BITSAT Mathematics Principle Of Mathematical Induction MCQs

Question: If  then P(n) is true for

• a) 
• b) n > 0
• c) n < 0
• d)

  

Answer: 

Question: The greatest positive integer, which divides n(n +1)(n + 2)(n + 3) for all n€N , is

• a) 2
• b) 6
• c) 24
• d) 120

Answer: 24

Question: Let T(k) be the statement 1 + 3 + 5 + ... + (2k – 1)= k² +10

Which of the following is correct?

• a) T(1) is true
• b) T(k) is true Þ T(k + 1) is true
• c) T(n) is true for all n €N
• d) All above are correct

Answer: T(k) is true Þ T(k + 1) is true

Question: For n€ N, xⁿ⁺¹ + (x + 1)^2n–1 is divisible by

• a) x
• b) x + 1
• c) x² + x + 1
• d) x² – x + 1

Answer: x² + x + 1

Question: 10ⁿ + 3(4ⁿ⁺²) + 5 is divisible by (n €N)

• a) 7
• b) 5
• c) 9
• d) 17

Answer: 9

Question: If 

having n radical signs then by methods of mathematical induction which is true

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Let S(k) = 1+ 3+ 5...+ (2k -1) = 3 + k² . Then which of the following is true?

• a) Principle of mathematical induction can be used to prove the formula
• b)

  

• c)

  

• d) S(1) is correct

Answer:

Question: The inequality n! > 2^n–1 is true for

• a) n > 2
• b) n€ N
• c) n > 3
• d) None of these

Answer: n > 2

Question: 10ⁿ + 3(4ⁿ⁺²) + 5 is divisible by (n €N)

• a) 7
• b) 5
• c) 9
• d) 17

Answer: 9

Question: The greatest positive integer, which divides n(n +1)(n + 2)(n + 3) for all n€N , is

• a) 2
• b) 6
• c) 24
• d) 120

Answer: 24