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question_answer1)
If \[{{x}^{m}}\]occurs in the expansion of \[{{(x+1/{{x}^{2}})}^{2n}}\], then the coefficient of \[{{x}^{m}}\]is
A)
\[\frac{(2n)!}{(m)!(2n-m)!}\] done
clear
B)
\[\frac{(2n)!3!3!}{(2n-m)!}\] done
clear
C)
\[\frac{(2n)!}{\left( \frac{2n-m}{3} \right)!\left( \frac{4n+m}{3} \right)!}\] done
clear
D)
none of these done
clear
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question_answer2)
In the expansion of \[{{(1+3x+2{{x}^{2}})}^{6}}\], the coefficient of \[{{x}^{11}}\]is
A)
144 done
clear
B)
288 done
clear
C)
216 done
clear
D)
576 done
clear
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question_answer3)
The coefficient of the middle term in the binomial expansion in powers of x of \[{{(1+ax)}^{4}}\]and of \[{{(1-ax)}^{6}}\]is the same, if \[\alpha \]equals
A)
\[-\frac{5}{3}\] done
clear
B)
\[\frac{10}{3}\] done
clear
C)
\[-\frac{3}{10}\] done
clear
D)
\[\frac{3}{5}\] done
clear
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question_answer4)
The coefficient of \[{{x}^{5}}\]in the expansion of \[{{({{x}^{2}}-x-2)}^{5}}\]is
A)
-83 done
clear
B)
-82 done
clear
C)
-86 done
clear
D)
-81 done
clear
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question_answer5)
The coefficient of \[{{x}^{10}}\]in the expansion of \[{{(1+{{x}^{2}}-{{x}^{3}})}^{8}}\]is
A)
476 done
clear
B)
496 done
clear
C)
506 done
clear
D)
528 done
clear
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question_answer6)
If coefficient of \[{{a}^{2}}{{b}^{3}}{{c}^{4}}\]in \[{{(a+b+c)}^{m}}\] (where m\[\in \]N) is L (L\[\ne \]0), then in same expansion coefficient of \[{{a}^{4}}{{b}^{4}}{{c}^{1}}\]will be
A)
L done
clear
B)
\[\frac{L}{3}\] done
clear
C)
\[\frac{mL}{4}\] done
clear
D)
\[\frac{L}{2}\] done
clear
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question_answer7)
If the \[{{6}^{th}}\]term in the expansion of \[{{\left( \frac{1}{{{x}^{8/3}}}+{{x}^{2}}{{\log }_{10}}x \right)}^{8}}\]is 5600, then x equals
A)
1 done
clear
B)
\[{{\log }_{e}}10\] done
clear
C)
10 done
clear
D)
x does not exist done
clear
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question_answer8)
if\[I{{f}^{n+1}}{{C}_{r+1}}{{:}^{n}}{{C}_{r}}{{:}^{n-1}}{{C}_{r-1}}=11:6:3\], then nr=
A)
20 done
clear
B)
30 done
clear
C)
40 done
clear
D)
50 done
clear
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question_answer9)
The number of distinct terms in the expansion of \[{{\left( x+\frac{1}{x}+{{x}^{2}}+\frac{1}{{{x}^{2}}} \right)}^{15}}\]is/are (with respect to different power of x)
A)
255 done
clear
B)
61 done
clear
C)
127 done
clear
D)
none of these done
clear
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question_answer10)
If the sum of the coefficients in the expansion of \[{{(a+b)}^{n}}\]is 4096, then the greatest coefficient in the expansion is
A)
924 done
clear
B)
792 done
clear
C)
1594 done
clear
D)
none of these done
clear
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question_answer11)
The fractional part of \[{{2}^{4n}}/15\]is \[(n\in N)\]
A)
\[\frac{1}{15}\] done
clear
B)
\[\frac{2}{15}\] done
clear
C)
\[\frac{4}{15}\] done
clear
D)
none of these done
clear
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question_answer12)
The value of \[\frac{^{n}{{C}_{0}}}{n}+\frac{^{n}{{C}_{1}}}{n+1}+\frac{^{n}{{C}_{2}}}{n+2}+...+\frac{^{n}{{C}_{n}}}{2n}\]is equal to
A)
\[\int\limits_{0}^{1}{{{x}^{n-1}}{{(1-x)}^{n}}dx}\] done
clear
B)
\[\int\limits_{0}^{1}{{{x}^{n}}{{(x-1)}^{n-1}}dx}\] done
clear
C)
\[\int\limits_{0}^{1}{{{x}^{n-1}}{{(1+x)}^{n}}dx}\] done
clear
D)
\[\int\limits_{0}^{1}{{{(1-x)}^{n}}{{x}^{n-1}}dx}\] done
clear
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question_answer13)
