List of top Questions asked in JEE Main- 2026

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

Surface tension of soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is \( \alpha \pi \times 10^{-4} \) J. Find the value of \( \alpha \).

If \( z_1 \) lies on curve \( |z| = r \) and \( z_2 \) lies on curve \( |z - 3 - 4i| = 5 \), if minimum of \( |z_1 - z_2| = 2 \), then the maximum of \( |z_1 - z_2| \) is

A metal of work function 2.3 eV is irradiated with radiation of wavelength \( y \times 10^2 \) nm. The maximum kinetic energy of ejected electron is \( 2.8 \times 10^{-20} \) J. Then calculate \( y \) (in nearest integer).

Statement 1: The correct order of 2\(^\text{nd}\) ionization energy for boron family elements is: \( \text{B}>\text{Al}>\text{Ga} \).
Statement 2: The correct order of 1\(^\text{st}\) ionization energy for carbon family elements is: \( \text{Si}>\text{Ge}<\text{Pb}<\text{Sn} \).
Choose the correct option:

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

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

An ideal gas of 5 moles has \( C_p = 8 \, \text{cal/mol}^\circ \text{C} \). If its temperature changes from 10°C to 20°C, then calculate the change in its internal energy (in cal).

0.1 mole of \( H_2S \) is added in 1 liter of 0.1 HCl solution. Calculate the concentration of \( HS^{-} \).
[Given \( K_{a1} = 8.3 \times 10^{-8} \) and \( K_{a2} = 10^{-13} \)]

20 ml of 0.2 M HA (\( K_a = 5 \times 10^{-4} \)) is titrated with 10 ml of 0.2 M NaOH solution. Calculate the initial and final value of pH of the solution. [Given \( \log 5 = 0.7 \)]

Find speed of 1 kg object when it reaches close to Earth's surface from a long distance after it is released from rest as shown in the diagram. [Given \( R_e = 6400 \, \text{km}, g_s = 9.8 \, \text{m/s}^2 \)]

If matrices \( A = \begin{bmatrix} 2 & -2 \\ 4 & -2 \end{bmatrix} \) and \( B = \begin{bmatrix} 1 & 3 \\ 3 & 9 \end{bmatrix} \) are such that \( PA = B \) and \( AQ = B \), then \( \mathrm{tr}\bigl(2(P+Q)\bigr) \) is -

If the lines \( x + (k - 1)y + 3 = 0 \) \& \( 2x + k^2y - 4 = 0 \) are perpendicular and their point of intersection is the centre of a circle which passes through origin. If chord \( x - y + 2 = 0 \) intersects this circle at \( A \) \& \( B \) then \( (AB)^2 = ? \)

Force on a charge \( q = 10^{-9} \, \text{C} \) in uniform electric and magnetic fields is \( \vec{F} = (2 \times 10^{-10} \hat{i} + 3 \times 10^{-10} \hat{j}) \, \text{N} \).

Find the velocity (in m/s) of the charge if the electric field is \( 0.4 \hat{j} \, \text{V/m} \) and the magnetic field is \( 2 \times 10^{-3} \hat{k} \, \text{T} \).

If the system of equations \( x + 5y + 6z = 4 \), \( 2x + 2y + 4z = 1 \) and \( x + y + az = b \) has infinite numbers of solutions then point \( (a,b) \) lies on-

Let \( A = \{2,3,4,5,6\} \) be a set. Consider \( R \) be a relation on \( A \times A \) such that \( (x,y) \, R \, (a,b) \) implies \( x \) divides \( a \) and \( y \leq b \), then total number of elements in \( R \) is:

Parabola \( y = x^2 + px + q \) is passing through \( (1,-1) \) and vertex of parabola is at minimum distance from x-axis then \( p^2 + q^2 \) is

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.

A regular polygon with \( n \) sides is given. \( P_n \) denotes number of triangles formed by joining any three points of given regular polygon. If \( P_{n+1} - P_n = 66 \), then the sum of all prime divisors of \( n \) is

For given logic gate circuit, an equivalent gate will be

‘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: \( R = 0.083 \, \text{lit-bar/K-mol} \)}

If \( G \) is the Gravitational constant and \( h \) is Planck's constant, then the dimension of \( G \) is:

A hydrocarbon has mass ratio of C and H in 12 : 1.
Each molecule of hydrocarbon has 2 carbon atoms.
Calculate mass of \( CO_2 \) (in gm) produced, when 3.38 gm hydrocarbon undergoes combustion.

Organic compound (X) + KOH \( \overset{H^+}{\rightarrow} \) gives product \( P \) having the same molar ratio of C : H : O. Identify product \( P \).

What will be the mass of AgBr obtained when 1 gm of product is treated with AgNO₃ in the Carius method?