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CBSE Questions for Class 11 Engineering Maths Permutations And Combinations Quiz 9 - MCQExams.com

The number of such numbers which are even (all digits are different) is
  • 60
  • 96
  • 120
  • 204
10k=1k.k!=
  • 10!
  • 11!
  • 10!+1
  • 11!-1
Solve:
nCrnCr1=
  • nrr
  • n+r1r
  • nr+1r
  • nr1r
A double Decker is can accommodate 20 passengers 7 in the lower deck 13 in the upper deck. The number of ways the passengers can be accommodate if 5 want to sit only in lower deck and 8 want to sit only in upper deck is 
  • 7C5
  • 7C3
  • 7C1
  • 7C6
If nC4, nC5 and nC6 in A.P., then possible value of n is
  • 6
  • 12
  • 14
  • 21
If CARPET is coded as TCEAPR then the code for NATIONAL would be written as 
  • NLATNOIA
  • LANOITAN
  • LNAANTOI
  • LNOINTAA
How many 10 digits number can be written by using digits (9 and 2) ?
  • 10C1+9C2
  • 210
  • 10C2
  • 10!
All possible three digits even numbers which can be formed with the condition that if 5 is one of the digit, then 7 is the next digit is:
  • 5
  • 325
  • 345
  • 365
1+1.1!+2.2!+3.3!+...+n.n! is equal to 
  • n!
  • (n1)!
  • (n+1)!
  • n
A committee of 10 is to be formed from 8 women and 6 men. In how many of these committees the women are in majority?
  • 515
  • 545
  • 575
  • 595
A shelf contains 15 books, of which 4 are single volume and the others are 8 and 3 volumes respectively. In how many ways can these books be arranged on the shelf so that order of the volumes of same work is maintained ?
  • 4!
  • 8!
  • 3!
  • 4!8!3!3!
\displaystyle \sum^{n-1}_{r=0}\dfrac {^{n}C_{r}}{^{n}C_{r}+^{n}C_{r+1}}=
  • \dfrac {n}{2}
  • \dfrac {n+1}{2}
  • (n+1)\dfrac {n}{2}
  • \dfrac {n\ (n-1)}{2\ (n+1)}
If  a=\,^ { m }C _ { 2 } ,  then  ^ { a } C _ { 2 } is equal to
  • ^{m + 1}C _ { 4 }
  • ^{m+2} C _ { 4 }
  • 3.\, ^ { m + 2 } C _ { 4 }
  • 3. \,^ { m + 1 }C_4
^{ n }{ C }_{ 1 }.2+^{ n }{ C }_{ 2 }.\frac { { 2 }^{ 2 } }{ 3 } +^{ n }{ C }_{ 3 }.\frac { { 2 }^{ 3 } }{ { 3 }^{ 2 } } +......^{ n }{ C }_{ n }.\frac { { 2 }^{ n } }{ { 3 }^{ n-1 } } =
  • \frac { { 3 }^{ n }-{ 2 }^{ n } }{ { 3 }^{ n-1 } }
  • \frac { { 3 }^{ n }+{ 2 }^{ n } }{ { 3 }^{ n-1 } }
  • \frac { { 5 }^{ n }-{ 3 }^{ n } }{ { 3 }^{ n-1 } }
  • \frac { { 3 }^{ n }+{ 5 }^{ n } }{ { 3 }^{ n-1 } }
The number of seven letter words that can be formed by using the letters of the word  SUCCESS  that the two  C are together but no two  S  are together is
  • 24
  • 18
  • 54
  • none of these
Nine boys and 3 girls are to be seated in 2 vans, each having numbered seats, 3 in front and 4 at back. The number of ways of seating arrangements, if the girls should sit together in a back row on adjacent seats, is 
  • 12!
  • 3\times 11!
  • 4\times 11!
  • 3\times 9!
Six people are going to sit in a row on a bench. A and B are adjacent, C does not want to sit adjacent to D.E and F can sit anywhere. Number of ways in which these six people can be seated is 
  • 200
  • 144
  • 120
  • 56
How many different words can be formed by jumbling the letters in the word  MISSISSIPPI  in which no two  S  are adjacent ?
