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AA n in N, 49^(n) + 16n -1 is divisible ...

`AA n in N, 49^(n) + 16n -1` is divisible by

A

64

B

49

C

132

D

32

Text Solution

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The correct Answer is:
A
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By Mathematical Induction , show that 49^(n)+16n-1 is divisible by 64 for all positive Integer n .

A) 49^(n) + 16n +1 is divisible by A ( n in N) B) 3^(2n) + 7 is divisible by B ( n in N) C) 4^(n ) - 3n -1 is divisible by C ( n in n) D) 3^( 3n ) - 26 n - 1 is divisible by D (n in N) then the increasing order of A, B, C, D is

AAKASH SERIES-MATHEMATICAL INDUCTION-PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)
  1. If a,b and n are natural numbers then a^(2n-1) + b^(2n-1) is divisible...

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  2. If 'a' and 'b'are natural numbers such that a^(2) - b^(2) is prime num...

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  3. AA n in N, 49^(n) + 16n -1 is divisible by

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  4. AA n in , 7^(2n) + 3^(n-1) . 2^(3n-3) is divisible by

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  5. Sum of the cubes of three successive natural number is divisible by

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  6. For every natural number n, 3^(2n+2) - 8n -9 is divisible by

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  7. If 10^(n) + 3.4^(n) + x is divisible by 9 for all n in N, then least ...

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  8. AA n in N, 5^(2n+2) - 24n - 25 is divisible by

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  9. If y^(n) -1 is divisible by y+ a for all values of n in N, then a must...

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  10. 7^(13) + 6^(13) is divisible by

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  11. (1+ x)^(n) -nx -1 is divisible by (where n in N )

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  12. For a positive integer (n gt 1), Let a (n) = 1+ (1)/(2) + (1)/(3) + (1...

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  13. For all positive integers n gt 1, { x(x^(n-1) - n,a^(n-1) ) } + a^(n) ...

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  14. ((n+2)!)/( (n-1)!) is divisible by

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  15. When 2^( 301) is divided by 5, the least +ve remainder is

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  16. Statement -1 : For all n in N, x^( 2n+1) +y^(2n+1) is divisible by x+y...

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  17. Statement - 1 : For all n in N x^(n) - y^(n) is divisible by x-y Sta...

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  18. A) 49^(n) + 16n +1 is divisible by A ( n in N) B) 3^(2n) + 7 is divi...

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  19. Let S = (1)/( 1.4) + (1)/( 4.7) + (1)/(7.10) + .....n terms, Observe t...

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  20. The smallest +ve integer n for which n! lt ( (n+1)/( 2) )^(n) holds is

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