List of top Mathematics Questions on Algebra asked in IISER

मान लीजिए कि n = 2026 है। यदि 49n + 41n + 10n को 100 से भाग दें तो शेषफल कितना होगा?

मान लीजिए कि a1, a2, a3, . . . धनात्मक पूर्णांकों की एक गुणोत्तर श्रेणी है। यदि a1 = 3 है, तथा सभी धनात्मक पूर्णांकों n के लिए an+2 − 2an = an+1 है, तो a1 + a2 + a3 + a4 + a5 का मान क्या होगा?

यदि p(x) एक ऐसा द्विघातीय बहुपद है जिसके लिए p(1) = p(−1) = 0 है, तो p(x) में x का गुणांक क्या है?

Let $n = 20^{26}$. What is the remainder when $49^n + 41^n + 10n$ is divided by 100?

Let $a_1, a_2, a_3, \dots$ be a geometric progression of positive integers such that $a_1 = 3$ and $a_{n+2} - 2a_n = a_{n+1}$ for all positive integers $n$. What is the value of $a_1 + a_2 + a_3 + a_4 + a_5$?

Let $p(x)$ be a quadratic polynomial such that $p(1) = p(-1) = 0$. What is the coefficient of $x$ in $p(x)$?

Let $S_n$ denote the sum of the first $n$ terms of a sequence $a_1, a_2, a_3, \dots$. If $S_{n+3} - S_n = 13n + 7$ for all $n$, what is the value of $a_{13} - a_{10}$?

Let $n = \sum_{r=0}^{10} (-1)^r \binom{10}{r} \left(\frac{2}{3}\right)^{2r} 3^{20}$. Which one of the following statements is TRUE?

Let $a_1, a_2, a_3, \dots$ be a sequence of real numbers. Let $s_n = a_1 + a_2 + \dots + a_n$.
If $2s_n = n(c + a_n)$ for some real number $c$ and for all $n = 1, 2, 3, \dots$, then which one of the following statements is Correct?