CBSE Class 11 Mathematics Permutations and Combinations Assignment Set A

Question. The number of natural numbers less than 7,000 which can be formed by using the digits 0,1,3,7,9 (repetition of digits allowed) is equal to:
(a) 374
(b) 372
(c) 375
(d) 250
Answer : A

Question. Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are 
(a) 216
(b) 375
(c) 400
(d) 720 
Answer : D

Question. The sum of integers from 1 to 100 that are divisible by 2 or 5 is
(a) 3000
(b) 3050
(c) 3600
(d) 3250
Answer : B

Question. All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is :
(a) 180
(b) 175
(c) 160
(d) 162
Answer : A

Question. The number of ways of choosing 10 ob ects out of 31 ob ects of which 10 are identical and the remaining 21 are distinct is:
(a) 2^{20 –} 1
(b) 2²¹
(c) 2²⁰
(d) 2²⁰+1
Answer : C

Question. There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :
(a) 3000
(b) 1500
(c) 2255
(d) 2250
Answer : D

Question. If a, b and c are the greatest values of 19Cp, 20Cq and 21Cr respectively, then: 
(a) a/11 = b/22 = c/21
(b) a/10 = b/11 = c/21
(c) a/11 = b/22 = c/42
(d) a/10 = b/11 = c/42
Answer : C

Question. The number of ordered pairs (r, k) for which 6.³⁵Cr = (k² – 3).³⁶C_{r + 1}, where k is an integer, is:
(a) 3
(b) 2
(c) 6
(d) 4
Answer : A

Question. A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:
(a) m⁺ n = 68
(b) m = n = 78
(c) n = m – 8
(d) m = n = 68
Answer : B

Question. A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to :
(a) 28
(b) 27
(c) 25
(d) 24
Answer : C

Question. Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-ad acent pillars, then the total number of beams is :
(a) 170
(b) 180
(c) 210
(d) 190
Answer : A

Question. Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is : 
(a) 201
(b) 200
(c) 101
(d) 199
Answer : A

Question. There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is
(a) 12
(b) 11
(c) 9
(d) 7
Answer : A

Q3. Prove that n! +1 is not divisible by any natural number between 2 and n.

Q4. A room has 6 doors. In how many ways can a man enter the room through one door and come out through a different door?
Answer : 30

Q5. For a set of five true/false questions, no student has written all correct answers and no two students have given the same sequence of answers. What is the maximum number of students in a class, for this to be possible?
Answer : 31

Q6. How many numbers are there between 100 and 1000 such that at least one of their digits is 7?
Answer : 252.

Q7. In a class, there are 30 boys and 18 girls. The teacher wants to select one boy and one girl to represent the class for quiz competition. In how many ways can the teacher make this selection?
Answer : 540

Q8. How many two digit even numbers can be formed from the digit 1, 2, 3, 4 and 5 if the digit can be repeated?
Answer : 10

Q9. A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequence will be possible.
Answer : 720

Q10. Each of six squares in the strip shown in figure is to be coloured with any one of ten different colours so that no two adjacent squares have the same colour. Find the number of ways of colouring the strip.
Answer : 590490

Q17.The principal wants to arrange 5 students on the platform such that the boy ‘SALIM’ occupies second position and such that the girl ‘SITA’ is always adjacent to the girl ‘RITA’. How many such arrangements are possible? .
Answer : 8

Q18. Three married couples are to be seated in a row having six seats in a cinema hall. If the spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.
Answer : 48, 144

Q19. Find the number of 8-letter word formed from the letters of the word ‘TRIANGLE’ if each word is to
(i) have no two vowels together
(ii) have both consonants and vowels together
(iii) have the relative position of the vowels and consonants unaltered. .
Answer : 14400, 1440,720

Q20. There are three prizes to be distributed among six students. In how many ways can it be done when
(i) no students get more than one prize
(ii) there is no restriction as to the number of prizes any students gets.
(iii) No students get all the prizes. 
Answer : 30, 216,210

Q21. A polygon has 44 diagonals. Find the number of its sides .
Answer : 11

Q22. If the letter of the word ‘SACHIN’ are arranged in all possible ways and these words are written out as in dictionary. Prove that the word ‘SACHIN’ appear at serial number 601.

Q23. In the expansion of (1+x)ⁿ , the coefficient of the pth and qth terms are equal, prove that p+q=n+2 where p≠q

Q24. Using binomial theorem, prove that:- 3²ⁿ⁺²-8n-9 is divisible by 64 Where n is natural number.

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