List of top Questions asked in JEE Main

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 wire) is half of the maximum possible magnetic field, anywhere due to the wire, will be:

At the interface between two materials having refractive indices \( n_1 \) and \( n_2 \), the critical angle for reflection of an EM wave is \( \theta_c \). The \( n_1 \) material is replaced by another material having refractive index \( n_3 \), such that the critical angle at the interface between \( n_1 \) and \( n_3 \) materials is \( \theta_{c3} \). If \( n_1>n_2>n_3 \), \( \frac{n_2}{n_3} = \frac{2}{5} \), and \( \sin\theta_{c2} - \sin\theta_{c1} = \frac{1}{2} \), then \( \theta_{c1} \) is:

The pair of physical quantities not having same dimensions is:

Let \[ S = \left\{ m \in \mathbb{Z} : A m^2 + A^n = 31 - A^6 \right\}, \quad \text{where} \quad A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \] Then \( n(S) \) is equal to:

Match List - I with List - II.

In Carius method of estimation of halogen, 0.25 g of an organic compound gave 0.15 g of silver bromide (AgBr). The percentage of Bromine in the organic compound is \(\_\_\_\_\)times 10^{-1}% (Nearest integer). (Given: Molar mass of Ag is 108 and Br is 80 g mol^{-1}

The observed and normal molar masses of compound MX\(_2\) are 65.6 and 164 respectively. The percent degree of ionisation of MX\(_2\) is \(\_\_\_\_\)% (Nearest integer).

The possible number of stereoisomers for 5-phenylpent-4-en-2-ol is:

The hydrocarbon (X) with molar mass 80 g mol\(^{-1}\) and 90% carbon has \(\_\_\_\_\) degree of unsaturation.

Consider a complex reaction taking place in three steps with rate constants \(k_1\), \(k_2\), and \(k_3\) respectively. The overall rate constant \(k\) is given by the expression \( k = \sqrt{\frac{k_1 k_3}{k_2}} \). If the activation energies of the three steps are 60, 30, and 10 kJ mol\(^{-1}\) respectively, then the overall energy of activation in kJ mol\(^{-1}\) is \(\_\_\_\_\)(Nearest integer).

Acceleration due to gravity on the surface of earth is \( g \). If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is \_\_\_\_ g.

The temperature of a body in air falls from \( 40^\circ \text{C} \) to \( 24^\circ \text{C} \) in 4 minutes. The temperature of the air is \( 16^\circ \text{C} \). The temperature of the body in the next 4 minutes will be:

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is:

Let \( f : (0, \infty) \to \mathbb{R} \) be a twice differentiable function. If for some \( a \neq 0 \), \[ \int_0^a f(x) \, dx = f(a), \] and given that \[ f(1) = 1, \quad f(16) = \frac{1}{8}, \] then \[ 16 - f^{-1}\left( \frac{1}{16} \right) \] is equal to:

Let \[ S = \left\{ x : \cos^{-1}x = \pi + \sin^{-1}x + \sin^{-1}(2x+1) \right\}. \] Then \[ \sum_{x \in S} (2x - 1)^2 \] is equal to:

Let \( [t] \) be the greatest integer less than or equal to \( t \). Then the least value of \( p \in \mathbb{N} \) for which \[ \lim_{x \to \infty} \left( x \left( \left[ 1/x \right] + \left[ 2/x \right] + \cdots + \left[ p/x \right] \right) - x^2 \left( \frac{1}{x^2} + \frac{2}{x^2} + \cdots + \frac{p^2}{x^2} \right) \right) \geq 1 \] is equal to:

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 11th term is:

Let \[ A = \left[ a_{ij} \right] = \begin{bmatrix} \log_5 128 & \log_4 5 \\ \log_5 8 & \log_4 25 \end{bmatrix}. \] If \( A_{ij} \) is the cofactor of \( a_{ij} \), \( C_{ij} = \sum_{k=1}^{2} a_{ik} A_{jk} \), and \( C = [C_{ij}] \), then \( 8|C| \) is equal to:

Let \( y = y(x) \) be the solution of the differential equation \[ \cos(x \log_e (\cos x))^2 \, dy + (\sin x - 3 \sin x \log_e (\cos x)) \, dx = 0, \, x \in \left( 0, \frac{\pi}{2} \right) \] If \( y \left( \frac{\pi}{4} \right) = -1 \), then \( y \left( \frac{\pi}{6} \right) \) is equal to:

Let \( P \) be the set of seven-digit numbers with the 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:

Let \( ABC \) be a triangle formed by the lines \( 7x - 6y + 3 = 0 \), \( x + 2y - 31 = 0 \), and \( 9x - 2y - 19 = 0 \).
Let the point \( (h, k) \) be the image of the centroid of \( \triangle ABC \) in the line \( 3x + 6y - 53 = 0 \). Then \( h^2 + k^2 + hk \) is equal to:

Let \( f: \mathbb{R} \to \mathbb{R} \) be a function defined by \( f(x) = \left( 2 + 3a \right)x^2 + \left( \frac{a+2}{a-1} \right)x + b, a \neq 1 \). If \[ f(x + y) = f(x) + f(y) + 1 - \frac{2}{7}xy, \] then the value of \( 28 \sum_{i=1}^5 f(i) \) is:

Let \( T_r \) be the \( r^{th} \) term of an A.P. If for some \( m \), \( T_m = \frac{1}{25} \), \( T_{25} = \frac{1}{20} \), and \( \sum_{r=1}^{25} T_r = 13 \), then

\[ 5m \sum_{r=m}^{2m} T_r \text{ is equal to:} \]

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

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