JEE Main 2023 · 29 Jan 2023 · Shift 1

Q1.In a cuboid of dimension $2\mathrm{L}\times 2\mathrm{L}\times \mathrm{L}$, a charge q is placed at the centre of the surface ' $S$ ' having area of $4{\mathrm{L}}^2$. The flux through the opposite surface to ' S ' is given by

Q2.Ratio of thermal energy released in two resistor R and $3R$ connected in parallel in an electric circuit is :

Q3.A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve $z$ direction and lying in xy plane in shown in figure. The plot of $\hat{j}$ component of magnetic field (By) at a distance 'a' (less than radius of the coil) and on $yz$ p …

Q4.The magnitude of magnetic induction at mid-point O due to current arrangement as shown in Fig will be :

Q5.Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ' R ' is placed inside a large square loop of wire of side L $(\mathrm{L}\gg \mathrm{R})$. The loops are coplanar and their centres coincide :

Q6.Which of the following are true?
(A) Speed of light in vacuum is dependent on the direction of propagation.
(B) Speed of light in a medium in independent of the wavelength of light.
(C) The speed of light is independent of the motion of the source.
(D) The speed of light in a med …

Q7.In a Young's double slit experiment, two slits are illuminated with a light of wavelength 800 nm . The line joining ${\mathrm{A}}_1\mathrm{P}$ is perpendicular to ${\mathrm{A}}_1{\mathrm{A}}_2$ as shown in the figure. If the first minimum is detected at P , the value of slits …

Q8.A stone is projected at angle $30^{\circ }$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be :

Q9.A block of mass $m$ slides down the plane inclined at angle $30^{\circ }$ with an acceleration $\frac{\mathrm{g}}{4}$. The value of coefficient of kinetic friction will be :

Q10.A car is moving on a horizontal curved road with radius 50 m . The approximate maximum speed of car will be, if friction between tyres and road is 0.34 . [Take $\mathrm{g}=10{\mathrm{ms}}^{-2}$ ]

Q11.Two particles of equal mass ' $m$ ' move in a circle of radius ' $r$ ' under the action of their mutual gravitational attraction. The speed of each particle will be :

Q12.Surface tension of a soap bubble is $2.0\times 10^{-2}{\mathrm{Nm}}^{-1}$. Work done to increase the radius of soap bubble from 3.5 cm to 7 cm will be : [Take $\pi =\frac{22}{7}$]

Q13.Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If dQ and dW represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics …

Q14.A bicycle tyre is filled with air having pressure of 270 kPa at $27^{\circ }\mathrm{C}$. The approximate pressure of the air in the tyre when the temperature increases to $36^{\circ }\mathrm{C}$ is

Q15.A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of $30\mathrm{m}/\mathrm{s}$. If both trains emit sounds with frequency 300 Hz, (Speed of sound : $330\mathrm{m}/\mathrm{s}$) approximate difference of frequenci …

Q16.If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be :
Given : Earth's radius $=6.4\times 10^6\mathrm{m}$.

Q17.The threshold wavelength for photoelectric emission from a material is $5500\mathring{A}$. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a
A. 75 W infra-red lamp
B. 10 W infra-red lamp
C. 75 W ultra-violet lamp
D. 10 W ultra-violet …

Q18.If a radioactive element having half-life of 30 min is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 min. will be :

Q19.Which of the following statement is not correct in the case of light emitting diodes?
A. It is a heavily doped $\mathrm{p}-\mathrm{n}$ junction.
B. It emits light only when it is forward biased.
C. It emits light only when it is reverse biased.
D. The energy of the light emitte …

Q20.A radioactive element ${}_{92}^{242}\mathrm{X}$ emits two $\alpha$-particles, one electron and two positrons. The product nucleus is represented by ${}_{\mathrm{P}}^{234}\mathrm{Y}$. The value of P is

Q21.Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is ______ degree.

Q22.A body cools from $60^{\circ }\mathrm{C}$ to $40^{\circ }\mathrm{C}$ in 6 minutes. If, temperature of surroundings is $10^{\circ }\mathrm{C}$. Then, after the next 6 minutes, its temperature will be ______ ${}^{\circ }\mathrm{C}$.

Q23.A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ______ ${\mathrm{ms}}^{-1}$.

Q24.A 0.4 kg mass takes 8 s to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potential energy in the last second of fall is ______ J. [Take $g=10m/{\mathrm{s}}^2$]

Q25.A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2 s. The average acceleration during contact is ______ $\mathrm{m}{\mathrm{s}}^{-2}$. [Given $g=10\mathrm{m}{\mathrm{s}}^{-2}$]

Q26.A point charge $q_1=4q_0$ is placed at origin. Another point charge $q_2=-q_0$ is placed at $x=12\mathrm{cm}$. Charge of proton is $q_0$. The proton is placed on x-axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the …

Q27.In a metre bridge experiment the balance point is obtained if the gaps are closed by $2\Omega$ and $3\Omega$. A shunt of $X\Omega$ is added to $3\Omega$ resistor to shift the balancing point by 22.5 cm. The value of X is ______

Q28.A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field $B=0.8\mathrm{T}$. When released the radius of the loop starts shrinking at a constant rate of $2\mathrm{cm}{\mathrm{s}}^{-1}$. The induced em …

Q29.As shown in figures, three identical polaroids $P_1$, $P_2$ and $P_3$ are placed one after another. The pass axis of $P_2$ and $P_3$ are inclined at angle of $60^{\circ }$ and $90^{\circ }$ with respect to axis of $P_1$. The source S has an intensity of …

Q1.For 1 mol of gas, the plot of pV vs p is shown below. p is the pressure and V is the volume of the gas.

What is the value of compressibility factor at point A ?

Q2.The shortest wavelength of hydrogen atom in Lyman series is $\lambda$. The longest wavelength in Balmer series of ${\mathrm{He}}^{+}$ is

Q3.Which of the following salt solutions would coagulate the colloid solution formed when ${\mathrm{FeCl}}_3$ is added to NaOH solution, at the fastest rate?

Q4.The bond dissociation energy is highest for

Q5.The reaction representing the Mond process for metal refining is ____

Q6.Which of the given compounds can enhance the efficiency of hydrogen storage tank?

Q7.The correct order of hydration enthalpies is
(A) ${\mathrm{K}}^{+}$
(B) ${\mathrm{Rb}}^{+}$
(C) ${\mathrm{Mg}}^{2+}$
(D) ${\mathrm{Cs}}^{+}$
(E) ${\mathrm{Ca}}^{2+}$

Choose the correct answer from the options given below:

Q8.The magnetic behaviour of ${\mathrm{Li}}_2\mathrm{O}$, ${\mathrm{Na}}_2{\mathrm{O}}_2$ and ${\mathrm{KO}}_2$, respectively, are

Q9."A" obtained by Ostwald's method involving air oxidation of ${\mathrm{NH}}_3$, upon further air oxidation produces "B". "B" on hydration forms an oxoacid of Nitrogen along with evolution of "A". The oxoacid also produces "A" and gives positive brown ring test

Q10.The standard electrode potential ( ${\mathrm{M}}^{3+}/{\mathrm{M}}^{2+}$ ) for V , $\mathrm{Cr}$, $\mathrm{Mn}$ & $\mathrm{Co}$ are $-0.26\mathrm{V}$, $-0.41\mathrm{V}$, $+1.57\mathrm{V}$ and $+1.97\mathrm{V}$ , respectively. The metal ions which can liberate …

Q11.Correct statement about smog is

Q12.Chiral complex from the following is :

Here en = ethylene diamine

Q13.Identify the correct order for the given property for following compounds
(A) Boiling Point:
(see structures)
(B) Density:
(see structure)
(C) Boiling Point:
(see structure)
(D) Density:
(see structures)
(E) Boiling Point:
(see structure)

