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If…..is true and P(k) is true rArr P(k+...

If…..is true and P(k) is true `rArr ` P(k+1) is true, `k gt= - 1` , then for all `n in N cup {0,-1},P(n)` is true.

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KUMAR PRAKASHAN-OBJECTIVE SECTION AS PER NEW PAPER SCHEME -Principle of Mathematical Induction (Fill in the blanks)
  1. P(n):2^n - 1, for n = ……………it is a prime number.

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  2. If…..is true and P(k) is true rArr P(k+1) is true, k gt= - 1 , then f...

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  3. P(n) : n (n+1) is even number then P(3) = .........

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  4. P(n) : 1^(2) + 2^(2) + 3^(2) + .......+ n^(2) = n/6(n+1) (2n+1) n in N...

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  5. Statement P (n) : 10^(n) + 3(4^(n+2))+5 is divisible by n = ........

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  6. P(n) : 2n + 1, for n = …………it is not a prime number.

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  7. P(n) : 2^n gt n^2 , for n = ………it is true.

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  8. P(n):n^2 - n +41 , for n = ……, it is not prime number .

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  9. .........is the remainder if P (n) : 3^(2n+2) - 8n is divided by 64.

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  10. Statement P (n) : n^(3) +3n^2 + 5n +3 is multiple of .......smellest ...

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  11. P(n):2^n - 1, for n = ……………it is a prime number.

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  12. If…..is true and P(k) is true rArr P(k+1) is true, k gt= - 1 , then f...

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  13. P(n) : n (n+1) is even number then P(3) = .........

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  14. P(n) : 1^(2) + 2^(2) + 3^(2) + .......+ n^(2) = n/6(n+1) (2n+1) n in N...

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  15. Statement P (n) : 10^(n) + 3(4^(n+2))+5 is divisible by n = ........

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  16. P(n) : n (n+1) is even number then P(3) = .........

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  17. P(n) : 2^n gt n^2 , for n = ………it is true.

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  18. If a(1),a(2),a(3), . . . .,a(n+1) be (n+1) different prime numbers, t...

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  19. .........is the remainder if P (n) : 3^(2n+2) - 8n is divided by 64.

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  20. Statement P (n) : n^(3) +3n^2 + 5n +3 is multiple of .......smellest ...

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