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Find the value of tan^(-1)(x/y)-tan^(-1)...

Find the value of `tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))`

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Solve for x : 2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2

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  2. Prove the following: cot^(-1)[(sqrt(1+sinx )+sqrt(1-sinx))/(sqrt(1+sin...

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  3. Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

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  4. Using properties of determinants, prove the following |[x,x+y,x+2y],[x...

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  5. Consider f: R^+->[4,\ oo) given by f(x)=x^2+4 . Show that f is inverti...

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  6. Differentiate the following with respect to x : sin^(-1)((2^(x+1). 3^x...

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  7. If y^x=e^(y-x), prove that (dy)/(dx)=((1+logy)^2)/(logy)

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  8. Write the cartesian equation of a plane, bisecting the line segment...

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  9. Solve the following differential equation: y\ dx+xlog(y/x)dy=2x\ dy

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  10. Find the particular solution of the following differential equation...

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  11. Write the value of sin[pi/3-sin^(-1)(-1/2)]

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  12. For a\ 2\ xx\ 2\ matrix, A=[a(i j)], whose elements are given by a...

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  13. Evaluate: int1^3(2x^2+5x)dx as limit of a sum

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  14. State the reason for the relation R in the set {1, 2, 3} given by R=...

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  15. Write the value of intsecx\ (secx+tanx)\ dx

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  16. Write the value of int(dx)/(x^2+16)

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  17. For what value of x, the matrix [(5-x,x+1),(2,4)] is singular?

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  18. Write A^-1 for A=[(2,5),(1,3)]

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  19. For what value of a the vectors 2 hat i-\ 3 hat j+4 hat k and a h...

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  20. Write the direction cosines of the vector -2 hat i+ hat j-5 hat k

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