CBSE Questions for Class 11 Engineering Maths Permutations And Combinations Quiz 4 - MCQExams.com

If k is odd, then $$^k C_r$$ is maximum for r equal to
  • $$\dfrac{1}{2}(k-1)$$
  • $$\dfrac{1}{2}(k+1)$$
  • $$k-1$$
  • $$k$$
What is the sum of all 5 digit numbers which can be formed with digits 0, 1, 2, 3, 4 without repetition
  • 2599980
  • 2679980
  • 2544980
  • 2609980
Given:
(i) $$^n p_r=\angle r ^ n c_r$$
(ii) $$^n c_r + ^n c_{r-1} = ^{n+1}c_r$$
If $$^n p_r = 720$$ and $$^n c_r = 120$$, then what is the value of 'r'
  • $$6$$
  • $$9$$
  • $$3$$
  • $$\dfrac{n}{6}$$
How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)?
  • $$7920$$
  • $$330$$
  • $$14640$$
  • $$419430$$
In how many ways is it possible to choose a white square and a black square on a chessboards, so that the squares must not lie in the same row or column?
  • $$56$$
  • $$896$$
  • $$60$$
  • $$768$$
Find the number of rectangles formed on a chessboard:
  • 1296
  • 1452
  • 1528
  • 1614
If $$N$$ is the number of positive integral solutions of $$x_1\times x_2\times x_3\times x_4 = 770$$, then:
  • $$N$$ is divisible by $$4$$ district primes
  • $$N$$ is a perfect square
  • $$N$$ is a perfect fourth power
  • $$N$$ is a perfect $$8^{th}$$ power
Based on this information answer the questions given below.
A string of three English letters is formed as per the following rules:
(a) The first letter is any vowel.
(b) The second letter is $$m, n$$ or $$p$$.
(c) If the second letter is $$m$$ then the third letter is any vowel which is different from the first letter.
(d) If the second letter is $$n$$ then the third letter is $$e$$ or $$u$$.
(e) If the second letter is $$p$$ then the third letter is the same as the first letter.
How many strings of letters can possibly be formed using the above rules?
  • $$40$$
  • $$45$$
  • $$30$$
  • $$35$$
On the occasion of Dipawali festival each student of a class sends greeting cards to one another. If the postmen deliver $$1640$$ greeting cards to the students of this class, then the number of students in the class is
  • 39
  • 41
  • 51
  • 53
State true or false.
The product of any $$r$$ consecutive natural numbers is always divisible by $$r!$$.
  • True
  • False
We number both the rows and the columns of an $$8$$ $$\times$$ $$8$$ chess-board with the numbers $$1$$ to $$8$$. A number of grains are placed onto each square, in such a way that the number of grains on a certain square equals the product of its row and column numbers. How many grains are there on the entire chessboard?
  • $$1296$$
  • $$1096$$
  • $$2490$$
  • $$1156$$
In how many ways is it possible to choose a white square and a black square on a chess board  so that the squares must not lie in the same row or column -
  • $$56$$
  • $$896$$
  • $$60$$
  • $$768$$
A hall has 12 gates. In how many ways can a man enter the hall through one gate and come out through a different gate?
  • $$144$$
  • $$132$$
  • $$121$$
  • $$156$$
$$\displaystyle \frac{^{\alpha}C_{2}}{^{\alpha + 1}C_{4}}$$ =
  • $$\displaystyle\frac{1}{3}$$
  • $$\displaystyle\frac{12}{(\alpha+1)(\alpha-2)}$$
  • $$\displaystyle\frac{4}{(\alpha+1)(\alpha-3)}$$
  • $$\displaystyle\frac{12}{(\alpha+1)(\alpha-2)(\alpha-3)}$$
There are three stations $$A,\space B$$ and $$C$$, five routes for going from station $$A$$ to station $$B$$ and four routes for going from station $$B$$ to station $$C$$.
Find the number of different ways through which a person can go from station $$A$$ to $$C$$ via $$B$$
  • 10
  • 15
  • 20
  • 25
Given six line segments of length $$2, 3, 4, 5, 6, 7$$ units. Then the number of triangles that can be formed by joining these lines is
  • $$^6C_3 - 7$$
  • $$^6C_3 - 1$$
  • $$^6C_3$$
  • $$^6C_3 - 2$$
The number of different ways in which five "alike dashes" and eight "alike dots" can be arranged using only seven of these "dashes" and "dots" is
  • $$350$$
  • $$120$$
  • $$1287$$
  • None of these
Number of ways 6 rings can be worn on four fingers of one hand?
  • $$4095$$
  • $$4096$$
  • $$4097$$
  • $$4098$$
The value of $$\displaystyle ^{ 47 }{ { C }_{ 4 } }+\sum _{ r=1 }^{ 5 }{ ^{ 52-r }{ { C }_{ 3 } } } $$ is equal to
  • $$^{ 47 }{ { C }_{ 6 } }$$
  • $$^{ 52 }{ { C }_{ 5 } }$$
  • $$^{ 52 }{ { C }_{ 4 } }$$
  • none of these
If $$m$$ parallel lines in a plane are intersected by a family of $$n$$ parallel lines, the number of parallelograms than can be formed is
  • $$\dfrac {1}{4} mn(m - 1)(n - 1)$$
  • $$\dfrac {1}{2} mn (m - 1)(n - 1)$$
  • $$\dfrac {1}{4} m^{2}n^{2}$$
  • None of these
The total number of permutation of $$n$$ different things taken not more than $$r$$ at a time, where each thing may be repeated any number of times, is
  • $$\displaystyle \frac { n\left( { n }^{ n }-1 \right)  }{ n-1 } $$
  • $$\displaystyle \frac { \left( { n }^{ r }-1 \right)  }{ n-1 } $$
  • $$\displaystyle \frac { n\left( { n }^{ r }-1 \right)  }{ n-1 } $$
  • $$\displaystyle \frac { \left( { n }^{ n }-1 \right)  }{ n-1 } $$
The maximum number of points of intersection of five lines and four circles is
  • $$60$$
  • $$72$$
  • $$62$$
  • None of these
If $$\displaystyle ^nC_{r-1}=56$$, $$\displaystyle ^nC_r=28$$ and $$\displaystyle ^nC_{r+1}=8$$ then r is equal to
  • 8
  • 6
  • 5
  • None of these
If $$^nC_{r-1} = 36, \space ^nC_r = 84$$ and $$^nC_{r+1} = 126,$$ then find $$r$$.
  • 2
  • 3
  • 4
  • 5
The number of numbers of 9 different nonzero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than that in the middle is 
  • $$\displaystyle 2(4!)$$
  • $$\displaystyle (4!)^2$$
  • $$8!$$
  • none of these
In a packet there are m different books, n different pens and p different pencils. The number of selections of at least one article of each type from the packet is
  • $$\displaystyle 2^{m+n+p}-1$$
  • $$\displaystyle \left ( m+1 \right )\left ( n+1 \right )\left ( p+1 \right )-1$$
  • $$\displaystyle 2^{m+n+p}$$
  • $$(2^{m}-1)(2^{n}-1)(2^{p}-1)$$
The value of $$\displaystyle \sum_{r= 0}^{n}$$ $$\displaystyle ^{n+r}C_{r}$$ is equal to
  • $$\displaystyle ^{2n+1}C_{n}$$
  • $$\displaystyle ^{2n}C_{n-1}$$
  • $$\displaystyle ^{2n}C_{n+1}$$
  • $$\displaystyle ^{2n+1}C_{n-1}$$
The number of 5-digit even numbers that can be made with the digits 0,1,2 and 3 is
  • 384
  • 192
  • 768
  • none of these
If $$\displaystyle ^nC_4,^nC_5 $$ and $$ ^nC_6$$ are in AP then n is 
  • 8
  • 9
  • 14
  • 7
From a group of persons the number of ways of selecting 5 persons is equal to that of 8 persons. The number of persons in the group is
  • 13
  • 40
  • 18
  • 21
$$\displaystyle ^{n}C_{r+1}+^{n}C_{r-1}+2\times ^{n}C_{r}$$ is equal to
  • $$\displaystyle ^{n+2}C_{r+1}$$
  • $$\displaystyle ^{n+1}C_{r}$$
  • $$\displaystyle ^{n+1}C_{r+1}$$
  • $$\displaystyle ^{n+2}C_{r}$$
The number of different 6-digit numbers that can be formed using the three digits 0,1 and 2 is
  • $$\displaystyle 3^6$$
  • $$\displaystyle 2$$ x $$3^5$$
  • $$\displaystyle 3^5$$
  • none of these
The product of r consecutive integers is divisible by
  • r
  • $$\displaystyle \sum_{k=1}^{r-1}k$$
  • r!
  • none of these
The total number of $$9-$$digit numbers of different digits is
  • $$10 (9!)$$
  • $$8 (9!)$$
  • $$9 (9!)$$
  • none of these
For $$\displaystyle 2\leq r\leq n,\binom{n}{r}+2\binom{n}{r-1}+\binom{n}{r-2}$$ is equal to
  • $$\displaystyle \binom{n+1}{r-1}$$
  • $$\displaystyle 2\binom{n+1}{r+1}$$
  • $$\displaystyle 2\binom{n+2}{r}$$
  • $$\displaystyle \binom{n+2}{r}$$
The numbers of three digit number can be formed by using the digits 0, 1, 2, 3, 7, 9 if any digit can be used in any number of time, is

  • 180
  • 216
  • 120
  • 36
If $$n<p<2n$$ and $$p$$ is prime and $$N=^{ 2n }{ { C }_{ n } }$$, then
  • $$\displaystyle \frac { p }{ N } $$
  • $$p$$ does not divide $$N$$
  • $$\displaystyle \frac { p^2 }{ N } $$
  • $$p^2$$ does not divide $$N$$
The number of ways in which one or more letters be selected from the letters $$AAAABBCCCDEF$$ is
  • $$476$$
  • $$487$$
  • $$435$$
  • $$479$$
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is 
  • 360
  • 192
  • 96
  • 48
The number of even numbers with three digits such that if 3 is one of the digit then 5 is the next digit are 
  • 959
  • 285
  • 365
  • 512
The different six digit numbers whose 3 digits are even and 3 digits are odd is

  • 281250
  • 281200
  • 156250
  • none of these
A five-digit number divisible by $$3$$ is to be formed using the digits $$0, 1, 2, 3, 4$$ and $$5$$, without repetition. The total number of ways this can be done is
  • $$216$$
  • $$240$$
  • $$600$$
  • $$3125$$
If $$m=^{n}\textrm{C}_{2}$$, then $$^{m}\textrm{C}_{2}$$ equals
  • $$^{n+1}\textrm{C}_{4}$$
  • $$3\times ^{n+1}\textrm{C}_{4}$$
  • $$^{n}\textrm{C}_{4}$$
  • $$^{n+1}\textrm{C}_{3}$$
The domain and range of the function $$\displaystyle f\left ( x \right ) = \sqrt{^{x^{2}+4x}C_{2x^{2}+3}}$$ are
  • domain: $$1,2,3 $$, range: $$1,2\sqrt { 3 } $$
  • domain: $$1,2\sqrt {3} $$ range: $$1,2,3$$
  • domain: $$1,3$$ range: $$1$$
  • none of these
If $$^{ n }{ { C }_{ r-1 } }=\left( { k }^{ 2 }-8 \right) \left( ^{ n+1 }{ { C }_{ r } } \right) $$, then $$k$$ belongs to
  • $$[-3,-2\sqrt{2}]$$
  • $$[-3,-2\sqrt{2})$$
  • $$2\sqrt{2}.3]$$
  • $$(2\sqrt{2},3]$$
The mean of the values $$0, 1, 2, \cdots n$$, having corresponding weights $$^nC_0, ^nC_1, \cdots ^nC_n,$$ respectively is
  • $$\cfrac{n+1}{2}$$
  • $$\cfrac{2^{n-1}+1}{n+1}$$
  • $$\cfrac{2^n}{n}$$
  • $$\cfrac{n}{2}$$
An $$n-$$ digit number is a positive number with exactly $$n$$ digits. Nine hundred distinct n−digit numbers are to be formed using only the three digits 2,5 and 7. The smallest value of $$n$$ for which this is possible is
  • $$5$$
  • $$6$$
  • $$7$$
  • $$8$$
If $$^{20}C_{r\, +\, 2}\, =\, ^{20}C_{2r\, -\, 3}\,$$, find  $$\, ^{12}C_r$$.
  • $$792$$
  • $$795$$
  • $$790$$
  • None of these
A set contains $$(2n + 1)$$ elements. The number of subsets of the set which contain at most n elements is
  • $$2^{n}$$
  • $$2^{n\, +\, 1}$$
  • $$2^{n\, -\, 1}$$
  • $$2^{2n}$$
The number of such numbers which are divisible by two and five (all digits are not different) is
  • 125
  • 76
  • 65
  • 100
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Engineering Maths Quiz Questions and Answers