JEE Main 2023 · 12 Apr 2023 · Shift 1

Q1.An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12 cm. when viewed from the opposite side, the apparent distance of the bubble is observed as 4 cm. If the side of the ice cube is 24 cm, the refractive index of the ice cube is

Q2.Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be:

Q3.The amplitude of $15\sin (1000\pi t)$ is modulated by $10\sin (4\pi t)$ signal. The amplitude modulated signal contains frequencies of

1. 500 Hz.
2. 2 Hz
3. 250 Hz
4. 498 Hz
5. 502 Hz

Choose the correct answer from the options given below:

Q4.In an n-p-n common emitter (CE) transistor the collector current changes from 5 mA to 16 mA for the change in base current from $100\mu A$ and $200\mu A$, respectively. The current gain of transistor is ______.

Q5.If the r.m.s. speed of chlorine molecule is $490\text{ m/s}$ at $27^{\circ }C$, the r.m.s. speed of argon molecules at the same temperature will be (Atomic mass of argon $=39.9\text{ u}$, molecular mass of chlorine $=70.9\text{ u}$)

Q6.A proton and an $\alpha$-particle are accelerated from rest by 2 V and 4 V potentials, respectively. The ratio of their de-Broglie wavelength is:

Q7.Given below are two statements:

Statement I: The diamagnetic property depends on temperature.
Statement II: The induced magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field.
In the light of given statement, choose the correct answer from the …

Q8.A wire of resistance $160\Omega$ is melted and drawn in wire of one-fourth of its length. The new resistance of the wire will be

Q9.Three force $F_1=10\text{ N}$, $F_2=8\text{ N}$, $F_3=6\text{ N}$ are acting on a particle of mass 5 kg. The forces $F_2$ and $F_3$ are applied perpendicular so that particle remains at rest. If the force $F_1$ is removed, then the acceleration of the particle is:

Q10.A body cools from $80^{\circ }\mathrm{C}$ to $60^{\circ }\mathrm{C}$ in 5 minutes. The temperature of the surrounding is $20^{\circ }\mathrm{C}$. The time it takes to cool from $60^{\circ }\mathrm{C}$ to $40^{\circ }\mathrm{C}$ is:

Q11.An engine operating between the boiling and freezing points of water will have

1. efficiency more than $27\%$
2. efficiency less than the efficiency a Carnot engine operating between the same two temperatures.
3. efficiency equal to $27\%$
4. efficiency less than $27\%$

Q12.Given below are two statements:

Statement I: A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.

Statement II : A car moving towards east takes a turn and moves towar …

Q13.A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be:

Q14.A ball is thrown vertically upward with an initial velocity of $150\mathrm{m}/\mathrm{s}$. The ratio of velocity after 3 s and 5 s is $\frac{\mathrm{x}+1}{\mathrm{x}}$. The value of x is ____.

Take ( $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ ).

Q15.Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If an electric dipole of dipole moment $30\times 10^{-5}\mathrm{Cm}$ is enclosed by a closed surface, the net flux coming out of the surface will be zero.
Reason R …

Q16.Given below are two statement : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : EM waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology.
Reason R : Infrared EM waves are more energeti …

Q17.A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

Q18.The ratio of escape velocity of a planet to the escape velocity of earth will be:
Given : Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.

Q19.Given below are two statements :

Statement I : When the frequency of an a.c. source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases.

Statement II : In a series LCR circuit, the value of power factor at re …

Q20.For a certain organ pipe, the first three resonance frequencies are in the ratio of $1:3:5$ respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is $324{\mathrm{ms}}^{-1}$ the length of the organ pipe is ____ m.

Q21.For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{\mathrm{x}}{5}$. The value of $x$ is ____ .

Q22.A compass needle oscillates 20 times per minute at a place where the dip is $30^{\circ }$ and 30 times per minute where the dip is $60^{\circ }$. The ratio of total magnetic field due to the earth at two place respectively is $\frac{4}{\sqrt{x}}$. The value of $x$ is

Q23.A conducting circular loop is placed in a uniform magnetic field of 0.4 T with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of $1\mathrm{mm}/\mathrm{s}$. The magnitude of induced emf in the loop at an instant when …

Q24.To maintain a speed of $80\mathrm{km}/\mathrm{h}$ by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be
____ KJ. [The coefficient of friction between tyre of bus and road is 0.04].

