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Physics

Dimensions of universal gravitational constant \( (G) \) in terms of Planck’s constant \( (h) \), distance \( (L) \), mass \( (M) \) and time \( (T) \) are ________.

27.

A \( 0.5 \, \text{kg} \) mass is in contact against the inner wall of a cylindrical drum of radius \( 4 \, \text{m} \) rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is \( 5 \, \text{rad/s} \). The coefficient of friction between the drum’s inner wall surface and mass is _________. (Take \( g=10 \, \text{m/s}^{2} \))

28.

Two blocks of masses \( 2 \, \text{kg} \) and \( 1 \, \text{kg} \) respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in \( 2 \, \text{s} \) is _______ \( \text{m} \). (Take \( g=10 \, \text{m/s}^{2} \))

29.

A particle having charge \( 10^{-9}\, \text{C} \) moving in \( x\text{-}y \) plane in fields of \( 0.4\,\hat{\jmath}\, \text{N/C} \) and \( 4\times 10^{-3}\,\hat{k}\, \text{T} \) experiences a force of \( (4\hat{\imath}+2\hat{\jmath})\times 10^{-10}\, \text{N} \). The velocity of the particle at that instant is __________ \( \text{m/s} \).

30.

If \( X \) and \( Y \) are the inputs, the given circuit works as ________.

31.

If a body of mass \( 1 \, \text{kg} \) falls on the earth from infinity, it attains velocity \( (v) \) and kinetic energy \( (k) \) on reaching the surface of earth. The values of \( v \) and \( k \) respectively are _________.
(Take radius of earth to be \( 6400 \, \text{km} \) and \( g = 9.8 \, \text{m} / \text{s}^2 \) )

32.

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are \( 100 \) divisions in circular scale and pitch of screw gauge is \( 0.1 \, \text{mm} \). When diameter of a sphere is measured, the reading of main scale is \( 5 \, \text{mm} \) and \( 50^{\text{th}} \) division of circular scale coincides with the reference line of main scale. The diameter of sphere is ________ \( \text{mm} \).

33.

The surface tension of a soap bubble is \( 0.03 \, \text{N}/\text{m} \). The work done in increasing the diameter of bubble from \( 2 \, \text{cm} \) to \( 6 \, \text{cm} \) is \( \alpha \pi \times 10^{-4} \, \text{J} \). The value of \( \alpha \) is _________. (Take \( \pi = 3.14 \))

34.

A mixture of carbon dioxide and oxygen has volume \( 8310 \, \text{cm}^{3} \), temperature \( 300 \, \text{K} \), pressure \( 100 \, \text{kPa} \) and mass \( 13.2 \, \text{g} \). The number of moles of carbon dioxide and oxygen gases in the mixture respectively are ________.
(Assume both carbon dioxide and oxygen gases behave like ideal gases) \([ R = 8.31 \, \text{J}/(\text{mol}\cdot\text{K}) ]\)

35.

If an air bubble of diameter \( 2 \, \text{mm} \) rises steadily through a liquid of density \( 2000 \, \text{kg}/\text{m}^{3} \) at a rate of \( 0.5 \, \text{cm}/\text{s} \), then the coefficient of viscosity of liquid is ________ Poise. (Take \( g = 10 \, \text{m}/\text{s}^{2} \))

36.

A spherical ball of mass \( 2 \, \text{kg} \) falls from a height of \( 10 \, \text{m} \) and is brought to rest after penetrating \( 10 \, \text{cm} \) into sand. The average force exerted by sand on the ball is ________ \( \text{N} \). (Take \( g = 10 \, \text{m/s}^2 \))

37.

An electromagnetic wave travels in free space along the \( x \)-direction. At a particular point in space and time, \( \vec{B} = 2 \times 10^{-7} \, \hat{j} \, \text{T} \) is associated with this wave. The value of corresponding electric field \( \vec{E} \) at this point is ______ \( \text{V/m} \).

38.

Two resistors of \( 200\,\Omega \) and \( 400\,\Omega \) are connected in series with a battery of \( 100 \, \text{V} \). A bulb rated at \( 200 \, \text{V}, 100 \, \text{W} \) is connected across the \( 400\,\Omega \) resistance. The potential drop across the bulb is _______ \( \text{V} \).

39.

