WBCS Mains 2018 Official Paper-VI

A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight, and describes $88\text{m}$ when it traces $72^{\circ }$ at the centre, then the length of the rope is

What value of $m$ ensures that the two roots of the quadratic equation $4x^2+4(3m-1)x+(m+7)=0$ are reciprocal to each other?

The present price of a machine is $\text{Rs. }p$. If the price of the machine increases by $2r\%$ each year, the price of the machine after $n$ years will be

Ramen deposits $\text{Rs. }100$ on the first day of every month in a monthly savings scheme. In this way, he has deposited money for $1$ year. If the rate of simple interest is $6\%$ per annum, then the total amount he will get at the end of the year is

If $x=2+\sqrt{3}$, the value of $x+\frac{1}{x}$ is