Sequences And Series - Algebra - Mathematics Previous Year Questions

If $a, b, c$ are three consecutive terms of an AP and $x, y, z$ are three consecutive terms of a GP, then the value of $x^{b-c} \cdot y^{c-a} \cdot z^{a-b}$ is

The third term of a GP is 9. The product of its first five terms is

If the sum of \(n\) terms of an AP is given by \(S_n=n^2+n\), then the common difference of the \(\mathrm{AP}\) is

If the middle term of the AP is 300, then the sum of its first 51 terms is

If \(A=\{1,2,3, \ldots, 10\}\), then number of subsets of \(A\) containing only odd numbers is

If \(a_1, a_2, a_3, \ldots, a_{10}\) is a geometric progression and \(\frac{a_3}{a_1}=25\), then \(\frac{a_9}{a_5}\) equals

If the set \(x\) contains 7 elements and set \(y\) contains 8 elements, then the number of bijections from \(x\) to \(y\) is

If \(p\left(\frac{1}{q}+\frac{1}{r}\right), q\left(\frac{1}{r}+\frac{1}{p}\right), r\left(\frac{1}{p}+\frac{1}{q}\right)\) are in \(\mathrm{AP}\), then \(p, q, r\)

\(n\)th term of the series \(1+\frac{3}{7}+\frac{5}{7^2}+\frac{1}{7^2}+\ldots\) is

If $S_n$ stands for sum to $n$-terms of a GP with $a$ as the first term and $r$ as the common ratio, then $S_n: S_{2 n}$ is

If $4^{\text {th }}, 10^{\text {th }}$ and $16^{\text {th }}$ terms of a G.P. are $x, y$ and $z$ respectively, then