If A is any \(m \times n\) matrix and B is a matrix such that AB and BA are both defined, then B is a matrix of order :

If \(x=-4\) is a root of \(\left|\begin{array}{lll}x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x\end{array}\right|=0\) , then the sum of the other two roots is

The region represented by the system of inequalities \(x, y \geq 0 ;-2 x+y \leq 4 ; x+y \geq 3\) and \(x-2 y \leq 2\) is

Given that the value of a determinant of order three is zero; which one of the following is not correct?

A couple has 3 children each child is equally likely to be a boy or a girl. The probability that the eldest child is a girl glven that they have atleast one boy is :

The equation of the tangent, to the curve \(y=x^2-2 x-3\) which is perpendicular to the line x + 2y + 3 = 0, is:

The probability distribution of number of aces when two cards are drawn without replacement from a pack of 52 cards is:

Let \(A=\left[\begin{array}{ccc}2 & -1 & 3 \\ 1 & 2 & -1 \\ 4 & 1 & 2\end{array}\right]\). \(M_{i j}\) and \(A_{i j}\) respectively denote the minor and cofactor of an element \(a_{i j}\) of matrix \(A=\left[a_{i j}\right]\).
(A) \(M_{23}=6\)
(B) \(A_{22}=-8\)
(C) \(A_{13}=7\)
(D) \(M_{32}=-5\)
Choose the correct answer from the options given below:

Methyl bromide reacts with silver nitrite to form :

The kinetic energy of an electron in the ground state of hydrogen atom is \(1 3 . 6 ~ e V\). The potential energy (P.E) and total energy ( E ) of electron in this state is :

\(A\) and \(B\) are two independent events. The probability that both events \(A\) and \(B\) occur is \(\frac{1}{6}\) and the probability that neither of them occur is \(\frac{1}{3}\). If \(P(A)=x, P(B)=y\) then the value of \(x+y\) is.

Read the passage carefully and answer the Questions
Alcohols and phenols are obtained when a hydrogen atom in aliphatic and aromatic hydrocarbons respectively, is replaced by \(OH\) group. These compounds find wide applications in industry as well as in our daily life. You may notice that ordinary spirit is used for polishing wooden furniture which is chiefly a compound containing hydroxyl group. An alcohol contains one or more hydroxyl \((OH)\) group(s) directly attached to carbon atom(s), of an aliphatic system \((CH_3OH)\) while a phenol contains \(OH\) group(s) directly attached to carbon atom(s) of an aromatic system \((C_6H_5OH)\). Alcohols are prepared by the hydration of alkenes, fermentation of glucose, and reduction of carbonyl compounds. Alcohols produce alkenes upon dehydration whereas alkenes on acid catalyzed hydration convert into alcohols.
An alkyl halide can be converted into alcohol through:

A doctor is to visit a patient.
The probabilities that he comes by train, bus, scooter or other means are
\(\frac{3}{10}, \frac{1}{5}, \frac{1}{10}\) and \(\frac{2}{5}\) respectively.
The probabilities that he will be late are
\(\frac{1}{4}\) if he comes by train,
\(\frac{1}{3}\) if he comes by bus,
\(\frac{1}{12}\) if he comes by scooter.
If he comes by other means of transport, he will not be late.
When he arrives, he arrives late.
The probability that he comes by bus is: