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

Two circular coils of diameter 10 cm and 20 cm, carrying equal currents have the same number of turns. The ratio of magnetic fields produced at the center of coils, respectively will be

A uniform electric field exists in the positive x-direction. Let \( V_A = \) electric potential at (0, 0, 0) cm, \( V_B = \) electric potential at (5, 0, 0) cm and \( V_C = \) electric potential at (0, 5, 0) cm. The correct relationship between them is :

A slab of material of dielectric constant K has the same area as the plates of a parallel-plate capacitor but has a thickness \( \frac{1}{4}d \), where d is the separation between the plates. If the slab is inserted between the plates, the potential difference becomes:
(Given: Potential difference across the capacitor without dielectric is \( V_0 \))

Velocity of light in diamond, glass and water decreases in the following order :

Which of the following statements is correct about the effect of the presence of a third charge on Coulomb force between the two charges?

Identify the correct statement(s) among the following:
(A) The time taken by a light wave is \( 5 \times 10^{-9} \text{ s} \) to travel a thickness of 1 cm of glass having refractive index 1.5.
(B) Two similar waves of amplitude 3 mm and 5 mm reach a point in the same phase. The resultant amplitude will be 8 mm.
(C) Two waves of amplitude 2 mm each reach a point with a phase difference of \( \pi/2 \). The resultant amplitude is zero.
(D) If one of the slits is closed in Young's double slit experiment, the interference pattern will disappear.
Choose the correct answer from the options given below :

If \(D_1=\left|\begin{array}{ccc}\frac{1}{2} & \frac{1}{\sqrt{2}} & 0 \\ -\frac{1}{\sqrt{2}} & \frac{1}{2} & 0 \\ 0 & 0 & 1\end{array}\right|\) and \(D_2=\left|\begin{array}{ccc}\frac{1}{\sqrt{2}} & \frac{1}{2} & 0 \\ -\frac{1}{2} & \frac{1}{\sqrt{2}} & 0 \\ 0 & 0 & 1\end{array}\right|\), then \(D_1 D_2\) is equal to :

Arrange the following steps of sewage treatment in correct sequence:
A. Flocs consume organic matter and reduces the BOD.
B. Removal of floating debris and grit.
C. Bacterial flocs allowed to sediment.
D. Primary effluent passed into aeration tank and agitated mechanically.
E. Effluent after secondary treatment is released into water bodies.
Choose the correct answer from the options given below:

In Clemmensen reduction the carbonyl compound is treated with

Read the following passage carefully and answer the given questions.
Immune System in the Body
The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The primary lymphoid organs are bone marrow and thymus where immature lymphocytes differentiate into antigen-sensitive lymphocytes. After maturation the lymphocytes migrate to secondary lymphoid organs like spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells. The bone marrow is the main lymphoid organ where all blood cells including lymphocytes are produced. Each antibody molecule has four peptide chains, two small called light chains and two longer called heavy chains. Hence, an antibody is represented as H2L2. Different types of antibodies are produced in our body. IgA, IgM, IgE, IgG are some of them. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs.
Human immune system recognizes the viral proteins as:

Evaluate \(\int_1^{\sqrt{3}} \frac{1}{1+x^2} d x\)

The drift velocity of electrons in a copper wire of length 2 m under the application of a potential difference of 200 V is \( 0.5 \text{ ms}^{-1} \). The mobility of electrons in \( \text{m}^2\text{V}^{-1}\text{s}^{-1} \) is :