JEE Main 1 February 2023 Shift 1 Question Paper

Question 1

If $y=y(x)$ is the solution curve of the differential equation $\frac{dy}{dx}+y	an x=x\sec x$, $0\le x\le\frac{\pi}{3}$, $y(0)=1$, then $y\!\left(\frac{\pi}{6}ight)$ is equal to

Accepted Answer

(B) $\frac{\pi}{12}-\frac{\sqrt{3}}{2}\log_e\!\left(\frac{2}{e\sqrt{3}}\right)$

Answer

(A) $\frac{\pi}{12}-\frac{\sqrt{3}}{2}\log_e\!\left(\frac{2\sqrt{3}}{e}\right)$

Answer

(C) $\frac{\pi}{12}+\frac{\sqrt{3}}{2}\log_e\!\left(\frac{2}{e\sqrt{3}}\right)$

Answer

(D) $\frac{\pi}{12}+\frac{\sqrt{3}}{2}\log_e\!\left(\frac{2\sqrt{3}}{e}\right)$

Question 2

Let $R$ be a relation on $\mathbb{R}$, given by $R=\{(a,b):3a-3b+\sqrt{7}	ext{ is an irrational number}\}$. Then $R$ is

Accepted Answer

(C) reflexive but neither symmetric nor transitive

Answer

(A) an equivalence relation

Answer

(B) reflexive and symmetric but not transitive

Answer

(D) reflexive and transitive but not symmetric

Question 3

For a triangle $ABC$, the value of $\cos 2A+\cos 2B+\cos 2C$ is least. If its inradius is $3$ and incentre is $M$, then which of the following is NOT correct?

Accepted Answer

(D) area of $	riangle ABC$ is $\frac{27\sqrt{3}}{2}$

Answer

(A) perimeter of $	riangle ABC$ is $18\sqrt{3}$

Answer

(B) $\sin 2A+\sin 2B+\sin 2C=\sin A+\sin B+\sin C$

Answer

(C) $\overrightarrow{MA}\cdot\overrightarrow{MB}=-18$

Question 4

Let $S$ be the set of all solutions of the equation $\cos^{-1}(2x)-2\cos^{-1}\!\left(\sqrt{1-x^2}ight)=\pi$, $x\in\left[-	frac{1}{2},	frac{1}{2}ight]$. Then $\sum_{x\in S}2\sin^{-1}\!\left(x^2-1ight)$ is equal to

Accepted Answer

(A) $\pi-2\sin^{-1}\!\left(\frac{\sqrt{3}}{4}\right)$

Answer

(B) $\pi-\sin^{-1}\!\left(\frac{\sqrt{3}}{4}\right)$

Answer

(C) $\frac{-2\pi}{3}$

Answer

(D) $0$

Question 5

Let $S$ denote the set of all real values of $\lambda$ such that the system of equations $\lambda x+y+z=1$, $x+\lambda y+z=1$, $x+y+\lambda z=1$ is inconsistent, then $\sum_{\lambda\in S}\left(|\lambda|^2+|\lambda|\right)$ is equal to

Accepted Answer

(C) $6$

Answer

(A) $4$

Answer

(B) $12$

Answer

(D) $2$

Question 6

In a binomial distribution $B(n,p)$, the sum and the product of the mean and the variance are $5$ and $6$ respectively, then $6(n+p-q)$ is equal to

Accepted Answer

(A) $52$

Answer

(B) $50$

Answer

(C) $51$

Answer

(D) $53$

Question 7

The combined equation of the two lines $ax+by+c=0$ and $a'x+b'y+c'=0$ can be written as $(ax+by+c)(a'x+b'y+c')=0$. The equation of the angle bisectors of the lines represented by the equation $2x^2+xy-3y^2=0$ is

Accepted Answer

(A) $x^2-y^2-10xy=0$

Answer

(B) $x^2-y^2+10xy=0$

Answer

(C) $3x^2+5xy+2y^2=0$

Answer

(D) $3x^2+xy-2y^2=0$

Question 8

The area enclosed by the closed curve $C$ given by the differential equation $\frac{dy}{dx}+\frac{x+a}{y-2}=0$, $y(1)=0$ is $4\pi$. Let $P$ and $Q$ be the points of intersection of the curve $C$ and the $y$-axis. If normals at $P$ and $Q$ on the curve $C$ intersect $x$-axis at points $R$ and $S$ respectively, then the length of the line segment $RS$ is

Accepted Answer

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

Answer

(A) $2$

Answer

(C) $2\sqrt{3}$

Answer

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

Question 9

The value of $\frac{1}{1!\,50!}+\frac{1}{3!\,48!}+\frac{1}{5!\,46!}+\cdots+\frac{1}{49!\,2!}+\frac{1}{51!\,1!}$ is

Accepted Answer

(A) $\frac{2^{50}}{51!}$

Answer

(B) $\frac{2^{51}}{50!}$

Answer

(C) $\frac{2^{50}}{50!}$

Answer

(D) $\frac{2^{51}}{51!}$

Question 10

The mean and variance of $5$ observations are $5$ and $8$ respectively. If $3$ observations are $1, 3, 5$ then the sum of cubes of the remaining two observations is

Accepted Answer

(B) $1072$

Answer

(A) $1216$

Answer

(C) $1456$

Answer

(D) $1792$

Question 11

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

Accepted Answer

(A) $\frac{55}{111}$

Answer

(B) $\frac{56}{111}$

Answer

(C) $\frac{58}{111}$

Answer

(D) $\frac{59}{111}$

Question 12

The shortest distance between the lines $\frac{x-5}{1}=\frac{y-2}{2}=\frac{z-4}{-3}$ and $\frac{x+3}{1}=\frac{y+5}{4}=\frac{z-1}{-5}$ is

Accepted Answer

(C) $6\sqrt{3}$

Answer

(A) $5\sqrt{3}$

Answer

(B) $7\sqrt{3}$

Answer

(D) $4\sqrt{3}$

Question 13

$\lim_{n	o\infty}\left[\frac{1}{1+n}+\frac{1}{2+n}+\frac{1}{3+n}+\cdots+\frac{1}{2n}ight]$ is equal to

Accepted Answer

(A) $\log_e 2$

Answer

(B) $\log_e\!\left(\frac{2}{3}\right)$

Answer

(C) $\log_e\!\left(\frac{3}{2}\right)$

Answer

(D) $0$

Question 14

Let the image of the point $P(2,-1,3)$ in the plane $x+2y-z=0$ be $Q$. Then the distance of the plane $3x+2y+z+29=0$ from the point $Q$ is

Accepted Answer

(C) $3\sqrt{14}$

Answer

(A) $\frac{24\sqrt{2}}{7}$

Answer

(B) $2\sqrt{14}$

Answer

(D) $\frac{22\sqrt{2}}{7}$

Question 15

Let $f(x)=2x+	an^{-1}x$ and $g(x)=\log_e\!\left(\sqrt{1+x^2}+xight)$, $x\in[0,3]$. Then

Accepted Answer

(B) $\max f'(x)>\max g'(x)$

Answer

(A) $\min f'(x)=1+\max g'(x)$

Answer

(C) there exist $0<x_1<x_2<3$ such that $f(x)<g(x),\ \forall x\in(x_1,x_2)$

Answer

(D) there exists $\hat{x}\in[0,3]$ such that $f'(\hat{x})<g'(\hat{x})$

Question 16

If the orthocentre of the triangle, whose vertices are $(1,2)$, $(2,3)$ and $(3,1)$ is $(\alpha,\beta)$, then the quadratic equation whose roots are $\alpha+4\beta$ and $4\alpha+\beta$, is

Accepted Answer

(A) $x^2-20x+99=0$

Answer

(B) $x^2-19x+90=0$

Answer

(C) $x^2-22x+120=0$

Answer

(D) $x^2-18x+80=0$

Question 17

Let $S=\{x:x\in\mathbb{R}	ext{ and }(\sqrt{3}+\sqrt{2})^{x^2-4}+(\sqrt{3}-\sqrt{2})^{x^2-4}=10\}$. Then $n(S)$ is equal to

Accepted Answer

(A) $4$

Answer

(B) $0$

Answer

(C) $6$

Answer

(D) $2$

Question 18

If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha,\beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to

Accepted Answer

(B) $12$

Answer

(A) $11$

Answer

(C) $9$

Answer

(D) $10$

Question 19

Let $f(x)=\begin{vmatrix}1+\sin^2 x & \cos^2 x & \sin 2x\ \sin^2 x & 1+\cos^2 x & \sin 2x\ \sin^2 x & \cos^2 x & 1+\sin 2x\end{vmatrix}$, $x\in\left[\frac{\pi}{6},\frac{\pi}{3}ight]$. If $\alpha$ and $\beta$ respectively are the maximum and the minimum values of $f$, then

Accepted Answer

(B) $\beta^2-2\sqrt{\alpha}=\frac{19}{4}$

Answer

(A) $\alpha^2+\beta^2=\frac{9}{2}$

Answer

(C) $\alpha^2-\beta^2=4\sqrt{3}$

Answer

(D) $\beta^2+2\sqrt{\alpha}=\frac{19}{4}$

Question 20

The negation of the expression $q\vee((\sim q)\wedge p)$ is equivalent to

Accepted Answer

(D) $(\sim p)\wedge(\sim q)$

Answer

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

Answer

(B) $p\wedge(\sim q)$

Answer

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

Question 21

Let $\vec{v}=\alpha\hat{i}+2\hat{j}-3\hat{k}$, $\vec{w}=2\alpha\hat{i}+\hat{j}-\hat{k}$ and $\vec{u}$ be a vector such that $|\vec{u}|=\alpha>0$. If the minimum value of the scalar triple product $[\vec{u}\ \vec{v}\ \vec{w}]$ is $-\alpha\sqrt{3401}$, and $|\vec{u}\cdot\hat{i}|^2=\frac{m}{n}$ where $m$ and $n$ are coprime natural numbers, then $m+n$ is equal to _______ .

Accepted Answer

3501

Question 22

The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is _______ .

Accepted Answer

50400

Question 23

The remainder, when $19^{200}+23^{200}$ is divided by $49$, is _______ .

Accepted Answer

29

Question 24

The number of $3$-digit numbers, that are divisible by either $2$ or $3$ but not divisible by $7$, is _______ .

Accepted Answer

514

Question 25

Let $f:\mathbb{R}	o\mathbb{R}$ be a differentiable function such that $f'(x)+f(x)=\int_0^2 f(t)\,dt$. If $f(0)=e^{-2}$, then $2f(0)-f(2)$ is equal to _______ .

Accepted Answer

1

Question 26

If $f(x)=x^2+g'(1)x+g''(2)$ and $g(x)=f(1)x^2+xf'(x)+f''(x)$, then the value of $f(4)-g(4)$ is equal to _______ .

Accepted Answer

14

Question 27

Let $A$ be the area bounded by the curve $y=x|x-3|$, the $x$-axis and the ordinates $x=-1$ and $x=2$. Then $12A$ is equal to _______ .

Accepted Answer

62

Question 28

If $\int_0^1 (x^{21}+x^{14}+x^7)(2x^{14}+3x^7+6)^{1/7}\,dx=\frac{1}{l}(11)^{m/n}$ where $l,m,n\in\mathbb{N}$, $m$ and $n$ are coprime, then $l+m+n$ is equal to _______ .

Accepted Answer

63

Question 29

Let $a_1, a_2, a_3, \ldots, a_n$ be in A.P. If the sum of its first four terms is $50$ and the sum of its last four terms is $170$, then the product of its middle two terms is _______ .

Accepted Answer

754

Question 30

$A(2,6,2)$, $B(-4,0,\lambda)$, $C(2,3,-1)$ and $D(4,5,0)$, $|\lambda|\le 5$ are the vertices of a quadrilateral $ABCD$. If its area is $18$ square units, then $5-6\lambda$ is equal to _______ .

Accepted Answer

11

Question 31

A child stands on the edge of the cliff $10$ m above the ground and throws a stone horizontally with an initial speed of $5$ ms$^{-1}$. Neglecting the air resistance, the speed with which the stone hits the ground will be _______ ms$^{-1}$ (given, $g = 10$ ms$^{-2}$).

