Principle of Mathematical Induction Test

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Principle of Mathematical Induction Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

For all n ∈ N,2.4²ⁿ⁺¹ + 3³ⁿ⁺¹ is divisible by :

A
5

B
7

C
11

D
209

Solution

Replace n = 1 we get 209 which is divisible by 11.
Question 2
1 / -0

If 49ⁿ + 16n + λ is divisible by 64 for all n ∈ N , then the least negative integral value of λ is

A
-4

B
-3

C
-1

D
-2

Solution

When n = 1 we have the value of the expression as 65 . Given that the expression is divisible be 64. Hence the value is -1.
Question 3
1 / -0

10²ⁿ⁻¹ + 1∀n ∈ N is divisible by :

A
3

B
2

C
11

D
7

Solution

put n = 1 we get 11 .
Question 4
1 / -0

For all odd positive integers n , the number n(n² − 1) is divisible by :

A
16

B
9

C
36

D
24

Solution

When n = 1 we have 0 : When n = 2 we have 24. When n = 3 we have 120 .....where all these values are multiples of 24.
Question 5
1 / -0

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

A
5n-1

B
3n² + n

C
2n² + 2n

D
2n² + 2

Solution

When n = 1 we get 3. When n = 2 we get 12+2= 14...
Question 6
1 / -0

The product of three consecutive natural numbers is divisible by

A
11

B
8

C
3

D
6

Solution

By replacing n by 1 we get 6.
Question 7
1 / -0

For n ∈ N,3²ⁿ⁺² − 2³n − 9is divisible by

A
64

B
9

C
3

D
81

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.

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Re-Attempt Weekly Quiz Competition

Principle of Mathematical Induction Test - 7

Result

Principle of Mathematical Induction Test - 7

Score

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SHARING IS CARING

Question 1

5

7

11

209

Solution

Question 2

-4

-3

-1

-2

Solution

Question 3

3

2

11

7

Solution

Question 4

16

9

36

24

Solution

Question 5

5n-1

3n2 + n

2n2 + 2n

2n2 + 2

Solution

Question 6

11

8

3

6

Solution

Question 7

64

9

3

81

Solution

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3n² + n

2n² + 2n

2n² + 2