CBSE Questions for Class 11 Engineering Maths Permutations And Combinations Quiz 7 - MCQExams.com

If $$n$$ is an integer greater than $$1$$, then $$a-{ _{  }^{ n }{ C } }_{ 1 }(a-1)+{ _{  }^{ n }{ C } }_{ 2 }(a-2)+....+{ (-1) }^{ n }(a-n)$$ is equal to
  • $$a$$
  • $$0$$
  • $${a}^{2}$$
  • $${2}^{n}$$
Choose $$3, 4, 5$$ points other than vertices respectively on the sides $$AB, BC$$ and $$CA$$ of a $$\triangle ABC$$. The number of triangles that can be formed by using only these points as vertices, is
  • $$220$$
  • $$217$$
  • $$215$$
  • $$210$$
  • $$205$$
Total number of words that can be formed using all letters of the word $$\text{BRIJESH}$$ that neither begins with $$I$$ nor ends with $$B$$ is equal to.
  • $$4920$$
  • $$3720$$
  • $$3600$$
  • $$4800$$
If $$^{n}C_{15} = ^{n}C_{8}$$, then the value of $$^{n}C_{21}$$ is
  • $$254$$
  • $$250$$
  • $$253$$
  • None of these
What was the bus charge per student?
  • Rs 194
  • Rs 184
  • Rs 187
  • Rs 199
A village has $$10$$ players. A team of $$6$$ players is to be formed. $$5$$ members are chosen first out of these $$10$$ players and then the captain from the remaining players. Then the total number of ways of choosing such teams is
  • $$1260$$
  • $$210$$
  • $$({ _{ }^{ 10 }{ C } }_{ 6 })5!$$
  • $${ _{ }^{ 10 }{ C } }_{ 5 }6$$
An alphabet contains a $$A^{'s}$$ and b $$ B^{'s}$$ . (In all a+b letters ). The number of words each containing all the $$ A^{'s}$$ and any number of $$ B^{'s}$$, is 
  • $$^{a+b}C_b$$
  • $$^{a+b+1}C_a$$
  • $$^{a+b+1}C_b$$
  • none of these
The maximum number of intersection points of n circles and n straight lines , among themselves  is 80.The value of n is
  • $$7$$
  • $$6$$
  • $$5$$
  • $$8$$
The number of ways of distributing $$8$$ identical balls in $$3$$ distinct boxes, so that none of the boxes is empty is
  • $$5$$
  • $$21$$
  • $${ 3 }^{ 8 }$$
  • $$^{ 8 }{ { C }_{ 3 } }$$
If $$p> q$$, the number of ways of $$p$$ men and $$q$$ women can be seated in a row so that no two women sit together is
  • $$\cfrac { p!q! }{ \left( p+q \right) ! } $$
  • $$\cfrac { \left( p+q \right) ! }{ p!\left( q+! \right) ! } $$
  • $$\cfrac { p!\left( q+1 \right) ! }{ \left( p-q+1 \right) ! } $$
  • $$\cfrac { p!(p+1)! }{ \left( p-q+1 \right) ! } $$
Total number of arrangements of the letters of the word SUCCESS such that both $$C's$$ are together and no two $$S's$$ are together is
  • $$12$$
  • $$24$$
  • $$96$$
  • $$120$$
If $$\alpha ,\beta , \gamma $$ are three consecutive integers. If these integers are raised to first, second and third positive powers respectively, and added then they form a perfect square, the square root of which is equal to the sum of these integers. Also, $$\alpha < \beta < \gamma $$. Then, $$\gamma$$ is equals to:
  • $$3$$
  • $$14$$
  • $$5$$
  • $$11$$
Out of $$15$$ persons $$10$$ can speak Hindi and $$8$$ can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is
  • $$5/3$$
  • $$7/12$$
  • $$1/5$$
  • $$2/5$$
The value of $$^{50}C_4+\displaystyle\sum^{6}_{r=1}$$ $$^{56-r}C_3$$ is?
  • $$^{56}C_4$$
  • $$^{56}C_3$$
  • $$^{55}C_3$$
  • $$^{55}C_4$$
A telephone number $$d_1d_2d_3d_4d_5d_6d_7$$ is called memorable if the prefix sequence $$d_1d_2d_3$$ is exactly the same as either of the sequence $$d_4d_5d_6$$ or $$d_5d_6d_7$$(or possibly both). If each $$d_1\epsilon\{x|0\leq x\leq 9, x\epsilon W\}$$, then number of distinct memorable telephone number is(are).
  • $$19810$$
  • $$19,910$$
  • $$19,990$$
  • $$20,000$$
$$\sum _{ r=0 }^{ n-1 }{ \cfrac { { _{  }^{ n }{ C } }_{ r } }{ { _{  }^{ n }{ C } }_{ r }+{ _{  }^{ n }{ C } }_{ r+1 } }  } $$ is equal to
  • $$\cfrac { n }{ 2 } $$
  • $$\cfrac { n+1 }{ 2 } $$
  • $$\cfrac { n(n+1) }{ 2 } $$
  • $$\cfrac { n(n-1) }{ 2(n+1) } $$
A man $$x$$ has $$7$$ friends, $$4$$ of them are ladies and $$3$$ are men. His wife $$Y$$ also has $$7$$ friends, $$3$$ of them are ladies and $$4$$ are men. Assume $$X$$ and $$Y$$ have no common friends. Then, the total number of ways in which $$X$$ and $$Y$$ together can throw a party inviting $$3$$ ladies and $$3$$ men , so that $$3$$ friends of each of $$X$$ and $$Y$$ are in this party, is 
  • $$485$$
  • $$468$$
  • $$469$$
  • $$484$$
The sum $$^{20}C_0+^{20}C_1+^{20}C_2+..... +^{20}C_{10}$$ is equal to
  • $$2^{20}+\dfrac{20 \,!}{(10\,!)^2}$$
  • $$2^{19}+\dfrac{1}{2}.\dfrac{20\,!}{(10\,!)^2}$$
  • $$2^{19}+^{20}C_{10}$$
  • none of these
The value of $$\begin{pmatrix} 30 \\ 0 \end{pmatrix}\begin{pmatrix} 30 \\ 10 \end{pmatrix}-\begin{pmatrix} 30 \\ 1 \end{pmatrix}\begin{pmatrix} 30 \\ 11 \end{pmatrix}+\begin{pmatrix} 30 \\ 2 \end{pmatrix}\begin{pmatrix} 30 \\ 12 \end{pmatrix}-...+\begin{pmatrix} 30 \\ 20 \end{pmatrix}\begin{pmatrix} 30 \\ 30 \end{pmatrix}$$ is where $$\begin{pmatrix} n \\ r \end{pmatrix}={ _{  }^{ n }{ C } }_{ r }$$
  • $$\begin{pmatrix} 30 \\ 15 \end{pmatrix}$$
  • $$\begin{pmatrix} 60 \\ 15 \end{pmatrix}$$
  • $$\begin{pmatrix} 60 \\ 30 \end{pmatrix}$$
  • $$\begin{pmatrix} 30 \\ 10 \end{pmatrix}$$
Let $${ T }_{ n }$$ denotes the number of triangles which can be formed by using the vertices of a regular polygon of n sides. If $${ T }_{ n+1 }\ -\ { T }_{ n }=21$$, then $$n$$ is equal to
  • $$5$$
  • $$7$$
  • $$6$$
  • $$4$$
If $$15! =2^{\alpha}\cdot 3^{\beta}\cdot 5^{\gamma}\cdot 7^{\delta}\cdot 11^{\theta}\cdot 13^{\Phi}$$, then the value of expression $$\alpha -\beta +\gamma -\delta +\theta -\Phi$$ is
  • $$4$$
  • $$6$$
  • $$8$$
  • $$10$$
If $$\left( 2\le r\le n \right) $$, then $${ _{  }^{ n }{ C } }_{ r }+2{ _{  }^{ n }{ C } }_{ r+1 }+{ _{  }^{ n }{ C } }_{ r+2 }$$ is equal to
  • $$2.{ _{ }^{ n+2 }{ C } }_{ r+2 }\quad $$
  • $${ _{ }^{ n+r }{ C } }_{ r+1 }$$
  • $${ _{ }^{ n+2 }{ C } }_{ r+2 }$$
  • $${ _{ }^{ n+1 }{ C } }_{ r }$$
From a collection of $$20$$ consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is
  • $$284\times 17$$
  • $$285\times 17$$
  • $$284\times 16$$
  • $$285\times 16$$
The number of selection of $$n$$ objects from $$2n$$ objects of which $$n$$ are identical and the rest are different is
  • $${ 2 }^{ n }$$
  • $${ 2 }^{ n-1 }$$
  • $${ 2 }^{ n }-1\quad $$
  • $${ 2 }^{ n }+1\quad $$
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
Ramesh number of ways in which the letters of the word RAMESH can be placed in the squares of the given figure so that no row remains empty, is  
879345_b3c7249374504a4f9a5d29c37fb99d8b.png
  • 17280
  • 18720
  • 15840
  • 14400
Let n be the number of ways in which the letters of the word "RESONANCE" can be arranged so the vowels appear at the even places and m be the number of ways in which "RESONANCE" can arrange so that letters R,S,O,A appears in the order same as the word RESONANCE, then answers the following questions.
The value of n is 
  • 360
  • 720
  • 240
  • 840
For $$n$$ being natural number, if $$^{2n}C_r={}^{2n}C_{r+2}$$, find $$r$$.
  • $$n$$
  • $$n-1$$
  • $$n-2$$
  • $$n-3$$
How many different $$4$$-person committees can be chosen form the $$100$$ members of the Senate ?
