The number of distinct terms in the expansion of $${\left( {x + y - z} \right)^{16}}$$ is
A.
136
B.
153
C.
16
D.
17
Answer :
153
Solution :
$${\left( {x + y - z} \right)^{16}} = {\,^{16}}{C_0}{x^{16}} + {\,^{16}}{C_1}{x^{15}}\left( {y - z} \right) + ..... + {\,^{16}}{C_r}{x^{16 - r}}{\left( {y - z} \right)^r} + ..... + {\,^{16}}{C_{16}}{\left( {y - z} \right)^{16}}.$$
Clearly, all the terms are distinct.
∴ the number of distinct terms
$$ = 1 + 2 + 3 + ..... + 17 = \frac{{17 \times 18}}{2}.$$
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