A parallel combination of three resistors takes a current of 7.5 A from a 30 V battery.
If the resistances of two resistors are \( 12 \text{ } \Omega \) and \( 10 \text{ } \Omega \), then the resistance of the third resistor is:

A parallel plate capacitor of capacitance 2 \( \mu F \) has energy \( 10 \times 10^{-5} \, J \). The potential difference and the charge on the capacitor are:

The correct statement given below are :
(A) \(\chi = 1 + \mu_r\)
(B) \(\mu_r = 1 + \chi\)
(C) \(B = \mu_0(H + M)\)
(D) \(H = \frac{B_0}{\mu_0}\)
(E) \(B_0 = \mu_0 H\)
Here x = magnetic susceptibility
\(\mu_r\)= Relative magnetic permeability
B = Magnetic field
M = Magnetisation
H = Magnetic Intensity
\(\mu_0\)= Magnetic permeability
Choose the correct answer from the options given below:

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 convex lens of focal length 40 cm is placed in contact with a concave lens of focal length 20 cm. If an object is placed at 40 cm in front of the combination, the position of the image formed by the combination is

Identify the correct statements.
(A) The density of nuclear matter is independent of the size of the nucleus.
(B) Nuclear forces are charge independent and are non-central forces.
(C) The nuclides having the same mass number are called isotones.
(D) The mass of a nucleus can be less or more than the sum of the masses of nucleons present inside it.
Choose the correct answer from the options given below:

A current of \( 2 \times 10^{-5} \text{ A} \) produces 25 division deflection in a galvanometer. The resistance of the galvanometer coil is \( 4 \ \Omega \). The figure of merit of galvanometer is :

If A is a skew-symmetric matrix of order n, then

Choose the correct sequence for the increasing boiling point of the following compounds.
(A) Pentan-1-ol
(B) Butan-2-ol
(C) Ethanol
(D) Propan-1-ol
Choose the correct answer from the options given below:

Arrange the following steps for working of a full wave rectifier in correct sequence

(A) During the negative half cycle, \( D_1 \) is reverse biased while \( D_2 \) is forward biased.
(B) During the positive half cycle, \( D_1 \) is forward biased while \( D_2 \) is reverse biased.
(C) A pulsating d. c. voltage is obtained across \( R_L \).
(D) a. c. input is given to the primary of a centre-tap transformer.
Choose the correct answer from the options given below:

A photon has a momentum of \(3.3 \times 10^{-29} kg m / s\). The frequency of the waves associated with the photon will be (Given: \(h=6.6 \times 10^{-84} Js\) )

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:

If the radius of the spherical ball is increasing at the rate of 1 m/sec and the radius of the ball is 3 meter then the volume of the ball is increasing at the rate of