Mathematics Mock Test - 11

A line joining the points $(1,2,0)$ and $(4,13,5)$ is perpendicular to a plane. Then the coefficients of $x,y$ and $z$ in the equation of the plane are respectively:

The area of the region bounded by $Y$ -axis, $y=\cos x$ and $y=\sin x$ for $0\le x\le \frac{\pi }{4}$ is:

For an objective function $Z=x+y$ with constraints $2x+2y\le 5$ and $4x-3y\ge 3$ ($x,y\ge 0$), at what point(s) will $Z$ achieve its maximum value?

The present value of a perpetuity is $\text{₹}50,000$ when the payment of $\text{₹}1,000$ is made at the end of each period. Find the present value of the perpetuity if the payments are made at the beginning of each period.

The point that lies in the region bounded by the lines $7x+y\ge 40$ and $2x+3y\le 25$ is: