Question

Which of the following(s) pair have same number of terms $(x,y\in R)$

• A. $(x+y{)}^9-2,(2x-3y{)}^{10}$
• B. $1-(2+x{)}^m,(x^2+5{)}^m,$ where $m\in N$
• C. $(x^2-2x+1{)}^5,(x^2+1{)}^{10}$
• D. $(x^2-2x+1{)}^5,(x^2+1{)}^{11}$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $(x+y{)}^9-2,(2x-3y{)}^{10}$
B $1-(2+x{)}^m,(x^2+5{)}^m,$ where $m\in N$
C $(x^2-2x+1{)}^5,(x^2+1{)}^{10}$

Option $\left(A\right):$ The number of terms in $(x+y{)}^9-2$ is $(9+1)+1=11$ (one extra constant term added) and
number of terms in $(2x-3y{)}^{10}=10+1=11$

Option $\left(B\right)$: The number of terms in $1-(2+x{)}^m=m+1$ (as both the constant terms merged to a single term) and number of terms in $(x^2+5{)}^m=m+1$

Option $\left(C\right)$: The number of terms in $(x^2-2x+1{)}^5$ equal to the number of terms in $(x-1{)}^{10}=10+1=11$, and number of terms in $(x^2+1{)}^{10}=10+1=11$

Option $\left(D\right)$: The number of terms in $(x^2-2x+1{)}^5$ equal to the number of terms in $(x-1{)}^{10}=11$, and number of terms in $(x^2+1{)}^{11}=11+1=12$