Choose the correct answer from the optio …

Q14.The increasing order of ${\mathrm{pK}}_{\mathrm{a}}$ for the following phenols is
(1) 2, 4-Dinitrophenol
(2) 4 - Nitrophenol
(3) 2,4,5-Trimethylphenol
(4) Phenol
(5) 3-Chlorophenol

Q15.The major product 'P' for the following sequence of reactions is:
(see reaction scheme)

Q16.During the borax bead test with ${\mathrm{CuSO}}_4$, a blue green colour of the bead was observed in oxidising flame due to the formation of

Q17.Number of cyclic tripeptides formed with 2 amino acids $A$ and $B$ is:

Q18.Compound that will give positive Lassaigne's test for both nitrogen and halogen is

Q19.Millimoles of calcium hydroxyide required to produce 100 mL of the aqueous solution of pH 12 is $x\times 10^{-1}$. The value of $x$ is ______ (Nearest integer).

Assume complete dissociation.

Q20.The number of molecules or ions from the following, which do not have odd number of electrons are ______.
(A) ${\mathrm{NO}}_2$
(B) ${\mathrm{ICl}}_4^{-}$
(C) ${\mathrm{BrF}}_3$
(D) ${\mathrm{ClO}}_2$
(E) ${\mathrm{NO}}_2^{+}$
(F) NO

Q21.Consider the following reaction approaching equilibrium at $27^{\circ }\mathrm{C}$ and 1 atm pressure
$\mathrm{A}+\mathrm{B}\underset{{\mathrm{K}}_{\mathrm{r}}=10^2}{\stackrel{{\mathrm{K}}_{\mathrm{f}}=10^3}{\rightleftharpoons }}\mathrm{C}+\mathrm{D}$
The standard Gibb's energy …

Q22.Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at $100.15^{\circ }\mathrm{C}$. When 0.2 mol of NaCl is added to the resulting solution, it was observed that the solution froze at $-0.8^{\circ }\mathrm{C}$. The solutbility product of …

Q23.Water decomposes at 2300 K

The percent of water decomposing at 2300 K and 1 bar is ______ (Nearest integer).

Equilibrium constant for the reaction is …

Q24.Following figure shows dependence of molar conductance of two electrolytes on concentration. ${\Lambda }_{\mathrm{m}}^0$ is the limiting molar conductivity.

The number of Incorrect statement(s) from the following is ______
(A) ${\Lambda }_{\mathrm{m}}^0$ for electrolyte A is obtai …

Q25.The sum of bridging carbonyls in $\mathrm{W}(\mathrm{CO}{)}_6$ and ${\mathrm{Mn}}_2(\mathrm{CO}{)}_{10}$ is ______.

Q26.Following chromatogram was developed by adsorption of compound 'A' on a 6 cm TLC glass plate. Retardation factor of the compound 'A' is ______ $\times 10^{-1}$.

Q27.17 mg of a hydrocarbon (M.F. ${\mathrm{C}}_{10}{\mathrm{H}}_{16}$) takes up 8.40 mL of the ${\mathrm{H}}_2$ gas measured at $0^{\circ }\mathrm{C}$ and 760 mm of Hg. Ozonolysis of the same hydrocarbon yields

The number of double bond/s present in the hydrocarbon is ______.

Q1.The domain of $f(x)=\frac{{\log }_{(x+1)}(x-2)}{e^{2{\log }_{e}x}-(2x+3)},x\in R$ is

Q2.Let $f:R\to R$ be a function such that $f(x)=\frac{x^2+2x+1}{x^2+1}$. Then

Q3.For two non-zero complex number ${\mathrm{z}}_1$ and ${\mathrm{z}}_2$, if $\mathrm{Re}({\mathrm{z}}_1{\mathrm{z}}_2)=0$ and $\mathrm{Re}({\mathrm{z}}_1+{\mathrm{z}}_2)=0$, then which of the following are possible ?
(A) $\mathrm{Im}({\mathrm{z}}_1)>0$ …

Q4.Let $\lambda \ne 0$ be a real number. Let $\alpha ,\beta$ be the roots of the equation $14{\mathrm{x}}^2-31\mathrm{x}+3\lambda =0$ and $\alpha ,\gamma$ be the roots of the equation $35x^2-53x+4\lambda =0$. Then $\frac{3\alpha }{\beta }$ and …

Q5.Consider the following system of equations
$\alpha \mathrm{x}+2\mathrm{y}+\mathrm{z}=1$
$2\alpha \mathrm{x}+3\mathrm{y}+\mathrm{z}=1$
$3\mathrm{x}+\alpha \mathrm{y}+2\mathrm{z}=\beta$
For some $\alpha ,\beta \in \mathbb{R}$. Then which of the following is NOT correct …

Q6.Let $\alpha$ and $\beta$ be real numbers. Consider a $3\times 3$ matrix A such that ${\mathrm{A}}^2=3\mathrm{A}+\alpha \mathrm{I}$. If ${\mathrm{A}}^4=21\mathrm{A}+\beta \mathrm{I}$, then

Q7.Let $x=2$ be a root of the equation $x^2+px+q=0$ and $f(x)=\{\begin{array}{cc}\frac{1-\cos \left(x^2-4px+q^2+8q+16\right)}{(x-2p{)}^4},& x\ne 2p\\ 0,& x=2p\end{array}$

Then ${\lim }_{x\to 2p^{+}}[f(x)]$
where [ . ] denotes greatest i …

Q8.Let $f(x)=x+\frac{a}{{\pi }^2-4}\sin x+\frac{b}{{\pi }^2-4}\cos x$, $x\in \mathbb{R}$ be a function which satisfies $f(x)=x+{\int }_0^{\pi /2}\sin (x+y)f(y)dy$. Then $(\mathrm{a}+\mathrm{b})$ is equal to

Q9.Let $\Delta$ be the area of the region
$\left\{(\mathrm{x},\mathrm{y})\in {\mathbb{R}}^2:{\mathrm{x}}^2+{\mathrm{y}}^2\le 21,{\mathrm{y}}^2\le 4\mathrm{x},\mathrm{x}\ge 1\right\}.$ Then $\frac{1}{2}\left(\Delta -21{\sin }^{-1}\frac{2}{\sqrt{7}}\right)$ is …

Q10.A light ray emits from the origin making an angle $30^{\circ }$ with the positive x -axis. After getting reflected by the line $\mathrm{x}+\mathrm{y}=1$, if this ray intersects x -axis at Q , then the abscissa of Q is

Q11.Let B and C be the two points on the line $\mathrm{y}+\mathrm{x}=0$ such that B and C are symmetric with respect to the origin. Suppose A is a point on $\mathrm{y}-2\mathrm{x}=2$ such that $△\mathrm{ABC}$ is an equilateral triangle. Then, the area of the …

Q12.Let the tangents at the points $\mathrm{A}(4,-11)$ and $\mathrm{B}(8,-5)$ on the circle $x^2+y^2-3x+10y-15=0$, intersect at the point C. Then the radius of the circle, whose centre is C and the line joining A and B is its tangent, is equal to

Q13.If the vectors $\vec{a}=\lambda \hat{i}+\mu \hat{j}+4\hat{k},\vec{b}=-2\hat{i}+4\hat{j}-2\hat{k}$ and $\vec{c}=2\hat{i}+3\hat{j}+\hat{k}$ are coplanar and the projection of $\vec{a}$ on the vector $\vec{b}$ is $\sqrt{54}$ units, then the sum of all possible value …

Q14.Let $f(\theta )=3\left({\sin }^4\left(\frac{3\pi }{2}-\theta \right)+{\sin }^4(3\pi +\theta )\right)-2\left(1-{\sin }^{2}2\theta \right)$ and
$S=\left\{\theta \in [0,\pi ]:f^{\prime }(\theta )=-\frac{\sqrt{3}}{2}\right\}$. If $4\beta ={\sum }_{\theta \in S}\theta$, then …

Q15.If $p,q$ and $r$ are three propositions, then which of the following combination of truth values of $\mathrm{p},\mathrm{q}$ and r makes the logical expression $\{(p\vee q)\wedge ((\sim p)\vee r)\}\to ((\sim q)\vee r)$ false ?

Q16.Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If $\mu$ and ${\sigma }^2$ represent mean and variance of $X$, respectively, then …

Q17.Let $y=f(x)$ be the solution of the differential equation $y(x+1)dx-x^{2}dy=0,y(1)=e$. Then ${\lim }_{x\to 0^{+}}f(x)$ is equal to

Q18.Let the co-ordinates of one vertex of $△\mathrm{ABC}$ be $\mathrm{A}(0,2,\alpha )$ and the other two vertices lie on the line $\frac{x+\alpha }{5}=\frac{y-1}{2}=\frac{z+4}{3}$. For $\alpha \in \mathbb{Z}$, if the area of $△\mathrm{ABC}$ is 21 sq. units …

Q19.Let the equation of the plane P containing the line $\mathrm{x}+10=\frac{8-\mathrm{y}}{2}=\mathrm{z}$ be $\mathrm{ax}+\mathrm{by}+3\mathrm{z}=2(\mathrm{a}+\mathrm{b})$ and the distance of the plane P from the point $(1,27,7)$ be c. Then …

Q20.Suppose f is a function satisfying $\mathrm{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y})$ for all $x,y\in \mathbb{N}$ and $f(1)=\frac{1}{5}$. If ${\sum }_{n=1}^m\frac{f(n)}{n(n+1)(n+2)}=\frac{1}{12}$, then $m$ is equal to ______.

Q21.Let ${\mathrm{a}}_1,{\mathrm{a}}_2,{\mathrm{a}}_3,\dots$ be a GP of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then $a_1{a}_9+a_2{a}_4{a}_9+a_5+a_7$ is equal to ______.

Q22.Let $\vec{a},\vec{b}$ and $\vec{c}$ be three non-zero non-coplanar vectors. Let the position vectors of four points A, $B,C$ and $D$ be $\vec{a}-\vec{b}+\vec{c},\lambda \vec{a}-3\vec{b}+4\vec{c}$, $-\vec{a}+2\vec{b}-3\vec{c}$ and $2\vec{a}-4\vec{b}+6\vec{c}$ respectivel …

Q23.If all the six digit numbers ${\mathrm{x}}_1{\mathrm{x}}_2{\mathrm{x}}_3{\mathrm{x}}_4{\mathrm{x}}_5{\mathrm{x}}_6$ with $0<{\mathrm{x}}_1<{\mathrm{x}}_2<{\mathrm{x}}_3<{\mathrm{x}}_4<{\mathrm{x}}_5<{\mathrm{x}}_6$ are arranged in the increasing order, then the sum of the di …

Q24.Let $\mathrm{f}:\mathbb{R}\to \mathbb{R}$ be a differentiable function that satisfies the relation $\mathrm{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y})-1,\forall \mathrm{x}$, $y\in \mathbb{R}$. If $f^{\prime }(0)=2$, then $|f(-2)|$ is equal …

Q25.If the co-efficient of $x^9$ in ${\left(\alpha x^3+\frac{1}{\beta x}\right)}^{11}$ and the co-efficient of ${\mathrm{x}}^{-9}$ in ${\left(\alpha \mathrm{x}-\frac{1}{\beta {\mathrm{x}}^3}\right)}^{11}$ are equal, then $(\alpha \beta {)}^2$ is equal to ____.

Q26.Let the coefficients of three consecutive terms in the binomial expansion of $(1+2\mathrm{x}{)}^{\mathrm{n}}$ be in the ratio $2:5:8$. Then the coefficient of the term, which is in the middle of these three terms, is ____.

Q27.Five digit numbers are formed using the digits 1,2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1. Then the serial number of 35337 is ____.