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
  • $$60$$
  • $$96$$
  • $$120$$
  • $$204$$
$$\sum _{ k=1 }^{ 10 }{ k.k! } =$$
  • 10!
  • 11!
  • 10!+1
  • 11!-1
Solve:
$$\dfrac{^{n}C_{r}}{^{n}C_{r-1}}=$$
  • $$\dfrac{n-r}{r}$$
  • $$\dfrac{n+r-1}{r}$$
  • $$\dfrac{n-r+1}{r}$$
  • $$\dfrac{n-r-1}{r}$$
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 
  • $$^{7}C_{5}$$
  • $$^{7}C_{3}$$
  • $$^{7}C_{1}$$
  • $$^{7}C_{6}$$
If $$^{n}C_{4},\ ^{n}C_{5}$$ and $$^{n}C_{6}$$ 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) ?
  • $$^{10}C_1 + ^9C_2$$
  • $$2^{10}$$
  • $$^{10} C_2$$
  • $$10 !$$
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 
  • $$n!$$
  • $$(n-1)!$$
  • $$(n+1)!$$
  • $$n$$
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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