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Solve: tan^(-1)x+2cot^(-1)x=(2pi)/3...

Solve: `tan^(-1)x+2cot^(-1)x=(2pi)/3`

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SHARAM PUBLICATION-MODEL QUESTION PAPER-18-EXERCISE
  1. If F : R rarr R is given by f(x) = (3-x^(3))^(1//3) then find ( fof ) ...

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  2. Let * is the binary operation on N given by a**b=HCF (a, b), where a, ...

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  3. Solve: tan^(-1)x+2cot^(-1)x=(2pi)/3

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  4. Write the solution of the following L.P.P. Maximize z = 3x + 2y subj...

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  5. IF Ay is the cofactor of the element ay of the determinant |{:(2,-3,5)...

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  6. If A=[{:(2,0,1),(2,1,3),(1,-1,0):}] then find the value of A^(2)-3A+2I

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  7. Prove that |[x+y, x, x],[5x+4y, 4x, 2x], [10x+8y, 8x, 3x]|=x^3

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  8. Show that: abs((a,a^2,a^3),(b,b^2,b^3),(c,c^2,c^3))=abc(a-b)(b-c)(c-a)

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  9. Find the inverse of [(1, 3),(2, 7)] by using elementary row operation.

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  10. Find the vector vecp which is perpendicular to both vecalpha = 4hati +...

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  11. Find a unit vector perpendicular to both of the vectors veca + vecb an...

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  12. Show that the lines (x+3)/2=(y+5)/3=(z-7)/-3and (x+1)/4=(y+1)/5=(z+1)/...

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  13. Prove that the measure of the angle between two main diagonals of a cu...

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  14. Find the equation of the plane passing through the intersection of the...

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  15. If f(x) = {((1-cos4x)/x^2, when x<0),(a, when x=0),((sqrtx)/(sqrt(16 +...

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  16. If y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1), then find (dy)/(dx)

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  17. Show that the semi-vertical angle of the cone of the maximum volume an...

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  18. Evaluate the following integrals : Evaluate int(0)^(pi//2)(xsinxcosx...

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  19. Find the area of region in the first quadrant enclosed by the X-axis, ...

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  20. Solve the following differential x(dy)/(dx) = y - x tan (y/x).

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