Class 11 Mathematics Principle of Mathematical Induction Functions MCQs Set 02

Question: For all n ε N, n (n+ 1)(n + 5) is a multiple of
a) 4
b) 3
c) 5
d) 7
Answer: b

Question: For every positive integer n, n7/7 + n5/5 + 2n³/3 – n/105 is
a) an integer
b) a rational number
c) a negative real number
d) an odd integer
Answer: a

Question: For all n≥ 2,n n² (n⁴ > 1) is divisible by
a) 60
b) 50
c) 40
d) 70
Answer: a

Question: If n εN, 7²ⁿ – 48n – 1 is divisible by
a) 25
b) 26
c) 1234
d) 2304
Answer: d

Question: If x^{n – 1} is divisible by x – k, then the least positive integral value of k is
a) 1
b) 2
c) 3
d) 4
Answer: a

Question: For n ∈ N, (1/5)n5 +(1/3)n³ + (7/15)n is
a) an integer
b) a natural number
c) a positive fraction
d) None of the options
Answer: b

Question: If nεN, then the highest positive integer which dividesn(n – 1)(n – 2) is
a) 3
b) 6
c) 9
d) 12
Answer: b

Question: For positive integer n, 10^n-2 > 81 , if
a) n > 5
b) n ≥ 5
c) n < 5
d) n > 6
Answer: b

Question: For all n εN, 2,4²ⁿ⁺¹ + 3³ⁿ⁺¹ is divisible by
a) 2
b) 9
c) 3
d) 11
Answer: d

Question: If P(n) is a statement (n∈ N) such that, if P(k) is true, P(k +1) is true for k∈ N, then P(n) is true
a) for all n
b) for all n > 1
c) for all n > 2
d) Nothing can be said
Answer: d

Question: If m, n are any two odd positive integer with n m, then the largest positive integers which divides all the numbers of the type m² – n ² is
a) 4
b) 6
c) 8
d) 9
Answer: c

Question: Sⁿ is divisible by the multiple of
a) 5
b) 7
c) 24
d) None of the options
Answer: c

Question: For all nεN ,3.5²ⁿ⁺¹ +2³ⁿ⁺¹ is divisible by
a) 19
b) 17
c) 23
d) 25
Answer: b

Question: The smallest positive integer n for which n! < (n+1 / 2) holds, is
a) 1
b) 2
c) 3
d) 4
Answer: b

Question: For eachn n εN, 3²ⁿ-1 is divisible by
a) 8
b) 16
c) 32
d) None of the options
Answer: a

Question: If x^{2n – 1} + y^{2n – 1} is divisible by x + y, if n is
a) a positive integer
b) an even positive integer
c) an odd positive integer
d) None of the options
Answer: a

Question: x(x^n-1 -nα^n-1)1 is divisible by (x – α.)² for
a) n > 1
b) n > 2
c) all n ∈ N
d) None of the options
Answer: c

Question: 2³ⁿ – 7n 1 is divisible by
a) 64
b) 36
c) 49
d) 25
Answer: c

Question: For eachn n εN, 10²ⁿ-1 is divisible by
a) 11
b) 13
c) 9
d) None of the options
Answer: a

Question: If 49ⁿ + 16ⁿ k is divisible by 64 for n ∈ N, then the least negative integral value of k is
a) –1
b) –2
c) –3
d) –4
Answer: a

Question: For all n εN, 41ⁿ-14ⁿ is a multiple of
a) 26
b) 27
c) 25
d) None of the options
Answer: b

Question: For all positive integral values ofn n,3²ⁿ – 2n +1 is divisible by
a) 2
b) 4
c) 8
d) 12
Answer: a

Question: If P(n) is a statement such that P(3) is true.Assuming P(k) is true P(k + 1) is true for all k ε 3, then P(n) is true
a) for all n
b) for n ≥ 3
c) for n > 4
d) None of the options
Answer: b

Question: For each n ε N, the correct statement is
a) 2ⁿ < n
b) n² > 2n
c) n⁴ < n¹⁰
d) 2³ⁿ > 7n + 1
Answer: c

Question: The product of three consecutive natural numbers is divisible by
a) 2
b) 3
c) 6
d) 4
Answer(a,b,c)

Question: Let P(n) denotes the statement that n ²+n is odd. It is seen that P(n) P(n + 1), P(n) is true for all
a) n > 1
b) n
c) n > 2
d) None of the options
Answer: d

Question: Let P(n) : n²+n+1 is an even integer. If P(k) is assumed true ⇒P(k + 1) is true. Therefore, P(n) is true
a) for n > 1
b) for all n > N
c) for n > 2
d) None of the options
Answer: d

Question: The greatest positive integer, which divides (n + 2) (n + 3) (n + 4) (n + 5) (n + 6) for all n ε N, is
a) 4
b) 120
c) 240
d) 24
Answer: b

Question: If Sn is divisible for every n, then Sn is
a) > 0
b) > 1
c) > 5
d) None of the options
Answer: a

 Question: The inequality n ! > 2^n-1 is true for
a) n > 2
b) n > N
c) n > 3
d) None of the options
Answer: a