CBSE Questions for Class 11 Engineering Maths Permutations And Combinations Quiz 10 - MCQExams.com

If $$\alpha = ^{m}C_{2}$$, then $$^{\alpha}C_{2}$$ is equal to
  • $$^{m + 1}C_{4}$$
  • $$^{m - 1}C_{4}$$
  • $$3 \ \  ^{m + 2}C_{4}$$
  • $$3 \ \  ^{m + 1}C_{4}$$
All possible number are formed using the digits $$1,1,2,2,2,2,3,4,4$$ taken all at a time. The number of such number in which the odd digits occupy even places is:
  • $$175$$
  • $$162$$
  • $$160$$
  • $$180$$
There are $$31$$ objects in a bag in which $$10$$ are identical, then the number of ways of choosing $$10$$ objects from bag is?
  • $$2^{20}$$
  • $$2^{20}-1$$
  • $$2^{20}+1$$
  • $$2^{21}$$
A group of students comprises of $$5$$ boys and $$n$$ girls. If the number of ways, in which a team of $$3$$ students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is $$1750$$, then $$n$$ is equal to
  • $$25$$
  • $$28$$
  • $$27$$
  • $$24$$
A team of three persons with at least one boy and atleast one girl is to be formed from $$5$$ boys and $$n$$ girls. If the number of sum teams is $$1750$$, then the value of $$n$$ is
  • $$24$$
  • $$28$$
  • $$27$$
  • $$25$$
If $$a, b$$ and $$c$$ are the gratest values of $$^{19}C_p, \, ^{20}C_q$$ and $$^{21}C_r$$ respectively, then :
  • $$\dfrac{a}{10} = \dfrac{b}{11} = \dfrac{c}{21}$$
  • $$\dfrac{a}{10} = \dfrac{b}{11} = \dfrac{c}{42}$$
  • $$\dfrac{a}{11} = \dfrac{b}{22} = \dfrac{c}{21}$$
  • $$\dfrac{a}{11} = \dfrac{b}{22} = \dfrac{c}{42}$$
If $$\dfrac{1}{6!}+\dfrac{1}{7!}=\dfrac{x}{8!}$$, then $$x=?$$
  • $$32$$
  • $$48$$
  • $$56$$
  • $$64$$
$$\dfrac{^nC_r}{^nC_{r-1}}=?$$
  • $$\dfrac{n-r}{r}$$
  • $$\dfrac{n-r-1}{r}$$
  • $$\dfrac{n-r+1}{r}$$
  • None of these
$$^{36}C_{34}=?$$
  • $$1224$$
  • $$612$$
  • $$630$$
  • None of these
There are $$10$$ points in a plane, out of which $$4$$ points are collinear. The number of line segments obtained from the pairs of these points is?
  • $$39$$
  • $$40$$
  • $$41$$
  • $$45$$
If $$^{n}C_3=220$$, then $$n=?$$
  • $$9$$
  • $$10$$
  • $$11$$
  • $$12$$
If $$^nC_{10}={^{n}C_{14}}$$, then $$n=?$$
  • $$4$$
  • $$24$$
  • $$14$$
  • $$10$$
There are $$10$$ points in a plane, out of which $$4$$ points are collinear. The number of triangles formed with vertices as these point is?
  • $$20$$
  • $$120$$
  • $$116$$
  • None of these
If $$^{n}C_r+{^nC_{r+1}}={^{n+1}C_x}$$, then $$x=?$$
  • $$r-1$$
  • $$r$$
  • $$r+1$$
  • $$n$$
$$^{60}C_{60}=?$$
  • $$60!$$
  • $$1$$
  • $$\dfrac{1}{60}$$
  • None of these
Out of $$7$$ consonants and $$4$$ vowels, how many words of $$3$$ consonants and $$2$$ vowels can be formed?
  • $$330$$
  • $$1050$$
  • $$6300$$
  • $$25200$$
If $$^{n}C_{18}={^nC_{12}}$$, then $$^{32}C_n=?$$
  • $$248$$
  • $$496$$
  • $$992$$
  • None of these
If a denotes the number of permutation of $$x+2$$ things taken all at a time, $$b$$ the number of permutation of x things taken 11 at a time and c the number of permutation of $$x-11$$ things taken all at a time such that $$a=182 bc$$, then the value of $$x$$ is
  • $$15$$
  • $$12$$
  • $$10$$
  • $$18$$
How many $$3$$-digit numbers are there?
