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CBSE Questions for Class 11 Engineering Maths Permutations And Combinations Quiz 2 - MCQExams.com

From a well shuffled pack of 52 playing cards two cards drawn at random. The probability that either both are red or both are kings is: 
  • (26C2+4C2)52C2
  • (26C2+4C22C2)52C2
  • 30C252C2
  • 39C252C2
Number of odd numbers of five distinct digits can be formed by the digits 0,1,2,3,4, is 
  • 24
  • 120
  • 48
  • 36
The number of ways in which ten candidates A1,A2,......A10 can be ranked such that A1 is always above A10 is
  • 5!
  • 2(5!)
  • 10!
  • 12(10!)
3 letters are posted in 5 letters boxes. If all the letters are not posted in the same box, then number of ways of posting is
  • 120
  • 125
  • 130
  • 124
There are 10 trees between two stations A and B. Three of them are to be cut down then the total number of ways so that no two trees are to be cut consecutively, is
  • 8C3
  • 7C3
  • 10C3
  • 9C3
A _____ is an arrangement of all or part of set of object in a definite order.
  • permutation
  • function
  • combination
  • factorial
If n+1C3=4nC2 then n=
  • 12
  • 10
  • 16
  • 11
If the letter of the word LATE be permuted and the words so formed be arranged as in a dictionary . Then the rank of LATE is :
  • 12
  • 13
  • 14
  • 15
If \left( {n + 1} \right)! = 12 \times (n - 1)!\;then\;n =
  • 3
  • 4
  • 2
  • 5
How many chords can be drawn through 21 points on a circle ?
  • 301
  • 210
  • 111
  • 220
If {2n_{C}}_{4} : {n_{C}}_{3} = 21:1, then find the value of n.
  • 4
  • 5
  • 6
  • 7
If ^{ 28 }{ C }_{ 2r }:^{ 24 }{ C }_{ 2r }=225:11, then find the value of r
  • r = 4
  • r = 3
  • r = 7
  • r = 8
If P (n, n) denotes the number of permutations of n different things taken all at a time then P (n, n ) is also identical to:
  • P ( n - 1 , n - 1 )
  • P ( n , n - 1 )
  • \mathrm { r } ! \mathrm { P } ( \mathrm { n } , \mathrm { n } - \mathrm { r } )
  • ( n - r ) \cdot P ( n , r )
The no .of ways of selecting 3 men and 2 women from 6 men and 6 women.
  • ^6C_3 ^6C_2
  • ^{12} C_5
  • ^6C_5
  • None of these
How many six letter words be made out of the letters of ASSIST ? In how many words the alphabets S alternates with other letters ?
  • 120,6
  • 720,\,12
  • 120,\,12
  • 720,\,24
The number of ways in which 6 rings can be worn on the four fingers of one hand is 
  • { 4 }^{ 6 }
  • ^{ 6 }{ C }_{ 4 }
  • { 6 }^{ 4 }
  • None of these
If the coefficients of three consecutive terms in the expansion of  (1+x)^n are in the ratio of 1:7:42, then n is divisible by-
  • 95
  • 55
  • 35
  • 11
When we realize a specific implementation of a pancake algorithm, every move when we find the greatest of the sized array and flipping can be modeled through ____________.
  • Combinations
  • Exponential functions
  • Logarithmic functions
  • Permutations
Two persons entered a Railway compartment in which 7 seats were vacant.The number of ways in which they can be seated is
  • 30
  • 42
  • 720
  • 360
No. of permutations of 25 dissimilar things taken more than 15 at a time when repetitions are allowed is
  • \dfrac{25}{24}({25}^{25}-{25}^{15})
  • \dfrac{25}{24}({25}^{25}-{25}^{10})
  • \dfrac{25}{24}({25}^{25}+{25}^{15})
  • \dfrac{25}{24}({25}^{25}+{25}^{10})
There are 8 types of pant pieces and 9 types of shirt pieces with a man. The number of ways in which a pair (1 pant, 1 shirt) can be stitched by the tailor is
  • 17
  • 56
  • 64
  • 72
If ^nP_r = ^nP{_r}{_+}{_1} and   ^nC_r = ^nC{_r}{_-}{_1} , then the values of n and r are:
  • r , 3
  • 3, 2
  • 4, 2
  • 3, 4
Using the  digits 0,  2, 4, 6,  8 not  more than once in any number, the number of 5 digited numbers that can be formed is
  • 16
  • 24
  • 120
  • 96
The number of different signals that can be formed by using any number of flags from 4 flags of different colours is
  • 24
  • 256
  • 64
  • 60
The product of n consecutive natural numbers is always divisible by
  • 4n!
  • 3n!
  • 2n!
  • n!
The number of words that can be formed using any number of letters of the word "KANPUR" without repeating any letter is
  • 720
  • 1956
  • 360
  • 370
 The value of expression {^4}{^7}C_4 + \sum _{i=1}^{5} {^5}{^{2-i}}C_3 is:
  • {^5}{^2}C_4
  • {^5}{^2}C_3
  • {^5}{^3}C_4
  • {^5}{^3}C_3
The number of rational numbers \dfrac {p}{q}, where p,q \in {1, 2, 3, 4, 5, 6} is
  • 23
  • 32
  • 36
  • 63
\displaystyle ^{14}C_{ 4 }+\sum _{ j=1 }^{ 4 } \quad ^{ (18-j) }C_{ 3 }=                  
  • ^{14}C_5
  • ^{18}C_5
  • ^{18}C_4
  • ^{19}C_4
If {^2}{^n}C_3 : ^nC_2  = 44 :3, then n =
  • 6
  • 7
  • 8
  • 9
If   {^1}{^5}C{_3}{_r} = {^1}{^5}C{_r}{_+}{_3} , then r=
  • \dfrac{3}{2}
  • 3
  • 4
  • 5
The number of unsuccessful attempts that can be made by a thief to open a number lock having 3 rings in which each rings contains 6 numbers is
  • 205
  • 200
  • 210
  • 215
If n is an integer between 0 and 21 then the minimum value of n!(21-n)! is
  • 9!2!
  • 10!11!
  • 20!
  • 21!
There are 'mn' letters and n post boxes. The number of ways in which these letters can be posted is:
  • (mn)^n
  • (mn)^m
  • m{^m}{^n}
  • n{^m}{^n}
The maximum number of persons in a country in which no two persons have an identical set of teeth assuming that there is no person without a tooth is
  • 2{^3}{^2}
  • 2{^3}{^2} - 1
  • 32!
  • 32! - 1
If ^nC{_{r-1}}= 36, ^nC_r=84, ^nC{_{r+1}}= 126, then (n,r) =
  • (9,6)
  • (9,5)
  • (9,3)
  • (9,2)
The number of products that can be formed with 8 prime numbers is:
  • 247
  • 252
  • 5
  • 248
A  telegraph post has 5 arms, each arm is capable of four distinct positions including the position of rest. The total number of signals that can be made is:
  • 625
  • 1023
  • 1024
  • 930
Let y be an element of the set A=\left\{1,2,3,5,6,10,15,30\right\} and x_1,x_2,x_3 be integers such that x_1x_2x_3=y, then the number of positive integral solutions of x_1x_2x_3=y is
  • 64
  • 27
  • 81
  • None of these
lf m=^n{C_{2}}, then ^m{C_{2}} equals
  • ^{n+1}C_{4}
  • 3.^{ n+1}C_{4}
  • ^{n}C_{4}
  • ^{n+1}C_{3}
Match the following:
\\ A)^{ n }{ P_{ r } }\quad \quad \quad \quad \quad \quad \quad 1)^{n+1}C_{ r }\\ B)^nC_{ r }\quad \quad \quad \quad \quad \quad     2){ \dfrac { n! }{ (n-r)!{r}! }  }\\ C)^nC_{ r }+^{n}C_{ r-1 }\quad \quad \quad 3)^nC_{ r }r!\\ D){ \dfrac { ^nC_{ r } }{ ^n{ C_{ r-1 } } }  }\quad \quad \quad \quad \quad \quad 4){ \dfrac { r }{ n-r+1 }  }\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad   5){ \dfrac { n-r+1 }{ r }  }
  • A-3,B-2,C-1, D-4
  • A-3, B-2,C-1, D-5
  • A-3, B-2,C-4, D-5
  • A-3, B-4,C-1, D-5
If ^{n}P_{r} = 30240 and ^{n}C_{r} = 252, then the ordered pair (n , r) =
  • (12, 6)
  • (10, 5)
  • (9 , 4)
  • (16, 7)
If ^{n-1}C_3 + {^{n-1}C_4} > {^nC_3}, then the least value of n is
  • 7
  • 8
  • 9
  • 10
The value of \displaystyle E = \frac { (1+17)(1+\frac { 17 }{ 2 } )(1+\frac { 17 }{ 3 } )......(1+\frac { 17 }{ 19 } ) }{ (1+19)(1+\frac { 19 }{ 2 } )(1+\frac { 19 }{ 3 } ).....(1+\frac { 19 }{ 17 } ) }  is,
  • 1
  • ^{36}C_{17}
  • \dfrac {2}{19}
  • ^{36}C_{18}
The expansion ^n C_r + 4.^nC_{ r-1 } + 6.^nC_{ r-2 }+4.^nC_{r -3 }+^n{ C_{r-4}}=
  • ^{ n+4 }C_{ r }
  • 2. ^{ n+4 }C_{ r - 1}
  • 4. ^nc_r
  • 11. ^nc_r
The number of rational numbers lying in the interval (2002, 2003) all of whose digits after the decimal point are non-zero and are in decreasing order is
  • \sum _{ i=1 }^{ 9 } 9P_{ i }
  • \sum _{ i=1 }^{ 10 } 9P_{ i }
  • 2^{ 9 }-1
  • 2^{ 10 }-1
If  ^{ n }{ C_{ r-1 } }+^{ n+1 }C_{ r-1 }+^{ n+2 }C_{ r-1 }+.......+^{ 2n }{ C_{ r-1 } },=^{ 2n+1 }C_{ { r^{ 2 }-132 } }-^{ n }C_{ r }, then the value of r
  • 10
  • 11
  • 12
  • 13
 lf ^nC_{ 3 }=^{ n }C_{ 9  }, then   ^n C_{ 2 }=
  • 66
  • 132
  • 72
  • 98
If n and r are integers such that 1\le r \le n, then n . C (n-1, r-1) =
  • C (n, r)
  • n . C (n, r)
  • r C (n, r)
  • (n - 1) . C (n, r)
 If n and r are positive integers such that r < n, then   ^nC_r +  ^nC_{r-1}  =
  • ^{2n}C_{2r-1}
  • ^{(n +1)}C_r
  • ^nC_{r+1}
  • ^{(n+1)}C_{r+1}
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