JEE Main 2023 · 25 Jan 2023 · Shift 1

Q1.Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of ${\lambda }_{\mathrm{o}}$. If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be:

Q2.An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is:
(Take …

Q3.A Carnot engine with efficiency $50\%$ takes heat from a source at 600 K. In order to increase the efficiency to $70\%$, keeping the temperature of sink same, the new temperature of the source will be:

Q4.T is the time period of simple pendulum on the earth's surface. Its time period becomes xT when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of $x$ will be:

Q5.Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the mot …

Q6.A car travels a distance of 'x' with speed ${\mathrm{V}}_1$ and then same distance 'x' with speed ${\mathrm{V}}_2$ in the same direction. The average speed of the car is:

Q7.A parallel plate capacitor has plate area $40{\mathrm{cm}}^2$ and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is:

Q8.The root mean square velocity of molecules of gas is

Q9.In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes x times its initial resonant frequency ${\omega }_0$. The value of x is:

Q10.The ratio of the density of oxygen nucleus ${(}_8^{16}\mathrm{O})$ and helium nucleus ${(}_2^4\mathrm{He})$ is

Q11.A message signal of frequency 5 kHz is used to modulate a carrier signal of frequency 2 MHz. The bandwidth for amplitude modulation is:

Q12.All electromagnetic wave is transporting energy in the negative z direction. At a certain point and certain time the direction of electric field of the wave is along positive $y$ direction. What will be the direction of the magnetic field of the wave at that point and instant?

Q13.In Young's double slits experiment, the position of $5^{\text{th}}$ bright fringe from the central maximum is 5 cm. The distance between slits and screen is 1 m and wavelength of used monochromatic light is 600 nm. The separation between the slits is:

Q14.Given below are two statements: one is labeled as Assertion A and the other is labeled as Reason R
Assertion A: Photodiodes are used in forward bias usually for measuring the light intensity.
Reason R: For a p-n junction diode, at applied voltage V the current in the forward bias …

Q15.A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is:

Q16.A uniform metallic wire carries a current 2 A. when 3.4 V battery is connected across it. The mass of uniform metallic wire is $8.92\times 10^{-3}\mathrm{kg}$. density is $8.92\times 10^3\mathrm{kg}/{\mathrm{m}}^3$ and resistivity is $1.7\times 10^{-8}\Omega$-m. The l …

Q17.A bowl filled with very hot soup cools from $98^{\circ }\mathrm{C}$ to $86^{\circ }\mathrm{C}$ in 2 minutes when the room temperature is $22^{\circ }\mathrm{C}$. How long it will take to cool from $75^{\circ }\mathrm{C}$ to $69^{\circ }\mathrm{C}$ ?

Q18.A car is moving with a constant speed of 20 $\mathrm{m}/\mathrm{s}$ in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take …

Q19.A ray of light is incident from air on a glass plate having thickness $\sqrt{3}\mathrm{cm}$ and refractive index $\sqrt{2}$. The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the pl …

Q20.In the given circuit, the equivalent resistance between the terminal A and B is $\_\_\_\_$ $\Omega$.

Q21.As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45^{\circ }$ with the load axis. The length of wire is 62.8 cm and its diameter is 4 …

Q22.An object of mass '$m$' initially at rest on a smooth horizontal plane starts moving under the action of force $\mathrm{F}=2\mathrm{N}$. In the process of its linear motion, the angle $\theta$ (as shown in figure) between the direction of force and horizontal varies as …

Q23.The wavelength of the radiation emitted is ${\lambda }_0$ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation …

Q24.$I_{CM}$ is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. $I_{AB}$ is its moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance $\frac{2}{3}R$ from center. Wher …

Q25.The distance between two consecutive points with phase difference of $60^{\circ }$ in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is traveling is ______ km/s

Q26.A uniform electric field of $10\text{ N/C}$ is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ($\theta$) of deviation of th …

Q27.An LCR series circuit of capacitance 62.5 nF and resistance of $50\Omega$, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is ______ mH.
(take ${\pi }^2=10$)

Q28.If $\vec{P}=3\hat{i}+\sqrt{3}\hat{j}+2\hat{k}$ and $\vec{Q}=4\hat{i}+\sqrt{3}\hat{j}+2.5\hat{k}$ then, The unit vector in the direction of $\vec{P}\times \vec{Q}$ is $\frac{1}{x}(\sqrt{3}\hat{i}+\hat{j}-2\sqrt{3}\hat{k})$. The value of $x$ is

Q1.The compound which will have the lowest rate towards nucleophilic aromatic substitution on treatment with ${\mathrm{OH}}^{-}$ is

Q2.The variation of the rate of an enzyme catalyzed reaction with substrate concentration is correctly represented by graph

Q3.Identify the product formed (A and E)

Q4.Match List I with List II

List I: Elements
List II: Colour imparted to the flame

Choose the correct answer from the options given below:

Q5.Reaction of thionyl chloride with white phosphorus forms a compound [A], which on hydrolysis gives [B], a dibasic acid. [A] and [B] are respectively

Q6.A cubic solid is made up of two elements X and Y. Atoms of X are present on every alternate corner and one at the center of cube. $Y$ is at $\frac{2}{3}$ of the total faces. The empirical formula of the compound is

Q7.The radius of the $2^{\text{nd }}$ orbit of ${\mathrm{Li}}^{2+}$ is x. The expected radius of the $3^{\text{rd }}$ orbit of ${\mathrm{Be}}^{3+}$ is

Q8.Which of the following conformations will be the most stable?

Q9.Match items of Row I with those of Row II.

Row I:
(P) (see structure)
(Q) (see structure)
(R) (see structure)
(S) (see structure)

Row II:
(i) $\alpha$-D-(-) Fructofuranose.
(ii) $\beta$-D-(-) Fructofuranose
(iii) $\alpha$-D-(-) Glucopyranose.
(iv) β-D-(-) Glucopyranose

Correct …

Q10.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: Acetal/Ketal is stable in basic medium.
Reason R: The high leaving tendency of alkoxide ion gives the stability to acetal/ketal in basic medium.

In the light of the …

Q11.Inert gases have positive electron gain enthalpy. Its correct order is

Q12.Which one of the following reactions does not occur during extraction of copper?

Q13.The correct order in aqueous medium of basic strength in case of methyl substituted amines is :

Q14.'25 volume' hydrogen peroxide means

Q15.Which of the following statements is incorrect for antibiotics?

Q16.Compound A reacts with ${\mathrm{NH}}_4\mathrm{Cl}$ and forms a compound B . Compound B reacts with ${\mathrm{H}}_2\mathrm{O}$ and excess of ${\mathrm{CO}}_2$ to form compound C which on passing through or reaction with saturated NaCl solution forms sodium hydrogen carbonate. C …

Q17.Some reactions of ${\mathrm{NO}}_2$ relevant to photochemical smog formation are

Identify $\mathrm{A},\mathrm{B},\mathrm{X}$ and Y

Q18.In the cumene to phenol preparation in presence of air, the intermediate is

Q19.An athlete is given 100 g of glucose $({\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6)$ for energy. This is equivalent to 1800 kJ of energy. The $50\%$ of this energy gained is utilized by the athlete for sports activities at the event. In order to avoid storage of energy, the we …

Q20.A litre of buffer solution contains 0.1 mole of each of ${\mathrm{NH}}_3$ and ${\mathrm{NH}}_4\mathrm{Cl}$. On the addition of 0.02 mole of HCl by dissolving gaseous HCl , the pH of the solution is found to be ______ $\times 10^{-3}$ (Nearest integer)
[Given : …

Q21.How many of the following metal ions have similar value of spin only magnetic moment in gaseous state? ______
(Given: Atomic number : V, $23;\mathrm{Cr},24;\mathrm{Fe},26$; Ni, 28)
${\mathrm{V}}^{3+}.{\mathrm{Cr}}^{3+},{\mathrm{Fe}}^{2+},{\mathrm{Ni}}^{3+}$

Q22.The density of a monobasic strong acid (Molar mass 24.2 g mol ) is 1.21 kg L . The volume of its solution required for the complete neutralization of 25 mL of 0.24 M NaOH is ______ × $10^{-2}\mathrm{mL}$ (Nearest integer)

Q23.For the first order reaction $\mathrm{A}\to \mathrm{B}$ the half life is 30 min. The time taken for $75\%$ completion of the reaction is ______ min. (Nearest integer)

Given: $\log 2=0.3010$
$\log 3=0.4771$
$\log 5=0.6989$

Q24.The total number of lone pairs of electrons on oxygen atoms of ozone is ______

Q25.In sulphur estimation, 0.471 g of an organic compound gave 1.4439 g of barium sulphate.