Accepted Answer

(A) $15$

Answer

(B) $20$

Answer

(C) $30$

Answer

(D) $25$

Question 32

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in the figure. Then the electric fields in three different regions $E_I$, $E_{II}$ and $E_{III}$ are:

Accepted Answer

(C) $\vec{E}_I=-	frac{\sigma}{\varepsilon_0}\hat{n},\ \vec{E}_{II}=0,\ \vec{E}_{III}=	frac{\sigma}{\varepsilon_0}\hat{n}$

Answer

(A) $\vec{E}_I=	frac{2\sigma}{\varepsilon_0}\hat{n},\ \vec{E}_{II}=0,\ \vec{E}_{III}=	frac{2\sigma}{\varepsilon_0}\hat{n}$

Answer

(B) $\vec{E}_I=	frac{\sigma}{2\varepsilon_0}\hat{n},\ \vec{E}_{II}=0,\ \vec{E}_{III}=	frac{\sigma}{2\varepsilon_0}\hat{n}$

Answer

(D) $\vec{E}_I=0,\ \vec{E}_{II}=	frac{\sigma}{\varepsilon_0}\hat{n},\ \vec{E}_{III}=0$

Question 33

A mercury drop of radius $10^{-3}$ m is broken into $125$ equal size droplets. Surface tension of mercury is $0.45$ Nm$^{-1}$. The gain in surface energy is:

Accepted Answer

(D) $2.26	imes10^{-5}$ J

Answer

(A) $28	imes10^{-5}$ J

Answer

(B) $17.5	imes10^{-5}$ J

Answer

(C) $5	imes10^{-5}$ J

Question 34

If earth has a mass nine times and radius twice to that of a planet $P$, then $	frac{v_e}{3}\sqrt{x}$ ms$^{-1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of $P$, where $v_e$ is escape velocity on earth. The value of $x$ is:

Accepted Answer

(D) $2$

Answer

(A) $1$

Answer

(B) $3$

Answer

(C) $18$

Question 35

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is $\left(	ext{given},\ \gamma=	frac{3}{2}ight)$:

Accepted Answer

(B) $W=RT[2-\sqrt{2}]$

Answer

(A) $W=	frac{T}{R}[\sqrt{2}-2]$

Answer

(C) $W=TR[\sqrt{2}-2]$

Answer

(D) $W=	frac{R}{T}[2-\sqrt{2}]$

Question 36

$\left(P+	frac{a}{V^2}ight)(V-b)=RT$ represents the equation of state of some gases, where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $	frac{b^2}{a}$, will be:

Accepted Answer

(A) Compressibility

Answer

(B) Energy density

Answer

(C) Modulus of rigidity

Answer

(D) Bulk modulus

Question 37

The equivalent resistance between $A$ and $B$ of the network shown in the figure is:

Accepted Answer

(A) $	frac{8}{3}R$

Answer

(B) $21R$

Answer

(C) $14R$

Answer

(D) $11	frac{2}{3}R$

Question 38

Match List I (electrical machines and resonance phenomena) with List II (the underlying principle or condition). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 39

An object moves with speed $v_1$, $v_2$ and $v_3$ along a line segment $AB$, $BC$ and $CD$ respectively, where $AB=BC$ and $AD=3AB$. Then the average speed of the object will be:

Accepted Answer

(C) $	frac{3v_1v_2v_3}{(v_1v_2+v_2v_3+v_3v_1)}$

Answer

(A) $	frac{(v_1+v_2+v_3)}{3v_1v_2v_3}$

Answer

(B) $	frac{(v_1+v_2+v_3)}{3}$

Answer

(D) $	frac{v_1v_2v_3}{3(v_1v_2+v_2v_3+v_3v_1)}$

Question 40

'$n$' polarizing sheets are arranged such that each makes an angle $45^\circ$ with the preceeding sheet. An unpolarized light of intensity $I$ is incident into this arrangement. The output intensity is found to be $	frac{I}{64}$. The value of $n$ will be:

Accepted Answer

(D) $6$

Answer

(A) $4$

Answer

(B) $3$

Answer

(C) $5$

Question 41

Match List I (regions of the electromagnetic spectrum) with List II (their sources). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 42

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda$. An alpha particle having certain kinetic energy has the same de-Broglie wavelength $\lambda$. The ratio of kinetic energy of proton and that of alpha particle is:

