An ideal gas initially at \(0^{\circ} \mathrm{C}\) temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is \(3 / 2\), the change in temperature due to the thermodynamic process is _____ K.

A uniform disc with mass \(M=4\,kg\) and radius \(R=\) \(10\,cm\) is mounted on a fixed horizontal axle as shown in figure. A block with mass \(m =2\,kg\) hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is_______ \(N\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)

Consider two physical quantities A and B related to each other as \(E=\frac{B-x^2}{A t}\) where \(E, x\) and \(t\) have dimensions of energy, length and time respectively. The dimension of \(A B\) is _______.

In a series LCR circuit, a resistor of \(300 \Omega\), a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ \(\times 10^4\) radians \(\mathrm{s}^{-1}\).

In the given figure of meter bridge experiment, the balancing length \(AC\) corresponding to null deflection of the galvanometer is \(40\,cm\). The balancing length, if the radius of the wire \(AB\) is doubled, will be \(....cm\)

The ratio of mass densities of nuclei of \(^{40}Ca\) and \(^{16}O\) is close to

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 person lives in a high-rise building on the bank of a river \(50\, m\) wide. Across the river is a well lit tower of height \(40\, m\). When the person, who is at a height of \(10\, m\), looks through a polarizer at an appropriate angle at light of the tower reflecting from the river surface, he notes that intensity of light coming from distance \(X\) from his building is the least and this corresponds to the light coming from light bulbs at height \('Y'\) on the tower. The values of \(X\) and \(Y\) are respectively close to (refractive index of water \(  \simeq  \frac{4}{3})\)

For the circuit shown below, calculate the value of \({I}_{{z}}\) : (In \({mA}\))