CBSE Questions for Class 11 Engineering Maths Permutations And Combinations Quiz 6 - MCQExams.com

The value of $$\dfrac {(n + 2)! - (n + 1)!}{n!} $$ is:
  • $$(n + 2)!$$
  • $$(n + 1)!$$
  • $$(n + 2)^{2}$$
  • $$(n + 1)^{2}$$
  • $$n$$
Six points were chosen on a circle and every possible chord was drawn. Two chords, which do not have the common points are named separately. How many pairs of separate chords exist in the situation described above?
  • $$26$$
  • $$28$$
  • $$30$$
  • $$34$$
If 100! = $$\displaystyle { 2 }^{ a }{ 3 }^{ b }{ 5 }^{ c }{ 7 }^{ d }...$$, then
  • $$a=97$$
  • $$\displaystyle b=\frac { 1 }{ 2 } \left( a+1 \right) $$
  • $$\displaystyle c=\frac { 1 }{ 2 } b$$
  • $$\displaystyle d=\frac { 1 }{ 3 } b$$
In how many different orders can five boys stand on a line?
  • 40
  • 50
  • 80
  • 120
Let $$\boxed { n }$$ be defined as $$\frac{(n+2)!}{(n-1)!}$$, what is the value of $$\frac{\boxed{7}}{\boxed {3}}$$ ?
  • 4.4
  • 8.4
  • 12.4
  • 16.4
  • 20.4
If $$^6P_r = 360$$ and $$^6C_r =15$$,then find $$r?$$
  • $$5$$
  • $$6$$
  • $$4$$
  • $$3$$
Find the coefficient of the middle term of the expansion $$\left (x-\dfrac{1}{2y}\right)^{10}$$:
  • $$-\dfrac{63}{8}$$
  • $$24$$
  • $$-\dfrac{33}{4}$$
  • $$-33$$
A company has $$5$$ men and $$6$$ women. What are the number of ways of selecting a group of eight persons?
  • $$165$$
  • $$185$$
  • $$205$$
  • $$225$$
The value of $${ }^{10}C_1 +{ }^{10}C_2 + { }^{10}C_3 + ... + { }^{10}C_9$$ is
  • $$2^{10}$$
  • $$2^{11}$$
  • $$2^{10}-2$$
  • $$2^{10}-1$$
If $$^{40}C_{n+7} = ^{40}C_{4n-2},$$ then all the values of n are given by
  • $$28$$
  • $$3,6$$
  • $$3,7$$
  • $$6$$
Ten different letters of alphabet are given, words with five letters are formed with these given letters. Then the number of words which have at least one letter repeated
  • $$69760$$
  • $$30240$$
  • $$99748$$
  • $$42386$$
If, $$\dfrac{1}{^5C_r}+\dfrac{1}{^6C_r} = \dfrac{1}{^4C_r}$$, then the value of $$r$$ equals to
  • $$4$$
  • $$2$$
  • $$5$$
  • $$3$$
When listing the integers from $$1$$ to $$1000$$, how many times the digit $$5$$ be written?
  • $$297$$
  • $$243$$
  • $$300$$
  • $$273$$
If $$^nC_8 = ^nC_{27}$$, then what is the value of $$n?$$
  • $$35$$
  • $$22$$
  • $$28$$
  • $$41$$
The exponent of $$18$$ in $$200!$$, is
  • $$24$$
  • $$46$$
  • $$47$$
  • $$48$$
There are $$8$$ true/false questions in an examination.The number of ways in which this questions can be answered, is
  • $$256$$
  • $$1024$$
  • $$16$$
  • $$64$$
The total number of five digit numbers the sum of whose digits is odd is 
  • $$9\times 10^4$$
  • $$\dfrac{9\times 10^4}{2}$$
  • $$10^5$$
  • none of these
There are $$8$$ men and $$10$$ women and you need to form a committee of $$5$$ men and $$6$$ women. In how many ways can the committee be formed? 
  • $$10420$$
  • $$11420$$
  • $$11760$$
  • None of these
A box contains $$2$$ white balls,$$3$$ black balls and $$4$$ red balls.In how many ways can three balls can be drawn from the box if atleast one black ball is to be included in the draw?
  • $$32$$
  • $$48$$
  • $$64$$
  • $$96$$
The total number of five digit numbers the sum of whose digits is even is 
  • $$4.5\times {10}^4$$
  • $$9\times{10}^4$$
  • $${10}^5$$
  • none of these
How many quadrilaterals can be formed by joining the vertices of an octagon?
  • $$65$$
  • $$60$$
  • $$70$$
  • $$64$$
The number of values of $$r$$ satisfying the equation $$\:^{69}C_{3r-1}-\:^{69}C_{r^2}=\:^{69}C_{r^2-1}-\:^{69}C_{3r}$$ is:
  • $$1$$
  • $$2$$
  • $$4$$
  • $$7$$
An event manager has ten patterns of chairs and eight patterns of tables. In how many ways can he make a pair of table and chair?
  • $$100$$
  • $$80$$
  • $$110$$
  • $$64$$
Find the number of subsets of the set $${1,2,3,4,5,6,7,8,9,10,11}$$ having $$4$$ elements
  • $$330$$
  • $$320$$
  • $$310$$
  • $$300$$
When two coins are tossed and a cubical dice is rolled, then the total outcomes for the compound event is 
  • $$48$$
  • $$52$$
  • $$36$$
  • $$24$$
If $$^nC_{10} = ^nC_{12}$$, then find n?
  • $$120$$
  • $$22$$
  • $$12$$
  • $$2$$
Simplify: $${ _{  }^{ 34 }{ C } }_{ 5 }+\sum _{ r=0 }^{ 4 }{ { _{  }^{ (38-r) }{ C } }_{ 4 } } $$.
  • $${ }^{38}C_4$$
  • $${ }^{39}C_4$$
  • $${ }^{38}C_5$$
  • $${ }^{39}C_5$$
If $$C\left( 28,2r \right) =C\left( 28,2r-4 \right) $$, then what is $$r$$ equal to?
  • $$7$$
  • $$8$$
  • $$12$$
  • $$16$$
Out of $$7$$ consonants and $$4$$ vowels, words are formed each having $$3$$ consonants and $$2$$ vowels. The number of such words that can be formed is
  • $$210$$
  • $$25200$$
  • $$2520$$
  • $$302400$$
If $${ _{  }^{ n }{ C } }_{ 8 }={ _{  }^{ n }{ C } }_{ 5 }$$, then the value of $$n$$ is
  • $$2$$
  • $$3$$
  • $$1$$
  • $$13$$
Out of $$15$$ points in a plane, n points are in the same straight line, $$445$$ triangles can be formed by joining these points. What is the value of n?
  • $$3$$
  • $$4$$
  • $$5$$
  • $$6$$
Given that C(n, r) : C ( n, r + 1)=1 : 2 and C (n, r + 1) : C (n, r + 2) = 2 : 3. 
Find $$n.$$
  • $$11$$
  • $$12$$
  • $$13$$
  • $$14$$
If different words are formed with all the letters of the word 'AGAIN' and are arranged alphabetically among themselves as in a dictionary, the word at the 50th place will be
  • NAAGI
  • NAAIG
  • IAAGN
  • IAANG
The value of $$(^{21}C_1-^{10}C_1)+(^{21}C_2-^{10}C_2)+(^{21}C_3-^{10}C_3)+(^{21}C_4+^{10}C_4)+......+(^{21}C_{10}-^{10}C_{10})$$ is:
  • $$2^{21}-2^{11}$$
  • $$2^{21}-2^{10}$$
  • $$2^{20}-2^9$$
  • $$2^{20}-2^{10}$$
The number of six-digit numbers which have sum of their digits as an odd integer, is
  • $$45000$$
  • $$450000$$
  • $$97000$$
  • $$970000$$
If $$^nC_{r-1}=10, ^nC_r=45$$ and $$^nC_{r+1}=120$$, then $$r$$ equals to
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
If $$^nC_{12} = ^nC_8$$ then is equal to
  • $$12$$
  • $$26$$
  • $$6$$
  • $$20$$
The value of $$\left( \dfrac { ^{ 50 }{ C }_{ 0 } }{ 1 } +\dfrac {^{ 50 }{ C }_{ 2 } }{ 3 } +...+\dfrac {^{ 50 }{ C }_{ 50 } }{ 51 }  \right) $$ is
  • $$\dfrac { { 2 }^{ 50 } }{ 51 } $$
  • $$\dfrac { { 2 }^{ 50 }-1 }{ 51 } $$
  • $$\dfrac { { 2 }^{ 50 }-1 }{ 50 } $$
  • None of these
The number of positive integers satisfying the inequality $${ _{  }^{ n+1 }{ C } }_{ n-2 }-{ _{  }^{ n+1 }{ C } }_{ n-1 }\le 50$$ is
  • $$9$$
  • $$8$$
  • $$7$$
  • $$6$$
Find the term independent of $$x$$ in $${ \left( \cfrac { 3 }{ 2 } { x }^{ 2 }-\cfrac { 1 }{ 3x }  \right)  }^{ 9 }$$.
