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If `a x^2+b/xgeqc` for all positive `x` where `a >0` and `b >0,` show that `27 a b^2geq4c^3dot`

A

`27ab^2ge4c^3`

B

`27ab^2lt4c^3`

C

`4ab^2ge27c^3`

D

none of these

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OBJECTIVE RD SHARMA ENGLISH-MAXIMA AND MINIMA -Chapter Test
  1. The maximum value of ((1)/(x))^(2x^(2)) is

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  2. If a x^2+b/xgeqc for all positive x where a >0 and b >0, show that 27 ...

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  3. The greatest value of the funxtion f(x)=xe^(-x) " in " [0,oo] is

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  4. Let f(x)=x^3-6x^2+12x-3 . Then at x=2 f(x) has

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  5. In the right triangle BAC, angle A=pi/2 and a+b=8. The area of the tr...

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  6. The range of values of a for which the function f(x)=(a^2-7a+12)cosx...

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  7. If the function f(x) = (2a-3)(x+2 sin3)+(a-1)(sin^4x+cos^4x)+log 2...

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  8. The function y=(ax+b)/(x-1)(x-4) has turning point at P(2,-1) Then fin...

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  9. Find the least value of the expressions 2log(10)x-log(x)0.01, where xg...

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  10. The maximum value of the function f(x) given by f(x)=x(x-1)^2,0ltxlt...

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  11. The least value of a for which the equation 4/(sinx)+1/(1-sinx)=a has ...

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  12. The minimum value of f(x)=e^((x^4-x^3+x^2)) is

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  13. Let f(x)=a/x+x^2dot If it has a maximum at x=-3, then find the value o...

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  14. Find the maximum value of 4sin^(2)x+3cos^(2)x+sin""(x)/(2)+cos""(x)/(2...

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  15. The least value of the f(x) given by f(x)=tan^(-1)x-1/2 logex " in t...

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  16. The slope of the tangent to the curve y=e^x cosx is minimum at x= a,0 ...

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  17. The value of a for which the function f(x)={{:(tan^(-1)a -3x^2" , " ...

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  18. The minimum value of 27^(cos3x)81^(sin3x) is

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  19. If f(x)=(x^2-1)/(x^2+1) . For every real number x , then the minimum v...

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  20. f(x) = |x|+|x-1| +|x-2|, then which one of the following is not correc...

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