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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.

Show that the radius of the right cicular cylinder of greatest curved surface that can be inscribed in a given cone is half the redius of the base of the cone.

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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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

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  2. Find the extreme values of the function f(x)=x^2e^(-x^2) and show that...

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

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  4. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

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  5. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

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  6. If A [[1,2,0],[1,1,0],[-1,4,0]],B=[[1,2,3],[1,1,-1],[1,1,1]]"and"C=[[1...

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  7. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  8. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  9. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  10. Let f:RrightarrowR be defined as f(x)=3x. Then f is one-one and onto

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  11. Find the number of binary operations on the set {a,b}.

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  12. If A, B are symmetric matrices of same order, then find AB-BA.

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  13. Let A be square matrix of order 3times3, then find abs(KA) where, k is...

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  14. If A is an invertible matrix of order 2, then find det(A^(-1)).

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  15. Find intx^2e^(x^3)dx

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  16. Give an example of a homogeneous differential equation.

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  17. In triangle ABC, find vec(AB)+vec(BC)+vec(CA)

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  18. Let the vectors veca and vecb such that abs(veca)=3 and abs(vecb)=frac...

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  19. Are the planes 2x-y+4z=5 and 5x-25y+10z=6 are perpendicular?

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  20. Find fog(2) and gof(1), when f:RrightarrowR defined by f(x)=x^2+8 and ...

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