Principle of Mathematical Induction Test

Result

Principle of Mathematical Induction Test - 8

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Weekly Quiz Competition

Question 1
1 / -0

For all positive integers n, the number 4ⁿ + 15n − 1 is divisible by :

A
16

B
36

C
9

D
24

Solution

Replace n = 1 we get 18 n = 2 we get 45.... By the principle of mathematical induction it is divisible by 9.
Question 2
1 / -0

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

A
2304

B
26

C
25

D
1234

Solution

When n = 1 the value is 0. When n = 2 the value is 2304..... Hence by the principle of mathematical induction the expression is divisible by 2304.
Question 3
1 / -0

For all n ∈ N , 5²ⁿ − 1 is divisible by :

A
11

B
24

C
25

D
26

Solution

Replace n = 1,2 3.. the answers are divisible by 24.
Question 4
1 / -0

For all n ∈ N,3²ⁿ + 7 is divisible by :

A
11

B
8

C
3

D
none of these

Solution

When n =1 the value is 16 which is a multple of 8 , n = 2 the value is 88 which is a multiple of 8..... By PMI the expression is divisible by 8 for all natural numbers.
Question 5
1 / -0

For all n ∈ N,3n⁵ + 5n³ + 7n is divisible by :

A
5

B
10

C
15

D
3

Solution

For n = 1 the value is 15. For n = 2 the value is 150 which is a multiple of 15... By PMI the expression is divisible by 15.
Question 6
1 / -0

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

A
n² + n + 1

B
4n-1

C
n+2

D
none of these

Solution

Put n = 1 we have 3. When n = 2 , 4 + 2 + 1 = 7...
Question 7
1 / -0

The nth terms of the series 4+14+30+52+80+114+….. is =

A
2n² + 2n

B
2n² + 2

C
3n² + n

D
5n-1

Solution

When n = 1 we get 3. When n = 2 we get 12+2= 14...
Question 8
1 / -0

3+13+29+51+79+………..to n terms is

A
n² + 5n³

B
2n² + 7n

C
n³ + 2n²

D
none of these

Solution

When n = 1 we have 3 when n = 2 we have LHS : 3 + 13 = 16 RHS : 8 + 8 = 16 .....By PMI this is the sum of the n terms of the series.
Question 9
1 / -0

The sum of n terms of the series 1³ + 3³ + 5³ +......... is

A
n²(2n² − 1)

B
n²(2n² + 1)

C
n²(n² + 1)

D
none of these.

Solution

When n = 1 we get 1 . When n = 2 we get RHS : 4x7 = 28 LHS : 1+27 = 28...... By PMI this is true.
Question 10
1 / -0

If n is an odd positive integer, then aⁿ+ bⁿis divisible by :

A
a² + b²

B
a+b

C
a-b

D
none of these

Solution

Since when n = 1 we get a + b. Hence by the method of mathematical induction it is true.

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Re-Attempt Weekly Quiz Competition

Principle of Mathematical Induction Test - 8

Result

Principle of Mathematical Induction Test - 8

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Question 1

16

36

9

24

Solution

Question 2

2304

26

25

1234

Solution

Question 3

11

24

25

26

Solution

Question 4

11

8

3

none of these

Solution

Question 5

5

10

15

3

Solution

Question 6

n2 + n + 1

4n-1

n+2

none of these

Solution

Question 7

2n2 + 2n

2n2 + 2

3n2 + n

5n-1

Solution

Question 8

n2 + 5n3

2n2 + 7n

n3 + 2n2

none of these

Solution

Question 9

n2(2n2 − 1)

n2(2n2 + 1)

n2(n2 + 1)

none of these.

Solution

Question 10

a2 + b2

a+b

a-b

none of these

Solution

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n² + n + 1

2n² + 2n

2n² + 2

3n² + n

n² + 5n³

2n² + 7n

n³ + 2n²

n²(2n² − 1)

n²(2n² + 1)

n²(n² + 1)

a² + b²