Class 11MathematicsBinomial TheoremGeneral term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient
EasyThe coefficient of $x^5$ in the expansion of $(x + 3)^6$ is
- A$18$
- B$6$
- C$12$
- D$10$
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If $C_0, C_1, C_2, \ldots, C_8$ are the binomial coefficients in the expansion of $(1+x)^8$,then $\sum_{r=1}^8 r^3 \frac{C_r}{C_{r-1}} =$
If the numerically greatest term in the expansion of $(2-3x)^9$ when $x=1$ is $P_1^\alpha P_2^\beta P_3^\gamma P_4^\delta$ (where $P_1 < P_2 < P_3 < P_4$ are the first four prime numbers),then $\alpha+\beta+\gamma+\delta=$
The sum of the binomial coefficients of $[2x + \frac{1}{x}]^n$ is equal to $256$. The constant term in the expansion is
If the coefficients of $x^7$ and $x^8$ in $(2 + \frac{x}{3})^n$ are equal,then $n$ is
Easy
View SolutionFor a positive integer $n$,$(1+\frac{1}{x})^n$ is expanded in increasing powers of $x$. If three consecutive coefficients in this expansion are in the ratio $2:5:12$,then $n$ is equal to
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