A series LCR circuit with \(R = 20\ \Omega\), \(L = 1.6\text{ H}\) and \(C = 40\ \mu\text{F}\) is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _______ \(\Omega\).

A projectile is given an initial velocity of \((\hat i + 2\hat j)\ ms^{-1}\), where \(\hat i\) is along the ground and \(\hat j\) is along the vertical. If \(g = 10\ m/s^2\) , the equation of its trajectory is

To increase the resonant frequency in series \(LCR\) circuit,

The plot given below is of the average power delivered to an \(LRC\) circuit versus frequency. The quality factor of the circuit is

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is \(7 \times 10^8 \mathrm{~V} / \mathrm{s}\) then the integer value of the distance between the parallel plates is \(\left(\right.\) Take, \(\left.\epsilon_0=9 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}, \pi=\frac{22}{7}\right)\) ________ \(\mu \mathrm{m}\).

Equation of travelling wave on a stretched string of linear density \(5\,g/m\) is \(y = 0.03\,sin\,(450\,t -9x)\) where distance and time are measured in \(SI\) united. The tension in the string is ... \(N\)

Identify the logic operation performed by the given circuit.

A prism of refractive index \(n_{1}\) and another prism of refractive index \(n_{2}\) are stuck together (as shown in the figure). \(n_{1}\) and \(n_{2}\) depend on \(\lambda\), the wavelength of light, according to the relation \({n}_{1}=1.2+\frac{10.8 \times 10^{-14}}{\lambda^{2}} \text { and } {n}_{2}=1.45+\frac{1.8 \times 10^{-14}}{\lambda^{2}}\) The wavelength for which rays incident at any angle on the interface \(B C\) pass through without bending at that interface will be \(....\,nm.\)

The temperature dependence of resistances of \(Cu\) and undoped \(Si\) in the temperature range \(300-400\;K\), is best described by

\(200\,g\) water is heated from \(40\,^oC\) to \(60\,^oC.\) Ignoring the slight expansion of water, the change in its internal energy is close to ...... \(kJ\) (Given specific heat of water \(=4184\,J/kgK\) )

To find the focal length of a convex mirror, a student records the following data

Object Pin	Convex Lens	Convex Mirror	Image Pin
\(22.2\,cm\)	\(32.2\,cm\)	\(45.8\,cm\)	\(71.2\,cm\)

The focal length of the convex lens is \(f_1\)  and that of mirror is \(f_2\). Then taking index correction to be negligibly small, \(f_1\)  and  \(f_2\) are close to

A compressive force, \(F\) is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by \(\Delta T\). The net change in its length is zero. Let \(l\) be the length of the rod, \(A\) its area of cross- section, \(Y\) its Young's modulus, and \(\alpha \) its coefficient of linear expansion. Then, \(F\) is equal to