For the following probability distribution,

X	1	2	3	4
p(x)	\(\frac{1}{10}\)	\(\frac{1}{5}\)	\(\frac{3}{10}\)	\(\frac{2}{5}\)

The value of \(E\left(X^2\right)-[E(X)]^2\)

The derivative of \(\frac{\tan ^{-1} x}{1+\tan ^{-1} x}\) with respect to \(\tan ^{-1}\) is :

Match List - I with List - II.

LIST - I	LIST - II
(A) \((\hat{i} \times \hat{j})+(\hat{j} \times \hat{i})\)	(I) 1
(B) \(\hat{i} \cdot \hat{i}+\hat{j} \cdot \hat{j}+\hat{k} \cdot \hat{k}\)	(II) \(\hat{k}-\hat{j}\)
(C) \(\hat{i} \times(\hat{i}+\hat{j}+\hat{k})\)	(III) \(\overrightarrow{0}\)
(D) \(\hat{i} \cdot(\hat{i}+\hat{j}+\hat{k})\)	(IV) 3

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The area of the region given by \(\left\{(x, y): y \geq x^2, y \leq|x|+2\right\} \backslash-\backslash-\backslash-\backslash-\backslash-\) is

Kavya takes a personal loan of ₹ 10,00,000 at the rate of 12% per annum for 5 years, then the EMI by using flat rate method is:

Find the value of k making the following function continuous at x = 5
\(f(x)=\left\{\begin{array}{ll}2 k x-1, & x \geq 5 \\ 2 x+3, & x<5\end{array}\right.\)

Which of the following statements are true?
(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector \(3 \hat{i}+2 \hat{j}-8 \hat{k}\) is \(\vec{r}=(5 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(3 \hat{i}+2 \hat{j}-8 \hat{k})\)
(B) Vector form of the equation of line \(\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\) is \(\vec{r}=(5 \hat{i}-4 \hat{j}+6 \hat{k})+\lambda(3 \hat{i}+7 \hat{j}+2 \hat{k})\)
(C) The direction cosines of z-axis are (1, 1, 0).
(D) If a line has direction ratios 2, -1, -2, then its direction cosines are \(-2 / 3,-1 / 3,-2 / 3\).
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The corner points of the feasible region of a LPP are \(P(0, 5), Q(1, 5), R(4, 2)\) and \(S(12, 0)\).
The minimum value of the objective function \(Z = 2x + 5y\) is at the point:

The correct sequence for product formation according to the Collision theory of chemical reaction is
(A) Proper orientation
(B) Molecules collide with threshold energy
(C) Intermediate formation
(D) Formation of products
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The rate of formation of new organic matter by consumers in termed as:-

In hydrogen atom light corresponding to the transition \(n=4\) to \(n=2\) falls on cesium metal. The work function of the metal is 1.9 eV . What is the maximum kinetic energy of the photoelectrons emitted?

In the interval [-5, -3], the function f(x) = (x + 1)(x - 3) is:

Arrange the following compounds in the decreasing order of their reactivity towards Nucleophilic substitution reaction:
(A) Bromobenzene
(B) 4-Nitrobromobenzene
(C) 2,4,6-Trinitrobromobenzene
(D) 2,4-Dinitrobromobenzene
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