A charge of \( Q = 8.0 \times 10^{-9} \text{ C} \) is uniformly distributed on the surface of a spherical shell of radius \( R = 10 \text{ cm} \). The electric field at a distance of 10 cm from the outer surface of the shell is

A plane electromagnetic wave of frequency 30 MHz travels in free space along the \( x \)-direction.
At a particular point in space and time, \( \vec{E} = 6.3\hat{j} \text{ V/m} \).
The magnetic field \( \vec{B} \) at this point would be:

Photo electric effect reveals the:

There are two thin parallel charged sheets having surface charge density \( \sigma \) placed at a small distance apart. Which of the following statements are correct?
(A) If both the sheets are positively charged, then the electric field between them is \( \sigma/\epsilon_0 \)
(B) If both the sheets are negatively charged, then the electric field between them is \( \sigma/\epsilon_0 \)
(C) If the left sheet is positively charged and the right sheet is negatively charged the field between them is \( \sigma/\epsilon_0 \)
(D) If the right sheet is positively charged and the left sheet is negatively charged then the field between them is \( \sigma/\epsilon_0 \)
Choose the correct answer from the options given below:

A parallel plate capacitor whose capacitance C is 13.0 pF is charged by a battery to a potential difference V = 13.0 V between its plates. What is the potential energy of the capacitor ?

Which of the following statement is correct for a potentiometer ?

A short bar magnet placed with its axis at 30\(^\circ\) with an external field of 800G, experiences a torque of 0.016 Nm. Work done in moving it from its most stable to most unstable position is :

For the given five values 18, 25, 20, 36, 49, the three years moving averages are

A uniformly charged sphere of \( 80 \text{ } \mu\text{C} \) and radius 2 cm is placed in air.
The electric field intensity at a point 20 cm from the center of the sphere is:

If \(A = \begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix}\) and \(I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\), then the value of k so that \(A^2 = 6A + kI\) is given by:

If the matrix \(A=\left[\begin{array}{ccc}0 & x+y & 1 \\ 3 & z & 2 \\ x-y & -2 & 0\end{array}\right]\) is skew-symmetric, then:

Transmission of HIV-Infection occurs by-
(A). Using infected needles by the health staff or by drug abusers
(B). Transfusion of contaminated blood and blood product
(C). Sexual contact with infected person
(D). Sharing food and sanitation facilities
Choose the correct answer from the options given below:

An alternating voltage \( V = V_0 \sin(\omega t + \pi/2) \) is applied across an ac circuit. As a result, a current \( I = I_0 \sin(\omega t + \pi/6) \) flows in it. The power factor of the circuit is