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Show that the rectangle of maximum area ...

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

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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. If 2x=y^(1/m)+y^(-1/m) , then prove that (x^2-1)y(n+2)+(2n+1)xy(n+1)+(...

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  3. Show that the rectangle of maximum area that can be inscribed in a giv...

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  4. Prove the following by vector method. Altitudes of a triangle are conc...

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  5. Find the magnitude and equation of the line of shotest distance betwee...

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  6. Solve the following by matrix method x-y+z=4, 2x+y-3z=0, x+y+z=2

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  7. Prove that abs((-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c))=4(b+c)(c+a)(...

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  8. Show that the function f : R^+toR^+ defined by f (x) =x+1/x is injecti...

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  9. Solve "sin"^(-1)x-"cos"^(-1)x="cos"^(-1)sqrt(3)/(2)

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  10. Solve: 2sin^(-1) x +sin^(-1) (1-x)= pi/2

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  11. Evaluate intln(x^2+x+2)dx

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  12. int0^pi((xtanx)/(secx+tanx))dx

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  13. Solve the differential equation (dy)/(dx)= (y-x+1)/(y+x+5).

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  14. Differentiate cos^(-1)(sinx) w.r.t.x.

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  15. int(cot xdx)/(ln sin x) = ?

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  16. How many independent constants are there in the general equation of a ...

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  17. What is the range of the signum function?

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  18. If the vectors hati+2hatj+hatk & 2hati+3hatj+alphahatk are perpendicul...

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  19. Between tan 1 and tan^(-1)1, which is greater?

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  20. Answer the following: In which inverval does the determinant A =[[1...

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