CBSE Class 11 Mathematics Permutations And Combinations Worksheet Set D

Question. The number of divisors of 9600 including 1 and 9600 are:
a. 60
b. 58
c. 48
d. 46
Answer : C

Question. The number of ways of painting the faces of a cube with six different colours is:
a. 1
b. 6
c. 6!
d. ⁹C₂
Answer : A, D

Question. Sanjay has 10 friends among whom two are married to each other. She wishes to invite 5 of the them for a party. If the married couple refuse to attend separately, the number of different ways in which she can invite five friends is:
a. ⁸C₅
b. 2 × ⁸C₃
c. ¹⁰C₅ – 2 × ⁸C₄
d. none of these
Answer : B, C

Question. There are n seats round a table marked 1,2,3,…n. The number of ways in which m(≤n) persons can takes seats is:
a. ⁿP_m
b. ⁿC_m x (m - 1)^! 
c. ⁿC_m × m!
d. ^n-1p_m-1
Answer : A, C

Question. The number of ways in which 10 candidates A₁, A₂,…, A₁₀ can be ranked, so that A₁ is always above A₂ is:
a. 10!/2
b. 8! × ¹⁰C₂
c. ¹⁰p₂
d. ¹⁰p₂
Answer : 

Question. In a class tournament when the participants were to play one game with another, two class players fell ill, having played 3 games each. If the total number of games played is 84, the number of participants at the beginning was:
a. 15
b. 30
c. ⁶C₂
d. 48
Answer : A, C

Question. The number of ways of distributing 10 different books among 4 students (S₁ − S₄ ) such that S and 2 get 2 books each and S₃ and S₄ get books each is:
a. 12600/
b. 25200
c. ¹⁰C₄
D. 10!/2!2!3!3!
Answer : B, D

Question. The number of ways to select 2 numbers from {0,1,2,3,4}  such that the sum of the squares of the selected numbers is divisible by 5 are: (repetition of digits is allowed)
a. ⁹C1
b. ⁹C₈
c. 9
d. 7
Answer : A, B, C

Question. The number of ways of arranging seven persons (having A, B, C and D among them) in a row so that A, B, C and D are always in order A–B–C–D (not necessarily together) is:
a. 210
b. 5040
c. 6 × ₇C₄
d. ⁷C₃
Answer : A, C, D

Question. Total number of ways of giving at least one coin out of three 25 paise and two 50 pasise coins to a beggar is:
a. 32
b. 12
c. 11
d. ¹²P1 – 1
Answer : C, D

Question. If α = x₁ x₂ x₃ and β = y₁ y₂ y₃ be two three digits numbers, the number of pairs of α and β can be formed so thatα can be subtracted fromβ without borrowing is:
a. 2!10!10!
b. (45)(55)²
c. 3². 5³ .11²
d. 136125
Answer : B, C, D

Assertion and Reason

Note: Read the Assertion (A) and Reason (R) carefully to mark the correct option out of the options given below:
a. If both assertion and reason are true and the reason is the correct explanation of the assertion.
b. If both assertion and reason are true but reason is not the correct explanation of the assertion.
c. If assertion is true but reason is false.
d. If the assertion and reason both are false.
e. If assertion is false but reason is true.

Question. Assertion: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ⁹C₃
Reason: The number of ways of choosing 3 places from 9 different place is ⁹C₃
Answer : B

Question. Assertion: If p is a prime, the exponent of p in n! is [n/^p] + [n/p²] + [n/p³] +......
Reason: where [x] denotes the greatest integer ≤ x.
Answer : A

Question. Assertion: A student is allowed to select at most n books from a collection of (2n +1) books. If the total number of ways in which he can select at least one book is 255, thenn = 3.

Answer : D

Question. If the number of ways of selecting n coupons out of an unlimited number of coupons bearing the letters A, T, C so that they cannot be used to spell to the used CAT is 189, then Σn² must be:
Answer : 127

Question. The letters of the word PATNA are arrange in all possible ways as in a dictionary, then rank of the word PATNA from last is:
Answer : 19

Question. The number of integral solutions of a + b + c = 0, a ≥ −5, b ≥ −5, c ≥ −5 must be:
Answer : 136

Question. Let n₁ < n₂ < n₃ < n₄ < n₅ be positive integers such that n₁ + n₂ + n₃ + n₄ + n₅ = 20. The number of such distinct arrangements 1 2 3 4 5 (n₁, n₂ ,n₃, n₄, n₅) is:
Answer : 7

Question. Let n ≥ 2 be an integer. Taken n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is
Answer : 5