CUET Mathematics Mock Test - 4

If the expected value of a random variable $X$ is 2 and its variance is 1, then what will be the variance of $3X+4$?

The principal value of ${\sin }^{-1}\left(\frac{1}{\sqrt{17}}\right)+{\cos }^{-1}\left(\frac{5}{\sqrt{34}}\right)$ is:

A manufacturing company has its variable cost given by $C(x)=x(80-x^2)$ where $x$ is the number of quantities produced. The price per unit is $p(x)=5x$. The ratio of marginal cost and marginal revenue when 5 units were both produced and in demand is:

On the set of positive rational numbers, a binary operation $\ast$ is defined by $a\ast b=|a-b|$. If $5\ast p\le 5$, then the maximum value of $p$ is:

Let $S$ denote all integers. Define a relation $R$ on $S$ as $aRb$ if $ab\ge 0$ where $a,b\in S$. Then $R$ is: