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question_answer1) When \[{{2}^{301}}\] is divided by 5, then find least positive remainder.
question_answer2) The values of x, for which the 6th term in the expansion of \[{{\left( {{2}^{{{\log }_{2}}\sqrt{\left( {{9}^{x-1}}+7 \right)}}}+\frac{1}{{{2}^{\left( 1/5 \right){{\log }_{2}}\left( {{3}^{x-1}}+1 \right)}}} \right)}^{7}}\] is 84 are \[{{x}_{1}}\And {{x}_{2}}\] then find value of \[{{x}_{1}}+{{x}_{2}}\].
question_answer3) In the binomial expansion of\[{{\left( \sqrt[3]{2}+\frac{1}{\sqrt[3]{3}} \right)}^{n}}\], the ratio of the 7th term from the beginning to the 7th term from the end is 1: 6 ; then find n.
question_answer4) If \[{{a}^{2}}+b=2\] then maximum value of term independent of x in expression of \[{{(a{{x}^{1/6}}+b{{x}^{-1/3}})}^{9}}(a>0,\,b>0)\] is \[{{9}^{k}}+k+1\], then find value of k.
question_answer5) If the term independent of x in \[{{\left( \sqrt{x}-\frac{k}{{{x}^{2}}} \right)}^{10}}\]is 405, then find value of k.
question_answer6) Number of irrational terms in expansion of \[{{\left( \sqrt{3}+\sqrt{7} \right)}^{17}}\] is equal to \[3k+{{k}^{2}}\] then find value of k.
question_answer7) If the third term in the expansion of \[{{\left[ x+{{x}^{{{\log }_{10}}x}} \right]}^{5}}\] is equal to 10,00,000, then \[x=\]
question_answer8) If \[^{50}{{C}_{4}}+\sum\limits_{r=1}^{6}{^{56-r}{{C}_{3}}{{=}^{50+k}}{{C}_{4}}}\]then find k.
question_answer9) If\[{{\left( 1+x-2{{x}^{2}} \right)}^{6}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{12}}{{x}^{12}},\] then find the value of expression\[{{a}_{2}}+{{a}_{4}}+{{a}_{6}}+.....+{{a}_{12}}\].
question_answer10) If \[{{2.}^{10}}{{C}_{0}}+\frac{{{2}^{2}}}{2}{{.}^{10}}{{C}_{1}}+\frac{{{2}^{3}}}{3}{{.}^{10}}{{C}_{2}}+.....+{{\frac{2}{11}}^{11}}{{.}^{10}}{{C}_{10}}\]\[=\frac{{{3}^{k}}-1}{11}\]then find k.
question_answer11) If the coefficient of \[{{x}^{-7}}\] in \[{{\left( 2x-\frac{1}{3{{x}^{2}}} \right)}^{11}}\] is \[^{11}{{C}_{6}}\frac{{{2}^{5}}}{{{3}^{k}}}\] then find k.
question_answer12) The sum of the series \[^{10}{{C}_{1}}.4{{+}^{10}}{{C}_{2}}{{4}^{2}}+.....{{+}^{10}}{{C}_{10}}{{4}^{10}}\]is \[{{5}^{k}}-1\] then find k.
question_answer13) If the 17th and 18th terms of the expansion \[{{\left( 2+a \right)}^{50}}\]are equal, then find the value of 'a'.
question_answer14) Find the coefficient of \[{{x}^{5}}\]in the expansion of\[{{\left( 1+{{x}^{2}} \right)}^{4}}{{\left( 1+x \right)}^{5}}\].
question_answer15) Find the number of rational terms in the expansion of\[{{\left( {{7}^{1/3}}+{{11}^{1/9}} \right)}^{6561}}\].
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