Mathematics Mock Test - 10

Consider the objective function $z=3x+4y$ subject to $4x+3y\le 24$, $3x+4y\le 24$, and $x,y\ge 0$. The objective function $z$ is maximized:

A continuous random variable $x$ has the probability density function:$f(x)=\{\begin{array}{ll}{e}^x,& -1\le x<0\\ \frac{1}{1+x^2},& 0\le x<1\\ \text{elsewhere},& e-1-\frac{\pi }{4}\end{array}$$P(-1<x<1)$ is equal to:

Payment of a perpetuity is done on a quarterly basis at the end of each period. The annual interest rate is $100r\%$ and the present value of the perpetuity is Rs 10,00,000. If the regular quarterly payment is Rs 40,000, what is the value of $r$?

The cost of a cricket ball is Rs 500. If the price remains constant, its marginal revenue in Rs will be:

If $X=48,Y=15$, then the value of $k$ such that $X(\mathrm{mod}Y)=(X+kY)(\mathrm{mod}Y)$ is: