If \(X\) is a random variable and \(a, b\) are real numbers, then which of the following statements are correct?
(A) \(E[a X+b]=a E(X)+b\)
(B) \(\operatorname{Var}(a X+b)=a^2 \operatorname{Var}(X)+b\)
(C) \(\operatorname{Var}(a X+b)=a \operatorname{Var}(X)\)
(D) \(\operatorname{Var}(X)=E\left(X^2\right)-[E(X)]^2\)
Choose the correct answer from the options given below:

Let A be any skew-symmetric matrix (where \(A^T\) is Transpose of matrix A ), then which of the following statements are correct?
(A) \(A^2\) is a symmetric matrix
(B) \(A^2\) is a skew-symmetric matrix
(C) \(A^T A=-A^2\)
(D) \(A^T A-A A^T=O\)
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If \(A =\left(\begin{array}{cc}-a & b \\ c & a\end{array}\right)\) and \(A ^2= I\), where \(I\) is an Identity matrix of order 2, then which of the following is correct?

\(\int \tan ^{-1} \sqrt{x} d x\) equals to : (Here \(C\) is an arbitrary constant)

The probability distribution of a random variable X is given by

X	0	1	2
P(X)	\(1-7 a^2\)	\(\frac{1}{2} a+\frac{1}{4}\)	\(a^2\)

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

Which of the following is true?

The area bounded by the curve \(y=2 x-x^2\) and the straight line \(y=-x\) is :

Phytophagous insects feed on :

Paleontological evidence for evolution refers to.

Let \(F(z)\) be the cumulative density function of the standard normal variate \(Z\), then which of the following are correct?
(A) \(F(z)=\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^z e^{-t^2 / 2} d t,-\infty<Z<\infty\)
(B) \(F(-Z)=1-F(Z)\)
(C) \(F(0)=0\)
(D) \(F(\infty)=1\)
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Answer the question on basis of passage given below
The noble gases have closed shell electronic configuration and are monatomic gases under normal conditions. The low boiling points of lighter noble gases are due to the weak dispersion forces between the atoms and the absence of other inter atomic interaction. The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers \(+2, +4\) and \(+6\).
\(\text{XeF}_4\) reacts violently with water to give \(\text{XeO}_3\). The compound of Xenon exhibit stereoisomerism and their geometries can be deduced considering the total number of electrons in the valence shell.
Which noble gas is generally used in illuminating warning signals?

Two infinitely long parallel conductors carrying currents \(I_1\) and \(I_2\) are at distance d apart. The force F on length L of one conductor due to the other is :

Identify the statements relevant to Genetically Modified (GM) crops:
A. They have better pest resistance.
B. They have increased nutritional value.
C. They are more reliant on chemical fertilisers.
D. They have less post harvest losses.
Choose the correct answer from the options given below: