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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 .

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) . Find the volume of the largest cylinder inscribed in a sphere of radius R.

USHA PUBLICATION-PREVIOUS YEAR QUESTION 2016-PREVIOUS YEAR QUESTION
  1. Solve the following LPP graphically Maximize, Z=20x+30y Subject to...

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  2. Find the feasible region of the following system 2x+yge6,x-yle3,xge0...

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  3. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

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  4. Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[...

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  5. If A=[[alpha,0],[1,1]] and B=[[1,0],[5,1]], show that for no values of...

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  6. How many 4 digit numbers each greater than 6000 can be formed with be ...

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  7. If m=""^nC2, prove that ""^nC2=3(n+1)C4.

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  8. If the ratio of the 3rd term from the beginning to the 3rd term from t...

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  9. Let A and B be events with P(A)=1/3,P(AuuB)=3/4,P(AnnB)=1/4, find P(Au...

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  10. If X follows a binomial distribution with parameter n=6 and p with 4P(...

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  11. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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

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  13. Determine the area common to the parabola y^2=x and the circle x^2+y^2...

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  14. Find the solution of the following differential equations: x dy-ydx=sq...

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  15. Prove that vecaxx(vecbxxvecc)+ vecbxx(veccxxveca)+veccxx(vecaxxvecb) =...

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  16. A variable plane meets the coordinate axes at P, Q, R points. If the p...

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  17. Solve the following LPP graphically : Maximize : Z=5x1+3x2 subject to ...

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  18. Solve the following system of equations by the matrix inversion method...

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  19. Show that C0 Cr + C1 C(r+1) + C2 C(r+2) + ... + C(n-r) Cn = (2n!)/(...

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  20. Three persons hit a target with probability 1/2,1/3 and 1/4 respective...

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