An air filled parallel plate capacitor has a uniform electric field 'E' in the space between the plates. If the distance between the plates is 'd' and area of each plate is ' \(A^{\prime}\), the energy stored in the capacitor is \(\left(\epsilon_{0}=\right.\) permittivity of free space)

The rotational kinetic energy and translational kinetic energy of a rolling body are same, the body is

A toroidal solenoid with air core has an average radius ' \(\mathrm{R}^{\prime}\), number of turns ' \(\mathrm{N}^{\prime}\) and
area of cross-section 'A'. The self-inductance of the solenoid is (Neglect the field variation across the cross-section of the toroid)

The inductive reactance of a coil is ' R ' \(\Omega\). If inductance of a coil is tripled and frequency of a.c supply is also tripled, then new inductive reactance will be

In the given capacitive network the resultant capacitance between point
\(\mathrm{A}\) and \(\mathrm{B}\) is

What is the magnifying power of a simple microscope of focal length \(5 \mathrm{~cm}\), if the
image is formed at the distance of distinct vision?

What is change in volume of an iron sphere of volume \(500 \mathrm{~cm}^3\), when it is heated from \(0^{\circ} \mathrm{C}\) to \(\left(\alpha_{\text {Iron }}=12 \times 10^{-6 /{ }^{\circ}} \mathrm{C}\right)\) ?

Bernoulli's equation is conservation of

Let \(\quad \overline{\mathrm{a}}=\alpha \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}, \quad \overline{\mathrm{b}}=3 \hat{\mathrm{i}}-\beta \hat{\mathrm{j}}+4 \hat{\mathrm{k}} \quad\) and \(\overline{\mathrm{c}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\), where \(\alpha, \beta \in \mathbb{R}\), be three vectors. If the projection at \(\overline{\mathrm{a}}\) on \(\overline{\mathrm{c}}\) is \(\frac{10}{3}\) and \(\overline{\mathrm{b}} \times \overline{\mathrm{c}}=-6 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}\), then the value of \(\alpha^2+\beta^2-\alpha \beta\) is equal to

Flippers of penguin and dolphins is an example of ________.

Calculate the work done in kJ when 3 moles of an ideal gas at \(27^{\circ} \mathrm{C}\) expand isothermally and reversibly from 10 atm . to \(1 \mathrm{~atm}\left[\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]\)

How many molecules of \(NADPH _2\) will be required for synthesis of 10 glucose molecules

A line is drawn through a fixed point \(P(\alpha, \beta)\) to cut the circle \(x^{2}+y^{2}=r^{2}\) at \(A\) and \(B\). Then
\(P A \cdot P B\) is equal to