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Prove that among all the rectangles of t...

Prove that among all the rectangles of the given area, square has the least perimeter.

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SURA PUBLICATION-MODAL QUESTION PAPER-PART - IV
  1. If cot^(-1)((1)/(7))=theta, find the value of costheta.

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  2. For the ellipse 4x^(2)+y^(2)+24x-2y+21=0, find the centre, vertices, a...

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  3. Find the number of solution of the eqution tan^(-1)(x-1)+tan^(-1)x+tan...

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  4. Find the parametric form vector eqution and Cartesian equations of the...

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  5. Prove by vector method that the perpendiculars (altitudes) from the ve...

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  6. If a tangent to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 makes intercepts...

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  7. Solve the following systems of linear equation by Cramer's rule: 3x...

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  8. Test for consistency and if possible solve the following system of equ...

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  9. If z = x + iy and arg ((z-1)/(z+1))=pi/2, show that x^(2)+y^(2)-1=0.

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  10. Sketch the graph of sinx in [-pi/2,pi/2]andsin^(-1) in [-1, 1].

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  11. Find the equation of the ellipse whose eccentricity is 1/2, one of the...

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  12. A tunnel through a mountain for a four lane highway is to have a ell...

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  13. By vector method, Prove that sin(alpha-beta)=sinalphacosbeta-cosalphas...

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  14. Find the Vector and Cartesian equation of the plane containing the lin...

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  15. A conical water tank with vertex down of 12 meters height has a radius...

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  16. Prove that among all the rectangles of the given area, square has the ...

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  17. If u(x,y) = (x^(2) + y^(2))/sqrt(x+y), prove that x(del u)/(del x) + y...

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  18. Solve : dy/dx+2ycotx=3x^(2)"cosec"^(2)x.

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  19. The rate at which the population of a city increases at any time is pr...

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  20. Find the area of the region bounded by y=cosx,y=sinx, the lines x=pi/...

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