Permutation & Combination

Are you preparing for campus placements,Banking,SSC, IAS, Insurance,Defence and other competitive exams? Then, make sure to take some time in practicing the Permutation & Combination questions and answer in Quantitative Aptitude. Moreover, only those questions are included that are relevant and likely to be asked in any competitive exam. So, take these questions and answer, brush up your skills and practice to stay fully prepared for any your exam.

• Q22.For $2\le \text{r}\le \text{n},\left(\begin{array}{c}n\\ r\end{array}\right)+2\left(\begin{array}{c}n\\ r-1\end{array}\right)+\left(\begin{array}{c}n\\ r-2\end{array}\right)$ is equal to

  A) $\left(\begin{array}{c}n+1\\ r-1\end{array}\right)$
  B) $2\left(\begin{array}{c}n+1\\ r+1\end{array}\right)$
  C) $2\left(\begin{array}{c}n+r\\ r\end{array}\right)$
  D) $\left(\begin{array}{c}n+2\\ r\end{array}\right)$
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• Q23.The exponent of 5 in $${}^{100}{C}_{50}$$ is

  A) 1
  B) 2
  C) 3
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• Q24. Let f(x) denotes the No. of different ways the positive integer k can be expressed as the sum of 1’s and 2’s for x.
  f(x)=4
  4 = 1 + 1 + 1 + 1
  = 1 + 1 + 2
  = 1 + 2 + 1
  = 2 + 1 + 1
  = 2 + 2
  Then value of f (6) is

  A) 10
  B) 13
  C) 16
  D) 19
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• Q25.The No. of different ways the letters of the word SHWETA can be placed in the 8 boxes of the given below such that no row empty is equal to
  

  A) 26
  B) 26 × 6!
  C) 6!
  D) 2!× 6!
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• Q26.The least positive integral value of k which satisfies the inequality $${}^{10}{C}_{k–1}>{2.}^{10}{C}_k$$ is:

  A) 7
  B) 8
  C) 9
  D) 10
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• Q27. Find the number of one–one mappings from A to B such that $$f\left(a_i\right)\ne b_i,i=1,2,3,4,5,6,$$ given A =$$\left\{a_1,a_2,a_3,a_4,a_5,a_6\right\},B=\left\{b_1,b_2,b_3,b_4,b_5,b_6\right\}.$$

  A) 720
  B) 265
  C) 360
  D) 145
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• Q28.When simplified, the expression $${}^{47}{C}_4+{\displaystyle \sum }_{\text{p}=1}^5{}^{52-\text{p}}{\text{C}}_3$$ equals

  A) $${}^{47}{C}_{5 }$$
  B) $${}^{49}{C}_4$$
  C) $${}^{52}{C}_5$$
  D) $${}^{52}{C}_4$$
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