The percentage of sulphur in the compound is ______ (Nearest Integer)
(Given: Atomic mass Ba: $137$ u; S: $32$ u, O: $16$ u)

Q26.The number of paramagnetic species from the following is ______.
${\left[\mathrm{Ni}(\mathrm{CN}{)}_4\right]}^{2-}$, $\left[\mathrm{Ni}(\mathrm{CO}{)}_4\right]$, ${\left[{\mathrm{NiCl}}_4\right]}^{2-}$
${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{4-}$, …

Q27.Consider the cell


Given: …

Q28.For the conversion shown, $n$-heptane $\stackrel{\text{(reagents)}}{\to }$ $Q$ + $R$, where $Q$ is benzoic acid (${\mathrm{C}}_6{\mathrm{H}}_5\mathrm{COOH}$) and $R$ is benzyl alcohol (${\mathrm{C}}_6{\mathrm{H}}_5\mathrm{C}{\mathrm{H}}_2\mathrm{OH}$), the correct sequence of reagents for the preparation of $Q$ and $R$ is:

Q1.Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $S=\left\{x\in Z:x(66-x)\ge \frac{5}{9}M\right\}$ and the event $A=\{x\in S:x$ is a multiple of 3$\}$. Then $\mathrm{P}(\mathrm{A})$ is equal to

Q2.Let $\vec{a},\vec{b}$ and $\vec{c}$ be three non zero vectors such that $\vec{b}\cdot \vec{c}=0$ and $\vec{a}\times (\vec{b}\times \vec{c})=\frac{\vec{b}-\vec{c}}{2}$. If $\vec{d}$ be a vector such that $\vec{b}\cdot \vec{d}=\vec{a}\cdot \vec{b}$, then …

Q3.Let $y=y(x)$ be the solution curve of the differential equation $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y}}{\mathrm{x}}\left(1+{\mathrm{xy}}^2\left(1+{\log }_{\mathrm{e}}\mathrm{x}\right)\right)$, $x>0,y(1)=3$. Then $\frac{y^2(x)}{9}$ is equal to :

Q4.The value of
${\mathrm{Lim}}_{n\to \infty }\frac{1+2-3+4+5-6+\dots +(3n-2)+(3n-1)-3n}{\sqrt{2n^4+4n+3}-\sqrt{n^4+5n+4}}$ is :

Q5.The points of intersection of the line $\mathrm{ax}+$ by $=0$, $(\mathrm{a}\ne \mathrm{b})$ and the circle ${\mathrm{x}}^2+{\mathrm{y}}^2-2\mathrm{x}=0$ are $A(\alpha ,0)$ and $B(1,\beta )$. The image of the circle with AB as a diameter in the line $\mathrm{x}+\mathrm{y}+2=0$ …

Q6.The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2. then their new variance is equal to :

Q7.Let
$y(x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)\left(1+x^{16}\right)$.
Then ${\mathrm{y}}^{\prime }-{\mathrm{y}}^{\prime \prime }$ at $\mathrm{x}=-1$ is equal to

Q8.The vector $\vec{a}=-\hat{i}+2\hat{j}+\hat{k}$ is rotated through a right angle, passing through the y -axis in its way and the resulting vector is $\overrightarrow{\mathrm{b}}$. Then the projection of $3\vec{a}+\sqrt{2}\vec{b}$ on $\vec{c}=5\hat{i}+4\hat{j}+3\hat{k}$ is

Q9.The minimum value of the function $f(x)={\int }_0^2{e}^{|x-t|}dt$ is

Q10.Consider the lines ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ given by
${\mathrm{L}}_1:\frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}-3}{1}=\frac{\mathrm{z}-2}{2}$
${\mathrm{L}}_2:\frac{\mathrm{x}-2}{1}=\frac{\mathrm{y}-2}{2}=\frac{\mathrm{z}-3}{3}$
A line ${\mathrm{L}}_3$ having direction …

Q11.Let $\mathrm{x}=2$ be a local minima of the function $f(x)=2x^4-18x^2+8x+12,x\in (-4,4)$. If $M$ is local maximum value of the function f in $(-4,4)$, then $\mathrm{M}=$

Q12.Let ${\mathrm{z}}_1=2+3\mathrm{i}$ and ${\mathrm{z}}_2=3+4\mathrm{i}$. The set
$S=\left\{\mathrm{z}\in \mathrm{C}:{\left|\mathrm{z}-{\mathrm{z}}_1\right|}^2-{\left|\mathrm{z}-{\mathrm{z}}_2\right|}^2={\left|{\mathrm{z}}_1-{\mathrm{z}}_2\right|}^2\right\}$ represents a

Q13.The distance of the point $(6,-2\sqrt{2})$ from the common tangent $\mathrm{y}=\mathrm{mx}+\mathrm{c},\mathrm{m}>0$, of the curves $\mathrm{x}=2{\mathrm{y}}^2$ and $\mathrm{x}=1+{\mathrm{y}}^2$ is

Q14.Let ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ be respectively the sets of all $\mathrm{a}\in \mathrm{R}-\{0\}$ for which the system of linear equations
$ax+2ay-3az=1$
$(2a+1)x+(2a+3)y+(a+1)z=2$
$(3a+5)x+(a+5)y+(a+2)z=3$
has unique solution and infinitely ma …

Q15.Let $f(x)=\int \frac{2x}{\left(x^2+1\right)\left(x^2+3\right)}dx$.

If $f(3)=\frac{1}{2}\left({\log }_{e}5-{\log }_{e}6\right)$, then $f(4)$ is equal to

Q16.The statement $(\mathrm{p}\wedge (\sim \mathrm{q}))\Rightarrow (\mathrm{p}\Rightarrow (\sim \mathrm{q}))$ is

Q17.Let $f:(0,1)\to \mathbb{R}$ be a function defined by
$\mathrm{f}(\mathrm{x})=\frac{1}{1-{\mathrm{e}}^{-\mathrm{x}}}$, and
$g(x)=(f(-x)-f(x))$. Consider two statements
(I) g is an increasing function in $(0,1)$
(II) g is one-one in $(0,1)$

Then,

Q18.The distance of the point $\mathrm{P}(4,6,-2)$ from the line passing through the point $(-3,2,3)$ and parallel to a line with direction ratios $3,3,-1$ is equal to :

Q19.Let $x,y,z>1$ and …

Q20.If ${\mathrm{a}}_{\mathrm{r}}$ is the coefficient of ${\mathrm{x}}^{10-\mathrm{r}}$ in the Binomial expansion of $(1+x{)}^{10}$, then ${\sum }_{r=1}^{10}{r}^3{\left(\frac{a_r}{a_{r-1}}\right)}^2$ is equal to

Q21.Let $\mathrm{S}=\{1,2,3,5,7,10,11\}$. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is ______.

Q22.For some $\mathrm{a},\mathrm{b},\mathrm{c}\in \mathbb{N}$, let $\mathrm{f}(\mathrm{x})=\mathrm{ax}-3$ and
$g(x)=x^b+c,x\in \mathbb{R}$. If $(f\circ g{)}^{-1}(x)={\left(\frac{x-7}{2}\right)}^{1/3}$, then $(\mathrm{fg})(\mathrm{ac})+(\mathrm{gof})(\mathrm{b})$ is eq …

Q23.Let


Then the maximum value of $\beta$ for which the equation …

Q24.The constant term in the expansion of ${\left(2x+\frac{1}{x^7}+3x^2\right)}^5$ is ______.

Q25.Let ${\mathrm{A}}_1,{\mathrm{A}}_2,{\mathrm{A}}_3$ be the three A.P. with the same common difference d and having their first terms as $\mathrm{A},\mathrm{A}+1,\mathrm{A}+2$, respectively. Let $\mathrm{a},\mathrm{b},\mathrm{c}$ be the …

Q26.If the sum of all the solutions of
${\tan }^{-1}\left(\frac{2x}{1-x^2}\right)+{\cot }^{-1}\left(\frac{1-x^2}{2x}\right)=\frac{\pi }{3}$,
$-1<x<1,x\ne 0$, is $\alpha -\frac{4}{\sqrt{3}}$, then $\alpha$ is equal to ______.

Q27.Let the equation of the plane passing through the line
$x-2y-z-5=0=x+y+3z-5$ and parallel to the line $\mathrm{x}+\mathrm{y}+2\mathrm{z}-7=0=2\mathrm{x}+3\mathrm{y}+\mathrm{z}-2$ be $\mathrm{ax}+\mathrm{by}+\mathrm{cz}=65$. Then the distance of the point …

Q28.Let x and y be distinct integers where $1\le \mathrm{x}\le 25$ and $1\le y\le 25$. Then, the number of ways of choosing x and y, such that $\mathrm{x}+\mathrm{y}$ is divisible by 5, is ______.