A coil is placed in a magnetic field \(\overrightarrow{{B}}\) as shown below: A current is induced in the coil because \(\overrightarrow{{B}}\) is:

For a periodic motion represented by the equation \(Y=\sin \omega t+\cos \omega t\) The amplitude of the motion is 

A \(60\; HP\) electric motor lifts an elevator having a maximum total load capacity of \(2000\; \mathrm{kg}\). If the frictional force on the elevator is \(4000 \;\mathrm{N}\). the speed of the elevator at full load is close to ..............  \(\mathrm{m} / \mathrm{s}\) \(\left(1 \;\mathrm{HP}=746 \;\mathrm{W}, \mathrm{g}=10\; \mathrm{ms}^{-2}\right)\)

A bullet of mass \(200\,g\) having initial kinetic energy \(90\,J\) is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to \(40\,J\) within 1s, the minimum length of the pool, the bullet has a to travel so that it completely comes to rest is \(.....m\)

In the circuit shown, current (in \(A\)) through \(50\; V\) and \(30\; V\) batteries are, respectively

Which statements are correct about degrees of freedom? \(A.\) \(A\) molecule with \(n\) degrees of freedom has \(n^{2}\) different ways of storing energy. \(B.\) Each degree of freedom is associated with \(\frac{1}{2} RT\) average energy per mole. \(C.\) \(A\) monoatomic gas molecule has \(1\) rotational degree of freedom where as diatomic molecule has \(2\) rotational degrees of freedom \(D\) \(CH _{4}\) has a total to \(6\) degrees of freedom Choose the correct answer from the option given below:

A solid metallic cube having total surface area \(24\;m ^{2}\) is uniformly heated. If its temperature is increased by \(10\,^{\circ} C\), calculate the increase in volume of the cube \(\left(\right.\) Given \(\left.: \alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)\)

A particle executes simple harmonic motion represented by displacement function as \(x(t)=A \sin (\omega t+\phi)\) If the position and velocity of the particle at \(t=0\, {s}\) are \(2\, {cm}\) and \(2\, \omega \,{cm} \,{s}^{-1}\) respectively, then its amplitude is \(x \sqrt{2} \,{cm}\) where the value of \(x\) is ..... .

A Carnot engine operating between two reservoirs has efficiency \(\frac{1}{3}\). When the temperature of cold reservoir raised by \(x\), its efficiency decreases to \(\frac{1}{6}\). The value of \(x\), if the temperature of hot reservoir is \(99^{\circ}\,C\), will be \(........\,K\)

The electric current through a wire varies with time as \(I=I_0+\beta t\). where \(I_0=20 \mathrm{~A}\) and \(\beta=3 \mathrm{~A} / \mathrm{s}\). The amount of electric charge crossed through a section of the wire in \(20 \mathrm{~s}\) is :

The resultant of these forces \(\overrightarrow{O P}, \overrightarrow{O Q}, \overrightarrow{O R}, \overrightarrow{O S}\) and \(\overrightarrow{{OT}}\) is approximately \(\ldots \ldots {N}\). [Take \(\sqrt{3}=1.7, \sqrt{2}=1.4\) Given \(\hat{{i}}\) and \(\hat{{j}}\) unit vectors along \({x}, {y}\) axis \(]\)