Beta Question Bank for Engineering: Mathematics>Chapter 7 - Mathematical Induction>EXERCISE-1>Q 1

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The greatest positive integer, which divides $(n + 16) (n + 17) (n + 18) (n + 19),$ where $n \in N$ , is

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Important Questions on Mathematical Induction

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Beta Question Bank for Engineering: Mathematics>Chapter 7 - Mathematical Induction>EXERCISE-1>Q 2

Let

P (n) : n^{2} + n

is an odd integer. It is seen that truth of

P (n) \Rightarrow

the truth of

P (n + 1) .

Therefore,

P (n)

is true for all,

(

where

n \in N)

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Beta Question Bank for Engineering: Mathematics>Chapter 7 - Mathematical Induction>EXERCISE-1>Q 3

For every natural number

n

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Beta Question Bank for Engineering: Mathematics>Chapter 7 - Mathematical Induction>EXERCISE-1>Q 4

If

n \in N

, then

x^{2 n - 1} + y^{2 n - 1}

is divisible by-

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Beta Question Bank for Engineering: Mathematics>Chapter 7 - Mathematical Induction>EXERCISE-1>Q 5

The sum of the cubes of three consecutive natural numbers is divisible by-

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Beta Question Bank for Engineering: Mathematics>Chapter 7 - Mathematical Induction>EXERCISE-1>Q 6

If

n \in N,

then

11^{n + 2} + 12^{2 n + 1}

is divisible by

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Beta Question Bank for Engineering: Mathematics>Chapter 7 - Mathematical Induction>EXERCISE-1>Q 7

If

n \in N

, then

3^{4 n + 2} + 5^{2 n + 1}

is a multiple of-

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Beta Question Bank for Engineering: Mathematics>Chapter 7 - Mathematical Induction>EXERCISE-1>Q 8

For each

n \in N

,

10^{2 n + 1} + 1

is divisible by

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Beta Question Bank for Engineering: Mathematics>Chapter 7 - Mathematical Induction>EXERCISE-1>Q 9

The difference between an positive integer and its cube is divisible by