  • $$25$$
  • $$400$$
  • $$3,921,225$$
  • $$94,109,400$$
If the letterss of the word 'NAAGI' are arranged as in a dictionary then the rank of the given word is 
  • $$23$$
  • $$84$$
  • $$49$$
  • $$48$$
The number of ways in which we can select 5 letters of the word INTERNATIONAL is equal to
  • $$200$$
  • $$220$$
  • $$242$$
  • $$256$$
If $$^nC_r : ^nC_{r + 1} : ^nC_{r + 2} = 3 : 4: 5$$, then the value of $$2n + 3r$$ is
  • $$238$$
  • $$220$$
  • $$203$$
  • $$240$$

The total number of different combinations of one
or more letters which can be made from the letter of the word MISSISSIPPI is,
  • $$150$$
  • $$148$$
  • $$149$$
  • $$146$$
We wish to select $$6$$ persons from $$8$$, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
  • $$20$$
  • $$22$$
  • $$24$$
  • $$26$$
Number of arrangements of the letter $$HOLLYWOOD$$ in which all $$Os$$ are separated.
  • $$360\ ^{ 7 }{ C }_{ 3 }$$
  • $$15\ ^{ 7 }{ P }_{ 4 }$$
  • $$15\ ^{ 7 }{ C }_{ 4 }$$
  • $$30\ ^{ 7 }{ P }_{ 4 }$$
$$\dfrac { { C }_{ 1 } }{ { C }_{ 0 } } +2\dfrac { { C }_{ 2 } }{ { C }_{ 1 } } +3\dfrac { { C }_{ 3 } }{ { C }_{ 2 } } +....+15\dfrac { { C }_{ 15 } }{ { C }_{ 14 } }$$ is equal to
  • $$100$$
  • $$120$$
  • $$-120$$
  • $$None\ of\ these$$
If $$\dfrac { ^{ n }{ P }_{ r-1 } }{ a } =\dfrac { ^{ n }{ P }_{ r } }{ b } =\dfrac { ^{ n }{ P }_{ r+1 } }{ c } $$, then which of the following holds good:
  • $$c^{2}=a(b+c)$$
  • $$a^{2}=c(a+b)$$
  • $$b^{2}=c(a-b)$$
  • $$\dfrac {1}{a}+\dfrac {1}{b}+\dfrac {1}{c}=1$$
How many committee of five persons with a chairperson can be selected from $$12$$ persons.
  • $$924$$
  • $$825$$
  • $$736$$
  • $$643$$
The number of permutations of the letters of the word $$HONOLULU$$ taken $$4$$ at a time is
  • $$ 354$$
  • $$ 314$$
  • $$ 210$$
  • $$ 124$$
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet ?
  • $$50000$$
  • $$50100$$
  • $$50300$$
  • $$50400$$
Find the remainder when $$105!$$ is divided by $$214.$$ 
  • $$168$$
  • $$108$$
  • $$196$$
  • $$172$$
PQRS is a quadrilateral having $$3, 4, 5, 6$$ points in PQ, QR, RS and SP respectively. The number of triangles with vertices on different sides is?
  • $$220$$
  • $$270$$
  • $$282$$
  • $$342$$
How many $$3$$-digit even numbers can be formed from the digits $$1, 2, 3, 4, 5, 6$$ if the digits can be repeated?
  • 108
  • 98
  • 72
  • 112
The value of $$\sum\limits_{r = 1}^{10} r .\frac{{{}^n{C_r}}}{{{}^n{C_{r - 1}}}}$$ is equal to
  • $$5(2n-9)$$
  • $$10n$$
  • $$9(n-4)$$
  • $$n-2$$
Robert was asked to made a $$5$$ digit number from the digits $$2$$ and $$4$$ such that first digit cannot be $$4$$. Find the number of such $$5$$ digit numbers that can be formed .
  • $$10$$
  • $$12$$
  • $$16$$
  • $$18$$
  • None of these
The number of $$5$$ digit telephone numbers having least one of their digits repeated is 
  • $$ 90,000$$
  • $$ 100,000$$
  • $$ 30,240$$
  • $$ 69,760$$
If A and B are the sums of odd and even terms respectively in the expansion of $$(x+a)^n$$,then $$(x+a)^{2n} -(x-a)^{2n}$$ is equal to:
  • $$4(A+B)$$
  • $$4(A-B)$$
  • $$AB$$
  • $$4AB$$
Number of ways in which $$7$$ green bottles and $$8$$ blue bottles can be arranged in a row if exactly $$1$$ pair of green bottles is side by side is (Assume all bottles to be a like except for the colour).
  • $$84$$
  • $$360$$
  • $$504$$
  • None of the above
There are $$10$$ points in a plane of which no $$3$$ points are collinear and $$4$$ points are concylic. No. of different circles that can be drawn through atleast $$3$$ points of these given points is
  • $$\left( ^{ 8 }{ C }_{ 3 }-^{ 6 }{ C }_{ 3 } \right) +1$$
  • $$\left( ^{ 10 }{ C }_{ 3 }-^{ 4 }{ C }_{ 3 } \right) +1$$
  • $$\left( ^{ 6 }{ C }_{ 3 }-^{ 4 }{ C }_{ 3 } \right) +1$$
  • $$\left( ^{ 4 }{ C }_{ 3 }-^{ 2 }{ C }_{ 3 } \right) +1$$
The sides AB, BC, CA of a triangle ABC have $$3,4$$ and $$5$$ interior points respectively on them. The number of triangles that can be constructed using these points as vertices is-
  • $$205$$
  • $$210$$
  • $$315$$
  • $$216$$
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