A clock has \(75 \mathrm{~cm}, 60 \mathrm{~cm}\) long second hand and minute hand respectively. In \(30\) minutes duration the tip of second hand will travel \(x\) distance more than the tip of minute hand. The value of \(x\) in meter is nearly _______. (Take \(\pi=3.14\) )

Two conductors have the same resistances at \(0^{\circ} \mathrm{C}\) but their temperature coefficients of resistance are \(\alpha_1\) and \(\alpha_2\). The respective temperature coefficients for their series and parallel combinations are _______.

A \(220 \; V , 50 \; Hz\) AC source is connected to a \(25 \; V\), \(5 \; W\) lamp and an additional resistance \(R\) in series (as shown in figure) to run the lamp at its peak brightness, then the value of \(R\) (in ohm) will be

A diatomic gas \((\gamma=1.4)\) does 100 J of work when it is expanded isobarically. Then the heat given to the gas _________ J.

Consider a n-type semiconductor in which \(\mathrm{n}_{\mathrm{e}}\) and \(\mathrm{n}_{\mathrm{h}}\) are number of electrons and holes, respectively.
(A) Holes are minority carriers
(B) The dopant is a pentavalent atom
(C) \(\mathrm{n}_{\mathrm{e}} \mathrm{n}_{\mathrm{h}} \neq \mathrm{n}_{\mathrm{i}}^2\)
(where \(n_i\) is number of electrons or holes in semiconductor when it is intrinsic form)
(D) \(\mathrm{n}_{\mathrm{e}} \mathrm{n}_{\mathrm{h}} \geq \mathrm{n}_{\mathrm{i}}^2\)
(E) The holes are not generated due to the donors Choose the correct answer from the options given below :

Consider a badminton racket with length scales as shown in the figure.If the mass of the linear and circular portions of the badminton racket are same \((M)\) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, \(\frac{r}{2}\) distance from the end \(A\) of the handle will be ....... \(Mr^2\)?

Moment of inertia about an axis \(AB\) for a rod of mass \(40\) kg and length \(3\) m is same as that of a solid sphere of mass of \(10\) kg and radius \(R\) about an axis parallel to \(AB\) axis with separation of \(3\) m as shown in figure below. The value of \(R\) is given as \(\sqrt{\dfrac{\alpha}{2}}\). The value of \(\alpha\) is _______.

A thin prism \(P_1\) with an angle \(6^{\circ}\) and made of glass of refractive index \(1.54\) is combined with another prism \(P _2\) made from glass of refractive index \(1.72\) to produce dispersion without average deviation. The angle of prism \(P_2\) is \(........{}^{\circ}\)

A body falling under gravity covers two points \(A\) and \(B\) separated by \(80 \mathrm{~m}\) in \(2 \mathrm{~s}\). The distance of upper point A from the starting point is________ \(\mathrm{m}\) (use \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now ..... \(f\)

Two metallic blocks \(M_{1}\) and \(M_{2}\) of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of \(M _{2}\) is \(K\) then the thermal conductivity of \(M _{1}\) will be ]...............\(K\) [Assume steady state heat conduction]