What is the mean of the numbers obtained on throwing a die having written \(1\) on three faces, \(2\) on two faces and \(5\) on \(1\) face?

The value of \(\frac{3}{2}(\hat{i} \cdot \hat{i})+\frac{1}{2}(\hat{j} \cdot \hat{j})+\frac{|\hat{i} \times \hat{i}|}{(\hat{k} \cdot \hat{k})}+\frac{(\hat{k} \cdot \hat{i})}{|\hat{i} \times \hat{j}|}\) is:

The normal distribution curve is symmetrical about[ \(\mu=\) mean, \(\sigma=\) standard deviation]

The solution of the system of equations \(2 x+\frac{1}{2} y-z=1,2 y=3, x+2 z=4\) is :

\(\int\left(\frac{1+x+x^2}{1+x^2}\right) e^{\tan ^{-1} x} d x=\)

For the given five values 3.6, 4.3, 4.3, 3.4, 4.4, the three years moving averages are:

If \(x\) is real, the minimum value of \(f(x)=x^2-8 x+20\) is :

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.
Which one of the following technique is not useful for the detection of cancers of internal organs?

The region represented by the constraints \(x \geq 0, y \geq 0\) of an LPP is

Match List I with List II

LIST I	LIST II
A. Photodiode	I. junction area is kept much larger and biasing not required
B. Light emitting diode	II. used to detect intensity of radiation
C. Solar cell	III. Used as a voltage regulator
D. Zener diode	IV. emits spontaneous radiation under forward bias

Choose the correct answer from the options given below:

A circular loop of area \( A = 0.01 \text{ m}^2 \) carrying a current of \( I = 10 \text{ A} \), is held in a magnetic field of \( B = 0.1 \text{ T} \) parallel to the plane of the loop. The torque acting on the loop is-

The differential equation of the family of lines through the origin is:

Match List-l with List-II

List-I(Concentration term)	List-II(Formula)
(A) Mass percentage	(I) \(\frac{\text { Volume of solute }}{\text { Volume of solution }} \times 100\)
(B) Volume percentage	(II)\(\frac{\text {Moles of a component}}{\text {Total moles of all the components } \mathrm{}}\)
(C) Mole Fraction	(III) \(\frac{\text { Moles of solute }}{\text { Mass of solvent in } \mathrm{kg}}\)
(D) Molality	(IV) \(\frac{\text { Mass of solute }}{\text { Volume of solution × Density of solution }} \times 100\)

Choose the correct answer from the options given below: