A point charge of 17.7 \( \mu\text{C} \) is placed at a perpendicular distance of 5 cm from the centre of a square. The amount of electric flux going through the square will be: (Given \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2\text{N}^{-1}\text{m}^{-2} \))

In an ac circuit, a coil of self-inductance L is connected in series with an electric bulb of resistance R. If the frequency of ac supply increases, then

A battery of emf 3 V and internal resistance r is connected in series with a resistor of \( 55 \text{ } \Omega \). An ammeter of resistance \( 2 \text{ } \Omega \) connected in circuit reads 50 mA. The value of r is

Read the following statements carefully:
(A) The average power in an inductor over one complete cycle is zero.
(B) Self-inductance plays the role of inertia.
(C) Mutual inductance of a pair of coils depends on their separation as well as their relative orientation.
(D) The capacitive reactance increases with increase in frequency of applied a. c.
Choose the correct answer from the options given below :

Identify the correct statement(s) among the following:
(A) If three electrical cells each of emf, E and internal resistance r are connected in series to a resistance R, the current drawn from them is 3E/(R+3r).
(B) If these three cells are connected in parallel combination, across resistance R then the current drawn will be E/(3R+r).
(C) If the two cells are connected in series and then one in parallel which are then connected across resistance R, then the current drawn will be 2E/(2R+2r).
(D) In a mixed grouping of cells, current will be maximum when total external resistance is equal to total equivalent internal resistance.
Choose the correct answer from the options given below :

Match List - I with List - II.

List 1	List 2
(A) Infra red waves	(I) to detect fracture of bones
(B) Radio waves	(II) absorbed by the ozone layer of atmosphere
(C) X-rays	(III) to treat muscular pain
(D) Ultraviolet rays	(IV) for broadcasting

Choose the correct answer from the options given below :

Which of the following is not correct for an ac circuit ?

If the matrix \(\left[\begin{array}{ccc}x-y & 1 & -2 \\ 2 x-y & 0 & 3 \\ 2 & -3 & 0\end{array}\right]\) is skew-symmetric, then the values of \(x\) and \(y\) are respectively:

A long solenoid carrying a current produces a magnetic field B along its axis. If the value of current is halved and the number of turns per unit length is doubled then the new value of magnetic field is:

The refractive index of the material of an equilateral prism is \(\sqrt {2}\). The angle of minimum deviation of that prism is

Two antennas A and B have maximum line of sight range R = 45.5 km. If the height of antenna A is 32 m then the height of antenna B is : (Given radius of earth is = 6400 km)

In the species-area relationship equation, log S = log C + Z log A, 'Z' denotes -

In a linear programming problem (LPP), the maximum value of the objective function \(Z=2 x+5 y\) subjected to the constraints :
\(\begin{array}{l}2 x+3 y \leq 6 \\2 x+y \leq 4 \\x, y \geq 0\end{array}\)
is