Accepted Answer

(D) $4:1$

Answer

(A) $2:1$

Answer

(B) $1:2$

Answer

(C) $1:4$

Question 43

A block of mass $5$ kg is placed at rest on a table of rough surface. Now, if a force of $30$ N is applied in the direction parallel to surface of the table, the block slides through a distance of $50$ m in an interval of time $10$ s. Coefficient of kinetic friction is (given, $g=10$ ms$^{-2}$):

Accepted Answer

(D) $0.50$

Answer

(A) $0.60$

Answer

(B) $0.25$

Answer

(C) $0.75$

Question 44

Given below are two statements:
Statement I: Acceleration due to gravity is different at different places on the surface of earth.
Statement II: Acceleration due to gravity increases as we go down below the earth's surface.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

(C) Both Statement I and Statement II are false

Answer

(D) Both Statement I and Statement II are true

Question 45

Which of the following frequencies does not belong to FM broadcast?

Accepted Answer

(A) $64$ MHz

Answer

(B) $89$ MHz

Answer

(C) $99$ MHz

Answer

(D) $106$ MHz

Question 46

The mass of proton, neutron and helium nucleus are respectively $1.0073u$, $1.0087u$ and $4.0015u$. The binding energy of helium nucleus is:

Accepted Answer

(A) $28.4$ MeV

Answer

(B) $56.8$ MeV

Answer

(C) $14.2$ MeV

Answer

(D) $7.1$ MeV

Question 47

A steel wire with mass per unit length $7.0	imes10^{-3}$ kg m$^{-1}$ is under tension of $70$ N. The speed of transverse waves in the wire will be:

Accepted Answer

(A) $100$ m/s

Answer

(B) $10$ m/s

Answer

(C) $50$ m/s

Answer

(D) $200\pi$ m/s

Question 48

Match List I (type of semiconductor/conductor) with List II (position of the Fermi-level). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 49

Find the magnetic field at the point $P$ in the figure. The curved portion is a semicircle of radius $r$ connected to two long straight wires.

Accepted Answer

(B) $	frac{\mu_0 i}{2r}\left(	frac{1}{2}+	frac{1}{2\pi}ight)$

Answer

(A) $	frac{\mu_0 i}{2r}\left(1+	frac{2}{\pi}ight)$

Answer

(C) $	frac{\mu_0 i}{2r}\left(1+	frac{1}{\pi}ight)$

Answer

(D) $	frac{\mu_0 i}{2r}\left(	frac{1}{2}+	frac{1}{\pi}ight)$

Question 50

The average kinetic energy of a molecule of the gas is:

Accepted Answer

(A) proportional to absolute temperature

Answer

(B) proportional to pressure

Answer

(C) proportional to volume

Answer

(D) dependent on the nature of gas

Question 51

A small particle moves to position $5\hat{i}-2\hat{j}+\hat{k}$ from its initial position $2\hat{i}+3\hat{j}-4\hat{k}$ under the action of force $5\hat{i}+2\hat{j}+7\hat{k}$ N. The value of work done will be _______ J.

Accepted Answer

40

Question 52

A certain pressure '$P$' is applied to $1$ litre of water and $2$ litre of a liquid separately. Water gets compressed to $0.01\%$ whereas the liquid gets compressed to $0.03\%$. The ratio of Bulk modulus of water to that of the liquid is $	frac{3}{x}$. The value of $x$ is _______ .

Accepted Answer

1

Question 53

A light of energy $12.75$ eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $	frac{x}{\pi}	imes10^{-17}$ eVs. The value of $x$ is _______ (use $h=4.14	imes10^{-15}$ eVs, $c=3	imes10^8$ ms$^{-1}$).

Accepted Answer

828

Question 54

A charge particle of $2\,\mu C$ accelerated by a potential difference of $100$ V enters a region of uniform magnetic field of magnitude $4$ mT at right angle to the direction of field. The charge particle completes semicircle of radius $3$ cm inside magnetic field. The mass of the charge particle is _______ $	imes10^{-18}$ kg.

Accepted Answer

144

Question 55

The amplitude of a particle executing SHM is $3$ cm. The displacement at which its kinetic energy will be $25\%$ more than the potential energy is _______ cm.

Accepted Answer

2

Question 56

In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf $1.5$ V is found to be $60$ cm. If this cell is replaced by another cell of emf $E$, the length of null point increases by $40$ cm. The value of $E$ is $	frac{x}{10}$ V. The value of $x$ is _______ .

