Principle of Mathematical Induction - Online Test

Q1.  upto n terms is equal to
Answer : Option B
Explaination / Solution:

Replace n = 1 we have 1/2. When n = 2 we have 1/2+1/6=2/3,( by the principle of mathematical induction when n = 1 we need to take one term from LHS. and for n = 2 we need to take the sum of two terms from the LHS. .....)

Q2. up to n terms is equal to
Answer : Option A
Explaination / Solution:

By the process of mathematical induction when n = 1 we have 1/15. When n = 2 we have LHS : 1/15+1/35=2/21, RHS :2/(3(4+3))=2/21, which is true

Q3. The nth terms of the series 4+14+30+52+80+114+….. is =
Answer : Option B
Explaination / Solution:

When n = 1 we get 3. When n = 2 we get 12+2= 14...

Q4. The product of three consecutive natural numbers is divisible by
Answer : Option D
Explaination / Solution:

By replacing n by 1 we get 6.

Q5. For is divisible by
Answer : Option A
Explaination / Solution:

When n = 1 we get 64. When n = 2 we get 704 which is divisible by 64......... By the principle of mathematical induction it is divisible by 64.

Q6.

The statement  is true for all


Answer : Option A
Explaination / Solution:

When n = 1 8<3, is not true. When n = 2 16<9, is false. When n = 3 32<27, is not valid. But when n = 4 64<81, is true.

Q7. The smallest positive integer for which The statement  is true for
Answer : Option C
Explaination / Solution:

When n = 1 9<4 not valid. when n = 2 27<16 not true. when n = 3 81<64 is in correct. when n = 4 243<256, is true.

Q8. For all n  N , is divisible by
Answer : Option A
Explaination / Solution:

Replace n = 1 , we have 64.

Q9. 23n-1 is divisible by
Answer : Option B
Explaination / Solution:

If n = 1 we get 7. n = 2 we get 63 which is divisible by 7........

Q10.  is divisible by
Answer : Option D
Explaination / Solution:

when n = 1 , we have 50, which is divisible by 25.