IPMAT Indore 2023 (MCQ) PYQs

Let $S_n$ be sum of the first $n$ terms of an A.P. If $S_5 = S_9$, what is the ratio of $a_3 : a_5$

Let $S_1 = \{100, 105, 110, 115, ... \}$ and $S_2 = \{100, 95, 90, 85, ... \}$ be two series in arithmetic progression. If $a_k$ and $b_k$ are the $k$-th terms of $S_1$ and $S_2$, respectively, then $\sum_{k=1}^{20} a_k b_k$ equals __________.

If $(1 + x - 2x^2)^6 = A_0 + \sum_{r=1}^{12} A_r x^r$, then the value of $A_2 + A_4 + A_6 + \cdots + A_{12}$ is