Mathematics Mock Test - 9

Consider the probability distribution function defined as $f_X(x)=\{\begin{array}{ll}|x|,& |x|<1\\ 0,& \text{otherwise}\end{array}$. Which of the following is true?

Which of the following is true for binomial distribution?

A unit vector $\vec{a}$ makes angle $\pi /3$ with $\hat{i}$, $\pi /4$ with $\hat{j}$ and an acute angle $\theta$ with $\hat{k}$.I. The value of $\theta$ is $\pi /3$.II. The components of $\vec{a}$ are $(1/2,1/2,1/2)$.Which of the above statement(s) is/are correct?

The minimum value of $z=5x-7y$, subject to the constraints $x+y\le 7$, $2x-3y+6\ge 0$, $x\ge 0,y\ge 0$, is:

Let $A=\{x\in \mathbb{R}:x\ge 0\}$. A function $f:A\to {\mathbb{R}}^{+}$ is defined by $f(x)=x^2$. Which one of the following is correct?