A particle is projected at an angle of \(30^{\circ}\) from horizontal at a speed of \(60 \mathrm{~m} / \mathrm{s}\). The height traversed by the particle in the first second is \(\mathrm{h}_0\) and height traversed in the last second, before it reaches the maximum height, is \(h_1\). The ratio \(h_0: h_1\) is _________
[Take, \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) ]

A closed organ pipe \(150 \mathrm{~cm}\) long gives \(7\) beats per second with an open organ pipe of length \(350 \mathrm{~cm}\), both vibrating in fundamental mode. The velocity of sound is_________ \(\mathrm{m} / \mathrm{s}\).

The angle of projection for a projectile to have same horizontal range and maximum height is _______.

Angular momentum of a single particle moving with constant speed along circular path:

Two capacitors \(C_1\) and \(C_2\) are charged to \(120\ V\) and \(200\ V\) respectively. It is found that connecting them together the potential on each one can be made zero. Then

Four point charges \(-q, +q, +q\) and \(-q\) are placed on \(y\) axis at \(y = -2d\), \(y = -d, y = +d\) and \(y = +2d\), respectively. The magnitude of the electric field \(E\) at a point on the \(x -\) axis at \(x = D\), with \(D > > d\), will vary as

The potential energy of a particle of mass \(4\,kg\) in motion along the \(x\)-axis is given by \(U =4(1-\cos 4 x )\,J\). The time period of the particle for small oscillation \((\sin \theta \simeq \theta)\) is \(\left(\frac{\pi}{ K }\right)\,s\). The value of \(K\) is .......

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(\mathrm{R}\) Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.
Reason \(\mathrm{R}\) : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below

Four closed surfaces and corresponding charge distributions are shown below Let the respective electric fluxes through the surfaces be \({\phi _1},{\phi _2},{\phi _3}\) and \({\phi _4}\) . Then

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

Four capacitor each of capacitance \(16 \mu \mathrm{~F}\) are connected as shown in the figure. The capacitance between points A and B is : ______ (in \(\mu \mathrm{F}\)).

A particle of mass \(2\, kg\) is moving such that at time \(t\), its position, in meter, is given by \(\overrightarrow r \left( t \right) = 5\hat i - 2{t^2}\hat j\) . The angular momentum of the particle at \(t\, = 2\, s\) about the origin in \(kg\, m^{-2}\, s^{-1}\) is