JEE Main 2025 · 29 Jan 2025 · Shift 1

Q1.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household elect …

Q2.Two projectiles are fired with same initial speed from same point on ground at angles of $\left(45^{\circ }-\alpha \right)$ and ( $45^{\circ }+\alpha$ ), respectively, with the horizontal direction. The ratio of their maximum heights attained is :

Q3.An electric dipole of mass m , charge q , and length $l$ is placed in a uniform electric field $\overrightarrow{\mathrm{E}}={\mathrm{E}}_0\hat{\mathrm{i}}$. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will b …

Q4.The pair of physical quantities not having same dimensions is :

Q5.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason (R) : Time period of a simple pendulum decr …

Q6.The expression given below shows the variation of velocity ( $v$ ) with time ( t ), $v={\mathrm{At}}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}$.
The dimension of ABC is :

Q7.Consider ${\mathrm{I}}_1$ and ${\mathrm{I}}_2$ are the currents flowing simultaneously in two nearby coils $1\&2$, respectively. If $L_1=$ self inductance of coil 1 , ${\mathrm{M}}_{12}=$ mutual inductance of coil 1 with respect to coil 2 , then the value of induced emf in coil …

Q8.Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wi …

Q9.As shown below, bob A of a pendulum having massless string of length ' R ' is released from $60^{\circ }$ to the vertical. It hits another bob B of half the mass that is at rest on a friction less table in the centre. Assuming elastic collision, the magnitude of the velocity of bo …

Q10.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Emission of electrons in photoelectric effect can be suppressed by applying a sufficiently negative electron potential to the photoemissive substance.
Reason …

Q11.A coil of area A and N turns is rotating with angular velocity $\omega$ in a uniform magnetic field $\overrightarrow{\mathrm{B}}$ about an axis perpendicular to $\overrightarrow{\mathrm{B}}$. Magnetic flux $\phi$ and induced emf $\epsilon$ across it, at an instant when …

Q12.The fractional compression $\left(\frac{\Delta V}{V}\right)$ of water at the depth of 2.5 km below the sea level is $\_\_\_\_$ %. Given, the Bulk modulus of water $=2\times 10^9{\mathrm{Nm}}^{-2}$, density of water $=10^3\mathrm{kg}{\mathrm{m}}^{-3}$, acceleration due to gr …

Q13.If $\lambda$ and K are de Broglie Wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be :-

Q14.For the circuit shown above, equivalent GATE is :

Q15.A body of mass ' $m$ ' connected to a massless and unstretchable string goes in verticle circle of radius ' R ' under gravity g . The other end of the string is fixed at the center of circle. If velocity at top of circular path is $\mathrm{n}\sqrt{\mathrm{gR}}$, where, …

Q16.Let $u$ and $v$ be the distances of the object and the image from a lens of focal length $f$. The correct graphical representation of u and v for a convex lens when $|\mathrm{u}|>f$, is

Q17.Match List-I with List-II.

(A) Electric field inside (distance $\mathrm{r}>0$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$, and radius R .
(B) Electric field at distance $\mathrm{r}>0$ from a uniformly charged infinite plane sheet with …

Q18.The workdone in an adiabatic change in an ideal gas depends upon only :

Q19.Given below are two statements : one is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : Electromagnetic waves carry energy but not momentum.
Reason (R) : Mass of a photon is zero.
In the light of the above statements, choose the most appropriate ans …

Q20.The coordinates of a particle with respect to origin in a given reference frame is $(1,1,1)$ meters. If a force of $\vec{F}=\hat{i}-\hat{j}+\hat{k}$ acts on the particle, then the magnitude of torque (with respect to origin) in z -direction is $\_\_\_\_$ .

Q21.A container of fixed volume contains a gas at $27^{\circ }\mathrm{C}$. To double the pressure of the gas, the temperature of gas should be raised to $\_\_\_\_$ ${}^{\circ }\mathrm{C}$.

Q22.Two light beams fall on a transparent material block at point 1 and 2 with angle ${\theta }_1$ and ${\theta }_2$, respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given : the distance bet …

Q23.In a hydraulic lift, the surface area of the input piston is $6{\mathrm{cm}}^2$ and that of the output piston is $1500{\mathrm{cm}}^2$. If 100 N force is applied to the input piston to raise the output piston by 20 cm , then the work done is $\_\_\_\_$ kJ.

Q24.The maximum speed of a boat in still water is $27\mathrm{km}/\mathrm{h}$. Now this boat is moving downstream in a river flowing at $9\mathrm{km}/\mathrm{h}$. A man in the boat throws a ball vertically upwards with speed of $10\mathrm{m}/\mathrm{s}$. Range of the ball …

Q1.Total number of nucleophiles from the following is :
${\mathrm{NH}}_3,\mathrm{PhSH},{\left({\mathrm{H}}_3\mathrm{C}\right)}_2\mathrm{S},{\mathrm{H}}_2\mathrm{C}={\mathrm{CH}}_2,\stackrel{\ominus }{\mathrm{O}}\mathrm{H},{\mathrm{H}}_3{\mathrm{O}}^{\oplus }$, …

Q2.The standard reduction potential values of some of the p-block ions are given below. Predict the one with the strongest oxidising capacity.

Q3.The molar conductivity of a weak electrolyte when plotted against the square root of its concentration, which of the following is expected to be observed?

Q4.At temperature T, compound ${\mathrm{AB}}_{2(\mathrm{g})}$ dissociates as ${\mathrm{AB}}_{2(\mathrm{g})}\rightleftharpoons {\mathrm{AB}}_{(\mathrm{g})}+\frac{1}{2}{\mathrm{B}}_{2(\mathrm{g})}$ having degree of dissociation x (small compared to unity). The correct expression for …

Q5.Choose the correct statements.
(A) Weight of a substance is the amount of matter present in it.
(B) Mass is the force exerted by gravity on an object.
(C) Volume is the amount of space occupied by a substance.
(D) Temperatures below $0^{\circ }\mathrm{C}$ are possible in Celsiu …

Q6.The correct increasing order of stability of the complexes based on ${\Delta }_{\mathrm{o}}$ value is :
(I) ${\left[\mathrm{Mn}(\mathrm{CN}{)}_6\right]}^{3-}$
(II) ${\left[\mathrm{Co}(\mathrm{CN}{)}_6\right]}^{4-}$
(III) ${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{4-}$
(IV) …

Q7.In the following substitution reaction :

Product 'P' formed is :

Q8.For a $\mathrm{Mg}\left|{\mathrm{Mg}}^{2+}(\mathrm{aq})\Vert {\mathrm{Ag}}^{+}(\mathrm{aq})\right|\mathrm{Ag}$ the correct Nernst Equation is :

Q9.The correct option with order of melting points of the pairs $(\mathrm{Mn},\mathrm{Fe}),(\mathrm{Tc},\mathrm{Ru})$ and $(\mathrm{Re},\mathrm{Os})$ is :

Q10.1.24 g of ${\mathrm{AX}}_2$ (molar mass $124\mathrm{g}{\mathrm{mol}}^{-1}$) is dissolved in 1 kg of water to form a solution with boiling point of $100.0156^{\circ }\mathrm{C}$, while 25.4 g of ${\mathrm{AY}}_2$ (molar mass $250\mathrm{g}{\mathrm{mol}}^{-1}$) in 2 k …

Q11.500 J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm. The final temperature and the change in internal energy respectively are:

Given: $\mathrm{R}=8.3\mathrm{J}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$

Q12.The reaction ${\mathrm{A}}_2+{\mathrm{B}}_2\to 2\mathrm{AB}$ follows the mechanism
${\mathrm{A}}_2\underset{{\mathrm{k}}_{-1}}{\stackrel{{\mathrm{k}}_1}{\rightleftharpoons }}\mathrm{A}+\mathrm{A}$ (fast) …

Q13.If ${\mathrm{a}}_0$ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength ($\lambda$) of the electron present in the second orbit of hydrogen atom? [n: any integer]

Q14.The product (P) formed in the following reaction is:

Q15.An element 'E' has the ionisation enthalpy value of $374\mathrm{kJ}{\mathrm{mol}}^{-1}$. 'E' reacts with elements A, B, C and D with electron gain enthalpy values of $-328,-349$, -325 and $-295\mathrm{kJ}{\mathrm{mol}}^{-1}$, respectively.
The correct order of the produ …

Q16.Match List - I with List - II.

Choose the correct answer form the options given below:

Q17.The steam volatile compounds among the following are:
(A) (see structure)
(B) (see structure)
(C) (see structure)
(D) (see structure)

Choose the correct answer from the options given below:

Q18.Given below are two statements:

Statement (I): The radii of isoelectronic species increases in the order.
${\mathrm{Mg}}^{2+}<{\mathrm{Na}}^{+}<{\mathrm{F}}^{-}<{\mathrm{O}}^{2-}$
Statement (II): The magnitude of electron gain enthalpy of halogen decreases in the order. …

Q19.Given below are some nitrogen containing compounds.

Each of them is treated with HCl separately. 1.0 g of the most basic compound will consume ______ mg of HCl.
(Given molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ C: 12, H: 1, O: 16, Cl: 35.5)

Q20.The molar mass of the water insoluble product formed from the fusion of chromite ore $\left({\mathrm{FeCr}}_2{\mathrm{O}}_4\right)$ with ${\mathrm{Na}}_2{\mathrm{CO}}_3$ in presence of ${\mathrm{O}}_2$ is ______ $\mathrm{g}{\mathrm{mol}}^{-1}$.

Q21.The sum of sigma ($\sigma$) and pi($\pi$) bonds in Hex-1,3-dien-5-yne is ______.

Q22.If ${\mathrm{A}}_2\mathrm{B}$ is 30% ionised in an aqueous solution, then the value of van't Hoff factor (i) is ______ $\times 10^{-1}$.

Q23.0.1 mole of compound 'S' will weigh ______ g.
(Given molar mass in $\mathrm{g}{\mathrm{mol}}^{-1}$ C: 12, H: 1, O: 16)

Q24.Match List-I with List-II:
List-I (Complex): (A) [MnBr₄]²⁻ (B) [FeF₆]³⁻ (C) [Co(CO)₄]³⁻? [Co(C₂O₄)₃]³⁻ (D) [Ni(CO)₄]
List-II (Hybridisation & Magnetic character): (I) d²sp³ & diamagnetic (II) sp³d² & paramagnetic (III) sp³ & diamagnetic (IV) sp³ & paramagnetic
Choose the …

Q1.Let the line $x+y=1$ meet the circle $x^2+y^2=4$ at the points A and B . If the line perpendicular to AB and passing through the mid point of the chord AB intersects is the circle at C and D , then the area of the quadrilateral ADBC is equal to

Q2.Let M and m respectively be the maximum and the minimum values of
$f(x)=\left|\begin{array}{ccc}1+{\sin }^{2}x& {\cos }^{2}x& 4\sin 4x\\ {\sin }^{2}x& 1+{\cos }^{2}x& 4\sin 4x\\ {\sin }^{2}x& {\cos }^{2}x& 1+4\sin 4x\end{array}\right|,x\in R$
Then …

Q3.Two parabolas have the same focus $(4,3)$ and their directrices are the $x$-axis and the $y$-axis, respectively. If these parabolas intersects at the points A and B , then $(\mathrm{AB}{)}^2$ is equal to

Q4.Let ABC be a triangle formed by the lines $7\mathrm{x}-6\mathrm{y}+3=0,\mathrm{x}+2\mathrm{y}-31=0$ and $9\mathrm{x}-2\mathrm{y}-19=0$, Let the point $(\mathrm{h},\mathrm{k})$ be the image of the centroid of $△\mathrm{ABC}$ in the line …

Q5.Let $\vec{a}=2\hat{i}-\hat{j}+3\hat{k},\vec{b}=3\hat{i}-5\hat{j}+\hat{k}$ and $\vec{c}$ be a vector such that $\vec{a}\times \vec{c}=\vec{c}\times \vec{b}$ and …

Q6.Let P be the set of seven digit numbers with sum of their digits equal to 11 . If the numbers in P are formed by using the digits 1,2 and 3 only, then the number of elements in the set P is :

Q7.Let the area of the region $\left\{(x,y):2y\le x^2+3,\mathrm{y}+|\mathrm{x}|\le 3,\mathrm{y}\ge |\mathrm{x}-1|\right\}$ be A. Then 6A is equal to:

Q8.The least value of n for which the number of integral terms in the Binomial expansion of $(\sqrt[3]{7}+\sqrt[12]{11}{)}^{\mathrm{n}}$ is 183 , is :

Q9.The number of solutions of the equation $\left(\frac{9}{\mathrm{x}}-\frac{9}{\sqrt{\mathrm{x}}}+2\right)\left(\frac{2}{\mathrm{x}}-\frac{7}{\sqrt{\mathrm{x}}}+3\right)=0$ is :

Q10.Let $y=y(x)$ be the solution of the differential equation $\cos x{\left({\log }_e(\cos x)\right)}^{2}dy+\left(\sin x-3y\sin x{\log }_e(\cos x)\right)dx=0$, $x\in \left(0,\frac{\pi }{2}\right)$. If $y\left(\frac{\pi }{4}\right)=\frac{-1}{{\log }_{e}2}$, then …

Q11.Define a relation R on the interval $\left[0,\frac{\pi }{2}\right)$ by x R y if and only if ${\sec }^{2}x-{\tan }^{2}y=1$. Then $R$ is :

Q12.Let the ellipse, $E_1:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$ and ${\mathrm{E}}_2:\frac{{\mathrm{x}}^2}{{\mathrm{A}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{B}}^2}=1,\mathrm{A}<\mathrm{B}$ have same eccentricity $\frac{1}{\sqrt{3}}$. Let the product of their lengths of …

Q13.Consider an A.P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its $11^{\text{th}}$ term is :

Q14.Let $\vec{a}=\hat{i}+2\hat{j}+\hat{k}$ and $\vec{b}=2\hat{i}+7\hat{j}+3\hat{k}$. Let $L_1:\vec{r}=(-\hat{i}+2\hat{j}+\hat{k})+\lambda \vec{a},\lambda \in R$ and $L_2:\vec{r}=(\hat{j}+\hat{k})+\mu \vec{b},\mu \in R$ be two lines. If the line $L_3$ passes through the …

Q15.The value of ${\lim }_{n\to \infty }\left({\sum }_{K=1}^n\frac{k^3+6k^2+11k+5}{(k+3)!}\right)$ is :

Q16.The integral $80{\int }_0^{\frac{\pi }{4}}\left(\frac{\sin \theta +\cos \theta }{9+16\sin 2\theta }\right)d\theta$ is equal to :

Q17.Let ${\mathrm{L}}_1:\frac{\mathrm{x}-1}{1}=\frac{\mathrm{y}-2}{-1}=\frac{\mathrm{z}-1}{2}$ and ${\mathrm{L}}_2:\frac{\mathrm{x}+1}{-1}=\frac{\mathrm{y}-2}{2}=\frac{\mathrm{z}}{1}$ be two lines.

Let ${\mathrm{L}}_3$ be a line passing through the point $(\alpha ,\beta ,\gamma )$ …

Q18.Let ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots \dots {\mathrm{x}}_{10}$ be ten observations such that ${\sum }_{i=1}^{10}\left(x_i-2\right)=30,{\sum }_{i=1}^{10}{\left(x_i-\beta \right)}^2=98,\beta >2$ and their variance is $\frac{4}{5}$. If $\mu$ and ${\sigma }^2$ are respectively the …

Q19.Let $\left|{\mathrm{z}}_1-8-2\mathrm{i}\right|\le 1$ and $\left|{\mathrm{z}}_2-2+6\mathrm{i}\right|\le 2$, ${\mathrm{z}}_1,{\mathrm{z}}_2\in \mathrm{C}$. Then the minimum value of $\left|{\mathrm{z}}_1-{\mathrm{z}}_2\right|$ is :

Q20.Let $\mathrm{A}=\left[{\mathrm{a}}_{\mathrm{ij}}\right]=\left[\begin{array}{cc}{\log }_{5}128& {\log }_{4}5\\ {\log }_{5}8& {\log }_{4}25\end{array}\right]$.

If ${\mathrm{A}}_{\mathrm{ij}}$ is the cofactor of …

Q21.Let $\mathrm{f}:(0,\infty )\to \mathrm{R}$ be a twice differentiable function. If for some $\mathrm{a}\ne 0,{\int }_0^1\mathrm{f}(\lambda \mathrm{x})\mathrm{d}\lambda =\mathrm{af}(\mathrm{x})$, $f(1)=1$ and $f(16)=\frac{1}{8}$, then …

Q22.Let $S=\left\{m\in Z:A^{m^2}+A^m=3I-A^{-6}\right\}$, where $\mathrm{A}=\left[\begin{array}{cc}2& -1\\ 1& 0\end{array}\right]$. Then $\mathrm{n}(S)$ is equal to ______.

Q23.Let $[t]$ be the greatest integer less than or equal to $t$. Then the least value of $p\in N$ for which …

Q24.The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is ______.

Q25.Let $\mathrm{S}=\left\{\mathrm{x}:{\cos }^{-1}\mathrm{x}=\pi +{\sin }^{-1}\mathrm{x}+{\sin }^{-1}(2\mathrm{x}+1)\right\}$.

Then ${\sum }_{\mathrm{x}\in \mathrm{S}}(2\mathrm{x}-1{)}^2$ is equal to ______.