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If [(4a^2,4a,1),(4b^2,4b,1),(4c^2,4c,1)...

If `[(4a^2,4a,1),(4b^2,4b,1),(4c^2,4c,1)][(f(-1)),(f(1)),(f(2))][(3a^2+3a),(3b^2+3b),(3c^2+3c)] ` ,`f(x)` is a quadratic function and its maximum valueoccurs at a point V.A is a point of intersection of `y = f (x)` with X-axis and point B is such that chord AB subtendsa right angle at V. Find the area enclosed by f(x) andchord AB.

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A DAS GUPTA-Miscellaneous Exercises-Exercise
  1. f: [0.4]-> R is a differentiable function. Then prove that for some a,...

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  2. Given a function f:[0,4]toR is differentiable ,then prove that for som...

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  3. If f: R to [0,∞) be a function such that f(x -1) + f(x + 1) = sqrt3(f...

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  4. Using Rolles theorem, prove that there is at least one root in (45^(1/...

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  5. A=[(a,1,0),(1,b,d),(1,b,c)],B=[(a,1,1),(0,d,c),(f,g,h)],U=[(f),(g),(h)...

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  6. Find the equation of circle touching the line 2x + 3y + 1=0 at the poi...

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  7. (int(sin^(3/2)x+cos^(3/2)x)dx)/(sqrt(sin^(3)x cos^(3)x sin(x-alpha)))

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  8. T is a parallelepiped in which A,B,C and D are vertices of one face an...

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  9. f'(0) = lim(n->oo) nf(1/n) and f(0)=0 Using this, find lim(n->oo)((...

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  10. If y(x)=int(pi^2/16)^(x^2) (cosx cos sqrt(theta))/(1+sin^2 sqrt(theta)...

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  11. At any point P on the parabola y^2 -2y-4x+5=0 a tangent is drawn which...

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  12. If a DeltaABC remains always similar to a given triangle and the point...

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  13. Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)

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  14. if |f(x1)-f(x2)|<=(x1-x2)^2Find the equation of gent to the curve y= f...

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  15. Find the equation of the common tangent to the circle x^2 + y^2 = 16 a...

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  16. If [(4a^2,4a,1),(4b^2,4b,1),(4c^2,4c,1)][(f(-1)),(f(1)),(f(2))][(3a^2...

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  17. The total number of runs scored If n matches is (n+1)/4(2^(n+1)-n-2),w...

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  18. A square circumscribes the circle |z -1| = sqrt2. If one of the vertic...

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  19. Evaluate int(0)^(pi)e^(|cosx|)(2"sin"(1/2cosx)+3"cos"(1/2cosx))sinx dx...

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  20. If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)=g(x).g(y)+f(x).f(y) for all x...

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