Which of the following statement is/are correct?
(A) A square matrix \(A=\left[a_{i j}\right]\) is called a symmetric matrix if \(a_{i j}=a_{j i}\) for all \(i, j\).
(B) \(A=\left[a_{i j}\right]_{m \times m}\) is a diagonal matrix if \(a_{i j}=0\) when \(i=j\).
(C) A square matrix \(A=\left[a_{i j}\right]\) is called a skew symmetric matrix if \(a_{i j}=-a_{j i}\) for all \(i, j\).
(D) The multiplication of diagonal matrices of same order is commutative.
Choose the correct answer from the options given below :

The area bounded by the curve y = 3 cos x and the x-axis between x = 0 and \(x=2 \pi\) is:

If A is a square matrix of order 3 and |A| = 5, then | adj A| is:

The value of the integral \(I=\int \frac{(\log x)^3}{x} d x\) is :

In reference to the Inferential Statistics, which of the following is NOT correct?

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	k	2k	3k

If \(k>0\), then \(P(0 < X \leq 2)\) is equal to

Maximize \(z=2 x-y\)
Subject to constraints
\(x+y \leq 4, \quad x+3 y \leq 6, \quad x \geq 0, \quad y \geq 0 .\)
The corner points of the feasible region are:

A money lender charges Rs 10 for Rs 100 per month in advance then effective rate of interest per annum charged by money lender is : \(\left[\right.\) given \(\left.\left(\frac{10}{9}\right)^{12}=3.541\right]\)

Read the passage and answer the question : There are thousands of varieties of rice in India alone. The diversity of rice in India is one of the richest in the world. Basmati rice is distinct for its unique aroma and flavour and 27 documented varieties of Basmati are grown in India. There is reference to Basmati in ancient texts, folklore and poetry, as it has been grown for centuries. Several attempts have also been made to patent uses, products and processes based on Indian traditional herbal medicine, e.g. turmeric, neem. There has been growing realisation of the injustice, inadequate compensation and benefit sharing between developed and developing countries. The Indian Parliament has recently cleared a Bill that takes such issues into consideration, including patent terms emergency provisions and research and development initiative.
How many varieties of rice India has?

If \(|\vec{a}|=a\), then the value of \(|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2\) is :

If the sequence of one strand of DNA is written as: 5'-ATCGTGCTATGAGCATGC-3'.
The sequence of its complementary strands will be?

Which of the following statements are correct for dilute solutions?
(A) The elevation in boiling point is directly proportional to the molality of the solution.
(B) The elevation in boiling point is inversely proportional to the molality of the solution.
(C) The depression in freezing point is directly proportional to the molality of the solution.
(D) The depression in freezing point is inversely proportional to the molality of the solution.
Choose the correct answer from the options given below:

Photoelectric current depends on
(A) the intensity of incident light
(B) the potential difference applied between the two electrodes
(C) the nature of the emitter material
(D) the conductivity of the emitter material
Choose the correct answer from the options given below: