Principle of Mathematical Induction

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Question

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Question 1 :

For principle of mathematical induction to be true, what type of number should ‘n’ be?

1. Whole number
2. Natural number
3. Rational number
4. Any form of number
Answer
7911

Question 2 :

7²ⁿ + 2^{2n – 2} . 3^{n – 1} is divisible by 50 by principle of mathematical induction.

1. True
2. False
3. Both
4. None
Answer
7912

Question 3 :

By principle of mathematical induction, 2^4n-1 is divisible by which of the following?

1. 3
2. 5
3. 7
4. 8
Answer
7913

Question 4 :

 If 10³ⁿ + 2^{4k + 1}. 9 + k, is divisible by 11, then what is the least positive value of k?

1. 4
2. 6
3. 8
4. 10
Answer
7914

Question 5 :

P(n) = n(n² – 1). Which of the following does not divide P(k+1)?

1. k
2. k + 2
3. k + 3
4. k + 1
Answer
7915