A discrete random variable \(X\) has the distribution \(B(15, p)\). Given that \(\operatorname{Var}(X)=3.15\). Then, the two possible values of \(p\) are

The general solution of the equation \(\frac{d y}{d x}+\frac{1}{x} y=\frac{1}{x} e^x\) is

If \(\tan \left(\frac{x}{2}\right)=\frac{m}{n}\), then the value of \(m\) \(\sin (x)+n \cos (x)\) is equal to

If $A+B+C=\pi ,\cos B=\cos A \cos C$, then $\tan A \tan C=$

The distance between the tangents of the hyperbola \(2 x^2-3 y^2=6\) which are perpendicular to the line \(x-2 y+5=0\) is

For \(A \neq 0, x < 0, \lim _{n \rightarrow \infty} \frac{\sin x-e^{n x}}{1+A e^{n x}}=\)

77. If \(5 f(x)+3 f\left(\frac{1}{x}\right)=2-\frac{1}{x}, x \neq 0\), then \(\int_1^2 f\left(\frac{1}{x}\right) d x=\)

\(X\) litre of carbon monoxide is present at STP. It is completely oxidized to \(\mathrm{CO}_2\). The volume of \(\mathrm{CO}_2\) formed is 11.207 litres. What is the value of \(X\) in litres?

Two towers \(A\) and \(B\), each of height \(20 \mathrm{~m}\) are situated a distance \(200 \mathrm{~m}\) apart. A body thrown horizontally from the top of the tower \(A\) with a velocity \(20 \mathrm{~ms}^{-1}\) towards the tower \(B\) hits the ground at point \(P\) and another body thrown horizontally from the top of tower \(B\) with a velocity \(30 \mathrm{~ms}^{-1}\) towards the tower \(A\) hits the ground at point \(Q\). If a car starting from rest from \(P\) reaches \(Q\) in 10 seconds, then the acceleration of the car is \(\left(\right.\) acceleration due to gravity \(\left.=10 \mathrm{~ms}^{-2}\right)\)

When photons of energy \(5 \mathrm{eV}\) incident on a photo metal of work function \(4.36 \mathrm{eV}\), photo electrons are emitted. The maximum impulse of the metal surface is

At \(1000 \mathrm{~K}\), if the equilibrium constant \(K_p\) for the reaction.
\(2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_2(g)\)
is \(4.157 \times 10^{-4}\) bar, the \(K_C\left(\right.\) in \(\mathrm{mol} \mathrm{L}^{-1}\) ) is \(\left(R=0.083 \mathrm{~L} \mathrm{bar} \mathrm{K}^{-1} \mathrm{~mol}^{-1}\right)\)

In a binomial distribution, the difference between the mean and standard deviation is 3 and the difference between their squares is 21 , then \(\mathrm{P}(x=1): \mathrm{P}(x=2)=\)

The values of \(a\) and \(b\) for which the function
\(f(x)=\left\{\begin{array}{cc}
1+|\sin x|^{a/|\sin x|}, & \frac{-\pi}{6} \lt x \lt 0 \\
b, & x=0 \\
e^{\tan 2 x / \tan 3 x}, & 0 \lt x \lt \frac{\pi}{6}
\end{array}\right.\)
is continuous at \(x=0\) are