Q25.A common example of alpha decay is
${}_{92}^{238}\mathrm{U}⟶{}_{90}^{234}\mathrm{Th}+{}_2{\mathrm{He}}^4+\mathrm{Q}$
Given :
${}_{92}^{238}\mathrm{U}=238.05060\mathrm{u}$,
${}_{90}^{234}\mathrm{Th}=234.04360\mathrm{u}$, …

Q26.The current flowing through a conductor connected across a source is 2 A and 1.2 A at $0^{\circ }\mathrm{C}$ and $100^{\circ }\mathrm{C}$ respectively. The current flowing through the conductor at $50^{\circ }\mathrm{C}$ will be ____ $\times 10^2\mathrm{mA}$.

Q27.Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at ____ cm from the first lens.

Q28.Glycerine of density $1.25\times 10^3\mathrm{kg}{\mathrm{m}}^{-3}$ is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends is $10{\mathrm{cm}}^2$ and $5{\mathrm{cm}}^2$ and pressure drop across its length is …

Q29.64 identical drops each charged upto potential of 10 mV are combined to form a bigger dorp. The potential of the bigger drop will be ____ mV .

Q1.Four gases A, B, C and D have critical temperatures 5.3, 33.2, 126.0 and 154.3 K respectively.
For their adsorption on fixed amount of charcoal, the correct order is :

Q2.Given below are two statement: one is labelled as
Assertion A and the other is labelled as Reason R
Assertion A: 5f electrons can participate in bonding to a far greater extent than 4f electrons
Reason R: 5f orbitals are not as buried as 4f orbitals
In the light of the above stat …

Q3.The incorrect statement regarding the reaction given below is

Q4.Match List I with List II

LIST I (Complex) | LIST II (CFSE (${\Delta }_0$))
A. ${\left[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_6\right]}^{2+}$ | I. -0.6
B. ${\left[\mathrm{Ti}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{3+}$ | II. -2.0
C. …

Q5.Match List I with List II

LIST I (Examples) | LIST II (Type)
A. 2-Chloro-1,3-butadiene | I. Biodegradable polymer
B. Nylon 2-nylon 6 | II. Synthetic Rubber
C. Polyacrylonitrile | III. Polyester
D. Dacron | IV. Addition Polymer

Choose the correct answer from the options given be …

Q6.The density of alkali metals is in the order

Q7.Given below are two statements:
Statement I: ${\mathrm{SbCl}}_5$ is more covalent than ${\mathrm{SbCl}}_3$
Statement II: The higher oxides of halogens also tend to be more stable than the lower ones.
In the light of the above statements, choose the most appropriate answer fro …

Q8.A metal chloride contains 55.0% of chlorine by weight. 100 mL vapours of the metal chloride at STP weigh 0.57 g. The molecular formula of the metal chloride is
(Given: Atomic mass of chlorine is 35.5 u)

Q9.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: In the Ellingham diagram, a sharp change in slope of the line is observed for $\mathrm{Mg}\to \mathrm{MgO}$ at $\sim 1120^{\circ }\mathrm{C}$
Reason R: Th …

Q10.Match List I with List II

LIST I | LIST II
A. Nitrogen oxides in air | I. Eutrophication
B. Methane in air | II. pH of rain water becomes 5.6
C. Carbon dioxide | III. Global warming
D. Phosphate fertilisers in water | IV. Acid rain

Choose the correct answer from the options giv …

Q11.For lead storage battery pick the correct statements
A. During charging of battery, ${\mathrm{PbSO}}_4$ on anode is converted into ${\mathrm{PbO}}_2$
B. During charging of battery, ${\mathrm{PbSO}}_4$ on cathode is converted into ${\mathrm{PbO}}_2$
C. Lead storage battery …

Q12.2-hexene $\underset{\text{(ii) }{\mathrm{H}}_2\mathrm{O}}{\overset{\text{(i) }{\mathrm{O}}_3}{\to }}$ Products

The two products formed in above reaction are -

Q13.Correct statements for the given reaction are :

Squaric acid $\stackrel{\text{2 eq. base}}{\to }$ 'B' (aromatic dianion)

