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show that the semi vertical angle of a right circular cone of given total surface area and max volume is `sin^-1 (1/3)`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. If xsqrt(1+y)+ysqrt(1+x)=0, find ("dy")/("dx") . To prove (dy)/(dx)=...

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  2. Find the maximum are of the isosceles triangle inscribed in the ell...

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  3. show that the semi vertical angle of a right circular cone of given ...

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  4. If the equation of a line "A B" is ("x"-3)/1=("y"+2)/(-2)=("z"-5)/4...

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  5. If "f"("x") is an invertible function, find the inverse of "f"("x")...

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  6. If [[(x+3y),y],[7-x,4]]=[(4,-1),(0,1)], find the values of x and y.

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  7. Solve for x: tan^-1((1-x)/(1+x))=1/2 tan^-1 x, x > 0

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  8. Evaluate: int("x"+cos6"x")/(3"x"^2+sin6"x")" dx"

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  9. Form the differential equation representing the parabolas having ve...

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  10. Solve the following differential equation: (3"x y"+"y"^2)"dx"+("x"^...

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  11. If int("e"^("a x")+"b x")"dx"=4"e"^(4"x")+(3"x"^2)/2"\ ","\ " find the...

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  12. A and B throw a pair of die turn by turn. The first to throw 9 is a...

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  13. Find the equation of the line passing through the point "P"(4,6,2) ...

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  14. Find the distance of the point (-2,3,-4) from the line ("x"+2)/3=(2"...

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  15. Evaluate: int0^pi(xtanx)/(secx+tanx)\ dxdot

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  16. Find the area of that part of the circle "x"^2+"\ y"^2=16 which is ...

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  17. A man is known to speak truth 3 out of 4 times. He throws a die and...

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  18. An aeroplane can carry a maximum of 200 passengers. A profit of Rs....

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  19. Prove that tan(pi/4+1/2 cos^-1(a/b))+tan(pi/4-1/2 cos^-1(a/b))=(2b)/a

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  20. Solve tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1) (8/31)

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