A projectile is thrown upward at an angle \( 60^{\circ} \) with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is \( 45^{\circ} \) with the horizontal. The initial speed of the projectile is __________ in m/s.

A student determined Young's Modulus of elasticity using the formula \(Y=\frac{M g L^{3}}{4 b d^{3} \delta} .\) The value of \(g\) is taken to be \(9.8 \,{m} / {s}^{2}\), without any significant error, his observation are as following.

Physical Quantity	Least count of the Equipment used for measurement	Observed value
Mass \(({M})\)	\(1\; {g}\)	\(2\; {kg}\)
Length of bar \((L)\)	\(1\; {mm}\)	\(1 \;{m}\)
Breadth of bar \((b)\)	\(0.1\; {mm}\)	\(4\; {cm}\)
Thickness of bar \((d)\)	\(0.01\; {mm}\)	\(0.4 \;{cm}\)
Depression \((\delta)\)	\(0.01\; {mm}\)	\(5 \;{mm}\)

Then the fractional error in the measurement of \({Y}\) is

In photo electric effect \(A.\) The photocurrent is proportional to the intensity of the incident radiation. \(B.\) Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light. \(C.\) Max. \(K.E\) with which photoelectrons are emitted depends on the frequency of incident light. \(D.\) The emission of photoelectrons require a minimum threshold intensity of incident radiation. \(E.\) Max. K.E of the photoelectrons is independent of the frequency of the incident light. Choose the correct answer from the options given below:

A thin half ring of radius \(35\) cm is uniformly charged with a total charge of \(Q\) coulomb. If the magnitude of the electric field at centre of the half ring is \(100\) V/m, then the value of \(Q\) is _______ nC. (\(\epsilon_o = 8.85 \times 10^{-12}\) C\(^2\)/Nm\(^2\) and \(\pi = 3.14\))

Eight mercury drops, each of radius \(r\), coalesce to form a bigger drop. The surface energy released in this process is _______. (\(S\) is the surface tension of mercury).

A vertical closed cylinder is separated into two parts by a frictionless piston of mass \(m\) and of negligible thickness. The piston is free to move along the length of the cylinder .The length of the cylinder above the piston is \(l_1,\) and that below the piston is \(l_2,\) such that \(l_1 > l_2.\) Each part of the cylinder contains \(n\) moles of an ideal gas at equal temperature \(T.\) If the piston is stationary, its mass, \(m,\) will be given by: ( \(R\) is universal gas constant and \(g\) is the acceleration due to gravity)

From the \(v\) - \(t\) graph shown. the ratio of distance to displacement in \(25\,s\) of motion

The parameter that remains the same for molecules of all gases at a given temperature is _______.

The initial speed of a bullet fired from a rifle is \(630\, m/s\). The rifle is fired at the centre of a target \(700\, m\) away at the same level as the target. How far above the center of the target (in \(m\)) the rifle must be aimed in order to hit the target? (Take \(g=10 \;m/s^2\))

A particle of mass \(20\,g\) is released with an initial velocity \(5\,m/s\) along the curve from the point \(A,\) as shown in the figure. The point \(A\) is at height \(h\) from point \(B.\) The particle slides along the frictionless surface. When the particle reaches point \(B,\) its angular momentum about \(O\) will be ......... \(kg - m^2/s\). [Take \(g = 10\,m/s^2\) ]