Class 12 | JEE Board | Mixed Level Practice Test - 25 Questions (2026)

A particle of mass $m$ is moving in a circular path of radius $r$ with a constant speed $v$. The work done by the centripetal force in moving the particle over half the circle is:

The equilibrium constant for the reaction $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$ is $K$. What is the equilibrium constant for the reaction $\frac{1}{2}N_2(g) + \frac{3}{2}H_2(g) \rightleftharpoons NH_3(g)$?

If $f(x) = \begin{cases} x^2\sin(\frac{1}{x}), & x eq 0 \\ 0, & x = 0 \end{cases}$, then which of the following is true?

A parallel plate capacitor has a capacitance $C$. If the distance between the plates is doubled and the area of each plate is halved, the new capacitance will be:

What is the major product formed when 2-methylpropene is reacted with HBr in the presence of peroxide?

Evaluate the integral $\int_0^{\pi/2} \sin^2(x) dx$.

A diatomic gas undergoes adiabatic compression. Its volume is reduced to $\frac{1}{8}$ of its initial volume. If the initial pressure is $P_0$, the final pressure is:

Which of the following compounds will give a positive iodoform test?

Find the area of the region bounded by the curve $y = x^2$ and the line $y = 4$.

A ball is dropped from a height $h$ above the ground. If the coefficient of restitution is $e$, the height to which the ball rises after the first bounce is:

What is the pH of a $10^{-8} M$ solution of HCl?

If the lines $ax + by + c = 0$ and $lx + my + n = 0$ are perpendicular, then which of the following is true?

A particle executes simple harmonic motion with an amplitude $A$. At what displacement from the mean position is its kinetic energy equal to its potential energy?

What is the standard electrode potential for the reaction $Zn^{2+}(aq) + 2e^- \rightarrow Zn(s)$ if the standard Gibbs free energy change ($\Delta G^\circ$) is -147 kJ/mol?

The value of $\lim_{x \to 0} \frac{e^x - (1 + x)}{x^2}$ is:

A particle of mass $m$ is moving in a circular path of radius $R$ with angular velocity $\omega$. It collides perfectly inelastically with another particle of the same mass $m$ initially at rest at the end of the diameter. The new angular velocity of the system will be:

One mole of an ideal monoatomic gas undergoes a reversible adiabatic expansion from an initial volume $V_1$ to a final volume $V_2 = 8V_1$. If the initial temperature is $T_1$, then the change in internal energy is:

The de Broglie wavelength of an electron accelerated from rest by a potential difference of $V$ volts is:

The rate constant for a first-order reaction is $k = 2.303 \times 10^{-3} s^{-1}$. The time required for 75% completion of the reaction is:

The pH of a buffer solution containing 0.1 M $CH_3COOH$ and 0.2 M $CH_3COONa$ is ($pK_a$ of $CH_3COOH$ = 4.74):

The number of geometrical isomers possible for the complex $[Co(en)_2Cl_2]^+$ is:

If $f(x) = \begin{cases} x^2 \sin(\frac{1}{x}), & x eq 0 \\ 0, & x = 0 \end{cases}$, then $f'(0)$ is:

The value of $\int_{0}^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx$ is:

The area of the region bounded by the curves $y = x^2$ and $y = |x|$ is:

If the vectors $\vec{a} = 2\hat{i} - \hat{j} + \hat{k}$, $\vec{b} = \hat{i} + 2\hat{j} - 3\hat{k}$, and $\vec{c} = 3\hat{i} + \lambda \hat{j} + 5\hat{k}$ are coplanar, then the value of $\lambda$ is: