List of top Questions asked in JEE Main- 2026

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 \( \alpha \).

Find sum up to 8 terms of the series
\[ \frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\cdots \]

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 \( (AB)^2 = ? \)

Side of square is \( L \) and \( R \ll L \).
Find mutual inductance of the system shown in the figure.

Let \( P = \{\theta \in [0, 4\pi] : \tan^2\theta \neq 1\} \)
\( S = \{ a \in \mathbb{Z} : (\cos^2\theta - \sin^2\theta)\sec 2\theta = a^2,\ \theta \in P \} \)
then \( n(S) \) equals

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:

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

Work function for an object is 2.3 eV. If maximum kinetic energy of ejected electrons is 0.18 eV, find wavelength \( \lambda \) of incident photon on object.

A hollow cylinder of radius 1m is rotating with angular velocity \( \omega = 10 \) rad/sec. Find minimum coefficient of friction \( \mu \) so that the block remains at rest w.r.t. the cylinder.

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 \( R_e = 6400 \, \text{km}, g_s = 9.8 \, \text{m/s}^2 \)]

A small ball of mass 1 kg is released from a height of 20 m on the sand. It penetrates 10 cm in the sand and comes to rest. Find the average force exerted by the sand on the ball. (g = 10 m/s\(^2\))

Find \( \frac{BE}{A} \) of \( {}^{83}\text{Bi}^{209} \).
Given: \( M_{\text{Bi}} = 208.9804 \, \text{amu}, \, m_p = 1.007276 \, \text{amu}, \, m_n = 1.008665 \, \text{amu}, \, 1 \, \text{amu} = 931 \, \text{MeV} \)

A cell is formed using the below half-cell reactions, and the cell is working with 80% efficiency. Work obtained is utilized for isothermal expansion of gas against external pressure of 1 kPa. Find \( \Delta V \) (in \( \text{m}^3 \)). \[ \frac{1}{2} O_2 + 2H^+ + 2e^- \rightarrow H_2O; \, E^\circ = 1.23 \, \text{V} \] \[ 6H^+ + CO_2 + 6e^- \rightarrow CH_3OH + H_2O; \, E^\circ = 0.02 \, \text{V} \]

Let \( f(x) \) be a polynomial of degree \( 5 \) having extreme values at \( x = 1 \) and \( x = -1 \). If \[ \lim_{x \to 0} \frac{f(x)}{x^3} = -5, \] then the value of \( f(B) - f(-2) \) is

Which of the following are iso-structural with \( \text{SF}_4 \)?

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

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 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

There is a thin layer of refractive index \( \mu \) below the base of an equilateral prism. The path of a ray is shown in the figure. Find out \( \mu \).

As shown in the figure in YDSE experiment, if intensity is \( \frac{3}{4} \) of maximum intensity at point P, and path difference at point 'P' is \( \Delta x = \frac{\lambda}{\alpha} \). Find the value of "α". (where \( \lambda \) is wavelength of light)

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:

If the area bounded by two curves \( \dfrac{x^2}{9} - \dfrac{y^2}{16} = 1 \) and \( 8x - 3y = 24 \) is \( A - 6\log_e 3 \), then \( A \) is equal to

A paper is placed in front of lens at a distance 30 cm, such that paper gets burned in minimum time. Radius of curvature of bi-convex lens is 60 cm. If refractive index of lens is \( \mu = \frac{\alpha}{10} \), then value of \( \alpha \) is?