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A DAS GUPTA-Miscellaneous Exercises-Exercise
- Solve - frac{sin^(3) frac{x}{2} -cos^(3) frac{x}{2}}{2 +sinx} = cosx/3
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- let f(x) be the polynomial function. It satisfies the equation 2 +f(x)...
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- Evaluate int(0)^(pi)(e^(cosx))/(e^(cosx)+e^(-cosx))dx.
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- Find the co-ordinates of all the points P on the ellipse, x^2/a^2+y^2/...
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- Find the equation of a curve passing through the point (1.1) if the pe...
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- Solve: (x^2 + 4y^2 + 4xy) dy = (x + 2y + 1) dx.
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- If the normal to the ellipse (x^(2))/9+(y^(2))/4=1 which is farthest f...
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- sum(n=0)^oo1/(n !)[sum(k=0)^n(k+1)int0^1 2^(-(k+1)x)dx]
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- Consider the family of circles x^2 + y^2= r^2 2 lt r lt 5. If in the f...
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- Let T1, T2 and be two tangents drawn from (-2, 0) onto the circle C:x^...
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- The equation of two equal sides AB and AC of an isosceies triangle ABC...
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- 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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