A block of mass \(m\) is kept on a platform which starts from rest with constant acceleration \(g/2\) upward, as shown in figure. Work done by normal reaction on block in time \(t\) is

As per the given figure, two blocks each of mass \(250\,g\) are connected to a spring of spring constant \(2\,Nm ^{-1}\). If both are given velocity \(V\) in opposite directions, then maximum elongation of the spring is:

A monoatomic gas of mass \(4.0\, u\) is kept in an insulated container. Container is moving with velocity \(30 \,m / s\). If container is suddenly stopped then change in temperature of the gas \(\left( R =\right.\) gas constant) is \(\frac{ x }{3 R } .\) Value of \(x\) is ..........

The velocity of a particle executing simple harmonic motion along \(x\)-axis is described as \(v^2 = 50 - x^2\), where \(x\) represents displacement. If the time period of motion is \(\dfrac{x}{7}\) s, the value of \(x\) is _____.

Consider a rectangular sheet of solid material of length \(\ell=9 \mathrm{~cm}\) and width \(\mathrm{d}=4 \mathrm{~cm}\). The coefficient of linear expansion is \(\alpha=3.1 \times 10^{-5} \mathrm{~K}^{-1}\) at room temperature and one atmospheric pressure. The mass of sheet \(\mathrm{m}=0.1 \mathrm{~kg}\) and the specific heat capacity \(\mathrm{C}_{\mathrm{v}}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}\). If the amount of heat supplied to the material is \(8.1 \times 10^2 \mathrm{~J}\) then change in area of the rectangular sheet is :-

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A :\) Photodiodes are preferably operated in reverse bias condition for light intensity measurement. Reason \(R\) : The current in the forward bias is more than the current in the reverse bias for a \(p - n\) junction diode. In the light of the above statement, choose the correct answer from the options given below :

A poly-atomic molecule ( \(C_V=3 R, C_P=4 R\), where \(R\) is gas constant) goes from phase space point \(\mathrm{A}\left(\mathrm{P}_{\mathrm{A}}=10^5 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{A}}=4 \times 10^{-6} \mathrm{~m}^3\right)\) to point \(\mathrm{B}\left(\mathrm{P}_{\mathrm{B}}=5 \times 10^4 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{B}}=6 \times 10^{-6} \mathrm{~m}^3\right)\) to point \(\mathrm{C}\left(\mathrm{P}_{\mathrm{C}}=10^4\right.\) \(\left.\mathrm{Pa}, \mathrm{V}_{\mathrm{C}}=8 \times 10^{-6} \mathrm{~m}^3\right)\). A to B is an adiabatic path and \(B\) to \(C\) is an isothermal path. The net heat absorbed per unit mole by the system is :

In the reported figure, two bodies \(A\) and \(B\) of masses \(200\, {g}\) and \(800\, {g}\) are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be \(.....\,{rad} / {s}\) when \({k}=20 \,{N} / {m} .\)

If \(15 \sin ^{4} \alpha+10 \cos ^{4} \alpha=6,\) for some \(\alpha \in R ,\) then the value of \(27 \sec ^{6} \alpha+8 \operatorname{cosec}^{6} \alpha\) is equal to ....... .

Heat energy of \(184\,kJ\) is given to ice of mass \(600\,g\) at \(-12^{\circ}\,C\), Specific heat of ice is \(2222.3\,J\,kg ^{-1^{\circ}}\,C ^{-1}\) and latent heat of ice in \(336\,kJ / kg ^{-1}\) \((A)\) Final temperature of system will be \(0^{\circ} C\). \((B)\) Final temperature of the system will be greater than \(0^{\circ} C\). \((C)\) The final system will have a mixture of ice and water in the ratio of \(5: 1\). \((D)\) The final system will have a mixture of ice and water in the ratio of \(1: 5\). \((E)\) The final system will have water only. Choose the correct answer from the options given below:

A \(200\,\Omega \) resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be .............. \(\Omega\)

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative \(z\)-axis and magnetic field is along the positive \(x\)-axis. Then the direction of propagation of electromagnetic wave is

An infinite number of point charges, each carrying \(1 \,\mu C\) charge, are placed along the y-axis at \(y=1\, m , 2\, m , 4 \,m , 8\, m \ldots \ldots \ldots \ldots \ldots\) The total force on a \(1 \,C\) point charge, placed at the origin, is \(x \times 10^{3}\, N\). The value of \(x\), to the nearest integer, is ......... [Take \(\left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \,Nm ^{2} / C ^{2}\right]\)