1
Two straight lines are drawn perpendicular to each other in $X-Y$ plane. If $\alpha$ and $\beta$ are the acute angles the straight lines make with the $\text{X-}$ axis, then $\alpha + \beta$ is_______. $60^{\circ}$ $90^{\circ}$ $120^{\circ}$ $180^{\circ}$
2
The figure below shows an annular ring with outer and inner as $b$ and $a$, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum $n$ ... $\pi [(b^{2}-a^{2})+n(b-a)^{2}]$
Find the inverse function of $f(x) = x^3 +1.$
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
Consider the grammar given below: $S \rightarrow Aa$ $A \rightarrow BD$ $B \rightarrow b \mid \epsilon$ $D \rightarrow d \mid \epsilon$ Let $a,b,d$ and $\$ be indexed as follows:$\begin{array}{|l|l|l|l|} \hline a & b & d & \$ \\ \hline 3 & 2 & 1 & ... $)$ , then the answer should be $3210$)
Two cars at the same time from the same location and go in the same direction. The speed of the first car is $50$ km/h and the speed of the second car is $60$ km/h. The number of hours it takes for the distance between the two cars to be $20$ km is _____. $1$ $2$ $3$ $6$