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question_answer1) If \[^{n}{{C}_{r}}={{\,}^{n}}{{C}_{r-1}}\] and \[^{n}{{P}_{r}}{{=}^{n}}{{P}_{r+1}}\], then the value of n is
question_answer2) \[^{n}{{P}_{r}}{{\div }^{n}}{{C}_{r}}\] = [MP PET 1984]
question_answer3) The number of numbers of 4 digits which are not divisible by 5 are
question_answer4) If \[^{n}{{P}_{r}}=840,{{\,}^{n}}{{C}_{r}}=35,\] then \[n\] is equal to [EAMCET 1986]
question_answer5) If \[^{n}{{P}_{3}}{{+}^{n}}{{C}_{n-2}}=14n\], then \[n=\]
question_answer6) In how many ways can Rs. 16 be divided into 4 person when none of them get less than Rs. 3
question_answer7) A set contains \[(2n+1)\] elements. The number of sub-sets of the set which contain at most \[n\] elements is
question_answer8) The number of divisors of 9600 including 1 and 9600 are [IIT Screening 1993]
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
question_answer10) If\[^{n}{{P}_{4}}=30{{\,}^{n}}{{C}_{5}}\], then \[n=\] [MP PET 1995]
question_answer11) The number of ordered triplets of positive integers which are solutions of the equation \[x+y+z=100\] is
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
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]
question_answer14) Number of divisors of \[n=38808\] (except 1 and n) is [RPET 2000]
question_answer15) If \[^{n}{{P}_{4}}=24.{{\,}^{n}}{{C}_{5}},\] then the value of n is [Karnataka CET 2001]
question_answer16) If \[^{n}{{P}_{r}}\]= 720.\[^{n}{{C}_{r}},\] then r is equal to [Kerala (Engg.) 2001]
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]
question_answer18) The sum of all positive divisors of 960 is [Karnataka CET 2000]
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]
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]
question_answer21) If \[P(n,r)=1680\] and \[C(n,r)=70\], then \[69n+r!=\] [Kerala (Engg.)2005]
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