The number of all possible matrices of order \(3 \times 4\) with each entry 1, 2 or 3 are:

The solution of the differential equation \(\frac{d y}{d x}-\frac{y}{x}=2 \log _e x\)

The maximum value of \((\sin x)(\cos x)\) is :

In a LPP:
If two corner points yield the same maximum value of the objective function of an LPP then :
(A) the LPP has unique solution
(B) the LPP has 2 solutions
(C) the LPP has 3 solutions
(D) the LPP has infinite many solutions
Choose the correct answer from the options given below :

A random variable X has the following probability distribution

X	0	1	2	3	4	5
P(X)	0.1	k	0.2	2k	0.3	k

Then \(P(X<3)\) is

If \(f(x)=3 x^2+10 x-5\), then by using differentials the appropriate value of \(f(2.03)\) is

The equation of a curve passing through the point \((-1,3)\), given that the slope of the tangent to the curve at any point \((x, y)\) is \(\frac{2 x}{y^2}\), is :

The correct statement (s) for cubic close packed (ccp) three dimensional structure are :
(A) The number of the neighbours of an atom present in the top most layer is 12.
(B) The efficiency of atom packing is \(74\%\).
(C) The number of octahedral and tetrahedral voids per atom are 1 & 2, respectively.
(D) The unit cell edge length is \(2\sqrt{2}\) times the radius of the atom.
(E) The metals like Be, Cd, Mg, Zn have cubic close packed (ccp) structure.
Choose the correct answer from the options given below :

For a substance at a given temperature, the osmotic pressure of its concentrated solution:

Read the following passage carefully and answer the given questions.
The B-lymphocytes produce an army of proteins in response to pathogens. Each antibody molecule has four peptide chains, two small called light chains and two longer called heavy chains. Virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Symptoms of allergic reactions include sneezing, watery eyes, running nose and difficulty in breathing. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Lymphoid organs are the organs where origin and/or maturation and proliferation of lymphocytes occur. The primary lymphoid organs are bone marrow and thymus. After maturation the lymphocytes migrate to secondary lymphoid organs like spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. Heroin commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine, which is extracted from the latex of poppy plant Papaver somniferum.
Heroin, commonly called smack and chemically is -

Match List-I with List-II

List-I (Materials)	List-II (Band Gap (eV))
(A) Germanium	(I) 1.42 eV
(B) Gallium Arsenide	(II) > 3 eV
(C) Insulator	(III) 1.1 eV
(D) Silicon	(IV) 0.7 eV

Choose the correct answer from the options given below :

Which of the following is a factor of the determinant \(\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|\)?

Which one of the following seeds is an example of non-albuminous seed?