CAT (QA) PYQs

The equation $x^3 + (2r + 1)x^2 + (4r - 1)x + 2 = 0$ has $- 2$ as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of $r$ is

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 equations $3x^2 - 5x + p = 0$ and $2x^2 - 2x + q = 0$ have one common root. The sum of the other roots of these two equations is