List of top Questions asked in JEE Main

‘x’ be the osmotic pressure of a solution formed by dissolving 1g of a protein (M = 50,000 g/mol) in 0.5 litre and ‘y’ be the osmotic pressure of solution formed by dissolving 2g of the same protein in 1 litre at 300 K. If ‘z’ be the osmotic pressure of solution formed by mixing above two solutions. Then the value of ‘x’, ‘y’ and ‘z’ respectively are.
\text{Use: $ R = 0.083 \, \text{lit-bar/K-mol} $}

Find the ratio of electric flux passing through two spheres centered at the origin, having radii 4 m and 6 m respectively, with charges $ q_1 = 8 \, \mu C $ and $ q_2 = 2 \, \mu C $ respectively.

Molarity of $ H_2SO_4 (aq.) $ solution is 4.9 M. If the density of the solution is 1.40 g/mL, then molality and mole fraction of solute in the solution is:
(Molar mass of $ H_2SO_4 = 98 \, \text{g mol}^{-1} $)

Let $ \overrightarrow{PS} = \hat{i} + \hat{j} $ and $ \overrightarrow{PQ} = -\hat{j} + \hat{k} $. If $ \overrightarrow{PS} $ must be rotated by an angle $ \alpha $ such that $ \overrightarrow{PS} $ is perpendicular to $ \overrightarrow{PQ} $, then $ \left( \sin^2 \frac{5\alpha}{2} - \sin^2 \frac{\alpha}{2} \right) $ equals

The value of $ \int_{0}^{20\pi} \left( \sin^4 x + \cos^4 x \right)\, dx $ is equal to

If $ {}^{30}C_{30-r} + 3 \cdot {}^{30}C_{31-r} + 3 \cdot {}^{30}C_{32-r} + {}^{30}C_{33-r} = {}^{n}C_{r} $, then value of $ n $ is

Let `C' be a circle with radius `6' units centred at origin. Let $ A(3,0) $ be a point. If $ B $ is a variable point in xy-plane such that circle drawn taking $ AB $ as diameter touches the circle $ C $, then eccentricity of the locus of point `B' is

Match List I with List II.

Predict expression for $ \alpha $ in terms of $ K_{eq} $ and concentration
C: $ A_2B_3 \, (aq) \rightleftharpoons 2A^{3+} (aq) + 3B^{2-} (aq) $

What is the equivalent gate for the following digital circuit?

In an equilateral prism the path of a ray is shown in the figure. Determine the refractive index of the prism.

Consider two arrangements of wires. Find the ratio of magnetic field at the centre of the semi–circular part.

Object is placed at $40 \text{ cm}$ from spherical surface whose radius of curvature is $20 \text{ cm}$. Find height of image formed.

Foot of perpendicular from origin on a line passing through $(1, 1, 1)$ having direction ratios $\langle 2, 3, 4 \rangle$, is:

A line through $(1, 1, 1)$ and perpendicular to both $\hat{i} + 2\hat{j} + 2\hat{k}$ and $2\hat{i} + 2\hat{j} + \hat{k}$, let $(a, b, c)$ be foot of perpendicular from origin then $34 (a + b + c)$ is: