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Prove by the principle of mathematical i...

Prove by the principle of mathematical induction that `2^ n >n` for all n∈N.

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ALLEN-TEST PAPER-Chemistry
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  4. The equation x(x+2)(x ^2 −x)=−1 , has all roots imaginary ...

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  5. The value of sin50^∘−sin70^∘ +sin10^∘ is

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  6. What is the value of sin ^2 25^0+sin^2 65^0?

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  7. Find dy/dx :6x−9+8y=0

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  8. The roots of the equation cos ^7x+sin^4x=1 in the interval (−π,π...

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  9. If (i ^413)(i ^x )=1 , then determine the one possible value of x.

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  10. Express the given complex number 3(7+i7)+i(7+i7) in the form a...

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  11. 1/(i-1) + 1/(i+1) is a. purely imaginary b. purely rational number....

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  12. |{:(,"List-I(Atom/Ions)",,"List-II(Electron Affinity in eV/atom and co...

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  13. |{:(,"List-I(Orbitals)",,"List-II"),(,"(Approach axis is z-axis)",,"(T...

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  14. Let alpha and beta be the roots of the equation x^2+(2-costheta)x-(1+c...

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  15. If 2p=x+1/x and 2q=y+1/y, then the value of ((pq+sqrt((p^2-1)(q^2-1)))...

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  16. Let P be minimum value of 9sin^2x+16cosec^2x and S be the minimum valu...

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  17. The values of a for which the equation 2(log(3)x)^(2)-|log(3)x|+a=0 po...

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  18. Number of integers satisfying the inequality log((x+3))(x^2-x) lt 1 is

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  19. If x and y are positive real numbers such that x^3+8y^3+24xy=64 , then...

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  20. Which of the following set of quantum numbers, an electron will have l...

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