A simple harmonic motion is represented by \(y\, = 5\,(\sin \,3\pi t\, + \,\sqrt 3 \,\cos \,3\pi t)\,cm\) The amplitude and time period of the motion are

A sphere of radius \('a'\) and mass \('m'\) rolls along a horizontal plane with constant speed \(v_{0}\). It encounters an inclined plane at angle \(\theta\) and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

Two waves of intensity ratio \(1: 9\) cross each other at a point. The resultant intensities at the point, when (a) Waves are incoherent is \(I_1\) (b) Waves are coherent is \(I_2\) and differ in phase by \(60^{\circ}\). If \(\frac{I_1}{I_2}=\frac{10}{x}\), then \(x=\) _______.

The ratio of momentum of the photons of the \(1^{st}\) and \(2^{nd}\) line of Balmer series of Hydrogen atoms is \(\alpha/\beta\). The possible values of \(\alpha\) and \(\beta\) are:-

Which of the following are true? \(A.\) Speed of light in vacuum is dependent on the direction of propagation. \(B.\) Speed of light in a medium in independent of the wavelength of light. \(C.\) The speed of light is independent of the motion of the source. \(D.\) The speed of light in a medium is independent of intensity. Choose the correct answer from the option given below :

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 torque meter is calibrated to reference standards of mass, length and time each with \(5 \%\) accuracy. After calibration, the measured torque with this torque meter will have net accuracy of\(............\%\)

The maximum rated power of the LED is \(2\) mW and it is used in the circuit with input voltage of \(5\) V as shown in the figure below. The current through resistance \(R_S\) is \(0.5\) mA. The minimum value of the resistance of \(R_S\), to ensure that the LED is not damaged is _______ k\(\Omega\).

The electric flux is \(\phi=\alpha \sigma+\beta \lambda\) where \(\lambda\) and \(\sigma\) are linear and surface charge density, respectively. \(\left(\frac{\alpha}{\beta}\right)\) represents

Nitrogen gas is at \(300^{\circ} C\) temperature. The temperature (in \(K\)) at which the \(rms\) speed of a \(H _{2}\), molecule would be equal to the \(rms\) speed of a nitrogen molecule, is........ (Molar mass of \(N _{2}\) gas \(28\, g\) )

A resonance circuit having inductance and resistance \(2 \times 10^{-4} H\) and \(6.28 \Omega\) respectively oscillates at \(10\, MHz\) frequency. The value of quality factor of this resonator is ......... \([\pi=3.14]\)

At room temperature a diatomic gas is found to have an \(r.m.s.\) speed of \(1930\,ms^{-1}\). The gas is