The electric potential due to an electric dipole depends on

The magnifying power of a telescope is 6 in normal adjustment. The distance between its two lenses is 35 cm. The focal lengths of objective and eye-piece are, respectively:

An electron (mass \(9 \times 10^{-31} \text{ kg}\) and charge \(1.6 \times 10^{-19} \text{ C}\)) moving with a speed of \(5.0 \times 10^7 \text{ m/s}\) enters a region of uniform magnetic field of strength 0.04 T which is perpendicular to its velocity. The radius of the circular path it follows is:

The main causes of energy loss in transformers are
1. Hysteresis loss
2. Flux leakage
3. Eddy current
4. Damping
Choose the correct answer from the options given below :

A circular loop of conducting wire is placed near a current carrying wire as shown in the figure. Both are in the same plane. If the current flowing through the wire is suddenly increased.

What will be the minimum length of antenna required to transmit a radio signal of frequency 10 MHz ?

The point charges \( 5 \times 10^{-11} \, \text{C} \) and \( -5 \times 10^{-11} \, \text{C} \) are placed along z-axis at z = 3 cm and z = -3 cm respectively. What will be the electric field intensity at a point (0, 4)

There are four media in which light is traveling. The speed of light in each medium along with relative permeability of the medium are given as below. Arrange the relative permittivity of each of the medium in increasing order.
(A) Medium I: \( v_1 = 2 \times 10^8 \, \text{m/s}, \mu_r = 1 \)
(B) Medium II: \( v_{II} = 1.5 \times 10^8 \, \text{m/s}, \mu_r = 1 \)
(C) Medium III: \( v_{III} = 3 \times 10^8 \, \text{m/s}, \mu_r = 1 \)
(D) Medium IV: \( v_{IV} = 2 \times 10^8 \, \text{m/s}, \mu_r = 2 \)

Read the following passage carefully and answer the given questions.
During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. The BOD test measures the rate of uptake of oxygen by micro-organisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
Cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by -

Low concentration of oxygen in the blood and tissues of people living at high altitude is due to :

Which intra uterine contraceptive device is responsible for making the cervix hostile to sperms and uterus unsuitable for implantation?

The corner points of the bounded feasible region determined by the system of linear constraints are (0,10), (5, 5), (15, 15), (0, 20). Let \(z=p x+q y\) where \(p, q>0\). Then the condition on p and q so that the maximum value of z occurs at (15, 15) and (0, 20) is

For \(x \in[-2,2]\), let \(f(x)=x^2+2\).
A. \(f(x)\) is continuous in \([-2,2]\)
B. \(f(x)\) is differentiable in \((-2,2)\)
C. \(f(-2)=f(2)=6\)
D. \(f^{\prime}(1)=0\)
Choose the correct answer from the options given below: