If number of terms in the expansion of $${\left( {x - 2y + 3z} \right)^n}$$ is 45, then $$n =$$
A.
$$7$$
B.
$$8$$
C.
$$9$$
D.
$$6^{10}$$
Answer :
$$8$$
Solution :
No. of terms in the expansion $$ = {\,^{n + 3 - 1}}{C_{3 - 1}}$$
$$\eqalign{
& \therefore {\,^{n + 2}}{C_2} = 45 \cr
& \Rightarrow n = 8 \cr} $$
Releted MCQ Question on Algebra >> Binomial Theorem
Releted Question 1
Given positive integers $$r > 1, n > 2$$ and that the co - efficient of $${\left( {3r} \right)^{th}}\,{\text{and }}{\left( {r + 2} \right)^{th}}$$ terms in the binomial expansion of $${\left( {1 + x} \right)^{2n}}$$ are equal. Then
If in the expansion of $${\left( {1 + x} \right)^m}{\left( {1 - x} \right)^n},$$ the co-efficients of $$x$$ and $${x^2}$$ are $$3$$ and $$- 6\,$$ respectively, then $$m$$ is