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GradeCoefficients of Terms in Binomial Expansion

TopicLatest Questions

The coefficients of \[{x^7}\] in the expansion of \[(1 - {x^4}){(1 + x)^9}\] is equal to

A.27

B.-24

C.48

D.-48

A.27

B.-24

C.48

D.-48

In the expansion of \[{{\left( 1+a \right)}^{m+n}}\] prove that coefficients of \[{{a}^{m}}\] and \[{{a}^{n}}\] are equal.

The sum ${}^{20}{C_0} + {}^{20}{C_1} + {}^{20}{C_2} + .....{}^{20}{C_{10}}$ is equal to

A.${2^{20}} + \dfrac{{20!}}{{2{{\left( {10!} \right)}^2}}}$

B.${2^{19}} + \dfrac{1}{2}.\dfrac{{20!}}{{{{\left( {10!} \right)}^2}}}$

C.${2^{19}} + {}^{20}{C_{10}}$

D.None of these

A.${2^{20}} + \dfrac{{20!}}{{2{{\left( {10!} \right)}^2}}}$

B.${2^{19}} + \dfrac{1}{2}.\dfrac{{20!}}{{{{\left( {10!} \right)}^2}}}$

C.${2^{19}} + {}^{20}{C_{10}}$

D.None of these

Simplify the expressions of the sums ${{\cot }^{2}}\dfrac{\pi }{2n+1}+{{\cot }^{2}}\dfrac{2\pi }{2n+1}+{{\cot }^{2}}\dfrac{3\pi }{2n+1}+......+{{\cot }^{2}}\dfrac{n\pi }{2n+1}=$

A. $\dfrac{n\left( 2n+1 \right)}{3}$

B. $\dfrac{n\left( 2n+1 \right)}{6}$

C. $\dfrac{n\left( 2n-1 \right)}{3}$

D. $\dfrac{n\left( 2n-1 \right)}{6}$

A. $\dfrac{n\left( 2n+1 \right)}{3}$

B. $\dfrac{n\left( 2n+1 \right)}{6}$

C. $\dfrac{n\left( 2n-1 \right)}{3}$

D. $\dfrac{n\left( 2n-1 \right)}{6}$

The number of rational terms in the expansion of ${{\left( \sqrt[4]{5}+\sqrt[5]{4} \right)}^{100}}$ is

(a) 50

(b) 5

(c) 6

(d) 51

(a) 50

(b) 5

(c) 6

(d) 51

What is the remainder when ${{14}^{{{15}^{16}}}}$ is divided by $5$ ?

Find the coefficient of \[{x^2}\] in \[{\left( {\sqrt {\dfrac{x}{3}} + \dfrac{3}{{2x}}} \right)^{10}}\].

In the binomial expression ${{\left( 1+\dfrac{k}{6} \right)}^{n}}$ what is the value of n given the fact that the coefficient of the third term is twice the coefficient of the fourth term?

The term independent of x in the expansion of ${{\left( 1-x \right)}^{2}}.{{\left( x+\dfrac{1}{x} \right)}^{10}}$ is?

What is the Binomial expansion of ${{\left( 2x+3 \right)}^{4}}$?

What is the binomial expansion of ${{\left( 2x-1 \right)}^{5}}$ ?

How do you use Pascalâ€™s triangle to expand${(2x - y)^3}$?

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