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Evaluate: int(dx)/(x(x^5+3))...

Evaluate: `int(dx)/(x(x^5+3))`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Consider f: R+ rarr [4, oo] given by f(x)=x^2+4. Show that f is inv...

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  2. What are the direction cosines of a line, which makes equal angles ...

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  3. Evaluate: int(dx)/(x(x^5+3))

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  4. Find the value of k so that the function f defined by f(x)={(kcosx)/(...

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  5. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

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  6. Find the vector and cartesian equations of the line passing through...

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  7. Evaluate: |(cos15^0,sin15^0),(sin75^0,cos75^0)|

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  8. What is the principal value of cos^(-1)cos((2pi)/3)+sin^(-1)sin((2p...

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  9. Let A = {1, 2, 3}, B = {4, 5, 6, 7}and let f = {(1, 4), (2, 5), (3, 6)...

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  10. Evaluate: int0^4(|x|+|x-2|+|x-4|)\ dx

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  11. Evaluate: int(dx)/(sqrt(1-x^2))

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  12. Evaluate: int(a x+b)^3dx

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  13. If a matrix has 5 elements, write all possible orders it can have.

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  14. If A=[[2, 3],[ 5,-2]], write A^(-1) in terms of A

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  15. Using properties of determinants, prove the following: |[1,x,x^2],[...

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  16. Write the projection of the vector hat i- hat j on the vector ha...

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  17. Write the direction-cosines of the line joining the points (1, 0, 0...

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  18. Differentiate the following function with respect to x : (log\ x)^...

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  19. If y=log[x+sqrt(x^2+a^2)\ ] , show that ((x^2+a^2)(d^2\ y)/(dx^2)+x(dy...

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  20. Evaluate: int0^(pi/4)(cos^2x)/(cos^2x+4sin^2x)dx\

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