JEE Advanced 2025 Paper 1 Question Paper

Question 1

Let R denote the set of all real numbers. Let $a_i, b_i \in R$ for $i \in \{1, 2, 3\}$. Define the function f: R → R, g : R → R, and h : R → R by
$f(x) = a_1 + 10x + a_2x^2 + a_3x^3 + x^4$,
$g(x) = b_1 + 3x + b_2x^2 + b_3x^3 + x^4$,
$h(x) = f(x + 1) - g(x + 2)$.
If $f(x) 
eq g(x)$ for every $x \in R$, then the coefficient of $x^3$ in h(x) is

Accepted Answer

(C) − 4

Answer

(A) 8

Answer

(B) 2

Answer

(D) − 6

Question 2

Three students $S_1$, $S_2$ and $S_3$ are given a problem to solve. Consider the following events:
U: At least one of $S_1$, $S_2$, and $S_3$ can solve the problem,
V: $S_1$ can solve the problem, given that neither $S_2$ nor $S_3$ can solve the problem,
W: $S_2$ can solve the problem and $S_3$ cannot solve the problem,
T: $S_3$ can solve the problem.
for any event E, let P(E) denote the probability of E. If $P(U) = \frac{1}{2}$, $P(V) = \frac{1}{10}$, and $P(W) = \frac{1}{12}$,
then P(T) is equal to

Accepted Answer

(A) $\frac{13}{36}$

Answer

(B) $\frac{1}{3}$

Answer

(C) $\frac{19}{60}$

Answer

(D) $\frac{1}{4}$

Question 3

Consider the matrix $P = \begin{pmatrix} 2 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 3 \end{pmatrix}$. Let the transpose of a matrix X be denote by $X^{T}$. Then the number of $3 	imes 3$ invertible matrices Q with integer entries, such that $Q^{-1} = Q^{T}$ and $PQ = QP$, is

Accepted Answer

(C) 16

Answer

(A) 32

Answer

(B) 8

Answer

(D) 24

Question 4

Let $L_1$ be the line of intersection of the planes given by the equations $2x + 3y + z = 4$ and $x + 2y + z = 5$. Let $L_2$ be the line passing through the point $P(2, -1, 3)$ and parallel to $L_1$. Let M denote the plane given by the equation $2x + y - 2z = 6$. Suppose that the line $L_2$ meets the plane M at the point Q. Let R be the foot of the perpendicular drawn from P to the plane M. The which of the following statements is (are) TRUE?

Accepted Answer

(A) The length of the line segment PQ is $9\sqrt{3}$

Accepted Answer

(C) The area of ΔPQR is $\frac{3}{2}\sqrt{234}$

Answer

(B) The length of the line segment QR is 15

Answer

(D) The acute angle between the line segments PQ and PR is $\cos^{-1}\left(\frac{1}{2\sqrt{3}}\right)$

Question 5

Let N denote the set of all natural numbers, and Z denote the set of all integers. Consider the functions $f: N 	o Z$ and $g: Z 	o N$ defined by
$f(n) = \begin{cases} (n+1)/2 & 	ext{if } n 	ext{ is odd,} \ (4-n)/2 & 	ext{if } n 	ext{ is even,} \end{cases}$
and
$g(n) = \begin{cases} 3 + 2n & 	ext{if } n \geq 0, \ -2n & 	ext{if } n < 0. \end{cases}$
Define $(g \circ f)(b) = g(f(n))$ for all $n \in N$, and $(f \circ g(n)) = f(g(n))$ for all $n \in Z$.
Then which of the following statements is (are) TRUE?

Accepted Answer

(A) $g \circ f$ is NOT one-one and $g \circ f$ is NOT onto

Accepted Answer

(D) $f$ is NOT one-one but $f$ is onto

Answer

(B) $f \circ g$ is NOT one-one but $f \circ g$ is onto

Answer

(C) g is one-one and g is onto

Question 6

Let R denote the set of all real numbers. Let $z_1 = 1 + 2i$ and $z_2 = 3i$ be two complex numbers, where $i = \sqrt{-1}$. Let
$S = \{(x, y) \in R 	imes R : |x + iy - z_1| = 2|x + iy - z_2|\}$.
Then which of the following statements is(are) TRUE ?

Accepted Answer

(A) S is a circle with centre $\left(-\frac{1}{3}, \frac{10}{3}\right)$

Accepted Answer

(D) S is a circle with radius $\frac{2\sqrt{2}}{3}$

Answer

(B) S is a circle with centre $\left(\frac{1}{3}, \frac{8}{3}\right)$

Answer

(C) S is a circle with radius $\frac{\sqrt{2}}{3}$

Question 7

Let the set of all relation R on the set $\{a, b, c, d, e, f\}$, such that R is reflexive and symmetric, and R contains exactly 10 elements be denoted by S.
Then the number of elements is S is __________ .

Accepted Answer

105

Question 8

For any two points M and N in the XY –plane, let $\overrightarrow{MN}$ denote the vector from M to N, and $\vec{0}$ denote the zero vector. Let P, Q and R be three distinct points in the XY-plane. Let S be a point inside the triangle ΔPQR such that
$\overrightarrow{SP} + 5\overrightarrow{SQ} + 6\overrightarrow{SR} = \vec{0}$.
Let E and F be the mid-points of the sides PR and QR, respectively. Then the value of $\frac{	ext{length of the line segment EF}}{	ext{length of the line segment ES}}$ is __________.

Accepted Answer

1.20

Question 9

Let S be the set of all seven-digit numbers that can be formed using the digits 0, 1 and 2. For example, 2210222 is in S, but 0210222 is NOT is S.
Then the number of elements x in S such that at least one of the digits 0 and 1 appears exactly twice in x, is equal to _________ .

Accepted Answer

762

Question 10

Let α and β be the real numbers such that
$\lim_{x 	o 0} \frac{1}{x^3}\left( \frac{\alpha}{2} \int_0^x \frac{1}{1-t^2} dt + \beta x \cos x ight) = 2$.
Then the value of α + β is _______ .

Accepted Answer

2.4

Question 11

Let R denote the set of all real numbers. Let $f: R 	o R$ be a function such that $f(x) > 0$ for all $x \in R$, and $f(x + y) = f(x) f(y)$ for all $x, y \in R$.
Let the real numbers $a_1$, $a_2$, ....., $a_{50}$ be in an arithmetic progression. If $f(a_{31}) = 64 f(a_{25})$, and
$\sum_{i=1}^{50} f(a_i) = 3\left(2^{25} + 1ight)$,
then the value of $\sum_{i=6}^{30} f(a_i)$ is ________ .

Accepted Answer

96

Question 12

For all $x > 0$, let $y_1(x)$, $y_2(x)$, and $y_3(x)$ be the functions satisfying
$\frac{dy_1}{dx} - \left(\sin xight)^2 y_1 = 0$, $y_1(1) = 5$,
$\frac{dy_2}{dx} - \left(\cos xight)^2 y_2 = 0$, $y_2(1) = \frac{1}{3}$,
$\frac{dy_3}{dx} - \left(\frac{2 - x^3}{x^3}ight) y_3 = 0$, $y_3(1) = \frac{3}{5e}$,
respectively. Then $\lim_{x 	o 0^{+}} \frac{y_1(x) y_2(x) y_3(x) + 2x}{e^{3x} \sin x}$ is equal to __________ .

Accepted Answer

2

Question 13

Consider the following frequency distribution:
Value | 4 | 5 | 8 | 9 | 6 | 12 | 11
Frequency | 5 | $f_1$ | $f_2$ | 2 | 1 | 1 | 3
Suppose that the sum of the frequencies is 19 and the median of this frequency distribution is 6. For the given frequency distribution, let α denote the mean deviation about the mean, β denote the mean deviation about the median, and $\sigma^2$ denote the variance.

Match each entry in List-I to the correct entries in List-II.

The correct option is:

Accepted Answer

(C) (P) → (5), (Q) → (3), (R) → (2), (S) → (1)

Answer

(A) (P) → (5), (Q) → (3), (R) → (2), (S) → (4)

Answer

(B) (P) → (5), (Q) → (2), (R) → (3), (S) → (1)

Answer

(D) (P) → (3), (Q) → (2), (R) → (5), (S) → (4)

Question 14

Let R denote the set of all real numbers. For a real number x, let [x] denote the greatest integer less than or equal to x. Let n denote a natural number.

Match each entry in List-I to the correct entries in List-II and choose the correct option.

The correct option is:

Accepted Answer

(B) (P) → (2), (Q) → (1), (R) → (4), (S) → (3)

Answer

(A) (P) → (1), (Q) → (3), (R) → (2), (S) → (5)

Answer

(C) (P) → (5), (Q) → (1), (R) → (4), (S) → (3)

Answer

(D) (P) → (2), (Q) → (3), (R) → (1), (S) → (5)

Question 15

Let $\vec{w} = \hat{i} + \hat{j} - 2\hat{k}$, and $\vec{u}$ and $\vec{v}$ be two vectors, such that $\vec{u} 	imes \vec{v} = \vec{w}$ and $\vec{v} 	imes \vec{w} = \vec{u}$. Let α, β, γ, and t be real numbers such that $\vec{u} = \alpha\hat{i} + \beta\hat{j} + \gamma\hat{k}$, $-t\alpha + \beta + \gamma = 0$, $\alpha - t\beta + \gamma = 0$, and $\alpha + \beta - t\gamma = 0$.

Match each entry in List-I to the correct entries in List-II and choose the correct option.

The correct option is:

Accepted Answer

(A) (P) → (2), (Q) → (1), (R) → (4), (S) → (5)

Answer

(B) (P) → (2), (Q) → (4), (R) → (3), (S) → (5)

Answer

(C) (P) → (2), (Q) → (1), (R) → (4), (S) → (3)

Answer

(D) (P) → (5), (Q) → (4), (R) → (1), (S) → (3)

Question 16

The center of a disk of radius r and mass m is attached to a spring of spring constant k, inside a ring of radius R > r as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following the Hooke's law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $T = \frac{2\pi}{\omega}$. The correct expression for $\omega$ is ( g is the acceleration due to gravity):

Accepted Answer

(A) $\sqrt{\frac{2}{3}\left(\frac{g}{R-r}+\frac{k}{m}\right)}$

Answer

(B) $\sqrt{\frac{2g}{3(R-r)}+\frac{k}{m}}$

Answer

(C) $\sqrt{\frac{1}{6}\left(\frac{g}{R-r}+\frac{k}{m}\right)}$

Answer

(D) $\sqrt{\frac{1}{4}\left(\frac{g}{R-r}+\frac{k}{m}\right)}$

Question 17

In a scattering experiment, a particle of mass 2m collides with another particle of mass m, which is initially at rest. Assuming the collision to be perfectly elastic, the maximum angular deviation $	heta$ of the heavier particle, as shown in the figure, in radians is:

Accepted Answer

(D) $\frac{\pi}{6}$

Answer

(A) $\pi$

Answer

(B) $	an^{-1}\left(\frac{1}{2}ight)$

Answer

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

Question 18

A conducting square loop initially lies in the XZ plane with its lower edge hinged along the X-axis. Only in the region y ≥ 0, there is a time dependent magnetic field pointing along the z-direction, $\vec{B}(t) = B_{0}(\cos\omega t)\hat{k}$, where $B_{0}$ is a constant. The magnetic field is zero everywhere else. At time t = 0, the loop starts rotating with constant angular speed $\omega$ about the X axis in the clockwise direction as viewed from the +X axis (as shown in the figure). Ignoring self-inductance of the loop and gravity, which of the following plots correctly represents the induced e.m.f. (V) in the loop as a function of time:

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 19

Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to the measurement of diameter D of a tube. The measured value of D is:

Accepted Answer

(C) 0.13 cm

Answer

(A) 0.12 cm

Answer

(B) 0.11 cm

Answer

(D) 0.14 cm

Question 20

A conducting square loop of side L, mass M and resistance R is moving in the XY plane with its edges parallel to the X and Y axes. The region y ≥ 0 has a uniform magnetic field, $\vec{B} = B_{0}\hat{k}$. The magnetic field is zero everywhere else. At time t = 0, the loop starts to enter the magnetic field with an initial velocity $v_{0}\hat{j}$ m/s, as shown in the figure. Considering the quantity $K = \frac{B_{0}^{2}L^{2}}{RM}$ in appropriate units, ignoring self-inductance of the loop and gravity, which of the following statements is/are correct:

Accepted Answer

(B) When the complete loop is inside the region of magnetic field, the net force acting on the loop is zero.

Accepted Answer

(D) If $v_{0}$ = 3KL, the complete loop enters inside the region of magnetic field at time $t = \left(\frac{1}{K}\right)\ln\left(\frac{3}{2}\right)$.

Answer

(A) If $v_{0}$ = 1.5 KL, the loop will stop before it enters completely inside the region of magnetic field.

Answer

(C) If $v_{0} = \frac{KL}{10}$, the loop comes to rest at $t = \left(\frac{1}{K}\right)\ln\left(\frac{5}{2}\right)$.

Question 21

Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm , 0.05 mm , and 6.0 μm, respectively. Which of the following option(s) give(s) the volume of the strip in $	ext{cm}^{3}$ with correct significant figures:

Accepted Answer

(D) $3 	imes 10^{-5}$

Answer

(A) $3.2 	imes 10^{-5}$

Answer

(B) $32.0 	imes 10^{-6}$

Answer

(C) $3.0 	imes 10^{-5}$

Question 22

Consider a system of three connected strings, $S_{1}$, $S_{2}$ and $S_{3}$ with uniform linear mass densities μ kg/m, 4μ kg/m and 16μ kg/m, respectively, as shown in the figure. $S_{1}$ and $S_{2}$ are connected at the point P, whereas $S_{2}$ and $S_{3}$ are connected at the point Q, and the other end of $S_{3}$ is connected to a wall. A wave generator O is connected to the free end of $S_{1}$. The wave from the generator is represented by $y = y_{0}\cos(\omega t - kx)$ cm, where $y_{0}$, $\omega$ and k are constants of appropriate dimensions. Which of the following statements is/are correct:

Accepted Answer

(A) When the wave reflects from P for the first time, the reflected wave is represented by $y = \alpha_{1}y_{0}\cos(\omega t + kx + \pi)$ cm, where $\alpha_{1}$ is a positive constant.

Accepted Answer

(D) When the wave transmits through Q for the first time, the transmitted wave is represented by $y = \alpha_{4}y_{0}\cos(\omega t - 4kx)$ cm, where $\alpha_{4}$ is a positive constant.

Answer

(B) When the wave transmits through P for the first time, the transmitted wave is represented by $y = \alpha_{2}y_{0}\cos(\omega t - kx)$ cm, where $\alpha_{2}$ is a positive constant.

Answer

(C) When the wave reflects from Q for the first time, the reflected wave is represented by $y = \alpha_{3}y_{0}\cos(\omega t - kx + \pi)$ cm, where $\alpha_{3}$ is a positive constant.

Question 23

A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg. Suppose that the variation of the height y (in m ) of the elevator, from the ground, with time t (in s) is given by $y = 8\left[1 + \sin\left(\frac{2\pi t}{T}ight)ight]$, where T = 40 $\pi$ s. Taking acceleration due to gravity, g = 10 $	ext{m/s}^{2}$, the maximum variation of the object's weight (in N ) as observed in the experiment is _____

Accepted Answer

2

Question 24

A cube of unit volume contains $35	imes 10^{7}$ photons of frequency $10^{15}$ Hz . If the energy of all the photons is viewed as the average energy being contained in the electromagnetic waves within the same volume, then the amplitude of the magnetic field is $\alpha	imes 10^{-9}$ T. Taking permeability of free space $\mu_{0} = 4\pi	imes 10^{-7}$ Tm/A, Planck's constant $h = 6	imes 10^{-34}$ Js and $\pi = \frac{22}{7}$, the value of $\alpha$ is____

Accepted Answer

23

Question 25

Two identical plates P and Q, radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures $T_{P}$ and $T_{Q}$, respectively, with $T_{Q} < T_{P}$, as shown in Fig. 1. The radiated power transferred per unit area from P to Q is $W_{0}$. Subsequently, two more plates, identical to P and Q, are introduced between P and Q, as shown in Fig. 2. Assume that heat transfer takes place only between adjacent plates. If the power transferred per unit area in the direction from P to Q (Fig. 2) in the steady state is $W_{S}$, then the ratio $\frac{W_{0}}{W_{S}}$ is _____

Accepted Answer

3

Question 26

A solid glass sphere of refractive index $n = \sqrt{3}$ and radius R contains a spherical air cavity of radius $\frac{R}{2}$, as shown in the figure. A very thin glass layer is present at the point O so that the air cavity (refractive index n = 1) remains inside the glass sphere. An unpolarized, unidirectional and monochromatic light source S emits a light ray from a point inside the glass sphere towards the periphery of the glass sphere. If the light is reflected from the point O and is fully polarized, then the angle of incidence at the inner surface of the glass sphere is θ. The value of sin θ is ______

Accepted Answer

0.75

Question 27

A single slit diffraction experiment is performed to determine the slit width using the equation, $\frac{bd}{D} = m\lambda$, where b is the slit width, D the shortest distance between the slit and the screen, d the distance between the $m^{th}$ diffraction maximum and the central maximum, and λ is the wavelength. D and d are measured with scales of least count of 1 cm and 1 mm, respectively. The values of λ and m are known precisely to be 600 nm and 3, respectively. The absolute error (in μm) in the value of b estimated using the diffraction maximum that occurs for m = 3 with d = 5 mm and D = 1 m is ______

Accepted Answer

75.6

Question 28

Consider an electron in the n = 3 orbit of a hydrogen-like atom with atomic number Z. At absolute temperature T, a neutron having thermal energy $k_{B}T$ has the same de Broglie wavelength as that of this electron. If this temperature is given by $T = \frac{z^{2}h^{2}}{\alpha\pi^{2}a_{0}^{2}m_{N}k_{B}}$, (where h is the Planck's constant, $k_{B}$ is the Boltzmann constant, $m_{N}$ is the mass of the neutron and $a_{0}$ is the first Bohr radius of hydrogen atom) then the value of $\alpha$ is

Accepted Answer

72

Question 29

List-I shows four configurations, each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of magnitude  p, oriented as marked by arrows in the figures. In all the configurations the dipoles are fixed such that they are at a distance 2r apart along the x direction.
The midpoint of the line joining the two dipoles is X. The possible resultant electric fields $\vec{E}$ at X are given in List-II.
Choose the option that describes the correct match between the entries in List-I to those in List-II.

Accepted Answer

(C) (P) → (2), (Q) → (1), (R) → (4), (S) → (5)

Answer

(A) (P) → (3), (Q) → (1), (R) → (2), (S) → (4)

Answer

(B) (P) → (4), (Q) → (5), (R) → (3), (S) → (1)

Answer

(D) (P) → (2), (Q) → (1), (R) → (3), (S) → (5)

Question 30

A circuit with an electrical load having impedance Z is connected with an AC source as shown in the diagram. The source voltage varies in time as V(t) = 300 sin(400t) V, where t is time in s. List-I shows various options for the load. The possible currents i(t) in the circuit as a function of time are given in List-II.
Choose the option that describes the correct match between the entries in List-I to those in ListII.

Accepted Answer

(A) (P) → (3), (Q) → (5), (R) → (2), (S) → (1)

Answer

(B) (P) → (1), (Q) → (5), (R) → (2), (S) → (3)

Answer

(C) (P) → (3), (Q) → (4), (R) → (2), (S) → (1)

Answer

(D) (P) → (1), (Q) → (4), (R) → (2), (S) → (5)

Question 31

The heating of $NH_4NO_2$ at 60–70°C and $NH_4NO_3$ at 200–250°C is associated with the formation of nitrogen containing compounds X and Y, respectively. X and Y, respectively, are

Accepted Answer

(A) $N_2$ and $N_2O$

Answer

(B) $NH_3$ and $NO_2$

Answer

(C) $NO$ and $N_2O$

Answer

(D) $N_2$ and $NH_3$

Question 32

The correct order of the wavelength maxima of the absorption band in the ultraviolet -visible region for the given complexes is

Accepted Answer

(A) $[Co(CN)_6]^{3-} < [Co(NH_3)_6]^{3+} < [Co(NH_3)_5(H_2O)]^{3+} < [Co(NH_3)_5(Cl)]^{2+}$

Answer

(B) $[Co(NH_3)_5(Cl)]^{2+} < [Co(NH_3)_5(H_2O)]^{3+} < [Co(NH_3)_6]^{3+} < [Co(CN)_6]^{3-}$

Answer

(C) $[Co(CN)_6]^{3-} < [Co(NH_3)_5(Cl)]^{2+} < [Co(NH_3)_5(H_2O)]^{3+} < [Co(NH_3)_6]^{3+}$

Answer

(D) $[Co(NH_3)_6]^{3+} < [Co(CN)_6]^{3-} < [Co(NH_3)_5(Cl)]^{2+} < [Co(NH_3)_5(H_2O)]^{3+}$

Question 33

One of the products formed from the reaction of permanganate ion with iodide ion in neutral aqueous medium is

Accepted Answer

(B) $IO_3^-$

Answer

(A) $I_2$

Answer

(C) $IO_4^-$

Answer

(D) $IO_2^-$

Question 34

Consider the depicted hydrogen (H) in the hydrocarbons given below. The most acidic hydrogen (H) is

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 35

Regarding the molecular orbital (MO) energy levels for homonuclear diatomic molecules, the INCORRECT statement(s) is(are)

Accepted Answer

(B) The highest occupied molecular orbital (HOMO) of $F_2$ is σ-type.

Accepted Answer

(C) Bond energy of $O_2^+$ is smaller than the bond energy of $O_2$.

Answer

(A) Bond order of $Ne_2$ is zero.

Answer

(D) Bond length of $Li_2$ is larger than the bond length of $B_2$.

Question 36

The pair(s) of diamagnetic ions is(are)

Accepted Answer

(A) $La^{3+}, Ce^{4+}$

Accepted Answer

(B) $Yb^{2+}, Lu^{3+}$

Answer

(C) $La^{2+}, Ce^{3+}$

Answer

(D) $Yb^{3+}, Lu^{2+}$

Question 37

For the reaction sequence given below, the correct statement(s) is(are)
(In the options, X is any atom other than carbon and hydrogen, and it is different in P, Q and R)

Accepted Answer

(B) C−X bond enthalpy in P, Q and R follows the order R > P > Q.

Answer

(A) C−X bond length in P, Q and R follows the order Q > R > P.

Answer

(C) Relative reactivity toward $S_N2$ reaction in P, Q and R follows the order P > R > Q.

Answer

(D) $pK_a$ value of the conjugate acids of the leaving groups in P, Q and R follows the order R > Q > P.

Question 38

In an electrochemical cell, dichromate ions in aqueous acidic medium are reduced to $Cr^{3+}$. The current (in amperes) that flows through the cell for 48.25 minutes to produce 1 mole of $Cr^{3+}$ is ______.
Use: 1 Faraday = 96500 C $mol^{-1}$

Accepted Answer

100.00

Question 39

At 25°C, the concentration of $H^+$ ions in $1.00 	imes 10^{-3}$ M aqueous solution of a weak monobasic acid having acid dissociation constant $(K_a)$ of $4.00 	imes 10^{-11}$ is $X 	imes 10^{-7}$ M. The value of X is ______.
Use: Ionic product of water $(K_w) = 1.00 	imes 10^{-14}$ at 25°C.

Accepted Answer

2.24

Question 40

Molar volume $(V_m)$ of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_m$ as the variable. The ratio (in mol $dm^{-3}$) of the coefficient of $V_m^2$ to the coefficient of $V_m$ for a gas having van der Waals constant $a = 6.0$ $dm^6$ atm $mol^{-2}$ and $b = 0.060$ $dm^3$ $mol^{-1}$ at 300 K and 300 atm is ______.
Use: Universal gas constant (R) = 0.082 $dm^3$ atm $mol^{-1}$ $K^{-1}$.

Accepted Answer

-7.1

Question 41

Considering ideal gas behavior, the expansion work done (in kJ) when 144 g of water is electrolyzed completely under constant pressure at 300 K is ______.
Use: Universal gas constant (R) = 8.3 J $K^{-1}$ $mol^{-1}$; Atomic mass (in amu) : H = 1, O = 16

Accepted Answer

29.88

Question 42

The monomer (X) involved in the synthesis of Nylon 6,6 gives positive carbylamine test. If 10 moles of X are analyzed using Dumas method, the amount (in grams) of nitrogen gas evolved is ______.
Use: Atomic mass of N (in amu) = 14

Accepted Answer

280

Question 43

The reaction sequence given below is carried out with 16 moles of X. The yield of the major product in each step is given below the product in parentheses. The amount (in grams) of S produced is ______.
Use: Atomic mass (in amu) : H = 1, C = 12, O = 16, Br = 80

Accepted Answer

175

Question 44

The correct match of the group reagents in List-I for precipitating the metal ion given in List-II from solutions, is

Accepted Answer

(A) P → 3; Q → 4; R → 2: S → 1

Answer

(B) P → 4; Q → 2; R → 3: S → 1

Answer

(C) P → 3; Q → 4; R → 1: S → 5

Answer

(D) P → 5; Q → 3; R → 2: S → 4

Question 45

The major products obtained from the reactions in List-II are the reactants for the named reactions mentioned in List-I. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

Accepted Answer

(B) P → 2; Q → 3; R → 4: S → 1

Answer

(A) P → 2; Q → 4; R → 1: S → 3

Answer

(C) P → 5; Q → 3; R → 4: S → 2

Answer

(D) P → 5; Q → 4; R → 2: S → 1

Question 46

Match the compounds in List-I with the appropriate observations in List-II and choose the correct option.

Accepted Answer

(B) P → 2; Q → 5; R → 1: S → 3

Answer

(A) P → 1; Q → 5; R → 4: S → 2

Answer

(C) P → 5; Q → 2; R → 1: S → 4

Answer

(D) P → 2; Q → 1; R → 5: S → 3

List-I	List-II
P.see figure	1. $\vec{E} = 0$
Q.see figure	2. $\vec{E} = -\frac{p}{2\pi\varepsilon_{0}r^{3}}\hat{j}$
R.see figure	3. $\vec{E} = -\frac{p}{4\pi\varepsilon_{0}r^{3}}(\hat{i} - \hat{j})$
S.see figure	4. $\vec{E} = \frac{p}{4\pi\varepsilon_{0}r^{3}}(2\hat{i} - \hat{j})$
	5. $\vec{E} = \frac{p}{\pi\varepsilon_{0}r^{3}}\hat{i}$

List-I	List-II
P.see figure	1.see figure
Q.see figure	2.see figure
R.see figure	3.see figure
S.see figure	4.see figure
	5.see figure

List-I	List-II
P.Passing $H_2S$ in the presence of $NH_4OH$	1. $Cu^{2+}$
Q. $(NH_4)_2CO_3$ in the presence of $NH_4OH$	2. $Al^{3+}$
R. $NH_4OH$ in the presence of $NH_4Cl$	3. $Mn^{2+}$
S.Passing $H_2S$ in the presence of dilute HCl	4. $Ba^{2+}$
	5. $Mg^{2+}$

List-I	List-II
P.Stephen reaction	1.see figure
Q.Sandmeyer reaction	2.see figure
R.Hoffmann bromamide degradation reaction	3.see figure
S.Cannizzaro reaction	4.see figure
	5.see figure

List-I	List-II
P.see figure	1.Reaction with phenyl diazonium salt gives yellow dye.
Q.see figure	2.Reaction with ninhydrin gives purple color and it also reacts with $FeCl_3$ to give violet color.
R.see figure	3.Reaction with glucose will give corresponding hydrazone.
S.see figure	4.Lassiagne extract of the compound treated with dilute HCl followed by addition of aqueous $FeCl_3$ gives blood red color.
	5.After complete hydrolysis, it will give ninhydrin test and it DOES NOT give positive phthalein dye test.

JEE Advanced 2025 Paper 1 Question Paper with Answers

Physics — JEE Advanced 2025 Paper 1

Chemistry — JEE Advanced 2025 Paper 1

Mathematics — JEE Advanced 2025 Paper 1

Chapters tested in this paper

Attempt JEE Advanced 2025 Paper 1 under exam timing.

List-I	List-II
P. $7f_1 + 9f_2$ is equal to	1.146
Q.19α is equal to	2.47
R.19β is equal to	3.48
S. $19\sigma^2$ is equal to	4.145
	5.55

List-I	List-II
P.The minimum value of n for which the function $f(x) = \left[\frac{10x^3 - 45x^2 + 60x + 35}{n}\right]$ is continuous on the interval [1, 2], is	1.8
Q.The minimum value of n for which $g(x) = (2n^2 - 13n - 15)(x^3 + 3x)$ , $x \in R$ , is an increasing function on R, is	2.9
R.The smallest natural number n which is greater than 5, such that $x = 3$ is a point of local minima of $h(x) = (x^2 - 9)^n(x^2 + 2x + 3)$ , is	3.5
S.Number of $x_0 \in R$ such that $l(x) = \sum_{k=0}^{4}\left( \sin\|x - k\| + \cos\left\|x - k + \frac{1}{2}\right\| \right)$ , $x \in R$ , In NOT differentiable at $x_0$ is	4.6
	5.10

List-I	List-II
P. $\|\vec{v}\|^2$ is equal to	1.0
Q.If $\alpha = \sqrt{3}$ , then $\gamma^2$ is equal to	2.1
R.If $\alpha = \sqrt{3}$ , then $(\beta + \gamma)^2$ is equal to	3.2
S.If $\alpha = \sqrt{2}$ , then $t + 3$ is equal to	4.3
	5.5