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Find the intervals in which the function `f` given by `f(x)=sinx+cosx ,\ \ 0lt=x\ lt=2pi` is strictly increasing or strictly decreasing.

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. If x=a^(sin^-1 t) ,\ y=a^(cos^-1t) ,\ show that (dy)/(dx)=-y/x

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

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

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

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

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  6. 2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

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

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

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

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

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

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  12. If the binary operation * on the set Z of integers is defined ...

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

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

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

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  16. Write the value of the area of the parallelogram determined by the v...

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  17. Write the value of ( hat ixx hat j). hat k+( hat jxx hat k).\ hati

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  18. If log (x^2+y^2)=2t a n^(-1)\ (y/x), then show that (dy)/(dx)=(x+y)/(x...

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  19. Prove that tan^-1((cosx)/(1+sinx))=pi/4-x/2,\ x in (-pi/2,pi/2)

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  20. Using integration, find the area of the following region : {(x , y...

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