  • $$648$$
  • $$729$$
  • $$900$$
  • $$1000$$
When simplified, the expression 
$$^{ 47 }{ C }_{ 4 }+\sum _{ j=1 }^{ 5 }$$   $$^{ 52-j }{ C }_{ 3 } $$ equals to
  • $$^{ 47 }{ C }_{ 5 }$$
  • $$^{ 49 }{ C }_{ 4 }$$
  • $$^{ 52 }{ C }_{ 5 }$$
  • $$^{ 52 }{ C }_{ 4 }$$
The total number of 5- digit telephone numbers that can be composed with distinct digits, is
  • $$ ^{10}P_{2}$$
  • $$ ^{10}P_{5}$$
  • $$ ^{10}C_{2}$$
  • None of these
If $$^{ n }{ C }_{ r-1 }=10,$$ $$^{ n }{ C }_{ r }=45,$$ and $$^{ n }{ C }_{ r+1 }=120,$$ then r equals
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
In an examination, a candidate has to pass in each of the five subjects. In how many ways can he fail?
  • $$5$$
  • $$10$$
  • $$21$$
  • $$31$$
A committee of $$5$$ is to be formed out of $$6$$ gents and $$4$$ ladies. In how many ways can this be done when each committee may have at the most $$2$$ ladies?
  • $$120$$
  • $$160$$
  • $$180$$
  • $$186$$
$$12$$ persons meet in a room and each shakes hands with all the others. How many handshakes are there?
  • $$144$$
  • $$132$$
  • $$72$$
  • $$66$$
In how many ways can a committee of $$5$$ members be selected from $$6$$ men and $$5$$ ladies, consisting of $$3$$ men and $$2$$ ladies?
  • $$25$$
  • $$50$$
  • $$100$$
  • $$200$$
Out of $$5$$ men and $$2$$ women, a committee of $$3$$ is to be formed. In how many ways can it be formed if at least one woman is included in each committee?
  • $$21$$
  • $$25$$
  • $$32$$
  • $$50$$
The exponent of 3 in $$100!$$ is 
  • $$12$$
  • $$24$$
  • $$48$$
  • $$96$$
The letters of word 'ZENITH' are written in all positive ways. If all these words are written in the order of a dictionary, then the rank of the word 'ZENITH' is
  • $$716$$
  • $$692$$
  • $$698$$
  • $$616$$
Find the values of $$ ^{61}C_{57} -^{60}C_{56} $$
  • $$ ^{61}C_{58} $$
  • $$ ^{60}C_{57} $$
  • $$ ^{60}C^{58} $$
  • $$ ^{60}C_{56} $$
If $$ ^{15}C_{3r} = ^{15}C_{r+3} $$ then r equal to :
  • $$ 5 $$
  • $$ 4 $$
  • $$ 3 $$
  • $$ 2 $$
$$ ^{ 47 }C_{ 4 }$$ +$$ \sum _{ r=1 }^{ 5 }$$ .$$^{ 52-r }C_{ 3 } $$is equal to :

  • $$ ^{51}C_4 $$
  • $$ ^{52}C_4 $$
  • $$ ^{53}C_4 $$
  • None of these
If $$_{  }^{ n+1 }{ { C }_{ r+1 } }$$: $$_{  }^{ n }{ { C }_{ r } }$$: $$_{  }^{ n-1 }{ { C }_{ r-1 } }=$$ 11: 6: 3 , then $$r=$$
  • 20
  • 30
  • 40
  • 5
lf $$\displaystyle x,y\in(0,30)$$ such that $$ [ \dfrac{x}{3}]+[\dfrac{3x}{2}]+[\dfrac{y}{2}]+[\dfrac{3y}{4}]=\dfrac{11x}{6}+\dfrac{5y}{4} $$ (where [x] denote greatest integer $$ \le x $$) then the number of ordered pairs $$(x, y)$$ is
  • 10
  • 20
  • 24
  • 28
If $$ n =  ^mC_2 $$, then the value of  $$ ^nC_2 $$ is given by
  • $$ ^{m+1}C_4 $$
  • $$ ^{m-1}C_4 $$
  • $$ ^{m+2}C_4 $$
  • $$ 3.^{m+1}C_4 $$
Let $$\displaystyle \mathrm{S}_{1}=\sum_{\mathrm{j}=1}^{10}j(j-1)^{10}\mathrm{C}_{\mathrm{j}}$$ , $$\displaystyle \mathrm{S}_{2}=\sum_{\mathrm{j}=1}^{10}j^{10}\mathrm{C}_{\mathrm{j}}$$ and $$\displaystyle \mathrm{S}_{3}=\sum_{\mathrm{j}=1}^{10}j^{2}10_{\mathrm{C}_{\mathrm{j}}}$$.
