Class 11 Mathematics Permutations and Combinations MCQs Set 03

Question. The number of 3 digit numbers having at least one of their digit as 5 are
(a) 250
(b) 251
(c) 252
(d) 253
Answer: c

Question. Number of ways in which 20 different pearls of two colours can be set alternately on a necklace, there being 10 pearls of each colour.
(a) 6 × (9!)²
(b) 12!
(c) 4 × (8!)²
(d) 5 × (9!)²
Answer: d

Question. If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number
(a) 601
(b) 600
(c) 603
(d) 602
Answer: a

Question. If ³⁰C_{r + 2} = ³⁰C_{r – 2}, then r equals:
(a) 8
(b) 15
(c) 30
(d) 32
Answer: b

Question. Number of words from the letters of the words BHARAT in which B and H will never come together is
(a) 210
(b) 240
(c) 422
(d) 400
Answer: b

Question. If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary. Then, what is the rank of the word RACHIT?
(a) 479
(b) 480
(c) 481
(d) 482
Answer: c

Question. The number of ways in which we can choose a committee from four men and six women so that the committee include at least two men and exactly twice as many women as men is
(a) 94
(b) 126
(c) 128
(d) None of these
Answer: a

Question. Determine n if ²ⁿC₃ : ⁿC₂ = 12 : 1
(a) 5
(b) 3
(c) 4
(d) 1
Answer: a

Question. If 1/6! + 1/7! = x/8! , then the value of x = 2^m. The value of m is
(a) 2
(b) 4
(c) 6
(d) 5
Answer: d

Question. Total number of eight digit numbers in which all digits are different is
(a) 8.7!/3
(b) 5.8!/3
(c) 8.9!/2
(d) 9.9!/2
Answer: d

Question. Let T_n denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If T_{n + 1} − T_n = 21, then n equals`
(a) 5
(b) 7
(c) 6
(d) 4
Answer: b

Question. If ^{n + 2}C₈ : ^{n – 2}P₄ = 57 : 16, then the value of n is:
(a) 20
(b) 19
(c) 18
(d) 17
Answer: b

Question. A father with 8 children takes them 3 at a time to the zoological garden, as often as he can without taking the same 3 children together more than once. The number of times he will go to the garden is
(a) 56
(b) 100
(c) 112
(d) None of these
Answer: a

Question. The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
(a) 6
(b) 18
(c) 12
(d) 9
Answer: b

Question. If ⁿC₉ = ⁿC₈, what is the value of ⁿC₁₇ ?
(a) 1
(b) 0
(c) 3
(d) 17
Answer: a

Question. Value of n!/(n− r)! when n = 6, r = 2 is 5 m. The value of m is
(a) 2
(b) 4
(c) 6
(d) 5
Answer: c

Question. The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is
(a) 72
(b) 96
(c) 90
(d) 98
Answer: c

Question. In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together? 
(a) 41472
(b) 41470
(c) 41400
(d) 41274
Answer: a

Question. If ⁿC_r denotes the number of combination of n things taken r at a time, then the expression ⁿC_r+1 + ⁿC_r–1 + 2 × ⁿC_r equals
(a)ⁿ⁺¹C_r+1
(b) ⁿ⁺²C_r
(c) ⁿ⁺²C_r+1
(d) ⁿ⁺¹C_r
Answer: c

Question . The sum of the digits in the unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time is
(a) 432
(b) 108
(c) 36
(d) 18
Answer: b

Question. In a small village, there are 87 families, of which 52 families have at most 2 children. In a rural development programme 20 families are to be chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
(a) ⁵²C₁₈ ³⁵C₂
(b) ⁵²C₁₈× ³⁵C₂+ ⁵²C₁₉× ³⁵C₁+ ⁵²C₂₀
(c) ⁵²C₁₈+ ³⁵C₂+ ⁵²C₁₉
(d) ⁵²C₁₈× ³⁵C₂+ ³⁵C₁× ⁵²C₁₉
Answer: b

Question. Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
(a) 60
(b) 120
(c) 7200
(d) 720
Answer: c

Question. For a game in which two partners play against two other partners, six persons are available. If every possible pair must play with every other possible pair, then the total number of games played is
(a) 90
(b) 45
(c) 30
(d) 60
Answer: b

Question. How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
(a) 8. ⁶C₄. ⁷C₄
(b) 6.7. ⁸C₄
(c) 6. 8. ⁷C₄.
(d) 7. 6C4. ⁸C₄
Answer: d

Question. Find n if n – ¹P₃ : ⁿP₄= 1 : 9
(a) 2
(b) 6
(c) 8
(d) 9
Answer: d

Question. Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side of the table. The number of ways in which the seating arrangement can be done equals
(a) ¹¹C₄ (9!)²
(b) ¹¹C₆ (9!)²
(c) ⁶P₀ × ⁵P₀
(d) None of these
Answer: b

STATEMENT TYPE QUESTIONS

Question. Consider the following statements.
I. If there are n different objects, then ⁿC_r = ⁿC_n−r 0 ≤ r ≤ n.
II. If there are n different objects, then ⁿC_r + ⁿC_{r– 1} = ⁿ⁺¹C_r, 0 ≤ r ≤ n
Choose the correct option.
(a) Both are false.
(b) Both are true.
(c) Only I is true.
(d) Only II is true.
Answer: b

Question. Consider the following statements.
I. If ⁿP_r = ⁿP_r+1 and ⁿC_r = ⁿC_r–1, then the values of n and r are 3 and 2 respectively.
II. From a class of 32 students, 4 are to be chosen for a competition. This can be done in ³²C₂ ways.
Choose the correct option.
(a) Only I is true.
(b) Only II is true.
(c) Both are false.
(d) Both are true.
Answer: a

Question. The number of 4 letter words that can be formed from letters of the word ‘PART’, when:
Statement I : Repetition is not allowed is 24.
Statement II : Repetition is allowed is 256.
Which of the above statement(s) is/are true?
(a) Only I
(b) Only II
(c) Both I and II
(d) Neither I nor II
Answer: c

Question. Consider the following statements.
I. If n is an even natural number, then the greatest among ⁿC₀, ⁿC₁ , ⁿC₂, …, ⁿC_n is ⁿC_n/2.
II. If n is an odd natural number, then the greatest among ⁿC₀, ⁿC₁ , ⁿC₂, …, ⁿC_n is ⁿC_n−1/2 or ⁿC_{n+ 1}/2.
Choose the correct option.
(a) Only I is false.
(b) Only II is true.
(c) Both are true.
(d) Both are false.
Answer: c