List of practice Questions

Let \(x, y > 0\). If \(x^3y^2 = 2^{15}\), then the least value of \(3x + 2y\) is

Let \(x * y\) = \(x^2 + y^3\) and \((x * 1) * 1\) = \(x * (1 * 1)\). Then a value of \(2 sin^{-1}\bigg(\frac{x^4+x^2-2}{x^4+x^2+2}\bigg)\) is

A random variable \(X\) has the following probability distribution : 

x	0	1	2	3	4
P(x)	k	2k	4k	6k	8k

The value of \(P(1 < X < 4 | x ≤ 2)\) is equal to

Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is: