UPTET 2018 (Paper 2 - Maths & Science ) Previous Year Paper (2018)

Find the value of $K$ for which equation $x-Ky=2$, $3x+2y=5$ has unique solution.

A can do a work in $6$ days. $B$ takes $8$ days to complete it. $C$ takes as long as $A$ and $B$ would take working together. How long will it take $B$ and $C$ to complete the work together?

In an examination, the mean of marks scored by a class of $30$ students was calculated as $58.5$. Later on, it was detected that the marks of one student was wrongly copied as $57$ instead of $75$. Find the correct mean.

If centroid of the points $(3,5)$, $(6,y)$ and $(-3,4)$ is $(x,y)$, then find the values of $x$ and $y$.

The polynomial $a{x}^3+b{x}^2+x-6$ has $(x+2)$ as a factor and leaves remainder $4$ when divided by $(x-2)$. Find the value of $a$ and $b$.