Mathematics Tes...

If \({f}(2 {a}-{x})={f}({x})\) and \(\int_{0}^{a} f(x) d x=\lambda\) then \(\int_{0}^{2 a} f(x) d x\) is:

What is the value of the determinant \(\left|\begin{array}{ccc}\mathrm{i} & \mathrm{i}^{2} & \mathrm{i}^{3} \\ \mathrm{i}^{4} & \mathrm{i}^{6} & \mathrm{i}^{8} \\ \mathrm{i}^{9} & \mathrm{i}^{12} & \mathrm{i}^{15}\end{array}\right|\) where \(\mathrm{i}=\sqrt{-1} ?\)

What is the number of different messages that can be represented by three a’s and two b’s?

A bag contains \(2 n+1\) coins, \(n\) coins have tails on both sides, whereas \(n+1\) coins are fair. A coin is picked on random from the bag and tossed. If the probability that toss in tail is \(\frac{31}{42}\), total numbers of coins in the bag are:

If the feasible region for a solution of linear inequations is bounded, it is called as:

What is the probability of getting a sum 9 from two throws of a dice?

If \(\lim _{x \rightarrow 0} \frac{\log (1+\sin x)}{x}=k\), the value of \(k\) is:

If \(6 \sin ^{2} x-2 \cos ^{2} x=4\), then find the value of \(\tan x \).

Three planes x + y = 0, y + z = 0, and x + z = 0: