If order of matrix A is \(m \times p\) and order of matrix B is \(p \times n\), then what is the order of matrix AB ?

The variance of the number of heads in two tosses of a coin is :

Angle between tangents to the curve \(y=x^2-5 x+6\) at the points \((2,0)\) and \((3,0)\) is :

If \(\hat{i}, \hat{j}\) and \(\hat{k}\) are unit vectors along co-ordinates axes \(OX , OY\) and OZ respectively, then which of the following is/are true?
(A) \(\hat{i} \times \hat{i}=\overrightarrow{0}\)
(B) \(\hat{i} \times \hat{k}=\hat{j}\)
(C) \(i \cdot i=1\)
(D) \(\hat{ i } \cdot \hat{ j }=0\)
Choose the correct answer from the options given below:

The integrating factor of the differential equation \(\frac{d y}{d x}=x+x y\) is:

The solution set of the inequality \(2x + 3y < 4\) is :

The inverse of the matrix \(\left[\begin{array}{cc}5 & 11 \\ 1 & 2\end{array}\right]\) is:

Benzene ring in phenol is expected to give the characteristic substitution or replacement reactions i.e. halogenation, nitration, sulphonation, alkylation etc. In these reactions, the attacking reagent is electrophile. The phenolic group activates the ortho and para positions in the ring due to conjugation. Disubstitution reactions are quite fast as the electron density in the ring has increased considerably. Phenols do not respond to nucleophilic substitution reactions as it is influenced by phenolic group.
Victor Meyer test gives following observations. Match List I with List II:

List-I	List-II
A. Blood red colouration	I. Tertiary alcohol
B. Blue colouration	II. Phenols
C. Colourless solution	III. Primary alcohol
D. Violet colouration with \(\text{FeCl}_3\)	IV. Secondary alcohol

Choose the correct answer from the options given below:

Which of the following is NOT a sexually transmitted disease?

The vector equation of line passing through \((-1,3,-2)\) and perpendicular to the lines \(\frac{x+4}{1}=\frac{y}{2}=\frac{z-3}{3}\) and \(\frac{x+2}{-3}=\frac{y+5}{2}=\frac{z-6}{5}\) is

Which contrasting trait was not considered by Mendel in pea plant?

Match List I with List - II. -

List - I	List - II
(A) Leydig cells	(I) Human Chorionic Gonadotropin (hcg)
(B) Placenta	(II) Progesterone
(C) Corpus luteum	(III) Androgens
(D) Pituitary gland	(IV) Oxytocin

Choose the correct answer from the options given below :

Read the passage carefully and answer the questions
The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation r = k[A]^x[B]^y, where x and y are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is x + y. The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.
The role of a catalyst is to change