CUET Mathematics Mock Test - 4

In a $500\text{m}$ race, the ratio of the speeds of $P$ and $Q$ is $3:4$. When the race starts, $P$ is $140\text{m}$ ahead. What is the distance between $P$ and $Q$ when $P$ wins the race?

A piecewise-defined function is defined as:
$$f(x)=\{\begin{array}{ll}-1& \text{if }x\le 0\\ ax+b& \text{if }0<x<1\\ 1& \text{if }x\ge 1\end{array}$$
Where $a$ and $b$ are constants. If the function is continuous everywhere, what is the value of $a$?

If $x=3\tan t$ and $y=3\sec t$, then the value of $\frac{d^{2}y}{d{x}^2}$ at $t=\frac{\pi }{4}$ is:

For the linear programming problem:$\text{Maximize }Z=3X_1+2X_2$ Subject to:$-2X_1+3X_2\le 9$$X_1-5X_2\ge -20$$X_1,X_2\ge 0$ The above problem has: