A die is thrown twice. The probability of occurrence of 5 at least once is:

If \(A=\left[a_{i j}\right]\) is a square matrix of order 2 such that, \(a_{i j}=\left\{\begin{array}{ll}2, & \text { when } i \neq j \\ 0, & \text { when } i=j\end{array}\right.\), then \(\operatorname{det}\left(A^2\right)\) is:

The function \(f(x)=\frac{x}{2}+\frac{2}{x}, x \neq 0\) is increasing on :
(A) \((-\infty,-2)\)
(B) \((-2,2)\)
(C) \((2, \infty)\)
(D) \((-1,1)\)
Choose the correct answer from the options given below :

Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag is selected at random and then a ball is drawn from it. The probability that the ball drawn is black is :

The straight line \(\frac{x+3}{3}=\frac{y+2}{4}=\frac{z+1}{0}\) is

The constraints of the given shaded feasible region below of an L.P.P., for non-negative variable constraints \(x\) and \(y\) are

If \(\vec{a}, \vec{b}\) and \(\sqrt{3} \vec{a}+\vec{b}\) are unit vectors, then the angle between \(\vec{a}\) and \(\vec{b}\) is:

If \(A = [a_{ij}]\) be a square matrix of order n, then the correct statements are:
A. A is a symmetric matrix if and only if \(A^T = A\).
B. A is a skew-symmetric matrix if and only if \(A^T = -A\).
C. If order of A is n x n, then order of \(A^T\) is m \(\times\) n (m\(\neq\)n).
D. If \(\begin{bmatrix} 1 & 2 \\ 3 & 2x \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ 3 & 2x \end{bmatrix}\) then x = 4.
Choose the correct answer from the options given below.

The value of \(\left|\begin{array}{lll}1 & b & c+a \\ 1 & c & a+b\end{array}\right|\) is

Which of the following statements related to Wheatstone Bridge are correct?
(A).The bridge is most sensitive when all the four resistances are of the same order
(B). The internal resistance of the cell and the resistance of the galvanometer affect the null point
(C). It does not involve measurement of current and potential difference
(D).Resistances of ammeters and voltmeters do not affect the measurements
Choose the correct answer from the options given below:

A random variable X has the following probability distribution :

X	0	1	2	3	4	5	6	7	8
P(X)	a	3a	5a	7a	9a	11a	13a	15a	17a

Then the values of ' \(a\) ' and \(P(0<X<5)\) respectively are :

Which of the following statements are correct?
(A) The electrostatic repulsive force between the protons can be greater than the nuclear force to bind the nucleons together inside a nucleus.
(B) The repulsive electrostatic force between protons in smaller nuclei is much smaller than the nuclear force between nucleons inside a nucleus.
(C) The gravitational force between nucleons is much smaller than the nuclear force between the nucleons inside a nucleus.
(D) The binding energy per nucleon between nucleons is almost constant because the nuclear force is a long range force.
Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
The coordination compounds are of great importance. These compounds are widely present in the mineral, plants and animal world and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine. For example, coordination compounds find use in many qualitative and quantitative chemical analysis. Some important metal extraction and purification make use of complex formation. Hardness of water can be estimated by stable complex formation of Ca\(^{2+}\) and Mg\(^{2+}\)
From which coordination complex, gold is recovered by reducing this complex with Zn ?