List of top Questions asked in JEE Main

An aqueous solution of 0.1 M HA shows depression in freezing point of 0.2°C. If $ K_f $ (H$_2$O) = 1.86 K kg mol$^{-1}$ and assuming molarity = molality, find the dissociation constant of HA.

Consider the following cell: $ \text{Pt}(s) \, \text{H}_2 (1 \, \text{atm}) | \text{H}^+ (1 \, \text{M}) | \text{Cr}_2\text{O}_7^{2-}, \, \text{Cr}^{3+} | \text{H}^+ (1 \, \text{M}) | \text{Pt}(s) $
Given: $ E^\circ_{\text{Cr}_2\text{O}_7^{2-}/\text{Cr}^{3+}} = 1.33 \, \text{V}, \quad \left[ \text{Cr}^{3+} \right]^2 / \left[ \text{Cr}_2\text{O}_7^{2-} \right] = 10^{-7} $
At equilibrium: $ \left[ \text{Cr}^{3+} \right]^2 / \left[ \text{Cr}_2\text{O}_7^{2-} \right] = 10^{-7} $
Objective: $ \text{Determine the pH at the cathode where } E_{\text{cell}} = 0. $

The product of the last 2 digits of $ (1919)^{1919} $ is:

If a curve $ y = y(x) $ passes through the point $ \left(1, \frac{\pi}{2}\right) $ and satisfies the differential equation $$ (7x^4 \cot y - e^x \csc y) \frac{dx}{dy} = x^5, \quad x \geq 1, \text{ then at } x = 2, \text{ the value of } \cos y \text{ is:} $$

A radioactive material P first decays into Q and then Q decays to non-radioactive material R. Which of the following figure represents time dependent mass of P, Q and R?

x mg of Mg(OH)$_2$ (molar mass = 58) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is ____ mg. (Nearest integer) (Given: Mg(OH)$_2$ is assumed to dissociate completely in H$_2$O)

For $ n \geq 2 $, let $ S_n $ denote the set of all subsets of $ \{1, 2, 3, \ldots, n\} $ with no two consecutive numbers. For example, $ \{1, 3, 5\} \in S_6 $, but $ \{1, 2, 4\} \notin S_6 $. Then, find $ n(S_5) $.

The number of solutions of the equation $ 2x + 3\tan x = \pi $, $ x \in [-2\pi, 2\pi] - \left\{ \pm \frac{\pi}{2}, \pm \frac{3\pi}{2} \right\} $ is

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3 \times 10^{-7} \mathrm{~m}$ and $600 \mathrm{~m} / \mathrm{s}$, respectively. Find the frequency of its collisions.

Rate law for a reaction between $A$ and $B$ is given by $\mathrm{R}=\mathrm{k}[\mathrm{A}]^{\mathrm{n}}[\mathrm{B}]^{\mathrm{m}}$. If concentration of A is doubled and concentration of B is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction $\left(\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}\right)$ is

The shortest distance between the curves $ y^2 = 8x $ and $ x^2 + y^2 + 12y + 35 = 0 $ is:

Let $ \vec{a} = \hat{i} + 2\hat{j} + \hat{k} $, $ \vec{b} = 3\hat{i} - 3\hat{j} + 3\hat{k} $, $ \vec{c} = 2\hat{i} - \hat{j} + 2\hat{k} $ and $ \vec{d} $ be a vector such that $ \vec{b} \times \vec{d} = \vec{c} \times \vec{d} $ and $ \vec{a} \cdot \vec{d} = 4 $. Then $ |\vec{a} \times \vec{d}|^2 $ is equal to _______

A magnetic dipole experiences a torque of $ 80\sqrt{3} $ N m when placed in a uniform magnetic field in such a way that the dipole moment makes an angle of $ 60^\circ $ with the magnetic field. The potential energy of the dipole is:

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are : $ \frac{L_A}{L_B} = \frac{1}{2} $, $ \frac{r_A}{r_B} = 2 $, and $ \frac{K_A}{K_B} = \frac{1}{2} $. The free ends of rods A and B are maintained at $ 400 \, K $, $ 200 \, K $, respectively. The temperature of rods interface is ____ K, when equilibrium is established.

Choose the incorrect trend in the atomic radii (r) of the elements :

Let $ A = \begin{bmatrix} \alpha & -1 \\ 6 & \beta \end{bmatrix} , \ \alpha > 0 $, such that $ \det(A) = 0 $ and $ \alpha + \beta = 1. $ If $ I $ denotes the $ 2 \times 2 $ identity matrix, then the matrix $ (I + A)^8 $ is:

Let $ a \in \mathbb{R} $ and $ A $ be a matrix of order $ 3 \times 3 $ such that $ \det(A) = -4 $ and \[ A + I = \begin{bmatrix} 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 \end{bmatrix} \] where $ I $ is the identity matrix of order $ 3 \times 3 $.

If $ \det\left( (a + 1) \cdot \text{adj}\left( (a - 1) A \right) \right) $ is $ 2^m 3^n $, $ m, n \in \{ 0, 1, 2, \dots, 20 \} $, then $ m + n $ is equal to:

Let the point $ P $ of the focal chord $ PQ $ of the parabola $ y^2 = 16x $ be $ (1, -4) $. If the focus of the parabola divides the chord $ PQ $ in the ratio $ m : n $, gcd($m, n$) = 1, then $ m^2 + n^2 $ is equal to:

If the sum of the first 10 terms of the series \[ \frac{4 \cdot 1}{1 + 4 \cdot 1^4} + \frac{4 \cdot 2}{1 + 4 \cdot 2^4} + \frac{4 \cdot 3}{1 + 4 \cdot 3^4} + \ldots \] is $\frac{m}{n}$, where $\gcd(m, n) = 1$, then $m + n$ is equal to _____.

If the set of all $ a \in \mathbb{R} \setminus \{1\} $, for which the roots of the equation $ (1 - a)x^2 + 2(a - 3)x + 9 = 0 $ are positive is $ (-\infty, -\alpha] \cup [\beta, \gamma] $, then $ 2\alpha + \beta + \gamma $ is equal to ...........

Find the value of the integral $ \int_0^{\frac{\pi}{2}} \sin^2(x) \, dx $.

Statement 1: Fructose can give Tollens' test even though it does not have an aldehyde group.
Statement 2: When reacted with base, fructose can undergo rearrangement to produce an aldehyde group.

The area (in sq. units) of the region $(x, y) : 0 \leq y \leq 2|x| + 1, 0 \leq y \leq x^2 + 1, |x| \leq 3$ is:

Which of the following circuits has the same output as that of the given circuit?

The molecules having square pyramidal geometry are: