GATE EE 2015 Question Paper (07-Feb-2015) (Shift 2)

If $p,q,r,s$ are distinct integers such that:

$\begin{array}{l}f\left(p,q,r,s\right)=max\left(p,q,r,s\right)\\ g\left(p,q,r,s,\right)=min\left(p,q,r,s\right)\\ h\left(p,q,r,s\right)=remainderof\frac{p\times q}{r\times s}if\left(p\times q\right)>\left(r\times s\right)\\ \left(or\right)remainderof\frac{r\times s}{p\times q}if\left(r\times s\right)>\left(p\times q\right)\end{array}$

Also a function $fgh\left(p,q,r,s\right)=f\left(p,q,r,s\right)\times g\left(p,q,r,s\right)\times h\left(p,q,r,s\right)$

Also the same operations are valid with two variable function of the form $f\left(p,q\right)$.

What is the value of $fg\left(h\left(2,5,7,3\right),4,6,8\right)$?

Four branches of a company are located at M,N,O, and P. M is north of N at a distance of 4km; P is south of O at a distance of 2km; N is southeast of O by 1km. What is the distance between M and P in km?

Out of the following four sentences, select the most suitable sentence with respect to grammar and usage:

In a triangle $PQR$, $PS$ is the angle bisector of $\angle SPR$ and $\angle QPS=60$. What is the

length of $PS$?

If the list of letters, $P,R,S,T,U$ is an arithmetic sequence, which of the following

are also in arithmetic sequence?

I. $2P,2R,2S,2T,2U$

II. $P-3,R-3,S-3,T-3,U-3$

III. $P^2,R^2,S^2,T^2,U^2$