9}{\log_{e}(10)}$

Question 16

The area of the region $\left\{(x,\,y) : |\,x-1\,| \le y \le \sqrt{5-x^{2}}\right\}$ is equal to :

Accepted Answer

(D) $\frac{5\pi}{4}-\frac{1}{2}$

Answer

(A) $\frac{5}{2}\sin^{-1}\left(\frac{3}{5}\right)-\frac{1}{2}$

Answer

(B) $\frac{5\pi}{4}-\frac{3}{2}$

Answer

(C) $\frac{3\pi}{4}+\frac{3}{2}$

Question 17

Let the focal chord of the parabola P : $y^{2}=4x$ along the line L : $y = mx + c$, $m > 0$ meet the parabola at the points M and N. Let the line L be a tangent to the hyperbola H : $x^{2}-y^{2}=4$. If O is the vertex of P and F is the focus of H on the positive x-axis, then the area of the quadrilateral OMFN is :

Accepted Answer

(B) $2\sqrt{14}$

Answer

(A) $2\sqrt{6}$

Answer

(C) $4\sqrt{6}$

Answer

(D) $4\sqrt{14}$

Question 18

The number of points, where the function $f : \mathbf{R} \rightarrow \mathbf{R}$, $f(x) = |x-1|\cos|x-2|\sin|x-1| + (x-3)\left|x^{2}-5x+4\right|$, is NOT differentiable, is :

Accepted Answer

(B) 2

Answer

(A) 1

Answer

(C) 3

Answer

(D) 4

Question 19

Let $S = \{1,\,2,\,3,\,\ldots,\,2022\}$. Then the probability, that a randomly chosen number n from the set S such that HCF $(n,\,2022) = 1$, is :

Accepted Answer

(D) $\frac{112}{337}$

Answer

(A) $\frac{128}{1011}$

Answer

(B) $\frac{166}{1011}$

Answer

(C) $\frac{127}{337}$

Question 20

Let $f(x) = 3^{\left(x^{2}-2\right)^{3}+4}$, $x \in \mathbf{R}$. Then which of the following statements are true ?
P : $x = 0$ is a point of local minima of f
Q : $x = \sqrt{2}$ is a point of inflection of f
R : f' is increasing for $x > \sqrt{2}$

Accepted Answer

(D) All, P, Q and R

Answer

(A) Only P and Q

Answer

(B) Only P and R

Answer

(C) Only Q and R

Question 21

Let $S = \left\{	heta \in (0,\,2\pi) : 7\cos^{2}	heta - 3\sin^{2}	heta - 2\cos^{2}2	heta = 2ight\}$. Then, the sum of roots of all the equations $x^{2} - 2\left(	an^{2}	heta + \cot^{2}	hetaight)x + 6\sin^{2}	heta = 0$, $	heta \in S$, is __________.

Accepted Answer

16

Question 22

Let the mean and the variance of 20 observations $x_{1},\,x_{2},\ldots x_{20}$ be 15 and 9, respectively. For $\alpha \in R$, if the mean of $\left(x_{1}+\alpha\right)^{2},\,\left(x_{2}+\alpha\right)^{2},\ldots,\,\left(x_{20}+\alpha\right)^{2}$ is 178, then the square of the maximum value of $\alpha$ is equal to __________.

Accepted Answer

4

Question 23

Let a line with direction ratios a, –4a, –7 be perpendicular to the lines with direction ratios 3, –1, 2b and b, a, –2. If the point of intersection of the line $\frac{x+1}{a^{2}+b^{2}} = \frac{y-2}{a^{2}-b^{2}} = \frac{z}{1}$ and the plane $x - y + z = 0$ is $(\alpha,\,\beta,\,\gamma)$, then $\alpha + \beta + \gamma$ is equal to __________.

Accepted Answer

10

Question 24

Let $a_{1},\,a_{2},\,a_{3},\ldots$ be an A.P. If $\sum_{r=1}^{\infty}\frac{a_{r}}{2^{r}} = 4$, then $4a_{2}$ is equal to __________.

Accepted Answer

16

Question 25

Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of $\left(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}}\right)^{n}$, in the increasing powers of $\frac{1}{\sqrt[4]{3}}$ be $\sqrt[4]{6} : 1$. If the sixth term from the beginning is $\frac{\alpha}{\sqrt[4]{3}}$, then $\alpha$ is equal to __________.

Accepted Answer

84

Question 26

The number of matrices of order $3 	imes 3$, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is__________.

Accepted Answer

282

Question 27

Let p and p + 2 be prime numbers and let
$\Delta = \begin{vmatrix} p! & (p+1)! & (p+2)! \ (p+1)! & (p+2)! & (p+3)! \ (p+2)! & (p+3)! & (p+4)! \end{vmatrix}$
Then the sum of the maximum values of $\alpha$ and $\beta$, such that $p^{\alpha}$ and $(p+2)^{\beta}$ divide $\Delta$, is __________.

Accepted Answer

4

Question 28

If $\frac{1}{2 	imes 3 	imes 4} + \frac{1}{3 	imes 4 	imes 5} + \frac{1}{4 	imes 5 	imes 6} + \ldots + \frac{1}{100 	imes 101 	imes 102} = \frac{k}{101}$, then 34 k is equal to _____.

Accepted Answer

286

Question 29

Let $S = \{4,\,6,\,9\}$ and $T = \{9,\,10,\,11,\,\ldots,\,1000\}$. If $A = \left\{a_{1}+a_{2}+\ldots+a_{k} : k \in N,\; a_{1},\,a_{2},\,a_{3},\,\ldots,a_{k} \in S\right\}$, then the sum of all the elements in the set $T - A$ is equal to _______.

Accepted Answer

11

Question 30

Let the mirror image of a circle $c_{1} : x^{2}+y^{2}-2x-6y+\alpha = 0$ in line $y = x + 1$ be $c_{2} : 5x^{2}+5y^{2}+10gx+10fy+38 = 0$. If r is the radius of circle $c_{2}$, then $\alpha + 6r^{2}$ is equal to __________

Accepted Answer

12

Question 31

Given below are two statements : One is labelled as Assertion (A) and other is labelled as
Reason (R).
Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is p and radius of the drop is r, then $T = k\sqrt{\frac{pr^{3}}{S^{3/2}}}$ is dimensionally correct, where K is dimensionless.
Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

Accepted Answer

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

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

Question 32

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height $\frac{h}{3}$ while going up and coming down respectively.

Accepted Answer

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

Answer

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

Answer

(C) $\frac{\sqrt{3}-1}{\sqrt{3}+1}$

Answer

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

Question 33

If $t = \sqrt{x} + 4$, then $\left(\frac{dx}{dt}\right)_{t=4}$ is:

Accepted Answer

(B) Zero

Answer

(A) 4

Answer

(C) 8

Answer

(D) 16

Question 34

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v) ?

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 35

A ball is projected with kinetic energy E, at an angle of $60^{0}$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :

Accepted Answer

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

Answer

(A) Zero

Answer

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

Answer

(D) E

Question 36

Two bodies of mass 1 kg and 3 kg have position vectors $\hat{i} + 2\hat{j} + \hat{k}$ and $-3\hat{i} - 2\hat{j} + \hat{k}$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

Accepted Answer

(A) $\hat{i} - 2\hat{j} + \hat{k}$

Answer

(B) $-3\hat{i} - 2\hat{j} + \hat{k}$

Answer

(C) $-2\hat{i} + 2\hat{k}$

Answer

(D) $-2\hat{i} - \hat{j} + 2\hat{k}$

Question 37

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A) : Clothes containing oil or grease stains cannot be cleaned by water wash.
Reason (R) : Because the angle of contact between the oil/ grease and water is obtuse. In the light of the above statements, choose the correct answer from the option 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 true but (R) is true

Question 38

If the length of a wire is made double and radius is halved of its respective values. Then, the Young’s modules of the material of the wire will :

Accepted Answer

(A) Remains same

Answer

(B) Become 8 times its initial value

Answer

(C) Become $\frac{1^{th}}{4}$ of its initial value

Answer

(D) Become 4 times its initial value

Question 39

The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $\alpha$, is given by :

Accepted Answer

(A) $2\pi\sqrt{L/(g\cos\alpha)}$

Answer

(B) $2\pi\sqrt{L/(g\sin\alpha)}$

Answer

(C) $2\pi\sqrt{L/g}$

Answer

(D) $2\pi\sqrt{L/(g	an\alpha)}$

Question 40

A spherically symmetric charge distribution is considered with charge density varying as
$ho(r) = \begin{cases} ho_{0}\left(\frac{3}{4} - \frac{r}{R}ight) & 	ext{for } r \leq R \ 	ext{Zero} & 	ext{for } r > R \end{cases}$
Where, r(r < R) is the distance from the centre O (as shown in figure). The electric field at point P will be :

Accepted Answer

(C) $\frac{\rho_{0}r}{4\varepsilon_{0}}\left(1 - \frac{r}{R}\right)$

Answer

(A) $\frac{\rho_{0}r}{4\varepsilon_{0}}\left(\frac{3}{4} - \frac{r}{R}\right)$

Answer

(B) $\frac{\rho_{0}r}{3\varepsilon_{0}}\left(\frac{3}{4} - \frac{r}{R}\right)$

Answer

(D) $\frac{\rho_{0}r}{5\varepsilon_{0}}\left(1 - \frac{r}{R}\right)$

Question 41

Given below are two statements.
Statement I : Electric potential is constant within and at the surface of each conductor.
Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements, choose the most appropriate answer from the options give below.

Accepted Answer

(A) Both statement I and statement II are correct

Answer

(B) Both statement I and statement II are incorrect

Answer

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

Answer

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

Question 42

Two metallic wires of identical dimensions are connected is series. If $\sigma_{1}$ and $\sigma_{2}$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :

Accepted Answer

(B) $\frac{2\sigma_{1}\sigma_{2}}{\sigma_{1}+\sigma_{2}}$

Answer

(A) $\frac{\sigma_{1}\sigma_{2}}{\sigma_{1}+\sigma_{2}}$

Answer

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

Answer

(D) $\frac{\sigma_{1}+\sigma_{2}}{\sigma_{1}\sigma_{2}}$

Question 43

An alternating emf E = 440 sin 100πt is applited to a circuit containing an inductance of $\frac{\sqrt{2}}{\pi}$ H. If an a.c. ammeter is connected in the circuit, its reading will be :

Accepted Answer

(C) 2.2 A

Answer

(A) 4.4 A

Answer

(B) 1.55 A

Answer

(D) 3.11 A

Question 44

A coil of inductance 1 H and resistance 100 Ω is connected to a battery of 6 V. Determine approximately :
(a) The time elapsed before the current acquires half of its steady – state value
(b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on. (Given In2 = 0.693, $e^{-3/2} = 0.25$)

Accepted Answer

(C) t = 7 ms; U = 1 mJ

Answer

(A) t = 10 ms; U = 2 mJ

Answer

(B) t = 10 ms; U = 1 mJ

Answer

(D) t = 7 ms; U = 2 mJ

Question 45

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

Accepted Answer

(B) (a)–(ii), (b)-(i), (c)-(iii), (d)-(iv)

Answer

(A) (a)–(iii), (b)-(ii), (c)-(i), (d)-(iv)

Answer

(C) (a)–(ii), (b)-(iv), (c)-(iii), (d)-(i)

Answer

(D) (a)–(iii), (b)-(i), (c)-(ii), (d)-(iv)

Question 46

The kinetic energy of emitted electron is E when the light incident on the metal has wavelength $\lambda$. To double the kinetic energy, the incident light must have wavelength :

Accepted Answer

(B) $\frac{hc\lambda}{E\lambda + hc}$

Answer

(A) $\frac{hc}{E\lambda - hc}$

Answer

(C) $\frac{h\lambda}{E\lambda + hc}$

Answer

(D) $\frac{hc\lambda}{E\lambda - hc}$

Question 47

Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its(i) second permitted energy level to the first level,  and (ii) the highest permitted energy level to the first permitted level.

Accepted Answer

(A) 3 : 4

Answer

(B) 4 : 3

Answer

(C) 1 : 4

Answer

(D) 4 : 1

Question 48

Find the modulation index of an AM wave having 8 V variation where maximum amplitude of the AM wave is 9 V.

Accepted Answer

(A) 0.8

Answer

(B) 0.5

Answer

(C) 0.2

Answer

(D) 0.1

Question 49

A travelling microscope has 20 divisions per cm on the main scale while its Vernier scale has total 50 divisions and 25 Vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope ?

Accepted Answer

(C) 0.002 cm

Answer

(A) 0.001 cm

Answer

(B) 0.002 mm

Answer

(D) 0.005 cm

Question 50

In an experiment to find out the diameter of wire using screw gauge, the following observation were noted :
(a) Screw moves 0.5 mm on main scale in one complete rotation
(b) Total divisions on circular scale = 50
(c) Main scale reading is 2.5 mm
(d) $45^{th}$ division of circular scale is in the pitch line
(e) Instrument has 0.03 mm negative error
Then the diameter of wire is :

Accepted Answer

(C) 2.98 mm

Answer

(A) 2.92 mm

Answer

(B) 2.54 mm

Answer

(D) 3.45 mm

Question 51

An object is projected in the air with initial velocity u at an angle $	heta$. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be ________degree.

Accepted Answer

15

Question 52

If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth $\alpha$h (h << $R_e$) from the earth surface. The value of $\alpha$ will be __________.
(use $R_e$ = 6400 km)

Accepted Answer

2

Question 53

The pressure $P_1$ and density $d_1$ of diatomic gas $\left(\gamma = \frac{7}{5}\right)$ changes suddenly to $P_2(>P_1)$ and $d_2$ respectively during an adiabatic process. The temperature of the gas increases and becomes __________ times of its initial temperature.
(given $\frac{d_2}{d_1}$ = 32)

Accepted Answer

4

Question 54

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{\alpha^2}{4}$R  J/mol K; then the value of $\alpha$ will be ________. (Assume that the given diatomic gas has no vibrational mode.)

Accepted Answer

3

Question 55

The current I flowing through the given circuit will be __________ A.

Accepted Answer

2

Question 56

A closely wounded circular coil of radius 5 cm produces a magnetic field of 37.68 x $10^{-4}$ T at its center. The current through the coil is __________ A.
[Given, number of turns in the coil is 100 and $\pi$ = 3.14]

Accepted Answer

3

Question 57

Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is $\pi$. The difference of resultant intensities, at the point A and B, will be __________ I.

Accepted Answer

24

Question 58

A wire of length 314 cm carrying current of 14 A is bent to form a circle. The magnetic moment of the coil is ________ A-$m^2$. [Given $\pi$ = 3.14]

Accepted Answer

11

Question 59

The X-Y plane be taken as the boundary between two transparent media $M_1$ and $M_2$. $M_1$ in $Z \geq 0$ has a refractive index of $\sqrt{2}$ and $M_2$ with $Z < 0$ has a refractive index of $\sqrt{3}$. A ray of light travelling in $M_1$ along the direction given by the vector $\vec{A} = 4\sqrt{3}\hat{i} - 3\sqrt{3}\hat{j} - 5\hat{k}$, is incident on the plane of separation. The value of difference between the angle of incident in $M_1$ and the angle of refraction in $M_2$ will be ______________ degree.

Accepted Answer

15

Question 60

If the potential barrier across a p-n junction is 0.6 V. Then the electric field intensity, in the depletion region having the width of $6 	imes 10^{-6}$m, will be __________ $	imes 10^{5}$ N/C.

Accepted Answer

1

Question 61

Which of the following pair of molecules contain odd electron molecule and an expanded octet molecule?

Accepted Answer

(B) NO and $H_{2}SO_{4}$

Answer

(A) $BCl_{3}$ and $SF_{6}$

Answer

(C) $SF_{6}$ and $H_{2}SO_{4}$

Answer

(D) $BCl_{3}$ and NO

Question 62

$N_{2(g)}$ + $3H_{2(g)}$ ⇌ $2NH_{3(g)}$
20 g   5 g
Consider the above reaction, the limiting reagent of the reaction and number of moles of $NH_{3}$ formed respectively are:

Accepted Answer

(C) $N_{2}$, 1.42 moles

Answer

(A) $H_{2}$, 1.42 moles

Answer

(B) $H_{2}$, 0.71 moles

Answer

(D) $N_{2}$, 0.71 moles

Question 63

100 mL of 5% (w/v) solution of NaCl in water was prepared in 250 mL beaker. Albumin from the egg was poured into NaCl solution and stirred well. This resulted in a/ an :

Accepted Answer

(A) Lyophilic sol

Answer

(B) Lyophobic sol

Answer

(C) Emulsion

Answer

(D) Precipitate

Question 64

The first ionization enthalpy of Na, Mg and Si, respectively, are: 496, 737 and 786 kJ mo1$^{-1}$. The first ionization enthalpy (kJ mol$^{-1}$) of Al is:

Accepted Answer

(C) 577

Answer

(A) 487

Answer

(B) 768

Answer

(D) 856

List – I	List - II
a.UV rays	i.Diagnostic tool in medicine
b.X-rays	ii.Water purification
c.Microwave	iii.Communication, Radar
d.Infrared wave	iv.Improving visibility in foggy days

Experiment	[X] mol $L^{-1}$	[Y] mol $L^{-1}$	Initial rate mol $L^{-1}$ $min^{-1}$
I.	0.1	0.1	$2 \times 10^{-3}$
II.	L	0.2	$4 \times 10^{-3}$
III.	0.4	0.4	$M \times 10^{-3}$
IV.	0.1	0.2	$2 \times 10^{-3}$

JEE Main 29 July 2022 Shift 1 Question Paper with Answers

Physics — JEE Main 29 July 2022 Shift 1

Chemistry — JEE Main 29 July 2022 Shift 1

Mathematics — JEE Main 29 July 2022 Shift 1

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