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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 BOARD PREVIOUS YEAR PAPER ENGLISH-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: int1^3(x^2+x)dx

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

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

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  7. Find the equation of the plane which contains the line of intersecti...

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

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

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

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

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  12. Find the point on the curve y=x^2 where the slope of the tangent is eq...

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

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

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

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  16. 2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

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  17. Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

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

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  19. If x[[2],[ 3]]+y[[-1],[ 1]]=[[10],[ 5]], write the value of x.

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  20. If int0^a3x^2dx=8,\ write the value of a.

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