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The smallest +ve integer n for which n! ...

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

A

1

B

2

C

3

D

4

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The correct Answer is:
B
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AAKASH SERIES-MATHEMATICAL INDUCTION-PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)
  1. If 'a' and 'b'are natural numbers such that a^(2) - b^(2) is prime num...

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

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

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

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

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

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

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

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  9. 7^(13) + 6^(13) is divisible by

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  10. (1+ x)^(n) -nx -1 is divisible by (where n in N )

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

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

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

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

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

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

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

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

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

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  20. If n gt 1 then

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