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If y=log[x+sqrt(x^2+a^2)\ ] , show that ...

If `y=log[x+sqrt(x^2+a^2)\ ]` , show that (`(x^2+a^2)(d^2\ y)/(dx^2)+x(dy)/(dx)=0`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Write the direction-cosines of the line joining the points (1, 0, 0...

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

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

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  5. Evaluate: int1^3(x^2+x)dx

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  6. Show that of all the rectangles inscribed in a given fixed circle, ...

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  7. Using integration find the area of the triangular region whose side...

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  8. Show that the function f in A=|R-{2/3}\ defined as f(x)=(4x+3)/(6x-4)...

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  9. Find the equation of the plane which contains the line of intersect...

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  10. Find a unit vector perpendicular to each of the vector vec a+ vec ...

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  11. Find the angle between the following pair of lines: (-x+2)/(-2)=(y-...

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  12. Probabilities of solving a specific problem independently by A and ...

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  13. If x=a^s in^((-1))\ t ,\ y=a^cos^((-1))t ,\ show that (dy)/(dx)=-y/x

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  14. Find the points on the curve y=x^3 at which the slope of the tangen...

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  15. Find the intervals in which the function f given by f(x)=sinx+cosx ,\...

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  16. A factory makes tennis rackets and cricket bats. A tennis racket ta...

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  17. Suppose 5% of men and 0.25% of women have grey hair. A grey haired ...

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  18. 2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

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  19. Prove the following: cot^(-1)((sqrt(1+sinx)\ \ +\ \ sqrt(1-sinx))/(sqr...

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  20. Write the value of the following determinant: |[102, 18, 36],[ 1, 3,...

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