Principle of Mathematical Induction MCQs with answers

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Tutor II

Q. The sum of the series 1³ + 2³ + 3³ + ………..n³ is

(A) {(n + 1)/2}²
(B) {n/2}²
(C) n(n + 1)/2
(D) {n(n + 1)/2}²
Correct Answer - Option (D)

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Kirti • 10.37K Points
Tutor II

Q. If n is an odd positive integer, then an + bn is divisible by 

(A) a² + b²
(B) a + b
(C) a – b
(D) none of these
Correct Answer - Option (B)

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Kirti • 10.37K Points
Tutor II

Q. 1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)}

(A) n(n + 1)
(B) n/(n + 1)
(C) 2n/(n + 1)
(D) 3n/(n + 1)
Correct Answer - Option (B)

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Kirti • 10.37K Points
Tutor II

Q. The sum of the series 1² + 2² + 3² + ………..n² is

(A) n(n + 1)(2n + 1)
(B) n(n + 1)(2n + 1)/2
(C) n(n + 1)(2n + 1)/3
(D) n(n + 1)(2n + 1)/6
Correct Answer - Option (D)

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Kirti • 10.37K Points
Tutor II

Q. {1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =

(A) 1/(n + 1) for all n ∈ N
(B) 1/(n + 1) for all n ∈ R
(C) n/(n + 1) for all n ∈ N
(D) n/(n + 1) for all n ∈ R
Correct Answer - Option (A)

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Kirti • 10.37K Points
Tutor II

Q. For any natural number n, 7n – 2n is divisible by

(A) 3
(B) 4
(C) 5
(D) 7
Correct Answer - Option (C)

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Kirti • 10.37K Points
Tutor II

Q. 1/(1 ∙ 2 ∙ 3) + 1/(2 ∙ 3 ∙ 4) + …….. + 1/{n(n + 1)(n + 2)} =

(A) {n(n + 3)}/{4(n + 1)(n + 2)}
(B) (n + 3)/{4(n + 1)(n + 2)}
(C) n/{4(n + 1)(n + 2)}
(D) None of these
Correct Answer - Option (A)

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Kirti • 10.37K Points
Tutor II

Q. The nth terms of the series 3 + 7 + 13 + 21 +………. is

(A) 4n – 1
(B) n² + n + 1
(C) n + 2
(D) none of these
Correct Answer - Option (B)

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Kirti • 10.37K Points
Tutor II

Q. n(n + 1)(n + 5) is a multiple of ____ for all n ∈ N

(A) 2
(B) 3
(C) 5
(D) 7
Correct Answer - Option (B)

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Kirti • 10.37K Points
Tutor II

Q. Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.

(A) n(n+1)(n+2)/3
(B) n(n+1)(n+2)/6
(C) n(n+2)/6
(D) (n+1)(n+2)/6
Correct Answer - Option (B)

K

Kirti • 10.37K Points
Tutor II

Q. For any natural number n, 7n – 2n is divisible by

(A) 3
(B) 4
(C) 5
(D) 7
Correct Answer - Option (C)

K

Kirti • 10.37K Points
Tutor II

Q. (n² + n) is ____ for all n ∈ N.

(A) Even
(B) odd
(C) Either even or odd
(D) None of these
Correct Answer - Option (A)

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Kirti • 10.37K Points
Tutor II

Q. For all n ∈ N, 3×52n+1 + 23n+1 is divisible by

(A) 19
(B) 17
(C) 23
(D) 25
Correct Answer - Option (B)

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Kirti • 10.37K Points
Tutor II

Q. (1 + x)n ≥ ____ for all n ∈ N,where x > -1

(A) 1 + nx
(B) 1 – nx
(C) 1 + nx/2
(D) 1 – nx/2
Correct Answer - Option (A)

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Kirti • 10.37K Points
Tutor II

Q. 102n-1 + 1 is divisible by ____ for all N ∈ N

(A) 9
(B) 10
(C) 11
(D) 12
Correct Answer - Option (C)

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Kirti • 10.37K Points
Tutor II

Q. For all n∈N, 72n − 48n−1 is divisible by

(A) 25
(B) 2304
(C) 1234
(D) 26
Correct Answer - Option (B)

K

Kirti • 10.37K Points
Tutor II

Q. The sum of the series 1² + 2² + 3² + ………..n² is

(A) n(n + 1)(2n + 1)
(B) n(n + 1)(2n + 1)/2
(C) n(n + 1)(2n + 1)/3
(D) n(n + 1)(2n + 1)/6
Correct Answer - Option (D)

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Kirti • 10.37K Points
Tutor II

Q. {1/(3 ∙ 5)} + {1/(5 ∙ 7)} + {1/(7 ∙ 9)} + ……. + 1/{(2n + 1)(2n + 3)} =

(A) n/(2n + 3)
(B) n/{2(2n + 3)}
(C) n/{3(2n + 3)}
(D) n/{4(2n + 3)}
Correct Answer - Option (C)

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