If ab neq 0 and the sum of the coefficients o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The general term in the expansion of $\left(\frac{x^2}{a}-\frac{b}{x}\right)^{11}$ is given by $T_{r+1} = {}^{11}C_r \left(\frac{x^2}{a}\right)^{1

Vedclass · Accepted Answer

$ab=1$

Vedclass · Answer

(D) The general term in the expansion of $\left(\frac{x^2}{a}-\frac{b}{x}ight)^{11}$ is given by $T_{r+1} = {}^{11}C_r \left(\frac{x^2}{a}ight)^{11-r} \left(-\frac{b}{x}ight)^r = {}^{11}C_r \frac{(-b)^r}{a^{11-r}} x^{22-3r}$.For the coefficient of $x^7$,set $22-3r = 7$,which gives $3r = 15$,so $r = 5$.The coefficient is $C_1 = {}^{11}C_5 \frac{(-b)^5}{a^6} = -{}^{11}C_5 \frac{b^5}{a^6}$.For the coefficient of $x^4$,set $22-3r = 4$,which gives $3r = 18$,so $r = 6$.The coefficient is $C_2 = {}^{11}C_6 \frac{(-b)^6}{a^5} = {}^{11}C_6 \frac{b^6}{a^5}$.Given $C_1 + C_2 = 0$,we have $-{}^{11}C_5 \frac{b^5}{a^6} + {}^{11}C_6 \frac{b^6}{a^5} = 0$.Since ${}^{11}C_5 = {}^{11}C_6$,we can divide by ${}^{11}C_5 \frac{b^5}{a^6}$ (assuming $a, b 
eq 0$):$-1 + \frac{b^6}{a^5} \cdot \frac{a^6}{b^5} = 0$ $\Rightarrow -1 + ab = 0$ $\Rightarrow ab = 1$.

If $ab \neq 0$ and the sum of the coefficients of $x^7$ and $x^4$ in the expansion of $\left(\frac{x^2}{a}-\frac{b}{x}\right)^{11}$ is $0$,then

Similar Questions

In a permanent magnet at room temperature,

Photoelectric emission is observed from a metallic surface for frequencies $v_1$ and $v_2$ of the incident light $(v_1 > v_2)$. If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio $1: n$,then the threshold frequency of the metallic surface is

If $L = 2.331 \, cm$ and $B = 2.1 \, cm$,then $L + B = $ (in $, cm$)

If $x=\log _{0.1} 0.001$ and $y=\log _9 81$,then $\sqrt{x-2 \sqrt{y}}$ is equal to

$A$ particle of mass $5 \times 10^{-5} \ kg$ is placed at the lowest point of a smooth parabola $x^2 = 40y$ (where $x$ and $y$ are in $m$). If it is displaced slightly such that it is constrained to move along the parabola,the angular frequency of oscillation (in $rad/s$) will be approximately:

Vedclass Test Series

Exam Paper Generator

Online Exam Module