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Show that the semi-vertical angle of the...

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is `cos^(-1)(1/(sqrt(3)))`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Find the equations of the tangent and normal to the curve x=asin^3t...

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  2. Evaluate : int(pi/6)^(pi/3)(dx)/(1+sqrt(cotx))

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

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  4. Prove that cot^(-1)((sqrt(1+sin)+sqrt(1-sinx))/(1sqrt(1+sin)-sqrt(1...

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  5. Prove that 2tan^(-1)(1/5)+sec^(-1)((5sqrt(2))/7)+2tan^(-1)(1/8)=pi/4...

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  6. Prove that, for any three vectors vec a , vec b , vec c [ vec a+ v...

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  7. Vector vec a , vec b and vec c are such that vec a+ vec b+ vec c...

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  8. The sum of the perimeters of a circle and a square is k , where k is s...

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  9. Find the direction cosines of the line (x+2)/2=(2y-7)/6=(5-z)/6dot Als...

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  10. Solve for x: 2tan^(-1)(cosx)=tan^(-1)(2cos e cx)

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  11. Using differentials, find the approximate value of (3. 968)^(3/2)

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  12. Write the derivative of sinx w.r.t. cosxdot

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  13. Find : int(sin^2x-cos^2x)/(sin^2xcos^2x)dx

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  14. Write a vector in the direction of the vector hat i-2 hat j+2 hat k t...

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  15. Write the distance of a point P(a ,b ,c) from x-axis.

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  16. If, [xdoty4z+6x+y]=[8w0 6], write the value of (x+y+z)dot

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  17. Write the principal value of cos^(-1)[cos(680^@)]

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  18. Let R be the equivalence relation in the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5}...

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  19. Write a x2x matrix which is both symmetric and skew-symmetric.

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  20. Write the projection of the vector 2 hat i- hat j+ hat k on the vector...

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