IPMAT Indore 2023 (MCQ) PYQs

Let $\alpha, \beta$ be the roots of $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots of $x^2 - 4x + q = 0$ where p and q are integers. If $\alpha, \beta, \gamma, \delta$ are in geometric progression then $p + q$ is

The number of terms common to both the arithmetic progressions $2, 5, 8, 11, ..., 179$ and $3, 5, 7, 9, ..., 101$ is

The numbers $-16,2^{x+3}-2^{2 x-1}-16,2^{2 x-1}+16$ are in an arithmetic progression. Then $x$ equals ________.