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A DAS GUPTA-Miscellaneous Exercises-Exercise
- 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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- A right circular cone with radius R and height H contains a liquid whi...
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- If vecu, vercv, vecw be three noncoplanar unit vectors and alpha,beta,...
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- If P(1)=0a n d(d P(x))/(dx),sinx+2xgeq(3x(x+1))/pi . Explain the ident...
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- Normals are drawn from a point P with slopes m1,m2 and m3 are drawn fr...
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- Find a point on the curve x^2 + 2y^2 = 6, whose distance from the li...
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- If a function f: [-2a, 2a] -> R is an odd function such that, f(x) = f...
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- A is targeting to B, B and C are targeting to A. probability of hittin...
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- f: [0.4]-> R is a differentiable function. Then prove that for some a,...
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- Given a function f:[0,4]toR is differentiable ,then prove that for som...
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