If \(A=\left[\begin{array}{cc}1 & 0 \\ -1 & 7\end{array}\right]\) and \(A^2-8 A+K I=O\), then the value of \(K\) is:

Evaluate \(\int_1^{\sqrt{3}} \frac{1}{1+x^2} d x\)

If A and B are square matrix of order \(n \times n\), then \((A-B)^2\) is equal to
A. \(A^2-A B-B A+B^2\)
B. \(A^2-2 A B+B^2\)
C. \(A^2-2 B A+B^2\)
D. \(\quad A^2-B^2\)
E. \(A^2+2 A B+B^2\)
Choose the correct answer from the options given below:

For real numbers x and y, the relation R is defined as R = {(x, y) : x + y - \(\pi\) is an irrational number}, then the relation R is:

Let \(A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\), then \(\left(A^{-1}\right)^T\) equals

If \(x \neq y \neq z\) then \(\left|\begin{array}{lll}1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2\end{array}\right|\) is equal to

The general solution of the differential equation \(x d y+e^{-y} d x=x e^{x-y} d x\) is (given C is constant of integration)

Read the passage carefully and give the answers to the question :
Does the number of species in a community really matter to the functioning of the ecosystem? This is a question for which ecologists have not been able to give a definitive answer. For many decades, ecologists believed that communities with more species, generally, tend to be more stable than those with less species. According to the International Union for Conservation of Nature and Natural Resources (IUCN) (2004), the total number of plant and animal species described so far is more than 1.5 million.
The following are the various hypotheses proposed in explaining the greatest biological diversity in tropics except :

Internal resistance of a cell is:
A. decreases with increase in the distance between electrodes.
B. increases with increase in the area of electrodes inside electrolyte.
C. decreases with increase in temperature.
D. doesn't depend on the concentration of the electrolyte.
Choose the correct answer from the options given below:

Which one of the following structures is not the male sex accessory duct in human?

In angiosperms during micorsporogenesis, meiosis occurs in:

If \(y = x^2 \log_e x\), then \(\frac{d^2y}{dx^2}\) is equal to:

Work done in moving a charge q along a closed path of length l by an electric field \(\vec{E}\) is given by: