JEE Main & Advanced Mathematics Permutations and Combinations Question Bank

done Multinomial Theorem, Number of Divisors, Miscellaneous problems Total Questions - 21

• question_answer1)
  If \[^{n}{{C}_{r}}={{\,}^{n}}{{C}_{r-1}}\] and \[^{n}{{P}_{r}}{{=}^{n}}{{P}_{r+1}}\], then the value of n is
  A)
  3 done clear
  B)
  4 done clear
  C)
  2 done clear
  D)
  5 done clear
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• question_answer2)
  \[^{n}{{P}_{r}}{{\div }^{n}}{{C}_{r}}\] = [MP PET 1984]
  A)
  \[n\,!\] done clear
  B)
  \[(n-r)!\] done clear
  C)
  \[\frac{1}{r!}\] done clear
  D)
  \[r\,!\] done clear
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• question_answer3)
  The number of numbers of 4 digits which are not divisible by 5 are
  A)
  7200 done clear
  B)
  3600 done clear
  C)
  14400 done clear
  D)
  1800 done clear
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• question_answer4)
  If \[^{n}{{P}_{r}}=840,{{\,}^{n}}{{C}_{r}}=35,\] then \[n\] is equal to [EAMCET 1986]
  A)
  1 done clear
  B)
  3 done clear
  C)
  5 done clear
  D)
  7 done clear
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• question_answer5)
  If  \[^{n}{{P}_{3}}{{+}^{n}}{{C}_{n-2}}=14n\], then \[n=\]
  A)
  5 done clear
  B)
  6 done clear
  C)
  8 done clear
  D)
  10 done clear
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• question_answer6)
  In  how many ways can  Rs. 16 be divided into 4 person when none of them get less than Rs. 3
  A)
  70 done clear
  B)
  35 done clear
  C)
  64 done clear
  D)
  192 done clear
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• question_answer7)
  A set contains \[(2n+1)\] elements. The number of sub-sets of the set which contain at most \[n\] elements is
  A)
  \[{{2}^{n}}\] done clear
  B)
  \[{{2}^{n+1}}\] done clear
  C)
  \[{{2}^{n-1}}\] done clear
  D)
  \[{{2}^{2n}}\] done clear
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• question_answer8)
  The number of divisors of 9600 including 1 and 9600 are [IIT Screening 1993]
  A)
  60 done clear
  B)
  58 done clear
  C)
  48 done clear
  D)
  46 done clear
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• question_answer9)
  Number of ways of selection of 8 letters from 24 letters of which 8 are \[a\], 8 are \[b\] and the rest unlike, is given by
  A)
  \[{{2}^{7}}\] done clear
  B)
  \[8\ .\ {{2}^{8}}\] done clear
  C)
  \[10\ .\ {{2}^{7}}\] done clear
  D)
  None of these done clear
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• question_answer10)
  If\[^{n}{{P}_{4}}=30{{\,}^{n}}{{C}_{5}}\], then \[n=\] [MP PET 1995]
  A)
  6 done clear
  B)
  7 done clear
  C)
  8 done clear
  D)
  9 done clear
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• question_answer11)
  The number of ordered triplets of positive integers which are solutions of the equation \[x+y+z=100\] is
  A)
  6005 done clear
  B)
  4851 done clear
  C)
  5081 done clear
  D)
  None of these done clear
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• question_answer12)
  If \[a,\ b,\ c,\ d,\ e\] are prime integers, then the number of divisors of \[a{{b}^{2}}{{c}^{2}}de\] excluding 1 as a factor, is
  A)
  94 done clear
  B)
  72 done clear
  C)
  36 done clear
  D)
  71 done clear
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• question_answer13)
  An n-digit number is a positive number with exactly \[n\] digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of \[n\] for which this is possible is [IIT 1998]
  A)
  6 done clear
  B)
  7 done clear
  C)
  8 done clear
  D)
  9 done clear
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• question_answer14)
  Number of divisors of \[n=38808\] (except 1 and n) is [RPET 2000]
  A)
  70 done clear
  B)
  68 done clear
  C)
  72 done clear
  D)
  74 done clear
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• question_answer15)
  If \[^{n}{{P}_{4}}=24.{{\,}^{n}}{{C}_{5}},\] then the value of n is  [Karnataka CET 2001]
  A)
  10 done clear
  B)
  15 done clear
  C)
  9 done clear
  D)
  5 done clear
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• question_answer16)
  If \[^{n}{{P}_{r}}\]= 720.\[^{n}{{C}_{r}},\] then r is equal to [Kerala (Engg.) 2001]
  A)
  6 done clear
  B)
  5 done clear
  C)
  4 done clear
  D)
  7 done clear
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• question_answer17)
  The sum \[\sum\limits_{i=0}^{m}{\left( \begin{matrix}    10  \\    i  \\ \end{matrix} \right)}\,\left( \begin{matrix}    20  \\    m-i  \\ \end{matrix} \right)\,,\] \[\left( \text{where}\,\left( \begin{matrix}    p  \\    q  \\ \end{matrix} \right)\,=0\,\text{if}\,p<q \right)\], is maximum when m is [IIT Screening  2002]
  A)
  5 done clear
  B)
  15 done clear
  C)
  10 done clear
  D)
  20 done clear
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• question_answer18)
  The sum of all positive divisors of 960 is  [Karnataka CET 2000]
  A)
  3048 done clear
  B)
  3087 done clear
  C)
  3047 done clear
  D)
  2180 done clear
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• question_answer19)
  The number of way to sit 3 men and 2 women in a bus such that total number of sitted men and women on each side is 3 [DCE 2005]
  A)
  5! done clear
  B)
  \[^{6}{{C}_{5}}\times 5!\] done clear
  C)
  \[6!\,{{\times }^{6}}{{P}_{5}}\] done clear
  D)
  \[5!\,{{+}^{6}}{{C}_{5}}\] done clear
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• question_answer20)
  There is a rectangular sheet of dimension \[(2m-1)\]×\[(2n-1)\], (where \[m>0,n>0)\]. It has been divided into square of unit area by drawing lines perpendicular to the sides. Find number of rectangles having sides of odd unit length [IIT Screening 2005]
  A)
  \[{{(m+n+1)}^{2}}\] done clear
  B)
  \[mn(m+1)\,(n+1)\] done clear
  C)
  \[{{4}^{m+n-2}}\] done clear
  D)
  \[{{m}^{2}}{{n}^{2}}\] done clear
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• question_answer21)
  If \[P(n,r)=1680\] and \[C(n,r)=70\], then \[69n+r!=\] [Kerala (Engg.)2005]
  A)
  128 done clear
  B)
  576 done clear
  C)
  256 done clear
  D)
  625 done clear
  E)
  1152 done clear
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