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If a, b, c are in H.P. and they are dist...

If a, b, c are in H.P. and they are distinct and positive then prove that `a^n+c^n gt 2b^n`

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ML KHANNA-INEQUALITIES-PROBLEM SET (1)(TRUE AND FALSE)
  1. 3/(b+c+d)+3/(c+d+a)+3/(d+a+b)+3/(a+b+c)gt16/(a+b+c+d)

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  2. n(n+1)^(3)lt8(1^(3)+2^(3)+3^(3)+………+n^(3))

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  3. If a, b, c are in H.P. and they are distinct and positive then prove t...

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  4. Sum of the nth powers of the m^(th) power of n even numbers is gtn(n+1...

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  5. If a,b,c are real numbers such that a^(2)+b^(2)+c^(2)=1 then ab+bc+cag...

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  6. In any triangle the semi perimeter is greater than each of its sides.

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  7. The sum of the cubes of the legs of a right angled triangle is less th...

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  8. Thesum of the hypotenuse and the altitude of a right angled triangle d...

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  9. The area of an arbitrary triangle is less than one fourth the square o...

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  10. If x,y,z are all positive and x lt y lt z, then (x^(2))/zlt(x^(2)+y^(2...

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  11. If 0ltalpha(1)ltalpha(2)lt……….ltalpha(n)lt(pi)/2 then tan alpha(1)lt...

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  12. If A+B+C=pithen "tan"^(2)A/2+"tan"^(2)B/2+"tan"^(2)C/2ge1.

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  13. Prove that 2sinx + tanx ge3x, for all x in [0, pi/2].

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  14. (a(1)^(2)+a(2)^(2)+….a(n)^(2)) (b(1)^(2)+b(2)^(2)+…..+b(n)^(2))ge(a(1...

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  15. A.M. of the square root of products taken two together on n+ve quantit...

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  16. Given n^(4)lt10^(n) for a fixed positive integer nge2, then (n+1)^(4)l...

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  17. For real a,b and x -sqrt((a^(2)+b^(2))lea sin x +bcos x le sqrt((a^(2...

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  18. log(e)4+log(4)egt2 a. True b. False

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  19. 4 ^(sin ^(2)x ) + 4 ^(cos ^(2)x ) ge4 for all real x.

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  20. If y=sinnx+cosnx (x,n real0 then -sqrt(2)leylesqrt(2). a. True b. Fal...

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