  • 8 \times ^ { 6 } C _ { 4 } \times ^ { 7 } C _ { 4 }
  • 6 \times 7 \times ^ { 8 } C _ { 4 }
  • 6 \times 8 \times ^ { 7 } C _ { 4 }
  • 7\times ^{ { 6 } }{ C }_{ { 4 } }\times ^{ { 8 } }{ C }_{ { 4 } }
In the expansion of \left(x^3 - \dfrac{1}{x^2}\right)^{15}, the constant terms is
  • ^{15}C_6
  • -{^{15}C_6}
  • ^{15}C_4
  • -{^{15}C_4}
The value of ^{47}C_{4}+\displaystyle \sum _{ j=1 }^{ 5 }\ ^{ \left( 52-j \right)  } { C }_{ 3 } is
  • ^{47}C_{5}
  • ^{52}C_{5}
  • ^{52}C_{4}
  • ^{52}C_{3}
A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady. at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is :
  • 40
  • 41
  • 16
  • 32
The number of values of 'r' satisfying the equation, {^{39}C_{3r-1}}-{^{39}C_{r^2}}={^{39}C_{r^2-1}}-{^{39}C_{3r}} is?
  • 1
  • 2
  • 3
  • 4
The number lock of a suitcase has four wheels, each labelled with 10-digits i.e., from 0 toThe lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase 
  • \dfrac { 1 }{ 5040 }
  • \dfrac { 3 }{ 5040 }
  • \dfrac { 7 }{ 5040 }
  • None of these
An old man while dialing a 7 digit telephone number remembers that the first four digits consists of one 1's, one 2's and two 3's. He also remembers that the fifth digits is either a 4 or 5 while has no memorising of the sixth digit, he remembers that the seventh digit is 9 minus the sixth digit. Maximum number of distinct trials he has to try to make sure that he dials the correct telephone number, is
  • 360
  • 240
  • 216
  • None of these
The number of different seven digit numbers that can be written using only three digits 1, 2 & 3 under the condition that the digit 2 occurs exactly twice in each number is-
  • 672
  • 640
  • 512
  • None of these
If ^{8}C_{r}=^{8}C_{3}, then r is equal to 
  • 5
  • 4
  • 8
  • 6
Find x, if \dfrac {1}{4!}-\dfrac {1}{x}=\dfrac {1}{5!}.
  • 5
  • 4
  • 30
  • None
The value of  \sum _ { r = 1 } ^ { 5 } r \dfrac { ^ { n } C _ { r } } { ^ { n } C _ { r - 1 } } =?
  • 5 ( n - 3 )
  • 5 ( n - 2 )
  • 5 \mathrm { n }
  • 5 ( 2 n - 9 )
When n!+1 is divided by any natural number between 2 and n then remainder obtained is
  • 1
  • 2
  • 3
  • 4
If (1 + x)^n = \displaystyle \sum^{n}_{r = 0} {^nC_r} x^r then C^2_0 + \dfrac{C^2_1}{2} + \dfrac{C^2_2}{3} + ... + \dfrac{C^2_n}{n + 1} =
  • \dfrac{{2n}!}{n !)^2}
  • \dfrac{{2n + 1}!}{{(n + 1)^2}!}
  • \dfrac{{2n - 1}!}{{(n + 1)^2}!}
  • \dfrac{{n}!}{{(n - 1)^2}!}
Set of value of r for which, ^{18}C_{r-2}+2\cdot {^{18}C_{r-1}}+{^{18}C_{r}} \geq {^{20}C_{13}} contains?
  • 4 elements
  • 5 elements
  • 7 elements
  • 10 elements
The no.of triangles formed by selecting the points from Regular pentagon is 
  • 10
  • 12
  • 16
  • none
^{n}C_{r}+2^{n}C_{r+1}+^{n}C_{r+2} is equal to 
  • 2.^{n}C_{r+2}
  • ^{n+1}C_{r+1}
  • ^{n+2}C_{r+2}
  • none\ of\ these
Value of \displaystyle \sum _{ r=0 }^{ n} r.\left(^{n}C_{r}\right)^{2} is equal to
  • n.{^{2n}C_{r}}
  • \dfrac{n.{^{2n}C_{r}}}{2}
  • n^{2}.{^{2n}C_{r}}
  • \dfrac{n^{2}.{^{2n}C_{r}}}{2}
The no .of ways of selecting a prime numbers from First 10 natural numbers is 
  • ^{10}C_4
  • ^4C_{10}
  • ^{10}P_4
  • ^{10}C_5
A rectangle with sides 2m - 1 and 2n - 1 is divided into square of unit length by drawing parallel lines as shown in diagram, then the number of rectangles possible with odd side length is 
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  • (m+n-1)^2
  • 4^{m+n-1}
  • m^2-n^2
  • m(m+1)n(n+1)
How many integers are there such that 2 \le n \le 100 and the highest common factor of n and 36 is 1?
  • 166
  • 332
  • 331
  • 416
If ^mC_3+^mC_4>^{m+1}C_3, then least value of m is :
  • 6
  • 7
  • 5
  • None of these
The number of ways in which 9 persons can be divided into three equal groups, is
  • 1680
  • 840
  • 560
  • 280
The value of \left( \begin{matrix} 30 \\ 0 \end{matrix} \right) \left( \begin{matrix} 30 \\ 10 \end{matrix} \right) -\left( \begin{matrix} 30 \\ 1 \end{matrix} \right) \left( \begin{matrix} 30 \\ 11 \end{matrix} \right) +\left( \begin{matrix} 30 \\ 2 \end{matrix} \right) \left( \begin{matrix} 30 \\ 12 \end{matrix} \right) .....+\left( \begin{matrix} 30 \\ 20 \end{matrix} \right) \left( \begin{matrix} 30 \\ 30 \end{matrix} \right) is, where \left( \begin{matrix} n \\ r \end{matrix} \right) =^{ n }{ C }_{ r }.
  • \left( \begin{matrix} 30 \\ 10 \end{matrix} \right)
  • \left( \begin{matrix} 30 \\ 15\end{matrix} \right)
  • \left( \begin{matrix} 60 \\ 30\end{matrix} \right)
  • \left( \begin{matrix} 31\\ 10 \end{matrix} \right)
A school committee consists of 2 teachers and 4 students. The number of different committees that can be formed from 5 teachers and 10 students is
  • 200
  • 2100
  • 2000
  • 3200
Number of cyphers at the end of ^{2002} C_{1001} is
  • 0
  • 1
  • 2
  • None of these
If \displaystyle \sum _{ r=0 }^{ n }{ \left\{ \dfrac { { n{ C }_{ r-1 } } }{ n{ C }_{ r }+n{ C }_{ r-1 } }  \right\}  } =2 then n is equal to
  • 3
  • 4
  • 5
  • 6
The number of all the possible selection which a student can make for answering one or more questions out of eight given question in a paper, which each question has an alternative is 
  • 255
  • 6560
  • 6561
  • none of these
If $$\frac{3^{3 n} \cdot 2^{n}}{108}+\frac{3^{3 n}}{729}+\frac{3^{3 n} \cdot 2^{2 n}}{48}+\frac{2^{3 n} \cdot 3^{3 n}}{64}=37^{3} \cdot 3^{6}$$
, then find the value of n ?
  • 2
  • 3
  • 4
  • 5
  • none of these
^{n }{ C }_{ r }+^{ n }{ C }_{ r+1 } is equal to______________.
  • ^{ n }{ C }_{ R+1 }
  • ^{ n }{ C }_{ R+1 }
  • ^{ n+1 }{ C }_{ R+1 }
  • ^{ n-1 }{ C }_{ R+1 }
If ^{n}C_{3} + ^{n}C_{4} > ^{n + 1}C_{3}, then
  • n + 1
  • \dfrac {n}{2}
  • n + 2
  • None of these
\displaystyle\sum^{m}_{r=0}{^{n+r}C_n} is equal to?
  • ^{n+m+1}C_{n+1}
  • ^{n+m+2}C_n
  • ^{n+m+3}C_{n-1}
  • None of these
The number of permutations which can be formed out of the letters of the word "SERIES" three letters together, is:
  • 120
  • 60
  • 42
  • none
The coefficient of x^{18} in the expansion of (1+x)(1-x)^{10}\{(1+x+x^2)^9\} is?
  • 84
  • 126
  • -42
  • 42
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