CBSE Class 11 Mathematics Permutation And Combination Worksheet Set A

Question. Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?
(a) 2! 3! 4!
(b) (3!)³ × (4!)
(c) (3!)² × (4!)
(d) 3! (4!)³
Answer : B

Question. The value of (2. ¹P₀ -3. ²P₁ + 4. ³P2 - ... up to 51^th term) + (1! – 2! + 3! – ... up to 51^th term) is equal to :
(a) 1 – 51(51)!
(b) 1 + (51)!
(c) 1 + (52)!
(d) 1
Answer : C

Question. If the number of five digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to:
(a) 4
(b) 6
(c) 7
(d) 8
Answer : D

Question. The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3, 4, 5 (repetition of digits is allowed) is:
(a) 288
(b) 360
(c) 306
(d) 310
Answer : D

Question. The range of the function f(x) = ^{7 - x} P_x-3 is
(a) {1, 2, 3, 4, 5}
(b) {1, 2, 3, 4, 5, 6}
(c) {1, 2, 3, 4,}
(d) {1, 2, 3,}
Answer : D

Question. The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is
given by
(a) 6! × 5!
(b) 6 × 5
(c) 30
(d) 5 × 4
Answer : A

Question. Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:
(a) 9
(b) 18
(c) 36
(d) 32
Answer : C

Question. The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?
(a) 30
(b) 48
(c) 24
(d) 36
Answer : A

Question. How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order
(a) 480
(b) 240
(c) 360
(d) 120
Answer : C

Question. Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number is
(a) 125
(b) 105
(c) 374
(d) 625
Answer : C

Question. Consider three boxes, each containing 10 balls labelled 1, 2,..., 10. Suppose one ball is randomly drawn from each of the boxes. Denote by n_i, the label of the ball drawn from the i^th box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n₁ < n₂ < n₃ is :
(a) 120
(b) 82
(c) 240
(d) 164
Answer : A

Question. Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is:
(a) 1/2 (6!)
(b) 6!
(c) 56
(d) 5/2 (6!)
Answer : D

Question. The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated, is: 
(a) 72
(b) 60
(c) 48
(d) 36
Answer : B

Fill in The Blanks

Question. The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is ______.
Answer : (120.00)

Question. If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ________. 
Answer : 309

Question. The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ‘SYLLABUS’ such that two letters are distinct and two letters are alike, is ______. 
Answer : (240)

Question. A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is __________. 
Answer : (135)

Question. If C_r ≡ ²⁵Cr and C₀ + 5×C₁ + 9×C₂ + ... + (101)×C₂₅ = 2²⁵×k, then k is equal to ________. 
Answer : (51)

Question. An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is _________. 
Answer : (490)

Question. The total number of 3-digit numbers, whose sum of digits is 10, is _________. 
Answer : (54)

Question. The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word ‘EXAMINATION’ is _________.
Answer : (2454)

Please click on below link to download CBSE Class 11 Mathematics Permutation And Combination Worksheet Set A