Two equal resistances when connected in series to a battery, consume electric power of \(60\,W.\) If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be .............. \(W\)

A uniform cable of mass \(‘M’\) and length \(‘L’\) is placed on a horizontal surface such that its \({\left( {\frac{1}{n}} \right)^{th}}\)  part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be

Expression for an electric field is given by \(\vec{E}=4000 x^2 \hat{i} \frac{V}{m}\). The electric flux through the cube of side \(20\,cm\) when placed in electric field (as shown in the figure) is \(.........V cm\).

A \(0.4\,kg\) mass takes \(8 s\) to reach ground when dropped from a certain height ' \(P\) ' above surface of earth. The loss of potential energy in the last second of fall is \(..............J\). [Take \(g =10\,m / s ^2\) ]

A massless spring gets elongated by amount \(x_1\) under a tension of 5 N . Its elongation is \(x_2\) under the tension of 7 N . For the elongation of \(\left(5 x_1-2 x_2\right)\), the tension in the spring will be,

Two very long, straight and insulated wires are kept at \(90^o\) angle from each other In \(xy -\) plane as shown in the figure. These wires carry current of equal magnitude \(I\), whose directions are shown in the figure. The net magnetic field at point \(P\) will be

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion A : The nuclear density of nuclides \({ }_5^{10} B ,{ }_3^6 Li ,{ }_{26}^{56} Fe ,{ }_{10}^{20} Ne\) and \({ }_{83}^{209} Bi\) can be arranged as \(\rho_{ Bi }^{ N }>\rho_{ Fe }^{ N }>\rho_{ Ne }^{ N }>\rho_{ B }^{ N }>\rho_{ Li }^{ N }\). Reason \(R\) : The radius \(R\) of nucleus is related to its mass number \(A\) as \(R=R_0 A^{1 / 3}\), where \(R_0\) is a constant. In the light of the above statement, choose the correct answer from the options given below :

A coaxial cable consists of an inner wire of radius \('a'\) surrounded by an outer shell of inner and outer radii ' \({b}\) ' and '\(c\)' respectively. The inner wire carries an electric current is, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance \({x}\) from the axis when \((i)\) \({x}<{a}\) and \((ii)\) \({a}<{x}<{b}\) ?

A body of mass \(0.5\, kg\) travels on straight line path with velocity \(v =\left(3 x ^{2}+4\right) m / s\). The net workdone by the force during its displacement from \(x =0\) to \(x =2\, m\) is\(.......J\)

At \(40\,^oC\), a brass wire of \(1\, mm\) is hung from the ceiling. A small mass, \(M\) is hung from the free end of the wire. When the wire is cooled down from \(40\,^oC\) to \(20\,^oC\) it regains its original length of \(0.2\, m\). The value of \(M\) is close to ........\(kg\) (Coefficient of linear expansion and Young's modulus of brass are \(10^{-5}/^oC\) and \(10^{11}\, N/m^2\), respectively; \(g = 10\, ms^{-2}\))

Two planets \(A\) and \(B\) having masses \(m_1\) and \(m_2\) move around the sun in circular orbits of \(r_1\) and \(r_2\) radii respectively. If angular momentum of \(\mathrm{A}\) is \(\mathrm{L}\) and that of \(B\) is \(3L\), the ratio of time period \(\left(\frac{T_A}{T_B}\right)\) is _______.

A block of mass \(200\, g\) is kept stationary on a smooth inclined plane by applying a minimum horizontal force \(F =\sqrt{ x }N\) as shown in figure. The value of \(x =.....\)