BITSAT Mathematics Permutations and Combinations MCQs

Question: How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions ?

• a) 16
• b) 36
• c) 60
• d) 180

Answer: 60

Question: Statement 1 : A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 with repetition. The total number formed are 216. Statement 2 : If sum of digits of any number is divisible by 3 then the number must be divisible by 3.

• a) Statement-1 is true, Statement-2 is true and is a correct explanation for Statement -1
• b) Statement -1 is true, Statement -2 is true and is NOT a correct explanation for Statement - 1
• c) Statement - 1 is true, Statement- 2 is false
• d) Statement -1 is false, Statement -2 is true

Answer: Statement -1 is false, Statement -2 is true

Question: If

 then a – n is equal to

• a) 0
• b) 1
• c) 2
• d) None of these

Answer: 0 

Question: The number of values of r satisfying the equation is

• a) 1
• b) 2
• c) 3
• d) 4

Answer: 2

Question: All the words that can be formed using alphabets A, H, L, U and R are written as in a dictionary (no alphabet is repeated). Rank of the word RAHUL is

• a) 71
• b) 72
• c) 73
• d) 74

Answer: 74

Question: The total number of 4-digit numbers in which the digits are in descending order, is

• a) ¹⁰C₄ × 4!
• b) ¹⁰C₄
• c)

  

• d) None of these

Answer:   ¹⁰C₄

Question: The number of all three elements subsets of the set {a₁, a₂, a₃ . . . a_n} which contain a₃ is

• a) ⁿC₃
• b) ^{n – 1}C₃
• c) ^{n – 1}C₂
• d) None of these

Answer: ^{n – 1}C₂

Question: In how many ways can a committee of 5 made out 6 men and 4 women containing atleast one woman?

• a) 246
• b) 222
• c) 186
• d) None of these

Answer: 246

Question: In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls may be together ?

• a) 4!
• b) 5!
• c) 4! + 5!
• d) 4! × 5!

Answer: 4! × 5!

Question: A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

• a) 64
• b) 129
• c) 84
• d) None of these

Answer: 64

Question: In how many ways can 5 prizes be distributed among 4 boys when every boy can take one or more prizes ?

• a) 1024
• b) 625
• c) 120
• d) 600

Answer: 1024

Question: The number of positive integral solution of abc= 30 is

• a) 30
• b) 27
• c) 8
• d) None of these

Answer: 27

Question: If ²⁰C_r = ²⁰C_r–10 then ¹⁸C_r is equal to

• a) 4896
• b) 816
• c) 1632
• d) None of these

Answer: 816

Question: In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon is

• a) 20
• b) 28
• c) 8
• d) None of these

Answer: 20

Question: With 17 consonants and 5 vowels the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is

• a) 5780
• b) 2890
• c) 5440
• d) 2720

Answer: 5780

Question: The letters of the word TOUGH are written in all possible orders and these words are written out as in a dictionary, then the rank of the word TOUGH is

• a) 120
• b) 88
• c) 89
• d) 90

Answer: 89

Question: If ^{2n +1}P_n–1 : ^{2n – 1}P_n = 3 : 5 then the value of n is equal to

• a) 4
• b) 3
• c) 2
• d) 1

Answer: 4

Question: 3 integers are chosen at random from the set of first 20 natural numbers. The chance that their product is a multiple of 3, is –

• a) 194/285
• b) 1/57
• c) 13/19
• d) 3/4

Answer: 194/285

Question: If the total number of m elements subsets of the set A = {a₁, a₂, a₃, ...., a_n} is l times the number of 3 elements subsets containing a₄, then n is

• a) (m – 1) λ
• b) mλ
• c) (m + 1) λ
• d) 0

Answer: mλ

Question: The number of arrangements of the letters of the word BANANA is which the two ‘N’s do not appear adjacently is

• a) 40
• b) 60
• c) 80
• d) 100

Answer: 40