List of top Questions asked in JEE Main, KCET

For `C' molar solution of weak electrolyte \( A_xB_y \), dissociation constant is \( K \), then degree of dissociation of \( A_xB_y \) at equilibrium is

Column-I (Isothermal process)

For a certain decomposition
\[ X_2 Y_4 (g) \rightleftharpoons 2 XY_2 (g) \] Degree of dissociation of \( X_2 Y_4 \) is 75% at 1 bar and 600K. Find \( \Delta G^\circ \) of reaction in kJ/mol\(^{-1}\).

A block of mass 1 kg moving with velocity varies according to position as \( v = 2x^2 \). If the block goes from \( x = 0 \) to \( x = 5 \), find the work done by the block.

Which of the following is correct outputs for inputs (1, 1) and (0, 1)?

A cylindrical container has radius 40 cm and volume 528 \((\text{dm}^3)\). It is placed on a table of same height as of container. A hole is made 70 cm below from the free surface. Find range of efflux on ground if the container is filled completely.

Two particles of the same masses moving initially with velocity \( 4 \hat{i} \) and \( 4 \hat{j} \) m/s respectively.
Acceleration of the first particle is \( 6 \hat{i} + 6 \hat{j} \) and of the second is zero. Find the path of the center of mass of the system.

For a concave mirror of focal length 10cm, magnification is 2 for two positions of an object. Find the distance between these two positions (in cm).

2 moles of monoatomic ideal gas has temperature \(T\) and 6 moles of monoatomic ideal gas has temperature \(2T\). Find the temperature of mixture.

If error in diameter of a sphere is 2%, then find error in volume of the sphere.

An EM wave has angular frequency \( \omega \).
Propagation constant \( \mathbf{k} \) and electric field vector \( \mathbf{E} \) is given, then \( \mathbf{B} \) can be represented by:

When a mass of 200 gm hangs from the ceiling via spring in equilibrium, the extension in the spring is observed to be 2mm. Find angular frequency of its SHM and energy stored in equilibrium position respectively.

A weight \( W \) is connected to one end of a wire and the other end is fixed, length of wire is 1m. Area of cross-section is \( 10^{-5} \, \text{m}^2 \). Graph between change in length and weight is shown. Then calculate Young's modulus.

In YDSE, intensity of both coherent sources are \(I_0\). Separation between the two slits is 5 cm and screen is placed at a distance of 50 cm from the slit. Wavelength of light is 6000 \(\text{Å}\). If intensity for a point on the screen is \(I_0\), then find the path difference at point P.

On an incline plane of angle \(45^\circ\), time taken by an object is \(t\) if it is smooth and \(2t\) if it is rough. Find value of \(\alpha\) if friction coefficient is \(\frac{\alpha}{100}\).

Figure shows an adiabatic container which is divided into two equal parts by an adiabatic freely moving piston. Both sides contain same gas having \( \gamma = 1.5 \). If heat is supplied to left part such that its pressure becomes \( \frac{27P_0}{8} \), find volume of right part.

Consider two spheres A (solid sphere) and B (hollow sphere) each of radius \(R\), kept on a perfectly rough surface. Mass of sphere A is 5 m and that of B is 2 m. If the same force \(F\) is applied at the top tangentially, then find the ratio of acceleration of A to acceleration of B.

C = 100 pF, V = 100 V (given spherical capacitor).
Identical capacitor is touched with this capacitor. If change in total energy is α × 10^-7 J then find α = ?
(Combined capacitance = 200 pF)

Find magnetic field at mid point between two parallel infinite wires carrying current of 30 Amp as shown in the figure.

A square loop of side 2 cm makes angle 60° with magnetic field \( \mathbf{B} = 0.4 \sin(300t) \, T \). Find maximum induced EMF (in mV) in loop.

If a 6 kg block is released from rest as shown in the figure, then find the velocity of the 6 kg block just before hitting the ground.

In the given circuit, current passing through \( R \) is 1 ampere. Now polarity of one cell is reversed, then current through \( R \) becomes \( \frac{\alpha}{5} \) Amp, then find \( \alpha \).

A charge particle when accelerated from rest by a potential difference \(V_1\) has a de-Broglie wavelength \(\lambda_1\), and when accelerated by a potential difference \(V_2\) has a de-Broglie wavelength \(\lambda_2\). If \(\lambda_2 = \frac{3\lambda_1}{2}\), find the ratio \(\frac{V_1}{V_2}\).

For the reaction find energy released ²₁H + ²₁H → ⁴₂He BE/A for \(^2_1H = 1.1 \, \text{MeV}\) and for \(^4_2He = 7.2 \, \text{MeV}\):

Match the following quantities with their dimensions.