In the wave equation \(y =0.5 \sin \frac{2 \pi}{\lambda}(400 t - x )\,m\)  the velocity of the wave will be ......... \(m / s\)

One main scale division of a vernier callipers is \(a\) \(cm\) and \(n ^{\text {th }}\) division of the vernier scale coincide with \(( n -1)^{\text {th }}\) division of the main scale. The least count of the callipers in \(mm\) is

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is \(30^{\circ}\) in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is _______ \(\mu \mathrm{m}\).

In \(LC\) circuit the inductance \(\mathrm{L}=40\; \mathrm{mH}\) and capacitance \(\mathrm{C}=100\; \mu \mathrm{F} .\) If a voltage \(\mathrm{V}(\mathrm{t})=10 \sin (314 \mathrm{t})\) is applied to the circuit, the current in the circuit is given as 

Four particles \(A, B, C\) and \(D\) with masses \(m_A=m, m_B=2m, m_C=3m\) and \(m_D=4m\) are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

A moving proton and electron have the same deBroglie wavelength. If \({K}\) and \({P}\) denote the \({KE}\). and momentum respectively. Then choose the correct option :

Photons of an electromagnetic radiation has an energy \(11\, keV\) each. To which region of electromagnetic spectrum does it belong ?

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature \(\mathrm{R}=2 \mathrm{~m}\). Another car approaches him from behind with a uniform speed of \(90 \mathrm{~km} / \mathrm{hr}\). When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of 100 a is _______ \(\mathrm{m} / \mathrm{s}^2\).

A body is dropped on ground from a height \(h_1\) and after hitting the ground, it rebounds to a height \(h _2\) If the ratio of velocities of the body just before and after hitting ground is \(4\), then percentage loss in kinetic energy of the body is \(\frac{x}{4}\). The value of \(x\) is \(.......\)

Two coaxial discs, having moments of inertia \(I_1\) and \(\frac{I_1}{2}\) are a rotating with respectively angular velocities \(\omega_1\) and \(\frac{\omega_1}{2}\), about their common axes. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If \(E_f\) and \(E_i\) are the final and initial total energies, then \((E_f -E_i)\) is

In an \(LCR \) circuit as shown below both switches are open initially. Now switch \(S_1\) is closed, \(S_2\) kept open. ( \(q\) is charge on the capacitor and \(\tau = RC\) is Capacitive time constant). Which of the following statement is correct?