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A DAS GUPTA-Miscellaneous Exercises-Exercise
- Find the equation of the largest circle with centre (1, 0) that can be...
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- Prove that the circle x^2 + y^2 -6y + 4 = 0 and the parabola y^(2) = x...
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- Find the equation of the ellipse whose foci are the points (1, 2) and ...
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- Let ABC and PQR be any two triangles in the same plane. Assume that th...
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- An unbiased dice, with faces numbered 1, 2, 3, 4, 5, 6, is thrown n ti...
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- Find the smallest positive values of xa n dy satisfying x-y=pi/4a n dc...
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- log(3/4)log8(x^2+7)+log(1/2)log(1/4)(x^2+7)^(-1)=-2.
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- Total number of solutions of the equation x² -4-[x]=0 are (where (.) d...
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- Let a, b be the roots of the equation x^2 - kx + k = 0, k in R. If a^2...
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- Two parabola have the focus (3, 2). Their directrices are the x-axis a...
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- Let alpha in R. prove that a function f: R-R is differentiable at...
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- Find the lim(x to 0) frac{sqrt(x+2) -sqrt2}{root(3)(1-x) - sqrt(1+x)}.
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- Two parabolas y(2) = 4a(x – 1l(1)) and x(2) = 4a(y – l(2)) always touc...
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- Let 2x^2 +y^2-3xy = 0 be the equation of a pair of tangents drawn from...
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- Let f(x),xgeq0, be a non-negative continuous function, and let f(x)...
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- Let b!=0 and for j=0,1,2,....,n. Let S(j) be the area of the region bo...
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- Let P be a point on the ellipse x^2/a^2+y^2/b^2=1 , 0 < b < a and le...
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- A hemi-spherical tank of radius 2 m is initially full of water and ...
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- I(n) is the area of n sided refular polygon inscribed in a circle unit...
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- For the circle x^(2)+y^(2)=r^(2), find the value of r for which the ar...
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