A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be

The disintegration rate of a certain radioactive sample at any instant is \(4250\) disintegrations per minute.\(10\) minutes later, the rate becomes \(2250\) disintegrations per minute. The approximate decay cons \(.........\min^{-1}\)

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are :- \(A.\) Real \(B.\) Erect \(C.\) Smaller in size then object \(D.\) Laterally inverted Choose the most appropriate answer from the options given below :

One plano-convex and one plano-concave lens of same radius of curvature \(‘R’\) but of different materials are joined side by side as shown in the figure. If the refractive index of the material of \(1\) is \(\mu_1\) and that of \(2\) is \(\mu _2\), then the focal length of the combination is

A charged particle (mass \(m\) and charge \(q\) ) moves along \(X\) axis with velocity \(V _{0}\). When it passes through the origin it enters a region having uniform electric field \(\overrightarrow{ E }=- E \hat{ j }\) which extends upto \(x = d\). Equation of path of electron in the region \(x > d\) is 

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights \(h_{sph}\) and \(h_{cyl}\) on the incline. The radio \(\frac{{{h_{sph}}}}{{{h_{cyl}}}}\) is given by

A player kicks a football with an initial speed of \(25\, {ms}^{-1}\) at an angle of \(45^{\circ}\) from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g \(=10 \,{ms}^{-2}\) )

An inductor of \(0.5\,mH\), a capacitor of \(20\,\mu\,F\) and resistance of \(20\,\Omega\) are connected in series with a \(220\,V\) ac source. If the current is in phase with the emf, the amplitude of current of the circuit is \(\sqrt{x} A\). The value of \(x\) is -

The mass of a hydrogen molecule is \(3.32 \times 10^{-27 } \) \(kg\). If \(10^{23}\) hydrogen molecules strike, per second, a fixed wall of area \(2\) \(cm^2\) at an angle of \(45^o \) to the normal, and rebound elastically with a speed of \(10^3\ m/s\), then the pressure on the wall is nearly:

The pressure \(( P )\) and temperature \(( T )\) relationship of an ideal gas obeys the equation \(PT ^2=\) constant. The volume expansion coefficient of the gas will be:

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

This question has Statement \(- 1\) and Statement \(-2\). Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement \(1\) : The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.
Statement \(2\) : A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.