Question

Which of the following statements is/are true?

• A. The general term in the expansion of ${\left(x^2-y\right)}^6$ is ${}^{6}C$ $x^{10-2r}{y}^r(-1{)}^r$
• B. The general term in the expansion of ${\left(x^2-yx\right)}^{12},x\ne 0$ is ${}^{12}{C}_r(-1{)}^r{x}^{24-r}{y}^r$
• C. Both (a) and (b) are true
• D. Both (a) and (b) are false

Answer 1

Answer: (B)

(a) The general term of ${\left(x^2-y\right)}^6$ is
$T_{r+1}={}^6{C}_r{\left(x^2\right)}^{6-r}(-y{)}^r={}^6{C}_r{x}^{12-2r}(-1{)}^r{y}^r$
$={}^6{C}_r{x}^{12=2r}{y}^r(-1{)}^r$
(b) The general term of ${\left(x^2-yx\right)}^{12}$ is
$T_{r+1}={}^{12}{C}_r{\left(x^2\right)}^{12-r}(-yx{)}^r$
$={}^{12}{C}_r{x}^{24-2r}(-1{)}^r{y}^r{x}^r$
$={}^{12}{C}_r(-1{)}^r{x}^{24-2r+r}{y}^r$
$-{}^{12}{C}_r(-1{)}^r{x}^{24-r}{y}^r$
So, only (b) is correct.