If a straight conductor of length 0.5 m is moved with a speed of \( 6 \text{ m s}^{-1} \) perpendicular to direction of a magnetic field of \( 1 \text{ Wb m}^{-2} \), the emf induced is :

Choose the correct phase relationship between the current and the applied voltage in an a.c. circuit.
(A) In a pure resistive circuit, the current is in phase with the applied voltage.
(B) In a pure inductive circuit, the current lags behind the voltage by a phase angle of 90°.
(C) In a pure inductive circuit, the current leads the voltage by a phase angle of 90°.
(D) In a pure resistive circuit, the current is not in phase with the applied voltage.
Choose the correct answer from the options given below:

An armature coil consists of 20 turns of wire, each of area \( A = 0.09 \text{ m}^2 \) and total resistance \( 15 \ \Omega \).
It rotates in a magnetic field of 0.5 T perpendicular to the axis of rotation at a constant frequency \( \frac{150}{\pi} \text{ Hz} \). The value of maximum emf produced in the coil is:

A parallel plate capacitor made of circular plates each of radius 10.0 cm has a capacitance 200 pF . The capacitor is connected to a 200 V ac supply with an angular frequency of \(200 rad / s\). The amplitude of the current is :

Match List-I with List-II (Symbols have their usual meanings)

List-I (Physical Quantity)	List-II (Expression)
(A) Current density	(I) \( \frac{e E \tau}{m} \)
(B) Drift velocity	(II) \( \frac{n e^2 \tau}{m} \)
(C) Conductivity	(III) \( \frac{e \tau}{m} \)
(D) Mobility	(IV) \( n e v_d \)

Choose the correct answer from the options given below:

What will be the energy required to remove the electron from the first excited state of \( Li^{++} \), if the ground state energy of the electron in a hydrogen atom is -13.6 eV?

A parallel plate capacitor filled with oil of dielectric constant \( k = 3 \), has a capacitance \( C \). After removing the oil between the plates, the capacitance of the capacitor will become:

If \(A\) is a square matrix and \(|A|=4\), then the value of \(\left|A A^{\prime}\right|\) where \(A^{\prime}\) is transpose of \(A\) is:

Study the following figure and answer the questions:


In the figure correct labelling of \(A , B , C\) and D is:

The broadly utilitarian argument says that -

A small piece of metal wire is dragged in the region of magnetic flux \( 8 \times 10^{-4} \, \text{Wb} \) in 0.5 s. The length of the wire is perpendicular to the magnetic field. The emf induced in the wire would be:

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.
Maturation of lymphocytes takes place in:

Consider the LPP: Minimize \(Z=x+2 y\) subject to \(2 x+y \geq 3, x+2 y \geq 6, x, y \geq 0\). The optimal feasible solution occurs at: