# Recent questions tagged isi2016-mma

Suppose $a, b, c >0$ are in geometric progression and $a^p = b^q =c^r \neq 1$. Which one of the following is always true? $p, q, r$ are in geometric progression $p, q, r$ are in arithmetic progression $p, q, r$ are in harmonic progression $p=q=r$
The number of terms independent of $x$ in the binomial expansion of $\left(3x^2 + \dfrac{1}{x}\right)^{10}$ is $0$ $1$ $2$ $5$
Let $x$ and $y$ be real numbers satisfying $9x^2+16y^2=1$. Then $(x+y)$ is maximum when $y=9x/16$ $y=-9x/16$ $y=4x/3$ $y=-4x/3$