Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is _______.

A body of mass \(2\, {kg}\) moving with a speed of \(4\, {m} / {s}\). makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is \(\frac{x}{10} \,{m} / {s}\). Then the value of \(x\) is ..... .

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should by unbinding the strings to achieve a speed of \(4\,ms ^{-1}\), is\(........cm\). \(\left(\right.\) take \(\left.g=10\,ms ^{-2}\right)\)

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is

Choose the correct relationship between Poisson ratio \((\sigma)\). bulk modulus \(( K )\) and modulus of rigidity \((\eta)\) of a given solid object:

The threshold wavelength for photoelectric emission from a material is \(5500\,\mathring A\). Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a \(A.\) \(75\,W\) infra-red lamp \(B.\) \(10\,W\) infra-red lamp \(C.\) \(75\,W\) ultra-violet lamp \(D.\) \(10\,W\) ultra-violet lamp Choose the correct answer from the options given below :

Match List-I with List-II.

List-I	List-II
A. \(\sin^2 \omega t\)	I. Periodic with time period \(T = \dfrac{\pi}{\omega}\) but not simple harmonic motion (SHM)
B. \(\sin^3(2\omega t)\)	II. Periodic with time period \(T = \dfrac{2\pi}{\omega}\) but Not SHM
C. \(\sin(\omega t) + \cos(\pi \omega t)\)	III. Periodic with time period \(T = \dfrac{\pi}{\omega}\) and SHM
D. \(\cos\omega t + \cos 2\omega t\)	IV. Non-periodic

Choose the correct answer from the options given below :

In Young's double slit arrangement, slits are separated by a gap of \(0.5\, mm ,\) and the screen is placed at a distance of \(0.5\, m\) from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of \(5890\, A^o\) is

Which one is the correct option for the two different thermodynamic processes ?

In a uniform magnetic field, the magnetic needle has a magnetic moment \(9.85 \times 10^{-2} \,{A} / {m}^{2}\) and moment of inertia \(5 \times 10^{-6} \,{kgm}^{2}\). If it performs \(10\) complete oscillations in \(5\, seconds\) then the magnitude of the magnetic field is \(....\,mT.\) [ Take \(\pi^{2}\) as \(9.85\) ]

At the centre of a fixed large circular coil of radius \(R\), a much smaller circular coil of radius \(r\) is placed. The two coils are concentric and are in the same plane. The larger coil carries a current \(I\). The smaller coil is set to rotate with a constant angular velocity \(\omega \) about an axis along their common diameter. Calculate the \(emf\) induced in the smaller coil after a time \(t\) of its start of rotation

A particle moving in a circle of radius \(R\) with uniform speed takes time \(\mathrm{T}\) to complete one revolution. If this particle is projected with the same speed at an angle \(\theta\) to the horizontal, the maximum height attained by it is equal to \(4 R\). The angle of projection \(\theta\) is then given by _______.

The frequency of oscillation of a mass \(m\) suspended by a spring is \(v_1\). If the length of the spring is cut to half, the same mass oscillates with frequency \(v_2\). The value of \(v_2/v_1\) is ________.