New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Mathematical Induction and Binomial Theorem

8 questions · Mathematics · JEE Advanced

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Advanced
Mathematics
Mathematical Induction and Binomial Theorem

Mathematical Induction and Binomial Theorem

8 questions · Mathematics · JEE Advanced

Let $a_{0}, a_{1}, \dots, a_{23}$ be real numbers such that $(1 + \frac{2}{5} x)^{23} = i = 0 \sum 23 a_{i} x^{i}$ for every real number $x$ . Let $a_{r}$ be the largest among the numbers $a_{j}$ for $0 \leq j \leq 23$ . Then the…2025 · Shift 2 · Q26 · Numerical
Let $a$ and $b$ be two nonzero real numbers. If the coefficient of $x^{5}$ in the expansion of $(a x^{2} + \frac{70}{27 b x})^{4}$ is equal to the coefficient of $x^{- 5}$ in the expansion of $(a x - \frac{1}{b x ^{2}})^{7}$ , then…2023 · Shift 1 · Q30 · Numerical
For non-negative integers s and r, let $(s r) = {\frac{s !}{r ! ( s - r )!} 0 i f r \leq s, i f r > s$ For…2020 · Shift 2 · Q30 · Multiple correct
Let $X = (^{10} C_{1})^{2} + 2 (^{10} C_{2})^{2} + 3 (^{10} C_{3})^{2} + ... + 10 (^{10} C_{10})^{2}$ , where $^{10} C_{r}$ , r $\in$ {1, 2, ..., 10} denote binomial coefficients. Then, the value of $\frac{1}{1430} X$ is ..........2018 · Shift 2 · Q32 · Numerical
Let $m$ be the smallest positive integer such that the coefficient of $x^{2}$ in the expansion of $(1 + x)^{2} + (1 + x)^{3} + ........ + (1 + x)^{49} + (1 + m x)^{50}$ …2016 · Shift 1 · Q29 · Numerical
Coefficient of $x^{11}$ in the expansion of $(1 + x^{2})^{4} (1 + x^{3})^{7} (1 + x^{4})^{12}$ is2014 · Shift 2 · Q29 · MCQ
The coefficient of three consecutive terms of $(1 + x)^{n + 5}$ are in the ratio $5 : 10 : 14.$ Then $n$ =2013 · Shift 1 · Q25 · Numerical
For $r = 0, 1, ....,$ let $A_{r}, B_{r}$ and $C_{r}$ denote, respectively, the coefficient of $X^{r}$ in the expansions of $(1 + x)^{10}, (1 + x)^{20}$ and $(1 + x)^{30} .$ Then $r = 1 \sum 10 A_{r} (B_{10} B_{r} - C_{10} A_{r})$ …2010 · Shift 2 · Q25 · MCQ