A. Compound 'B' is aromatic
B. The completion of above reaction is very slow
C. 'A' shows tautomerism
D. The bond lengths C–C in compound B are found to be sa …

Q14.The bond order and magnetic property of acetylide ion are same as that of

Q15.In the given reaction cycle
${\mathrm{CaCl}}_2+{\mathrm{Na}}_2{\mathrm{CO}}_3⟶\underline{\mathrm{X}}+\underline{\mathrm{Y}}$
$\mathrm{X},\mathrm{Y}$ and Z respectively are

Q16.Given below are two statements :
Statement I: Boron is extremely hard indicating its high lattice energy
Statement II : Boron has highest melting and boiling point compared to its other group members.
In the light of the above statements, choose the most appropriate answer from t …

Q17.A in the above reaction is :

Q18.The major product ' P ' formed in the following sequence of reactions is
'P' (Major Product)

Q19.One mole of an ideal gas at 350 K is in a 2.0 L vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal reversible expansion from 2.0 L to 3.0 L (the pressure figure printed alongside is a redundant distractor and does not enter t …

Q20.The mass of ${\mathrm{NH}}_3$ produced when 131.8 kg of cyclohexanecarbaldehyde undergoes Tollen's test is $\_\_\_\_$ kg. (Nearest Integer)

Molar Mass of $\mathrm{C}=12\mathrm{g}/\mathrm{mol}$
$\mathrm{N}=14\mathrm{g}/\mathrm{mol}$ …

Q21.In an oligopeptide named Alanylglycylphenyl alanyl isoleucine, the number of ${\mathrm{sp}}^2$ hybridised carbons is $\_\_\_\_$ .

Q22.An analyst wants to convert. 1 L HCl of $\mathrm{pH}=1$ to a solution of HCl of pH 2 . The volume of water needed to do this dilution is $\_\_\_\_$ mL. (Nearest Integer)

Q23.Three organic compounds $\mathrm{A},\mathrm{B}$ and C were allowed to run in thin layer chromatography using hexane and gave the following result (see figure). The ${\mathrm{R}}_{\mathrm{f}}$ value of the most polar compound is
$\_\_\_\_$ $\times 10^{-2}$

Q24.80 mole percent of ${\mathrm{MgCl}}_2$ is dissociated in aqueous solution. The vapour pressure of 1.0 molal aqueous solution of ${\mathrm{MgCl}}_2$ at $38^{\circ }\mathrm{C}$ is
$\_\_\_\_$ mm Hg. (Nearest integer)

Given : Vapour pressure of water at $38^{\circ }\mathrm{C}$ is 50 …

Q25.The value of x in compound ' D ' is $\_\_\_\_$

Q26.At 600 K, the root mean square (rms) speed of gas X (molar mass $=40$) is equal to the most probable speed of gas $Y$ at 90 K. The molar mass of the gas Y is ______ ${\mathrm{g}\mathrm{mol}}^{-1}$. (Nearest integer)

Q27.The reaction $2\mathrm{NO}+{\mathrm{Br}}_2\to 2\mathrm{NOBr}$
takes places through the mechanism given below:
$\mathrm{NO}+{\mathrm{Br}}_2\iff {\mathrm{NOBr}}_2$ (fast)
${\mathrm{NOBr}}_2+\mathrm{NO}\to 2\mathrm{NOBr}$ (slow)

The overall order of th …

Q28.Values of work function $({\mathrm{W}}_0)$ for a few metals are given below

The number of metals which will show photoelec …

Q29.4-Bromopentan-2-one is treated as shown:

$\mathrm{C}{\mathrm{H}}_3-\mathrm{CO}-\mathrm{C}{\mathrm{H}}_2-\mathrm{CH}(\mathrm{C}{\mathrm{H}}_3)-\mathrm{Br}\underset{(ii){\mathrm{H}}_2\mathrm{O}}{\overset{(i)\mathrm{Mg}}{\to }}\text{’A’ (Major Product)}$

A is :

Q1.The number of five digit numbers, greater than 40000 and divisible by 5, which can be formed using the digits $0,1,3,5,7$ and 9 without repetition, is equal to

Q2.Let $\alpha ,\beta$ be the roots of the quadratic equation $x^2+\sqrt{6}x+3=0$. Then $\frac{{\alpha }^{23}+{\beta }^{23}+{\alpha }^{14}+{\beta }^{14}}{{\alpha }^{15}+{\beta }^{15}+{\alpha }^{10}+{\beta }^{10}}$ is equal to

Q3.Let $⟨a_n⟩$ be a sequence such that $a_1+a_2+\dots +a_n=\frac{n^2+3n}{(n+1)(n+2)}$. If $28{\sum }_{k=1}^{10}\frac{1}{a_k}=p_1{p}_2{p}_3\dots p_m$, where $p_1,p_2,\dots ,p_m$ are the first $m$ prime numbers, then $m$ is equal to

Q4.Let the lines $l_1:\frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha }{-2}$ and $l_2:3x+2y+z-2=0=x-3y+2z-13$ be coplanar. If the point $P(a,b,c)$ on $l_1$ is nearest to the point $Q(-4,-3,2)$, then $|a|+|b|+|c|$ is equal to

Q5.Let $P\left(\frac{2\sqrt{3}}{\sqrt{7}},\frac{6}{\sqrt{7}}\right),Q,R$ and $S$ be four points on the ellipse $9x^2+4y^2=36$. Let $PQ$ and $RS$ be mutually perpendicular and pass through the origin. If $\frac{1}{(PQ{)}^2}+\frac{1}{(RS{)}^2}=\frac{p}{q}$, where …

Q6.Let $a,b,c$ be three distinct real numbers, none equal to one. If the vectors $a\hat{i}+\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k}$ and $\hat{i}+\hat{j}+c\hat{k}$ are coplanar, then $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is equal to

Q7.If the local maximum value of the function $f(x)={\left(\frac{\sqrt{3e}}{2\sin x}\right)}^{{\sin }^{2}x},x\in \left(0,\frac{\pi }{2}\right)$, is $\frac{k}{e}$, then ${\left(\frac{k}{e}\right)}^8+\frac{k^8}{e^5}+k^8$ is equal to

Q8.Let $D$ be the domain of the function $f(x)={\sin }^{-1}\left({\log }_{3x}\left(\frac{6+2{\log }_{3}x}{-5x}\right)\right)$. If the range of the function $g:D\to \mathbb{R}$ defined by $g(x)=x-[x]$, ([x] is the greatest integer function), is $(\alpha ,\beta )$, t …

Q9.Let $y=y(x),y>0$, be a solution curve of the differential equation $(1+x^2)dy=y(x-y)dx$. If $y(0)=1$ and $y(2\sqrt{2})=\beta$, then

Q10.Among the two statements
(S1): $(p\Rightarrow q)\wedge (q\wedge (\sim q))$ is a contradiction and
(S2): $(p\wedge q)\vee ((\sim p)\wedge q)\vee (p\wedge (\sim q))\vee ((\sim p)\wedge (\sim q))$ is a tautology

Q11.Let $\lambda \in \mathbb{Z},\vec{a}=\lambda \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=3\hat{i}-\hat{j}+2\hat{k}$. Let $\vec{c}$ be a vector such that $(\vec{a}+\vec{b}+\vec{c})\times \vec{c}=\vec{0},\vec{a}\cdot \vec{c}=-17$ and $\vec{b}\cdot \vec{c}=-20$. Then …

Q12.The sum of the coefficients of the first 50 terms in the binomial expansion of $(1-x{)}^{100}$, is equal to

Q13.The area of the region enclosed by the curve $y=x^3$ and its tangent at the point $(-1,-1)$ is

Q14.Let $\mathrm{A}=\left[\begin{array}{cc}1& \frac{1}{51}\\ 0& 1\end{array}\right]$. If $\mathrm{B}=\left[\begin{array}{cc}1& 2\\ -1& -1\end{array}\right]\mathrm{A}\left[\begin{array}{cc}-1& -2\\ 1& 1\end{array}\right]$, then the sum of all the elements of the matrix …

Q15.Let the plane $\mathrm{P}:4\mathrm{x}-\mathrm{y}+\mathrm{z}=10$ be rotated by an angle $\frac{\pi }{2}$ about its line of intersection with the plane $\mathrm{x}+\mathrm{y}-\mathrm{z}=4$. If $\alpha$ is the distance of the point $(2,3,-4)$ from the new position of the …