Two metal plates (A, B) are kept horizontally with separation of \( \left( \dfrac{12}{\pi} \right) \, \text{cm} \), with plate A on the top. An atomizer jet sprays oil (density \( 1.5 \, \text{g/cm}^3 \)) droplets of radius \( 1 \, \text{mm} \) horizontally. All oil droplets carry a charge \( 5 \, \text{nC} \). The potentials \( V_A \) and \( V_B \) are required on plates A and B respectively in order to ensure the droplets do not descend. The values of \( V_A \) and \( V_B \) are ______. (Neglect the air resistance to the droplets and take \( g = 10 \, \text{m/s}^2 \))

40.

Two point charges \( 8\,\mu\text{C} \) and \( -2\,\mu\text{C} \) are located at \( x = 2 \, \text{cm} \) and \( x = 4 \, \text{cm} \), respectively on the \( x \)-axis. The ratio of electric flux due to these charges through two spheres of radii \( 3 \, \text{cm} \) and \( 5 \, \text{cm} \) with their centers at the origin is ______.

41.

One side of an equilateral prism is painted by a transparent material of refractive index \( n_{2} \). The refractive index of prism is \( 1.6 \). The minimum value of \( n_{2} \) required for total internal reflection from painted face is ______.

42.

The figure given below shows an LCR series circuit with two switches \( S_1 \) and \( S_2 \). When switch \( S_1 \) is closed keeping \( S_2 \) open, the phase difference \( (\phi) \) between the current and source voltage is \( 30^\circ \) and phase difference is \( 60^\circ \) when \( S_2 \) is closed keeping \( S_1 \) open. The value of \( \left(3L_1 - L_2\right) \) is ________ \( \text{H} \\).

43.

A circular current loop of radius \( R \) is placed inside square loop of side length \( L \) \( (L \gg R) \) such that they are co-planar and their centers coincide. The permeability of free space is \( \mu_0 \). The mutual inductance between circular loop and square loop is ________.

44.

The binding energy per nucleon of \( ^{209}_{83}\mathrm{Bi} \) is ________ \( \text{MeV} \).
[Take \( m\!\left(^{209}_{83}\mathrm{Bi}\right) = 208.980388\,\text{u} \), \( m_p = 1.007825\,\text{u} \), \( m_n = 1.008665\,\text{u} \), \( 1\,\text{u} = 931\,\text{MeV}/c^{2} \)]

45.

The equation of motion of a particle is given by \( x = a \sin\!\left(50 t + \dfrac{\pi}{3}\right)\, \text{cm} \). The particle will come to rest at time \( t_1 \) and it will have zero acceleration at time \( t_2 \). The \( t_1 \) and \( t_2 \) respectively are ________.

46.

In a Young’s double slit experiment, the intensity at some point on the screen is found to be \( \dfrac{3}{4} \) times of the maximum of the interference pattern. The path difference between the interfering waves at this point is \( \dfrac{\pi}{x} \) where \( \lambda \) is wavelength of the incident light. The value of \( x \) is __________.

47.

Using Bohr’s model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2^nd and \( 4 \)th orbits of hydrogen atom __________.

48.

\( 5 \) moles of unknown gas is heated at constant volume from \( 10^{\circ}\text{C} \) to \( 20^{\circ}\text{C} \). The molar specific heat of this gas at constant pressure \( C_{p}=8\ \text{cal}/\text{mol}\cdot{}^{\circ}\text{C} \) and \( R=8.36\ \text{J}/\text{mol}\cdot{}^{\circ}\text{C} \). The change in the internal energy of the gas is ______ calorie.

49.

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at \( 30\ \text{cm} \) above the paper. If the radius of curvature of the lens is \( 60\ \text{cm} \) then the refractive index of the lens material is \( \frac{\alpha}{10} \). The value of \( \alpha \) is __________.

50.

Moment of inertia about an axis \( AB \) for a rod of mass \( 40\ \text{kg} \) and length \( 3\ \text{m} \) is same as that of a solid sphere of mass \( 10\ \text{kg} \) and radius \( R \) about an axis parallel to \( AB \) axis with separation of \( 3\ \text{m} \) as shown in figure below. The value of \( R \) is given as \( \sqrt{\frac{\alpha}{2}} \). The value of \( \alpha \) is __________.

JEE Main 2026 2nd April Evening Shift

Mathematics Physics Chemistry

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The equation of motion of a particle is given by \( x = a \sin\!\left(50 t + \dfrac{\pi}{3}\right)\, \text{cm} \). The particle will come to rest at time \( t_1 \) and it will have zero acceleration at time \( t_2 \). The \( t_1 \) and \( t_2 \) respectively are ________.

JEE MainsJEE AdvanceBITSATJEE Mains | PYQ

JEE Mains JEE Advance BITSAT
JEE Mains | PYQ