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Shows that the triangle of greatest area...

Shows that the triangle of greatest area that can be inscribed in a circle is equilateral.

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Show that the rectangle of maximum area that can be inscribed in a given circle is a square.

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An isosceles triangle of vertical angle 2 theta is inscribed in a circle of radius a. Show that the area of triangle is maximum when theta = (pi)/(6) .

Find the area of greatest rectangle that can be inscribed in an ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 .

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MODERN PUBLICATION-TEST PAPER 9-EXERCISE
  1. Prove that [[b^2c^2, bc,b+c],[c^2a^2,ca,c+a],[a^2b^2,ab,a+b]] = 0

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  2. Find "a" and "b" such that the function f(x)={3ax+b, if x>1 11 if x=1 ...

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  3. If y= tan^-1 x then prove that (1+x^2) y(2) + 2xy(1) =0. Differentiate...

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  4. Find the point (S) on the curve x=(3at)/(1+t^2), y=(3at^2)/(1+t^2) whe...

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  5. Find the intervals in which the function y=(lnx)/(x) is increasing and...

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  6. Evaluate int (x+1)dx/sqrt(x^2+2x-3))

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  7. Evaluate: int(0)^(2π) dx/(1+e^sin x).

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  8. Solve: (1+x^2)dy/dx+2xy-x^3=0

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  9. If the sum of two unit vectors is a unit vectors find the magnitude of...

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  10. Prove by vector method that in аny ∆ АВС. а=Ь cos С +с cos В.

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  11. Find the equation of the plane passing through (1, 3,4), (2, 1.-1) an...

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  12. Obtain the co-ordinates of the foot of the perpendicular drawn from th...

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  13. Let A=Rxx R and be the binary operation on A defined by (a, b) *(c,d) ...

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  14. Prove that f:X rarr Y is injective iff for all subsets A,B of X,f(A n...

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  15. Use matrix product [(1,-1,2),(0,2,-3),(3,-2,4)] [(-2,0,1),(9,2,-3),(6,...

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  16. Prove that the following. [[b^2+c^2,ab,ac],[ab,c^2+a^2,bc],[ca,cb,a^2+...

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  17. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

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  18. Shows that the triangle of greatest area that can be inscribed in a ci...

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  19. Evaluate the following integrals int (d theta)/(2+3cos^2theta-4sin^2 t...

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  20. Find the equation of the straight line perpendicular to the line (x-2)...

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