Statement-1: $$\mathrm{S}_{3}=55\times 2^{9}$$
Statement-2: $$\mathrm{S}_{1}=90\times 2^{8}$$ and $$\mathrm{S}_{2}=10\times 2^{8}$$.
  • Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1
  • Statement-1 is true, Statement-2 is false
  • Statement-1 is false, Statement-2 is true
  • Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1
 If $$ ^{n-1}C_r=(k^2-3 ) ^nC_{r+1} $$, then $$ k\in $$
  • $$ (\infty ,-2) $$
  • $$ (2,\infty ) $$
  • $$ [-\sqrt { 3 } ,\sqrt { 3 } ] $$
  • $$ (\sqrt { 3 } ,2] $$
In a test there were $$n$$ questions. In the test $$ 2^{n - i} $$ students gave wrong answers to at least $$i$$ questions $$i = 1, 2, 3 .... n$$. If the total number of wrong answers given is $$2047$$, then $$n$$ is
  • $$12$$
  • $$11$$
  • $$10$$
  • $$13$$
Which of the following is equal to $$\dfrac{1.3.5....(2n-1)}{2.4.6....(2n)}$$?
  • $$(2n!) \div (2^n(n!))^2$$
  • $$(2n!) \div n!$$
  • $$(2n - 1) \div (n - 1)!$$
  • $$2^n$$
The value of $$x$$ in the equation $$3 \times ^{x+1}C_2 = 2\times ^{x+2}C_2, \space x\space \in N$$ is
  • $$x = 4$$
  • $$x = 5$$
  • $$x= 6$$
  • $$x= 7$$
The value of $$\displaystyle \sum_{r=0}^{n-1} {\;}^nC_r / (^nC_r+^nC_{r+1})$$ equals
  • $$n+1$$
  • $$n/2$$
  • $$n+2$$
  • none of these
How many different signals can be made by hoisting $$6$$ differently coloured flags one above the other, when any number of them may be hoisted at once?
  • 1956
  • 1955
  • 1900
  • 1901
$$14X's$$ have to be placed in the squares of the above figure such that each row contains at least one $$X$$. In how many ways can this be done?
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  • 96
  • 104
  • 112
  • 118
The letters of word $$OUGHT$$ are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word $$TOUGH$$ in this dictionary.
  • 89
  • 90
  • 91
  • 92
If all the permutations of the letters in the word 'OBJECT' are arranged (and numbered serially) in alphabetical order as in a dictionary, then the $$717^{th}$$ word is
  • TOJECB
  • TOEJBC
  • TOCJEB
  • TOJCBE
The value of $$^{47}C_4 + \displaystyle\sum_{r=1}^{5}{^{52-r}C_3}$$=
  • $$^{52}C_2$$
  • $$^{52}C_3$$
  • $$^{52}C_4$$
  • $$^{52}C_5$$
$$p$$ is a prime number and $$n < p < 2n$$. If $$N=^{2n}C_n$$, then 
  • $$p$$ divides $$N$$ completely
  • $$p^2$$ divides $$N$$ completely
  • $$p$$ cannot divide $$N$$
  • none of these
The rank of the word $$NUMBER$$ obtained, if the letters of the word $$NUMBER$$ are written in all possible orders and these words are written out as in a dictionary is

  • $$468$$
  • $$469$$
  • $$470$$
  • $$471$$
If the difference of the number of arrangements of three things from a certain number of dissimilar things and the number of selections of the same number of things from them exceeds $$ 100$$, then the least number of dissimilar things is
  • $$8$$
  • $$6$$
  • $$5$$
  • $$7$$
$$^nC_r + \displaystyle\sum_{j=0}^{3}{^{n+j}C_{r+1+j}} = $$_________________
  • $$^{n+3}C_{r+3}$$
  • $$^{n}C_{r+4}$$
  • $$^{n+1}C_{r+4}$$
  • $$^{n+4}C_{r+4}$$
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