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Choose the proposition among the followi...

Choose the proposition among the following that is not true for all `n in NN`

A

(a) `2^(n) gt n`

B

(b) `2^(n)gt n^(2)`

C

(c) `1+2+3+…+n lt (2n+1)^(2)`

D

(d) `(2n+7) lt (n+3)^(2)`

Text Solution

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The correct Answer is:
B
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AAKASH INSTITUTE ENGLISH-PRINCIPLE OF MATHEMATICAL -Section-B((Objective Type Questions (One option is correct))
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  2. (x^(n)+y^(n)) is divisible by (x+y) is true when n in NN is of the for...

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  3. The statement 2^(n) ge n^(2) (where n in N) is true for

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  4. Choose the statement which is correct for all n in N

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  5. n(n+1)(n+2) is divisible by k for AA n in N. The largest k is

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  6. Mathematical induction is a tool or technique which is used to prove a...

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  7. For each n in N, 3^(2n)-1 is divisible by

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  8. For each n in N, n(n+1) (2n+1) is divisible by

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  9. The statement n! gt 2^(n-1), n in N is true for

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  10. For all n in N, 3.5^(2n+1) + 2^(3n+1) is divisible by: (i) 17 (ii...

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  11. 3.6+6.9+9.12+....+3n(3n+3)=

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  12. Choose the proposition among the following that is not true for all n ...

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  13. Prove the following by the principle of mathematical induction: 7+7...

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  14. Choose the proposition among the following that is not true for n=1 bu...

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  15. Find the value of 1 xx 1!+2 xx 2!+3 xx 3!+........+n xx n!

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  16. Choose the proposition that is not true for n gt 1 (n in N).

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  17. Which of the following is true for n in N?

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  18. For all n( gt 1) in N, by using mathematical induction or otherwise 1+...

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  19. The sum of the square of three consecutive odd number increased by 1 i...

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  20. Choose the proposition among the following that is true for all n in N...

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