Embibe Experts Solutions for Chapter: Sequence and Series, Exercise 1: WBJEE 2019

Given that $n$ numbers of arithmetic means are inserted between two sets of numbers $a, 2b$ and $2a, b$ where $a,b\in R$. Suppose further that the $m^{\mathrm{th}}$ means between these sets of numbers are same, then the ratio $a: b$ equals

The three sides of a right angled triangle are in $GP$ (geometric progression). If the two acute angles be $\alpha$ and $\beta ,$ then $\tan \alpha$ and $\tan \beta$ are

Let $a=min\left\{x^2+2x+3:x\in R\right\}$ and $b=\underset{\theta \to 0}{\lim }\frac{1-\cos \theta }{{\theta }^2}.$ Then $\sum _{r=0}^n{a}^r{b}^{n-r}$ is

A particle starts at the origin and moves $1$ unit horizontally to the right and reaches $P_1,$ then it moves $\frac{1}{2}$ unit vertically up and reaches $P_2,$ then it moves $\frac{1}{4}$ unit horizontally to right and reaches $P_3,$ then it moves $\frac{1}{8}$ unit vertically down and reaches $P_4,$ then it moves $\frac{1}{16}$ unit horizontally to right and reaches $P_5$ and so on. Let $P_n=\left(x_n, y_n\right)$ and $\lim x_n=\alpha$ and $\underset{n\to \infty }{\lim }{y}_n=\beta .$ Then, $(\alpha , \beta )$ is

Let $x_1, x_2$ be the roots of $x^2-3x+a=0$ and $x_3, x_4$ be the roots of $x^2-12x+b=0$. If $x_1<x_2<x_3<x_4$ and $x_1, x_2, x_3, x_4$ are in $GP,$ then $ab$ equals

If $a$ and $b$ are arbitrary positive real numbers then the least possible value of $\frac{6a}{5b}+\frac{10b}{3a}$ is

Let $I\left(n\right)=n^n,J\left(n\right)=1.3.5\dots \dots ..(2n-1)$ for all $(n>1),n\in N,$ then