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: 
  • $$\dfrac{{\left( {^{26}{C_2} + \,{\,^4}{C_2}} \right)}}{{^{52}{C_2}}}$$
  • $$\dfrac{{\left( {^{26}{C_2} + {\,^4}{C_2} - {\,^2}{C_2}} \right)}}{{^{52}{C_2}}}$$
  • $$\dfrac{{^{30}{C_2}}}{{^{52}{C_2}}}$$
  • $$\dfrac{{^{39}{C_2}}}{{^{52}{C_2}}}$$
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 $$A_1, A_2,......A_{10}$$ can be ranked such that $$A_1$$ is always above $$A_{10}$$ is
  • $$5!$$
  • $$2(5!)$$
  • $$10!$$
  • $$\dfrac{1}{2}(10!)$$
$$3$$ 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
  • $$^{8}C_{3}$$
  • $$^{7}C_{3}$$
  • $$^{10}C_{3}$$
  • $$^{9}C_{3}$$
A _____ is an arrangement of all or part of set of object in a definite order.
  • permutation
  • function
  • combination
  • factorial
If $$^{n + 1}{C_3} = 4\,{\,^n}{C_2}$$ 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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