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Mathematics
Coefficients of terms in binomial expansion
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

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

Mathematics
Coefficients of terms in binomial expansion
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

Mathematics
Coefficients of terms in binomial expansion
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. $\dfrac{n\left( 2n-1 \right)}{6}$
Mathematics
Coefficients of terms in binomial expansion
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
Mathematics
Coefficients of terms in binomial expansion
What is the remainder when ${{14}^{{{15}^{16}}}}$ is divided by $5$ ?
Mathematics
Coefficients of terms in binomial expansion
Find the coefficient of \[{x^2}\] in \[{\left( {\sqrt {\dfrac{x}{3}} + \dfrac{3}{{2x}}} \right)^{10}}\].

Mathematics
Coefficients of terms in binomial expansion
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?

Mathematics
Coefficients of terms in binomial expansion
The term independent of x in the expansion of ${{\left( 1-x \right)}^{2}}.{{\left( x+\dfrac{1}{x} \right)}^{10}}$ is?
Mathematics
Coefficients of terms in binomial expansion
What is the Binomial expansion of ${{\left( 2x+3 \right)}^{4}}$?
Mathematics
Coefficients of terms in binomial expansion
What is the binomial expansion of ${{\left( 2x-1 \right)}^{5}}$ ?
Mathematics
Coefficients of terms in binomial expansion
How do you use Pascal’s triangle to expand${(2x - y)^3}$?
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