Accepted Answer

25

Question 57

A thin cylindrical rod of length $10$ cm is placed horizontally on the principal axis of a concave mirror of focal length $20$ cm. The rod is placed in such a way that mid point of the rod is at $40$ cm from the pole of mirror. The length of the image formed by the mirror will be $	frac{x}{3}$ cm. The value of $x$ is _______ .

Accepted Answer

32

Question 58

A solid cylinder is released from rest from the top of an inclined plane of inclination $30^\circ$ and length $60$ cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is _______ ms$^{-1}$ (given $g=10$ ms$^{-2}$).

Accepted Answer

2

Question 59

A series LCR circuit is connected to an ac source of $220$ V, $50$ Hz. The circuit contains a resistance $R=100\,\Omega$ and an inductor of inductive reactance $X_L=79.6\,\Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _______ $\mu$F.

Accepted Answer

40

Question 60

Two equal positive point charges are separated by a distance $2a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $q_0$ becomes maximum is $	frac{a}{\sqrt{x}}$. The value of $x$ is _______ .

Accepted Answer

2

Question 61

A solution of $	ext{FeCl}_3$ when treated with $	ext{K}_4[	ext{Fe(CN)}_6]$ gives a prussian blue precipitate due to the formation of:

Accepted Answer

(B) $	ext{Fe}_4[	ext{Fe(CN)}_6]_3$

Answer

(A) $	ext{K[Fe}_2(	ext{CN})_6]$

Answer

(C) $	ext{Fe[Fe(CN)}_6]$

Answer

(D) $	ext{Fe}_3[	ext{Fe(CN)}_6]_2$

Question 62

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Hydrogen is an environment friendly fuel.
Reason R: Atomic number of hydrogen is 1 and it is a very light element.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

(A) A is true but R is false

Answer

(B) A is false but R is true

Answer

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

Question 63

Resonance structures of the carbonate ion $(	ext{CO}_3^{2-})$ are shown in the figure. Which of the following is true?

Accepted Answer

(D) $	ext{CO}_3^{2-}$ has a single structure i.e., resonance hybrid of the above three structures.

Answer

(A) All these structures are in dynamic equilibrium with each other.

Answer

(B) It is possible to identify each structure individually by some physical or chemical method.

Answer

(C) Each structure exists for equal amount of time.

Question 64

Match List I (class of drug) with List II (its example or action). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

List I	List II
A.AC generator	I.Presence of both L and C
B.Transformer	II.Electromagnetic Induction
C.Resonance phenomenon to occur	III.Quality factor
D.Sharpness of resonance	IV.Mutual Induction

List I	List II
A.Microwaves	I.Radio active decay of the nucleus
B.Gamma rays	II.Rapid acceleration and deceleration of electron in aerials
C.Radio waves	III.Inner shell electrons
D.X-rays	IV.Klystron valve

List I	List II
A.Intrinsic semiconductor	I.Fermi-level near the valence band
B.n-type semiconductor	II.Fermi-level in the middle of valence and conduction band
C.p-type semiconductor	III.Fermi-level near the conduction band
D.Metals	IV.Fermi-level inside the conduction band

List I	List II
A.Tranquilizers	I.Anti blood clotting
B.Aspirin	II.Salvarsan
C.Antibiotic	III.antidepressant drugs
D.Antiseptic	IV.soframicine

List I	List II
A.Slaked lime	I. $\text{NaOH}$
B.Dead burnt plaster	II. $\text{Ca(OH)}_2$
C.Caustic soda	III. $\text{Na}_2\text{CO}_3\cdot 10\text{H}_2\text{O}$
D.Washing soda	IV. $\text{CaSO}_4$

JEE Main 1 February 2023 Shift 1 Question Paper with Answers

Physics — JEE Main 1 February 2023 Shift 1

Chemistry — JEE Main 1 February 2023 Shift 1

Mathematics — JEE Main 1 February 2023 Shift 1

Chapters tested in this paper

Attempt this paper under exam timing.

List I	List II
A.Molisch's Test	I.Peptide
B.Biuret Test	II.Carbohydrate
C.Carbylamine Test	III.Primary amine
D.Schiff's Test	IV.Aldehyde