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If x=a(cos t+tsint) and y=a(sint-tcost),...

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

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. If I is the identity matrix and A is a square matrix such that A...

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

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

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

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

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

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

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

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  9. If C=0.003x^3+0.02x^2+6x+250 gives the amount of carbon pollution in a...

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  10. Prove that s in^(-1)(8/(17))+sin^(-1)(3/5)=cos^(-1)((36)/(85))

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  11. Evaluate: int0^(pi//2)(2logsinx-logsin2x)dx

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  12. Find the point on the curve y=x^3-11 x+5 at which the equation of tang...

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  13. Using differentials, find the approximate value of sqrt(49. 5)

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  14. Using properties of determinants, prove the following: |[a^2 + 1,ab, ...

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  15. Show that the lines vec r=3 hat i+2 hat j-4 hat k+lambda( hat i+2 ha...

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  16. Find the particular solution of the differential equation satisfyin...

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  17. Find the general solution of the differential equation xlogx\ (dy)/...

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  18. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

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  19. If y="sin"(logx), then prove that (x^2d^2y)/(dx^2)+x(dy)/(dx)+y=0

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  20. Find the value of k , for which f(x)={(sqrt(1+k x)-\ sqrt(1-k x))/(x)...

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