  • $$\dfrac {6}{15}$$
  • $$\dfrac  {7}{18}$$
  • $$\dfrac {7}{8}$$
  • $$\dfrac {4}{9}$$
Write down and simplify:
The $$5^{th}$$ term of $${ \left( \cfrac { { x }^{ \frac { 3 }{ 2 }  } }{ { a }^{ \frac { 1 }{ 2 }  } } -\cfrac { { y }^{ \frac { 5 }{ 2 }  } }{ { b }^{ \frac { 3 }{ 2 }  } }  \right)  }^{ 8 }$$.
  • $$\dfrac {60x^6y^{5}}{a^2b^6}$$
  • $$\dfrac {70x^6y^{10}}{a^3b^5}$$
  • $$\dfrac {70x^5y^{5}}{a^2b^6}$$
  • $$\dfrac {70x^6y^{10}}{a^2b^6}$$
The number of positive integer satisfying the inequality $$^{n + 1}C_{n} - {}^{n + 1}C_{n - 1} \leq 100$$ is
  • $$9$$
  • $$8$$
  • $$5$$
  • None of these
The number of triangles that can be formed by choosing the vertices from a set of $$12$$ points of which $$7$$ points lie on a line is
  • $$185$$
  • $$175$$
  • $$115$$
  • $$105$$
Find the $$4^{th}$$ term of $${ \left( 9x-\cfrac { 1 }{ 3\sqrt { x }  }  \right)  }^{ 18 }$$.
  • $$16500$$
  • $$18564$$
  • $$16540$$
  • $$32600$$
If $$^{n}C_{r - 1} = 36$$ and $$^{n}C_{r} = 84$$, then
  • $$13r - n - 3 = 0$$
  • $$10r - 3n - 30 = 0$$
  • $$10r + 3n - 3 = 0$$
  • $$10r - 3n + 3 = 0$$
  • $$10r - 3n - 3 = 0$$
The arithmetic mean of $${ _{  }^{ n }{ C } }_{ 0 },{ _{  }^{ n }{ C } }_{ 1 },....{ _{  }^{ n }{ C } }_{ n }\quad $$, is
  • $$\cfrac { 1 }{ n } $$
  • $$\cfrac { { 2 }^{ n } }{ n } $$
  • $$\cfrac { { 2 }^{ n-1 } }{ n } $$
  • $$\cfrac { { 2 }^{ n+1 } }{ n } $$
If $$\quad { _{  }^{ n }{ C } }_{ 2 }+{ _{  }^{ n }{ C } }_{ 3 }={ _{  }^{ 6 }{ C } }_{ 3 }$$ and $${ _{  }^{ n }{ C } }_{ x }={ _{  }^{ n }{ C } }_{ 3 },x\neq 3$$ then the value of $$x$$ is
  • $$5$$
  • $$4$$
  • $$2$$
  • $$6$$
  • $$1$$
If $$\displaystyle \sum _{ k=0 }^{ 18 }{ \cfrac { k }{ { _{  }^{ 18 }{ C } }_{ k } }  } =a\sum _{ k=0 }^{ 18 }{ \cfrac { 1 }{ { _{  }^{ 18 }{ C } }_{ k } }  } $$, then the value of $$a$$ is
  • $$3$$
  • $$9$$
  • $$6$$
  • $$18$$
  • $$36$$
There are $$10$$ persons including $$3$$ ladies. A committee of 4 persons including atleast one lady is to be formed. The number of ways of forming such a committee is :
  • $$160$$
  • $$170$$
  • $$180$$
  • $$175$$
  • $$155$$
If PQRS is a convex quadrilateral with 3, 4, 5 and 6 points marked on side PQ, QR, RS and PS respectively. Then, the number of triangles with vertices on different sides is
  • $$220$$
  • $$270$$
  • $$282$$
  • $$342$$
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