Mathematics Tes...

The total number of injective mappings from a set with m elements to a set with n elements (m ≤ n) is equal to:

In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between \(x\) and \(y\) and choose the correct option.

I. \(x^{2}+5 x-36=0\)

II. \(y^{2}+24 y+135=0\)

Find the 8^th term in the following sequence whose nth term is\(a_{n}=\frac{n^{2}}{2^{n}}\).

The value of \(\left|\begin{array}{ccc}\sin ^2 x & \cos ^2 x & 1 \\ \cos ^2 x & \sin ^2 x & 1 \\ -10 & 12 & 2\end{array}\right|\)

The value of p for which the sum of the squares of the roots of the equation x² - (p - 2)x - p + 1 = 0 is minimum will be:

A tea party is arranged for \(16\) people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is:

What is the sum of the coefficients of first and last terms in the expansion of \((1+x)^{2 n}\), where \(n\) is a natural number?

A game consists of tossing a one rupee coin \(3\) times and noting its outcome each time. Aryan wins if all the tosses give the same result i.e. three heads or three tails and loses otherwise. Then the probability that Aryan will lose the game.

The line passing through the extremity \(A\) of the major axis and extremity \(B\) of the minor axis of the ellipse \(x^{2}+9 y^{2}=9\) meets its auxiliary circle at the point \(M\). Find the area of the triangle with vertices at \(A, M\) and the origin \(O\).

\(\int^{\pi}_{-\pi} \tan x \sec ^{2} x d x=?\)