JEE Mathematics Principles Of Mathematical Induction MCQs

Question:

• a) none of these
• b) for all n > 1
• c) for all n
• d) for all n > 2

Answer: none of these

Question:

• a) none of these
• b) for n > 1
• c) for n > 2
• d) Both

Answer: none of these

Question:

• a) none of these
• b) n ≥ 1
• c) n ≥ 3
• d) n ≥ 2

Answer: none of these

Question:

• a) 24
• b) 120
• c) 240
• d) 2

Answer: 24

Question:

• a)

  

• b)

  

• c) for all n
• d) none of these

Answer:

Question:

• a)

  

• b)

  

• c) n > 1
• d) n > 2

Answer:

Question: If n is a positive integer, then 2 . 4^{2n + 1} + 3^{3n + 1} is divisible by

• a) 11
• b) 2
• c) 7
• d) 27

Answer: 11

Question:

• a) 6
• b) 4
• c) 2
• d) 8

Answer: 6

More Questions............................

Question: 1+ 3+ 3² +.....+ 3^n-1 =

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) (n + 1)²
• b) (n + 1)³
• c) 2 (n + 1)²
• d) (n – 1)²

Answer: (n + 1)²

Question: 1.3 + 2.3² + 3.3³ + ........n.3ⁿ =

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) 24
• b) 2
• c) 6
• 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)

  

• b) T(1) is true
• c) All above are correct
• d)

  

Answer:

Question:

• a)

  

• b) for odd values of n
• c) for even values of n
• d) not true for any value of n

Answer:

Question: Let P(n) be statement 2n < n!. Where n is a natural number, then P(n) is true for:

• a) all n > 3
• b) all n
• c) all n > 2
• d) none of these

Answer: all n > 3

Question:

• a) for n ≥7
• b) for n ≥6
• c) for n ≥3
• d) for all n

Answer:  for n ≥7

Question:

• a) 11
• b) 9
• c) 13
• d) none of these

Answer: 11

Question:

Statement 1 : (n+2)!/(n-1)! is divisible by 6.

Statement 2 : Product of 3 consecutive integers is divisible by 3!

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.