JEE Advanced 2025 Paper 1 Online

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 = ...

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

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.

List–I
List–...

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

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

In an electrochemical cell, dichromate ions in aqueous acidic medium are reduced to Cr3+. The current (in amperes) that flows through the cell for 48.25 minutes to produce 1 mole of Cr3+ is ______.Use: 1 Faraday = 96500 C mol−1

Molar volume (Vm) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with Vm as the variable. The ratio (in mol dm−3) of the coefficient of Vm2 to the coefficient of Vm for a gas having van...

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)

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

At 25 °C, the concentration of H+ ions in 1.00 × 10−3 M aqueous solution of a weak monobasic acid having acid dissociation constant (Ka) of 4.00 × 10−11 is X × 10−7 M. The value of X is ______.Use: Ionic product of water (Kw) = 1.00 × 10−14...

The heating of NH4NO2 at 60–70 °C and NH4NO3 at 200–250 °C is associated with the formation of nitrogen containing compounds X and Y, respectively. X and Y, respectively, are

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

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

List–I
List–II


(P)
(1) Reaction with phenyl diazonium salt gives
yellow dye.



(Q)
(2) R...

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

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





List–I

List–II





(P) Passing $\mathrm{H_2S}$ in the presence of $\mathrm{NH_4OH}$

(1) $\ma...

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

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 equa...

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\(S = \{(x, y) \in \mathbb{R} \times \mathbb{R} : |x + iy - z_1| = 2|x + iy - z_2| \}.\)Then which of the followin...

For all x > 0, let y₁(x), y₂(x), and y₃(x) be the functions satisfying
$ \frac{dy_1}{dx} - (\sin x)^2 y_1 = 0, \quad y_1(1) = 5, $ $ \frac{dy_2}{dx} - (\cos x)^2 y_2 = 0, \quad y_2(1) = \frac{1}{3}, $ $ \frac{dy_3}{dx} - \frac{(2-x^3)}{x^3}...

Let ℕ denote the set of all natural numbers, and ℤ denote the set of all integers. Consider the functions f: ℕ → ℤ and g: ℤ → ℕ defined by$$ f(n) = \begin{cases} \frac{(n + 1)}{2} & \text{if } n \text{ is odd,} \\ \frac{(4-n)}{2} & \text{if...

Let ℝ denote the set of all real numbers. Let f: ℝ → ℝ be a function such that f(x) > 0 for all x ∈ ℝ, and f(x+y) = f(x)f(y) for all x, y ∈ ℝ.
Let the real numbers a₁, a₂, ..., a₅₀ be in an arithmetic progression. If f(a₃₁) = 64f(a₂₅), and
...

Let $\mathbb{R}$ denote the set of all real numbers. Define the function $f : \mathbb{R} \to \mathbb{R}$ by$f(x)=\left\{\begin{array}{cc}2-2 x^2-x^2 \sin \frac{1}{x} & \text { if } x \neq 0, \\ 2 & \text { if } x=0 .\end{array}\right.$Then ...

Let α and β be the real numbers such that
$ \lim\limits_{x \to 0} \frac{1}{x^3} \left( \frac{\alpha}{2} \int\limits_0^x \frac{1}{1-t^2} \, dt + \beta x \cos x \right) = 2. $
Then the value of α + β is ___________.

Let $\mathbb{R}$ 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 entry in List-II and cho...

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 denoted by $X^T$. Then the number of $3 \times 3$ invertible matrices $Q$ with integer entries, such that$$ ...

Let the set of all relations $R$ 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 $\mathcal{S}$.Then the number of elements in $\mathcal{S}$ is ______________...

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 in $S$.Then the number of elements $x$ in $S$ such that at least one of the digits $0$ ...

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 t...

Let $\mathbb{R}$ denote the set of all real numbers. Let $a_i, b_i \in \mathbb{R}$ for $i \in \{1, 2, 3\}$.
Define the functions $f: \mathbb{R} \to \mathbb{R}$, $g: \mathbb{R} \to \mathbb{R}$, and $h: \mathbb{R} \to \mathbb{R}$ by
$f(x) = a...

Consider the following frequency distribution:table {width: 100%;border-collapse: collapse;margin: 20px 0;} th {background-color: blue;color: white;border: 1px solid lightgrey;padding: 10px;} td {border: 1px solid lightgrey;padding: 10px;te...

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 th...

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

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 $V(t)=300 \sin (400 t) \mathrm{V}$, where $t$ is time in s . List-I shows various options fo...

List-I shows various functional dependencies of energy $(E)$ on the atomic number $(Z)$. Energies associated with certain phenomena are given in List-II.
Choose the option that describes the correct match between the entries in List-I to th...

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 $k_{\mathrm{B}} T$ has the same de Broglie wavelength as that of this electron. If this tem...

A conducting square loop initially lies in the $X Z$ plane with its lower edge hinged along the $X$-axis. Only in the region $y \geq 0$, there is a time dependent magnetic field pointing along the $Z$-direction, $\vec{B}(t)=B_0(\cos \omega ...

A conducting square loop of side $L$, mass $M$ and resistance $R$ is moving in the $X Y$ plane with its edges parallel to the $X$ and $Y$ axes. The region $y \geq 0$ has a uniform magnetic field, $\vec{B}=B_0 \widehat{k}$. The magnetic fiel...

A cube of unit volume contains $35 \times 10^7$ photons of frequency $10^{15} \mathrm{~Hz}$. 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 ampl...

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 ...

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 0 so that the air cavity (refractive index...

Two identical plates P and Q , radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures $\mathrm{T}_{\mathrm{P}}$ and $\mathrm{T}_{\mathrm{Q}}$, respectively, with $\mathrm{T}_{\mathrm{Q}}<\mathrm{T}_{\mathrm{...

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 θ of the heavier particle, as shown in the...

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 th...

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...

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:

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 cm3 with correct significant figures:

Consider a system of three connected strings, $S_1, S_2$ and $S_3$ with uniform linear mass densities $\mu$ $\mathrm{kg} / \mathrm{m}, 4 \mu \mathrm{~kg} / \mathrm{m}$ and $16 \mu \mathrm{~kg} / \mathrm{m}$, respectively, as shown in the fi...

A single slit diffraction experiment is performed to determine the slit width using the equation, $\frac{b d}{D}=$ $m \lambda$, where $b$ is the slit width, $D$ the shortest distance between the slit and the screen, $d$ the distance between...