If \[{{(1+x)}^{n}}={{C}_{0}}+{{C}_{1}}x+{{C}_{2}}{{x}^{2}}+....+{{C}_{n}}{{x}^{n}},\]then \[{{C}_{0}}{{C}_{2}}+{{C}_{1}}{{C}_{3}}+{{C}_{2}}{{C}_{4}}+...+{{C}_{n-2}}{{C}_{n}}=\]
A)
\[\frac{(2n)!}{{{(n!)}^{2}}}\] done
clear
B)
\[\frac{(2n)!}{(n-1)!(n+1)!}\] done
clear
C)
\[\frac{(2n)!}{(n-2)!(n+2)!}\] done
clear
D)
none of these done
clear
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question_answer14)
If \[{{(3+{{x}^{2008}}+{{x}^{2009}})}^{2010}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+....+{{a}_{n}}{{x}^{n}}\], then the value of \[{{a}_{0}}-\frac{1}{2}{{a}_{1}}-\frac{1}{2}{{a}_{2}}+{{a}_{3}}-\frac{1}{2}{{a}_{4}}-\frac{1}{2}{{a}_{5}}+{{a}_{6}}-...\]is
A)
\[{{3}^{2010}}\] done
clear
B)
1 done
clear
C)
\[{{2}^{2010}}\] done
clear
D)
none of these done
clear
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question_answer15)
The value of \[\sum\limits_{r=0}^{50}{{{(-1)}^{r}}}\]\[\frac{^{50}{{C}_{r}}}{r+2}\]is equal to
A)
\[\frac{1}{50\times 51}\] done
clear
B)
\[\frac{1}{52\times 50}\] done
clear
C)
\[\frac{1}{52\times 51}\] done
clear
D)
none of these done
clear
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question_answer16)
\[1+\frac{1}{3}x+\frac{1\times 4}{3\times 6}{{x}^{2}}+\frac{1\times 4\times 7}{3\times 6\times 9}{{x}^{3}}+...\]is equal to
A)
x done
clear
B)
\[{{(1+x)}^{1/3}}\] done
clear
C)
\[{{(1-x)}^{1/3}}\] done
clear
D)
\[{{(1-x)}^{-1/3}}\] done
clear
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question_answer17)
The coefficient of \[{{x}^{5}}\]in \[{{(1+2x+3{{x}^{2}}+...)}^{-3/2}}\]is \[\left( \left| x \right|<1 \right)\]
A)
21 done
clear
B)
25 done
clear
C)
26 done
clear
D)
none of these done
clear
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question_answer18)
If \[f(x)=1-x+{{x}^{2}}-{{x}^{3}}+...-{{x}^{15}}+{{x}^{16}}-{{x}^{17}}\]then the coefficient of \[{{x}^{2}}\]in f(x-1) is
A)
826 done
clear
B)
816 done
clear
C)
822 done
clear
D)
none of these done
clear
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question_answer19)
Let \[f(x)={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+...+{{a}_{n}}{{x}^{n}}+...\]and \[\frac{f(x)}{1-x}={{b}_{0}}+{{b}_{1}}x+{{b}_{2}}{{x}^{2}}+...+{{b}_{n}}{{x}^{n}}+....,\]then
A)
\[{{b}_{n}}={{b}_{n-1}}={{a}_{n}}\] done
clear
B)
\[{{b}_{n}}-{{b}_{n-1}}={{a}_{n}}\] done
clear
C)
\[{{b}_{n}}/{{b}_{n-1}}={{a}_{n}}\] done
clear
D)
none of these done
clear
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question_answer20)
p is a prime number and n<p<2n. if N=\[^{2n}{{C}_{n}}\], then
A)
p divides N done
clear
B)
\[{{p}^{2}}\]divides N done
clear
C)
p cannot divide N done
clear
D)
none of these done
clear
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question_answer21)
The sum of the coefficients of the first 10 terms in the expansion of (\[{{(1-x)}^{-3}}\] is ___________.
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question_answer22)
The number of distinct terms in the expansion of \[{{(x+{{y}^{2}})}^{13}}+{{({{x}^{2}}+y)}^{14}}\]is___.
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question_answer23)
If \[{{6}^{th}}\]term in the expansion of \[{{\left( \frac{3}{2}+\frac{x}{3} \right)}^{n}}\]is numerically greatest, when x=3, then the sum of possible integral values of 'n' is _____________.
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question_answer24)
The positive integer just greater than \[{{(1+0.0001)}^{10000}}\] is ____________.
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question_answer25)
If the sum of the coefficients in the expansion of (a+b) is 4096, then the greatest coefficient in the expansion is __________.
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