Which of the following statements are correct about the "Central Limit Theorem"?
(A) The sampling distribution of the sample mean approaches the normal distribution as the sample size gets larger.
(B) A sample size of 30 or more is considered to be sufficient to hold the "Central Limit Theorem".
(C) As the sample size becomes larger, the prediction of characteristics of the population becomes more accurate.
(D) The sampling distribution of the sample mean approaches bell shaped curveas the sample size gets larger.
Choose the correct answer from the options given below :

The side of an equilateral triangle is increasing at the rate of \(3 cm / sec\).
The rate at which the area of the triangle is increasing, when the side is 4 cm , is:

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

If the matrix \(A=\left[\begin{array}{cc}2-x & 3 \\ 2 & 1-x\end{array}\right]\) is singular, then value(s) of \(x\) are :

If \(A\) and \(B\) are matrices of same order, then ( \(A B^{ T }-B A^{ T }\) ) is always:

Let the degree and order of the differential equation \(2 x^3 \frac{d y}{d x}-5\left(\frac{d^2 y}{d x^2}\right)^2=6\left(\frac{d y}{d x}\right)^3\) be \(m\) and \(n\) respectively. Then
(A) \(m=2\)
(B) \(n=3\)
(C) \(m=3\)
(D) \(m n=4\)

The solution set of the inequality \(\frac{2 x+3}{x-1}<0\) is:

The product, when an alcoholic solution of sucrose is boiled with dilute hydrochloric acid or sulphuric acid is/are

Aqueous \(CuSO _4\) solution gives green precipitate of \(( X )\) with aqueous KF.
Correct formula of X is:

A nematode, Meloidogyne incognitia infects the roots of _______ and causes a great reduction in yield.

Read the following passage carefully and answer the given questions.
Cancerous cells just continue to divide giving rise to masses of cells called tumors. Benign tumors normally remain confined to their original location and do not spread to other parts of the body and cause little damage. The malignant tumors, on the other hand are a mass of proliferating cells called neoplastic or tumor cells. Transformation of normal cells into cancerous neoplastic cells may be induced by physical, chemical or biological agents. Ionising radiations like X-rays and gamma rays and non-ionizing radiations like UV cause cancer. Cancer-causing viruses are called oncogenic viruses which have viral oncogenes. The substances to which an immune response is produced are called allergens. The antibodies produced to these are of IgE type. Common examples of allergens are mites in dust, pollens, animal dander, etc. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells.
The primary lymphoid organs are:

If \(x_1, x_2, x_3,\)........,\(x_n\) are \(n\) observations in a sample then which of following is/are TRUE?
(A) The mean \(\bar{x}\) has \(n\) degree of freedom
(B) The mean \(\bar{x}\) has ( \(n-1\) ) degree of freedom
(C) The standard deviation of the sample has ( \(n-1\) ) degree of freedom
(D) The standard deviation of the sample has \(n\) degree of freedom
Choose the correct answer from the options given below :

Two similar coils of radius R are lying concentrically with their planes perpendicular to each other and carrying current I and 2I respectively. What is the resultant magnetic field at the center?