CAT (QA) PYQs

A tea shop offers tea in cups of three different sizes. The product of the prices, in INR, of three different sizes is equal to $800$. The prices of the smallest size and the medium size are in the ratio $2 : 5$. If the shop owner decides to increase the prices of the smallest and the medium ones by INR $6$ keeping the price of the largest size unchanged, the product then changes to $3200.$ The sum of the original prices of three different sizes, in INR, is:

If $f(x)=(x^2+3x)(x^2+3x+2)$, then the sum of all real roots of the equation $\sqrt{f(x)+1}=9701$, is

Let $f(x)$ be quadratic polynomial in $x$ such that $f(x) \geq 0$ for all real numbers $x$. if $f(2)=0$ and $f(4)=6$, then $f(-2)$ is equal to