List of top Questions asked in JEE Main

The magnetic field inside a 200 turns solenoid of radius 10 cm is \( 2.9 \times 10^{-4} \) Tesla. If the solenoid carries a current of 0.29 A, then the length of the solenoid is:

The truth table for the circuit given below is:

Choose the correct answer from the options given below:

If \(\alpha x + \beta y = 109\) is the equation of the chord of the ellipse \[ \frac{x^2}{9} + \frac{y^2}{4} = 1 \] whose midpoint is \(\left(\frac{5}{2}, \frac{1}{2}\right)\), then \(\alpha + \beta\) is equal to:

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R).

Three identical spheres of the same mass undergo one-dimensional motion as shown in the figure with initial velocities \( v_A = 5 \, \text{m/s}, v_B = 2 \, \text{m/s}, v_C = 4 \, \text{m/s} \). If we wait sufficiently long for elastic collision to happen, then \( v_A = 4 \, \text{m/s}, v_B = 2 \, \text{m/s}, v_C = 5 \, \text{m/s} \) will be the final velocities. Reason (R): In an elastic collision between identical masses, two objects exchange their velocities. In light of the above statements, choose the correct answer from the options given below:

If for the solution curve \( y = f(x) \) of the differential equation \[ \frac{dy}{dx} + (\tan x) y = 2 + \sec^2 x, \quad y(\frac{\pi}{3}) = \sqrt{3}, \] \(\text{then}\) \( y(\frac{\pi}{4}) \) is equal to:

Consider the following low-spin complexes \[ \text{K}_3[\text{Co(NO}_3)_6], \, \text{K}_4[\text{Fe(CN)}_6], \, \text{K}_3[\text{Fe(CN)}_6], \, \text{Cu}_2[\text{Fe(CN)}_6], \, \text{Zn}_2[\text{Fe(CN)}_6] \] The sum of the spin-only magnetic moment values of complexes having yellow colour is: \[ \text{B.M. (answer is nearest integer)} \]

Let \( a_1, a_2, \dots, a_{2024} \) be an Arithmetic Progression such that \[ a_1 + (a_1 + a_0 + a_1 + a_2 + \cdots + a_{2020} + a_{2024}) = 2233. \quad \text{Then} \quad a_1 + a_2 + a_3 + \dots + a_{2022} \] is equal to ____ :

Let \( S = \mathbb{N} \cup \{0\} \). Define a relation \( R \) from \( S \) to \( \mathbb{R} \) by: \[ R = \left\{ (x, y) : \log_e y = x \log_e \left(\frac{2}{5}\right), x \in S, y \in \mathbb{R} \right\}. \] Then, the sum of all the elements in the range of \( R \) is equal to:

A capacitor, \( C_1 = 6 \, \mu F \), is charged to a potential difference of \( V_1 = 5 \, \text{V} \) using a 5V battery. The battery is removed and another capacitor, \( C_2 = 12 \, \mu F \), is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges \( q_1 \) and \( q_2 \) on the capacitors \( C_1 \) and \( C_2 \) when equilibrium condition is reached?

A poly-atomic molecule (C\(_3\)R, \(C_v = 4R\), where \(R\) is gas constant) goes from phase space point A (\(P_A = 10^4 \, \text{Pa}, V_A = 4 \times 10^{-3} \, \text{m}^3\)) to point B (\(P_B = 5 \times 10^4 \, \text{Pa}, V_B = 6 \times 10^{-7} \, \text{m}^3\)) to point C (\(P_C = 10^4 \, \text{Pa}, V_C = 8 \times 10^{-3} \, \text{m}^3\)). A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is:

Drug X becomes ineffective after 50% decomposition. The original concentration of drug in a bottle was 16 mg/mL which becomes 4 mg/mL in 12 months. The expiry time of the drug in months is ____ . Assume that the decomposition of the drug follows first order kinetics.

If the domain of the function \( \log_5 (18x - x^2 - 77) \) is \( (\alpha, \beta) \) and the domain of the function \[ \log_{(x-1)} \left( \frac{2x^2 + 3x - 2}{x^2 - 3x - 4} \right) \] is \( (\gamma, \delta) \), then \( \alpha^2 + \beta^2 + \gamma^2 \) is equal to:

Let \( \hat{a} \) be a unit vector perpendicular to the vectors \[ \mathbf{b} = \hat{i} - 2\hat{j} + 3\hat{k} \quad \text{and} \quad \mathbf{c} = 2\hat{i} + 3\hat{j} - \hat{k}, \] \(\text{and makes an angle of}\) \( \cos\left( -\frac{1}{3} \right) \) \(\text{with the vector}\) \( \hat{i} + \alpha \hat{j} + \hat{k} \). \(\text{If}\) \( \hat{a} \) \(\text{makes an angle of}\) \( \frac{\pi}{3} \) \(\text{with the vector}\) \( \hat{i} + \alpha \hat{j} + \hat{k} \), then the value of \( \alpha \) \(\text{is:}\)

Isomeric hydrocarbons \( \rightarrow \) negative Baeyer's test (Molecular formula \( \text{C}_9\text{H}_{12} \)). The total number of isomers from above with four different non-aliphatic substitution sites is -