Two parallel long wires carry currents, \( i_1 \) and \( i_2 \) with \( i_1 > i_2 \). When the currents are in same direction, the magnetic field at a point midway between them is \( 10 \mu \text{T} \). If the direction of \( i_2 \) is reversed, the field becomes \( 30 \mu \text{T} \). The ratio of \( i_1/i_2 \) is:

In an LCR circuit, which of the following expression has the dimension of frequency :

The current through a 4/3 \(\Omega\) external resistance connected to a parallel combination of two cells with emfs of 2 V and 1 V, internal resistances 1 \(\Omega\) and 2 \(\Omega\) respectively, is :

Choose the incorrect statements from the following:
(A) The energy density of an electric field in electromagnetic waves is \( (\epsilon_0 E^2/2) \).
(B) The total energy of electromagnetic waves falling on a surface is \( E = 6.0 \times 10^5 \text{ J} \) and the momentum delivered to the surface, if absorbed fully, is \( p = 2 \times 10^3 \text{ kg m/s} \).
(C) The speed of the electromagnetic waves is \( E_0 / B_0 \).
(D) The energy density of magnetic field in electromagnetic Waves is \( (B^2 / \mu) \).
Choose the correct answer from the options given below:

An electric dipole consists of charges \( \pm 2 \times 10^{-6} \, \text{C} \), separated by a distance of 2 mm. It is placed on the right side near a long line charge of density \( 4 \times 10^{-4} \, \text{C m}^{-1} \). The negative charge of dipole is at a distance of 2 cm from the line charge as shown in figure. A positive charge (+2q) is placed on the left at 2 cm at point C. Given \( q = 2 \times 10^{-8} \, \text{C} \).

(A) Force \( |F_A| \) exerted on negative charge at point A due to line charge
(B) Force \( |F_B| \) exerted on positive charge at point B due to line charge
(C) Net force on the dipole \( |F_{net}| \) due to line charge
(D) Force \( |F_C| \) exerted on charge +2q at point C due to line charge
If the forces \( |F_A|, |F_B|, |F_C|, |F_{net}| \) are arranged in decreasing order, then:
Choose the correct answer from the options given below:

Arrange the following EM waves in increasing order of their frequency ?
A. Ultraviolet rays
B. Gamma rays
C. Radio waves
D. Infrared waves
E. X-rays
Chose the correct answer from the options given below:

A copper wire of area of cross-section \( 2 \times 10^{-6} \, \text{m}^2 \) and electron density \( 10^{28} \, \text{m}^{-3} \) carries a current of 1.6 A. Time taken by an electron to drift from one end of a 1.0 m long wire to its other end will be

At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 40000 ?

If \(X\) is a random variable and \(a, b\) are real numbers, then which of the following statements are correct?
(A) \(E[a X+b]=a E(X)+b\)
(B) \(\operatorname{Var}(a X+b)=a^2 \operatorname{Var}(X)+b\)
(C) \(\operatorname{Var}(a X+b)=a \operatorname{Var}(X)\)
(D) \(\operatorname{Var}(X)=E\left(X^2\right)-[E(X)]^2\)
Choose the correct answer from the options given below:

Which of the following is true for the given reaction?
\(\text{CH}_3-(\text{CH}_3)_3\text{C-N-CH}_3 + \text{Cl-SO}_2-\text{C}_6\text{H}_5 \rightarrow \text{No Reaction}\)

The large holes in 'Swiss Cheese' are due to the production of a large amount of CO2 by a bacterium named as

In a meter bridge, the null point is found at a distance of 60 cm from end A. If a \( 5 \text{ } \Omega \) resistor is now connected in series with S, the null point occurs at 50 cm. The values of R and S are, respectively

For the curve xy = 6, the value of \(\frac{d^2 y}{d x^2}\) at y = 3 is: