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:

The roots $\alpha, \beta$ of the equation $3 x^{2}+\lambda x-1=0$, satisfy $\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}}=15$. The value of $\left(\alpha^{3}+\beta^{3}\right)^{2}$, is

If $(3+2\sqrt{2})$ is a root of the equation $ax^2 + bx + c = 0$, and $(4+2\sqrt{3})$ is a root of the equation $ay^2 + my + n = 0$, where $a, b, c, m$ and $n$ are integers,
then the value of $(\frac{b}{m} + \frac{c-2b}{n})$ is