Two resistance 60.36 W and 30.09 W are
connected in par al lel. The equiv a lent
resistance is

If a refrigerator of coefficient of performance of 5 has a freezer at a temperature of \(-13^{\circ} \mathrm{C}\), then the room temperature is

A block of metal 4 kg is in rest on a frictionless surface. It was targeted by a jet releasing water of \(2 \mathrm{~kg} \mathrm{~s}^{-1}\) at a speed of \(10 \mathrm{~ms}^{-1}\). The acceleration of the block is

A Carnot's engine has an efficiency of \(25 \%\) when its sink is at \(27^{\circ} \mathrm{C}\). If it has to be increased to \(40 \%\), what should be the temperature of the sink keeping the temperature of the source constant?

The machine gun fires 240 bullets per minute. If the mass of each bullet is \(10 \mathrm{~g}\) and the velocity of the bullets is \(600 \mathrm{~ms}^{-1}\), the power (in kW) of the gun is

Three charged particles of each mass \(0.1 \mathrm{~g}\) and charge ' \(\mathrm{q}\) ' are suspended from a common rigid point by insulated massless threads of each \(1 \mathrm{~m}\) long. If the three particles are in equilibrium and are located at the corners of an equilateral triangle of side \(3 \mathrm{~cm}\), the charge ' \(q\) ' on each particle is ____ \(\mathrm{nC}\). (The angle made by the line joining the centroid of the triangle and the point of suspension with the vertical is very small).
(Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) and \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}\) )

Beats are produced by frequencies \(v_1\) and \(v_2\left(v_1>v_2\right)\). The duration of time between two successive minima is

The following series \(L-C-R\) circuit, when driven by an emf source of angular frequency 70 kilo-radians per second, the circuit effectively behaves like

\[
\int\left(\sec ^4 x+\tan ^4 x\right) d x=
\]

The molality of solution, when \(18 \mathrm{~g}\) of glucose is added to the \(18 \mathrm{~g}_{\text {of } \mathrm{H}_2 \mathrm{O} \text { is }}\)

A toy car of mass \(100 \mathrm{~g}\) is moving with velocity of \((\hat{i}+2 \hat{j}-3 \hat{k}) m\), then the kinetic energy of the car is

Which of the following is correct?

A carrier wave of peak voltage \(60 \mathrm{~V}\) is used to transmit a message signal. Then the peak voltage of the modulating signal in order to have a modulation index of \(90 \%\) is