Q16.If $\frac{1}{n+1}{}^n{C}_n+\frac{1}{n}{}^n{C}_{n-1}+\dots +\frac{1}{2}{}^{\mathrm{n}}{\mathrm{C}}_1+{}^{\mathrm{n}}{\mathrm{C}}_0=\frac{1023}{10}$ then n is equal to

Q17.Let C be the circle in the complex plane with centre ${\mathrm{z}}_0=\frac{1}{2}(1+3\mathrm{i})$ and radius $\mathrm{r}=1$. Let ${\mathrm{z}}_1=1+\mathrm{i}$ and the complex number ${\mathrm{z}}_2$ be outside the circle C such that …

Q18.If the point $\left(\alpha ,\frac{7\sqrt{3}}{3}\right)$ lies on the curve traced by the mid-points of the line segments of the lines x $\cos \theta +\mathrm{y}\sin \theta =7,\theta \in \left(0,\frac{\pi }{2}\right)$ between the coordinates axes, then $\alpha$ is equal to

Q19.Two dice A and B are rolled. Let the numbers obtained on A and B be $\alpha$ and $\beta$ respectively. If the variance of $\alpha -\beta$ is $\frac{p}{q}$, where $p$ and $q$ are coprime, then the sum of the positive divisors of p is equal to

Q20.In a triangle ABC, if $\cos \mathrm{A}+2\cos \mathrm{B}+\cos \mathrm{C}=2$ and the lengths of the sides opposite to the angles A and C are 3 and 7 respectively, then $\cos \mathrm{A}-\cos$ C is equal to

Q21.A fair $\mathrm{n}(\mathrm{n}>1)$ faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is $\frac{\mathrm{n}}{9}$, then n is equal to

Q22.Let the digits $\mathrm{a},\mathrm{b},\mathrm{c}$ be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

Q23.Let $[\mathrm{x}]$ be the greatest integer $\le \mathrm{x}$. Then the number of points in the interval $(-2,1)$, where the function $\mathrm{f}(\mathrm{x})=|[\mathrm{x}]|+\sqrt{\mathrm{x}-[\mathrm{x}]}$ is discontinuous is

Q24.Let the plane $\mathrm{x}+3\mathrm{y}-2\mathrm{z}+6=0$ meet the co-ordinate axes at the points $\mathrm{A},\mathrm{B},\mathrm{C}$. If the orthocentre of the triangle ABC is $\left(\alpha ,\beta ,\frac{6}{7}\right)$, then $98(\alpha +\beta {)}^2$ is equal to

Q25.Let $\mathrm{I}(\mathrm{x})=\int \sqrt{\frac{\mathrm{x}+7}{\mathrm{x}}}\mathrm{dx}$ and $\mathrm{I}(9)=12+7{\log }_{\mathrm{e}}7$. If $\mathrm{I}(1)=\alpha +7{\log }_e(1+2\sqrt{2})$, then ${\alpha }^4$ is equal to ______.

Q26.Let ${\mathrm{D}}_{\mathrm{k}}=\left|\begin{array}{ccc}1& 2\mathrm{k}& 2\mathrm{k}-1\\ \mathrm{n}& {\mathrm{n}}^2+\mathrm{n}+2& {\mathrm{n}}^2\\ \mathrm{n}& {\mathrm{n}}^2+\mathrm{n}& {\mathrm{n}}^2+\mathrm{n}+2\end{array}\right|$. If …

Q27.Let the positive numbers ${\mathrm{a}}_1,{\mathrm{a}}_2,{\mathrm{a}}_3,{\mathrm{a}}_4$ and ${\mathrm{a}}_5$ be in a G.P. Let their mean and variance be $\frac{31}{10}$ and $\frac{m}{n}$ respectively, where m and n are co-prime. If the mean of their reciprocals is …

Q28.The number of relations, on the set $\{1,2,3\}$ containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is ______.

Q29.If ${\int }_{-0.15}^{0.15}\left|100{\mathrm{x}}^2-1\right|\mathrm{dx}=\frac{\mathrm{k}}{3000}$, then k is equal to ______.

Q30.Two circles in the first quadrant of radii ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line $x+y=2$. Then $r_1^2+r_2^2-r_1{r}_2$ is equal to ______.