The value of \(k\) for which the function, defined by, \(f(x)=\left\{\begin{array}{ll}\frac{3 x+4 \tan x}{x} & : x \neq 0 \\ k & : x=0\end{array}\right.\) is continuous at \(x=0\), is

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

"The random variable \(X\) has a probability distribution \(P ( X )\) of the following form, where \(k\) is some number.
\(P(X=x)=\left\{\begin{array}{ll}k, & \text { if } x=0 \\2 k, & \text { if } x=1 \\3 k, & \text { if } x=2 \\0, & \text { otherwise }\end{array}\right.\)
Then \(P(x \leq 2)\) is :"

Which of the following statements are correct?
(A) If elements of a row (or column) of a determinant are multiplied with cofactors of any other row (or column), then their sum is zero.
(B) The value of determinant is equal to the sum of the product of elements of any row (or column) with their corresponding cofactors.
(C) If any two rows (or columns) of a determinant are interchanged, their sign of determinant does not change.
(D) The value of determinant remains unchanged if its rows and columns are interchanged.
(E) A square matrix A has inverse if and only if A is singular.
Choose the correct answer from the options given below:

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 :

The area of the region bounded by the curves \(x^2 = 4y\), the line \(x = 3\) and x axis is:

If \(\vec{a}\) and \(\vec{b}\) are unit vectors, then the angle between \(\vec{a}\) and \(\vec{b}\) for \(\vec{a}+\sqrt{3 b}\) to be a unit vector is given by :

\[\int e^x\left(1+x^2\right) d x=\]

Let \(x\) denote the number of heads in a simultaneous toss of three coins, then \(P(0 < x \leq 3)\)

What is an example of globular protein?
(A) Insulin
(B) Keratin
(C) Albumin
(D) Myosin
Choose the correct answer from the options given below :

The value of is \(\left|\begin{array}{cc}x^2-x+1 & x-1 \\ x+1 & x+1\end{array}\right|\) equal to

An electric dipole of dipole moment \(p\) is rotated in an electric field of magnitude \(E\) from the most stable orientation to most unstable orientation. The work done in the process is:

Match List - I with List - II.

List - I	List - II
(A) Transgenic mice	(I) Hereditary disease
(B) PCR	(II) Safety of Polio vaccine
(C) Golden rice	(III) Molecular Diagnosis
(D) Gene Therapy	(IV) Enhanced nutritional value

Choose the correct answer from the options given below: