JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank

done Expansion of binomial theorem Total Questions - 15

• question_answer1)
  \[{{(\sqrt{2}+1)}^{6}}-{{(\sqrt{2}-1)}^{6}}=\] [MP PET 1984]
  A)
  101 done clear
  B)
  \[70\sqrt{2}\] done clear
  C)
  \[140\sqrt{2}\] done clear
  D)
  \[120\sqrt{2}\] done clear
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• question_answer2)
  \[{{x}^{5}}+10{{x}^{4}}a+40{{x}^{3}}{{a}^{2}}+80{{x}^{2}}{{a}^{3}}\]\[+80x{{a}^{4}}+32{{a}^{5}}=\]
  A)
  \[{{(x+a)}^{5}}\] done clear
  B)
  \[{{(3x+a)}^{5}}\] done clear
  C)
  \[{{(x+2a)}^{5}}\] done clear
  D)
  \[{{(x+2a)}^{3}}\] done clear
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• 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
  A)
  \[b<a\] done clear
  B)
  \[a<b\] done clear
  C)
  \[|a|\,<\,|b|\] done clear
  D)
  \[|b|\,<\,|a|\] done clear
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• question_answer4)
  The total number of terms in the expansion of \[{{(x+a)}^{100}}+{{(x-a)}^{100}}\] after simplification will be  [Pb. CET 1990]
  A)
  202 done clear
  B)
  51 done clear
  C)
  50 done clear
  D)
  None of these done clear
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• question_answer5)
  \[\frac{1}{\sqrt{5+4x}}\]can be expanded by binomial theorem, if
  A)
  \[x<1\] done clear
  B)
  \[|x|<1\] done clear
  C)
  \[|x|\,\,<\frac{5}{4}\] done clear
  D)
  \[|x|<\frac{4}{5}\] done clear
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• question_answer6)
  The value of \[{{(\sqrt{5}+1)}^{5}}-{{(\sqrt{5}-1)}^{5}}\]is [MP PET 1985]
  A)
  252 done clear
  B)
  352 done clear
  C)
  452 done clear
  D)
  532 done clear
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• 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]
  A)
  \[^{n+1}{{C}_{k+1}}\] done clear
  B)
  \[^{n}{{C}_{k}}\] done clear
  C)
  \[^{n}{{C}_{n-k-1}}\] done clear
  D)
  None of these done clear
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• question_answer8)
  The larger of \[{{99}^{50}}+{{100}^{50}}\] and \[{{101}^{50}}\] is [IIT 1980]
  A)
  \[{{99}^{50}}+{{100}^{50}}\] done clear
  B)
  Both are equal done clear
  C)
  \[{{101}^{50}}\] done clear
  D)
  None of these done clear
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• question_answer9)
  \[{{(1+x)}^{n}}-nx-1\] divisible (where \[n\in N\])
  A)
  by \[2x\] done clear
  B)
  by \[{{x}^{2}}\] done clear
  C)
  by \[2{{x}^{3}}\] done clear
  D)
  All of these done clear
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• question_answer10)
  If \[{{T}_{0}},{{T}_{1}},{{T}_{2}},....{{T}_{n}}\] represent the terms in the expansion of \[{{(x+a)}^{n}}\], then \[{{({{T}_{0}}-{{T}_{2}}+{{T}_{4}}-....)}^{2}}\] \[+{{({{T}_{1}}-{{T}_{3}}+{{T}_{5}}-....)}^{2}}=\]
  A)
  \[({{x}^{2}}+{{a}^{2}})\] done clear
  B)
  \[{{({{x}^{2}}+{{a}^{2}})}^{n}}\] done clear
  C)
  \[{{({{x}^{2}}+{{a}^{2}})}^{1/n}}\] done clear
  D)
    \[{{({{x}^{2}}+{{a}^{2}})}^{-1/n}}\] done clear
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• 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]
  A)
  9 done clear
  B)
  0 done clear
  C)
  5 done clear
  D)
  10 done clear
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• question_answer12)
  The greatest integer which divides the number \[{{101}^{100}}-1\], is [MP PET 1998]
  A)
  100 done clear
  B)
  1000 done clear
  C)
  10000 done clear
  D)
  100000 done clear
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• question_answer13)
  The approximate value of (1.0002)3000 is  [EAMCET 2002]
  A)
  1.6 done clear
  B)
  1.4 done clear
  C)
  1.8 done clear
  D)
  1.2 done clear
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• question_answer14)
  The positive integer just greater than  (1 +  0.0001)10000 is  [AIEEE 2002]  
  A)
  4 done clear
  B)
  5 done clear
  C)
  2 done clear
  D)
  3 done clear
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• question_answer15)
  The last digit in \[{{7}^{300}}\] is [Karnataka CET 2004]
  A)
  7 done clear
  B)
  9 done clear
  C)
  1 done clear
  D)
  3 done clear
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