For a random variable \(X, E(X)=3\) and \(E\left(X^2\right)=11\), then variance of \(X\) is :

The effective rate per annum equivalent to a nominal rate of \(8 \%\) compounded semi-annually is

\(\cos \left(\frac{\pi}{6}-\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)\) is equal to:

For what value of \(k\), the matrix \(A=\left[\begin{array}{ll}1 & 3 \\ k & 4\end{array}\right]\) is singular ?

The value(s) of K, for which the system of linear equations 2x + y + x = 1, x + Ky - x = \(\frac{3}{2}\) and 3y - 5x = 9 does not possess a unique solution is

Objective function \(z=200 x+500 y\), subject to the constraints
\(x+2 y \geq 10, \quad 3 x+4 y \leq 24, \quad x \geq 0, \quad y \geq 0\),
the minimum value of \(z\) is :

If \(\int_0^a 3 x^2 d x=8\), then the value of \(a\) is:

The vector equation of a line passing through the point with position vector \(2 \hat{i}-\hat{j}+\hat{k}\) and parallel to the line joining the points with position vectors \(-\hat{i}+4 \hat{j}+\hat{k}\) and \(\hat{i}+2 \hat{j}+2 \hat{k}\) is:

Which one of the following sex determination systems is found in honey bee?

The condition where one species is harmed whereas the other is
unaffected is called

Read the passage carefully and answer the questions based on the passage:
Species diversity on earth is not uniformly distributed. It is generally highest in the tropics and decreases towards the poles. Earth's fossil history reveals the incidences of mass extinctions in the past. Earth's rich biodiversity is vital for the very survival of mankind. It is believed that communities with high diversity tend to be less variable and more productive. The reasons of conserving biodiversity are narrowly utilitarian, broadly utilitarian and ethical. Biodiversity conservation may be in-situ as well as ex-situ.
Which of the following might not account for the greater biological diversity in the tropic region?

The difference of two different skew-symmetric matrices is :

In Kirchhoff's loop rule