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If x=a^s in^((-1))\ t ,\ y=a^cos^((-1))t...

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

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Find the angle between the following pair of lines: (-x+2)/(-2)=(y-...

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

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

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

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

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

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

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  8. 2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

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

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

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

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  12. If int0^a3x^2dx=8,\ write the value of ' a^(prime)dot

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  13. If int((x-1)/(x^2))e^x dx=f(x)e^x+c , then write the value of f(x)dot

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  14. If the binary operation * on the set Z of integers is defi...

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  15. If I is the identity matrix and A is a square matrix such that A...

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  16. Write the value of "cot"(tan^(-1)a+cot^(-1)a)dot

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  17. If x=a(cos t+tsint) and y=a(sint-tcost), then find (d^2y)/(dx^2)

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  18. Write the value of the are of the parallelogram determined by the v...

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  19. Write the value of ( hat ixx hat j)dot hat k+( hat jxx hat k)dot\ hat...

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  20. Prove that the relation R in the set A={5,6,7,8,9} given by R={(a , b)...

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