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A differentiable function f defined for ...

A differentiable function f defined for all x > 0 and satisfies `f(x^2)=x^3` for all x > 0. What is the value f'(16) ?

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MODERN PUBLICATION-TEST PAPER 3-PROBLEM
  1. If | adj A | = 64 then find | A |

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  2. Evaluate the following : [[sin^2theta,cos^2theta,1],[cos^2theta,sin^2t...

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  3. A differentiable function f defined for all x > 0 and satisfies f(x^2)...

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  4. Write the minimum value of y2 where y=sin^2x cos^2x

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  5. Evaluate int-1^1e^|x| dx

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  6. Write the vector equation ofthe plane whose cartesian equation is x + ...

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  7. Let A (1,2,3). Then, find the number of equivalence relations containi...

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  8. Let f ,g: R rarr R be two functions defined as f(x) = |x| +x and g(x) ...

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  9. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

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  10. If the matrix A is such that [[1,-1],[2,3]]A=[[-4,1],[7,7]], find A.

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  11. Find the values of a and b, if the function f defined as f(x) {(x^2+3x...

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  12. Differentiate with respect to x: y=3^(x^2)+tan^-1((cosx+sinx)/(cosx-si...

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  13. Find the dy/dx when cos x = sqrt ((1)/(1+t^2)), sin y = (2t)/(1+t^2)

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  14. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

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  15. Show that 2sinx+tanxge3x for all x epsilon(0,(pi)/(2)).

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  16. Evaluate : int (xe^x)/(x+1)^(2) dx

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  17. Evaluate the following integrals int(x^2)dx/((x^2+3)(x^2+2))

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  18. Solve : dy/dx + 1 = e^(x+y)

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  19. Solve : (x + 2y^3)dy/dx = y.

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  20. Find the equation of the plane passing through the points (2,1,3), (3,...

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