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question_answer1) \[{{(\sqrt{2}+1)}^{6}}-{{(\sqrt{2}-1)}^{6}}=\] [MP PET 1984]
question_answer2) \[{{x}^{5}}+10{{x}^{4}}a+40{{x}^{3}}{{a}^{2}}+80{{x}^{2}}{{a}^{3}}\]\[+80x{{a}^{4}}+32{{a}^{5}}=\]
question_answer3) The formulae\[{{(a+b)}^{m}}={{a}^{m}}+m{{a}^{m-1}}b\]\[+\frac{m(m-1)}{1.2}{{a}^{m-2}}{{b}^{2}}+....\] holds when
question_answer4) The total number of terms in the expansion of \[{{(x+a)}^{100}}+{{(x-a)}^{100}}\] after simplification will be [Pb. CET 1990]
question_answer5) \[\frac{1}{\sqrt{5+4x}}\]can be expanded by binomial theorem, if
question_answer6) The value of \[{{(\sqrt{5}+1)}^{5}}-{{(\sqrt{5}-1)}^{5}}\]is [MP PET 1985]
question_answer7) In the expansion of the following expression\[1+(1+x)+\]\[{{(1+x)}^{2}}+.....+{{(1+x)}^{n}}\]the coefficient of \[{{x}^{k}}(0\le k\le n)\] is [RPET 2000]
question_answer8) The larger of \[{{99}^{50}}+{{100}^{50}}\] and \[{{101}^{50}}\] is [IIT 1980]
question_answer9) \[{{(1+x)}^{n}}-nx-1\] divisible (where \[n\in N\])
question_answer10) If \[{{T}_{0}},{{T}_{1}},{{T}_{2}},....{{T}_{n}}\] represent the terms in the expansion of \[{{(x+a)}^{n}}\], then \[{{({{T}_{0}}-{{T}_{2}}+{{T}_{4}}-....)}^{2}}\] \[+{{({{T}_{1}}-{{T}_{3}}+{{T}_{5}}-....)}^{2}}=\]
question_answer11) The number of non-zero terms in the expansion of \[{{(1+3\sqrt{2}x)}^{9}}+{{(1-3\sqrt{2}x)}^{9}}\] is [EAMCET 1991]
question_answer12) The greatest integer which divides the number \[{{101}^{100}}-1\], is [MP PET 1998]
question_answer13) The approximate value of (1.0002)3000 is [EAMCET 2002]
question_answer14) The positive integer just greater than (1 + 0.0001)10000 is [AIEEE 2002]
question_answer15) The last digit in \[{{7}^{300}}\] is [Karnataka CET 2004]
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