If number of terms in the expansion of ${(x - 2y + 3z)^n}$ are $45$, then $n=$
$7$
$8$
$9$
None of these
(b) $\frac{{(n + 1)(n + 2)}}{2} = 45$ or ${n^2} + 3n – 88 = 0 \Rightarrow n = 8$..
If the expansion in powers of $x$ of the function $\frac{1}{{\left( {1 – ax} \right)\left( {1 – bx} \right)}}$ is ${a_0} + {a_1}x + {a_2}{x^2} + \;{a_3}{x^3} + \; \ldots……$ then ${a_n}$ is
If $C_r= ^{100}{C_r}$ , then $1.C^2_0 – 2.C^2_1 + 3.C^2_3 – 4.C^2_0 + 5.C^2_4 – …. + 101.C^2_{100}$ is equal to
In the polynomial $(x – 1)(x – 2)(x – 3)………….(x – 100),$ the coefficient of ${x^{99}}$ is
Co-efficient of $\alpha ^t$ in the expansion of,
$(\alpha + p)^{m – 1} + (\alpha + p)^{m – 2} (\alpha + q) + (\alpha + p)^{m – 3} (\alpha + q)^2 + …… (\alpha + q)^{m – 1}$
where $\alpha \ne – q$ and $p \ne q$ is :
If $x + y = 1$, then $\sum\limits_{r = 0}^n {{r^2}{\,^n}{C_r}{x^r}{y^{n – r}}} $ equals
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