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question_answer1) The coefficient of \[{{t}^{4}}\] in the expansion of \[{{\left( \frac{1-{{t}^{6}}}{1-t} \right)}^{3}}\]is
question_answer2) Let \[{{(x+10)}^{50}}+{{(x-10)}^{50}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+....+{{a}_{50}}{{x}^{50}},\]for all \[x\in R;\] then \[\frac{{{a}_{2}}}{{{a}_{0}}}\] is equal to
question_answer3) The sum of the co-efficients of all even degree terms in x in the expansion of \[{{\left( x+\sqrt{{{x}^{3}}-1} \right)}^{6}}+{{\left( x-\sqrt{{{x}^{3}}-1} \right)}^{6}},\] \[(x>1)\] is equal to:
question_answer4) If the fourth term in the binomial expansion of \[{{\left( \sqrt{\frac{1}{{{x}^{1+{{\log }_{10}}x}}}}+{{x}^{\frac{1}{12}}} \right)}^{6}}\] is equal to 200, and \[x>1,\]then the value of x is
question_answer5) The expression \[{{[x+{{({{x}^{3}}-1)}^{1/2}}]}^{5}}+{{[x-{{({{x}^{3}}-1)}^{1/2}}]}^{5}}\]is a polynomial of degree
question_answer6) The remainder when \[{{27}^{40}}\] is divided by 12 is
question_answer7) If \[{{r}^{th}}\] and \[{{(r+1)}^{th}}\] terms in the expansion of \[{{(p+q)}^{n}}\] are equal, then \[\frac{(n+1)q}{r(p+q)}\] is
question_answer8) If the ratio of the coefficient of third and fourth term in the expansion of \[{{\left( x-\frac{1}{2x} \right)}^{n}}\] is \[~1:2,\] then the value of \[-n\] will be
question_answer9) Coefficient of \[{{x}^{5}}\] in \[{{(1+2x+3{{x}^{2}}+.......)}^{3/2}}\] is
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
question_answer11) For natural numbers m, n if \[{{(1-y)}^{m}}\,{{(1+y)}^{n}}\]\[=1+{{a}_{1}}y+{{a}_{2}}{{y}^{2}}+.....\] and \[{{a}_{1}}={{a}_{2}}=10,\] then \[(m+n)\] is
question_answer12) The coefficient of the middle term in the binomial expansion in powers of x of \[{{(1+\alpha x)}^{4}}\] and of \[{{(1-\alpha x)}^{6}}\] is the same, then \[-\alpha \] equals to
question_answer13) If the coefficient of \[{{x}^{7}}\] in \[{{\left[ a{{x}^{2}}+\left( \frac{1}{bx} \right) \right]}^{11}}\] equals the coefficient of \[{{x}^{-7}}\] in \[{{\left[ ax-\left( \frac{1}{b{{x}^{2}}} \right) \right]}^{11}},\] then a and b satisfy the relation
question_answer14) The number of integral terms in the expansion of \[{{(\sqrt{3}+\sqrt[8]{5})}^{256}}\] is
question_answer15) \[{{\left( \sqrt[6]{3}\,\sqrt{2}+\frac{1}{\sqrt[3]{3}} \right)}^{n}},\] \[\frac{{{t}_{7}}\text{from the }{{\text{1}}^{st}}}{{{t}_{7}}\text{from the last}}=\frac{1}{6},\] then the value of n is
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