List of top Questions asked in JEE Main

A container of initial volume $0.15 \text{ m}^3$ is expanded adiabatically from pressure 8 bar to final pressure 1 bar. If initial temperature is $140 \text{ K}$, then find work done by the gas :- ($C_P = 3R, C_V = 2R$) :-

For given Atwood machine. Find displacement (in m) of centre of mass after 2 sec of release.

If \( S_1 \) is closed and \( S_2 \) open, \( \theta \) is 30° and if \( S_1 \) is open and \( S_2 \) closed then \( \theta \) is 60°. Then find \( 3L_2 - L_1 \), if \( C = 100 \mu F \).

Position of a particle is given by \( x = A \sin \left( 50t + \frac{\pi}{3} \right) \). If speed and acceleration become 0 for the first time at \( t_1 \) and \( t_2 \) sec respectively, then find \( t_1 \) and \( t_2 \) (in sec):

At any instant, if \( \vec{B} = -2 \times 10^{-7} \hat{j} \, \text{T} \) and \( \vec{C} \) is along the +x axis, then \( \vec{E} \) at this instant is:

If foot of the perpendicular from a point \( P(a,b,0) \) on the line \( \dfrac{x-1}{2}=\dfrac{y-2}{1}=\dfrac{z-\alpha}{3} \) is \( A \) and mid-point of \( AP \) is \( \left(0,\dfrac{3}{4},-\dfrac{1}{4}\right) \), then the value of \( \left(a^2+b^2+\alpha^2\right) \) is -

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)

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 \( K_{a2} = 10^{-13} \)]

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 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:

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

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 \( \mu \).

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 \( (AB)^2 = ? \)

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

Arrange the following complexes in increasing order of C.F.S.E. (\( \Delta_0 \))
(a) \( [\text{Co}(\text{H}_2\text{O})_6]^{2+} \)
(b) \( [\text{Co}(\text{H}_2\text{O})_6]^{3+} \)
(c) \( [\text{Co}(\text{en})_3]^{3+} \)

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

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\(^2\))

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

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

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

For first order reaction:
2A(g) → 4B(g) + C(g)
Total pressure at \( t = 30 \, \text{sec} \) and \( t = \infty \) are 300 torr and 600 torr respectively. Calculate pressure of C(g) at 30 sec (in torr).

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

An air bubble of radius 1 mm is rising up with constant speed of 0.5 cm/s in a liquid of density \( \rho_{\text{liq}} = 2000 \, \text{kg/m}^3 \). Find the coefficient of viscosity \( \eta \) in poise.

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