The integral \(\int \frac{x^4+2}{x^2+1} d x\) is equal to

During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20\%\) respectively. He has option to choose any of the two options with equal probabilities. If Amit choose yoga to reduce the chance of heart attack, then the chance of heart attack is:During lockdown, Amit was suffering from heart problem. After proper check-up it was deducted that he has \(45\%\) chance of having heart attack, but yoga and meditation assumed to reduce the chance of heart attack by \(25\%\) and \(20 \%\) respectively. He has option to choose any of the two options with equal probabilities.
If Amit choose yoga to reduce the chance of heart attack, then the chance of heart attack is:

The particular solution of the differential equation \(x d y=\left(2 x^2+1\right) d x, x \neq 0\), given that \(y=1\) when \(x=1\) is:

Match List-I with List-II

List-I	List-II
(A) \(\int \frac{d x}{x^2-16}\)	(I) \(\frac{1}{8} \log \left|\frac{4+x}{4-x}\right|+c\)
(B) \(\int \frac{d x}{x^2+16}\)	(II) \(\log \left|x+\sqrt{x^2-16}\right|+c\)
(C) \(\int \frac{d x}{16-x^2}\)	(III) \(\frac{1}{8} \log \left|\frac{x-4}{x+4}\right|+c\)
(D) \(\int \frac{d x}{\sqrt{x^2-16}}\)	(IV) \(\frac{1}{4} \tan ^{-1}\left(\frac{x}{4}\right)+c\)

Choose the Correct answer from the options given below :

The relation \(R\) in the set \(A=\{1,2,3\}\) given by \(R=\{(1,2),(2,1)\}\) is :

A solenoid with \(2 \times 10^4\) turns per meter, diameter 0.1 m , has a coil of 100 turns and 0.01 m radius placed inside. If solenoid current decreases from 4 A to 0 in 0.05 s , total charge through coil is :

For the objective function \(Z = 4x + 6y\) subject to the constraints
\(3x + 2y ≥ 5, 7x + 2y ≤ 9, x ≥ 0, y ≥ 0\),
the maximum value of Z occurs at (a, b)
and the minimum value of Z occurs at (p, q)
then the value of \(\frac{a}{p}+\frac{b}{q}\) is:

The Galvanic cells will behave like an electrolytic cell when

Cloning of alien DNA by the host involves -

RNA interference involves silencing of a specific mRNA due to complementarity of

In the middle of the depletion layer of a reverse biased p-n junction, the:

The order of reaction will be if the value of rate constant is \(7.195 \times 10-4\) \(mol ^{-3} L^3 s^{-1}\)

A ray is incident normally on the face of an equilateral prism of refracting angle \(60^{\circ}\).
The refractive index of the prism is \(\frac{2}{\sqrt{3}}\).
The angle of deviation will be: