Two ideal gases A and B of same number of moles expand at constant temperatures \(T_1\) and \(T_2\) respectively such that the pressure of gas A decreases by \(50 \%\) and the pressure of gas B decreases by \(75 \%\). If the work done by both the gases is same, then \(T_1: T_2\)

Which quantity among the following has neither units nor dimensions?

A \(4 \mu \mathrm{F}\) capacitor is charged by a \(200 \mathrm{~V}\) battery. It is then disconnected from the supply and is connected to another uncharged \(2 \mu \mathrm{F}\) capacitor. During the process, loss of energy (in \(\mathrm{J}\) ) is

A steel wire of length 81 cm has a mass of \(5 \times 10^{-3} \mathrm{~kg}\). If the wire is under a tension of 50 N, then the speed of transverse waves on the wire is

The value of acceleration due to gravity \(g\) is maximum at

Names of units of some physical quantities are given in List-I and their dimensions formulae are given in List-Il. Match the correct pairs in the lists
\(\begin{array}{ll|ll}
\hline & \text{ List-I } & \text{ List-II } \\
\hline A. & \mathrm{Pa}-\mathrm{s} & (i) & {\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline B. & \mathrm{NmK}^{-1} & (ii) & {\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right]} \\
\hline C. & \mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1} & (iii) & {\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]} \\
\hline D. & \mathrm{Wm}^{-1} \mathrm{~K}^{-1} & (iv) & {\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline
\end{array}\)
\(\begin{array}{llll}A & B & C & D\end{array}\)

The angular frequency of a block of mass 0.1 kg oscillating with the help of a spring of force constant \(2.5 \mathrm{Nm}^{-1}\) is

The correct statement regarding X and Y formed in the following reaction is
\(\left(\mathrm{CH}_3\right)_3 \mathrm{COC}_2 \mathrm{H}_5 \xrightarrow[\Delta]{\mathrm{HI}}\) halide \((\mathrm{X})+\operatorname{alcohol}(\mathrm{Y})\)

The area of the triangle formed by the line \(x+y=4\) and angular bisectors of the pair of lines \(x^2-y^2+2 y-1=0\) is......... sq. units.

The values of \(p\) and \(q\) so that the system of equations \(2 x+p y+6 z=8\), \(x+2 y+q z=5\) and \(x+y+3 z=4\) may have no solution are

The time taken for a calorimeter containing \(75 \mathrm{~g}\) of water at \(62^{\circ} \mathrm{C}\) to \(\mathrm{cool}\) to \(58^{\circ} \mathrm{C}\) is 9 minutes. When the calorimeter contains \(105 \mathrm{~g}\) of water, it takes 12 minutes to cool from \(62^{\circ} \mathrm{C}\) to \(58^{\circ} \mathrm{C}\). The water equivalent of the calorimeter is

The degree of the polynomial \(\left(x+\sqrt{x^4-1}\right)^9+\left(x-\sqrt{x^4-1}\right)^9\) is

The magnitude of maximum acceleration is \(\pi\) times that of maximum velocity of a simple harmonic oscillator. The time period of the oscillator in seconds is