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Find the value of c in Rolle’s theorem f...

Find the value of c in Rolle’s theorem for the function `f(x) = x^3– 3x in [–sqrt3, 0]`.

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. Prove that tan(pi/4+1/2 cos^-1(a/b))+tan(pi/4-1/2 cos^-1(a/b))=(2b)/a

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  2. Using properties of determinants, prove the following: |xx+y x+2y\...

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  3. Find the value of c in Rolle’s theorem for the function f(x) = x^3– 3...

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  4. Differentiate the function (sin x)^x+ sin^(-1) sqrtx with respect to...

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  5. The volume of a cube is increasing at the rate of 9cm3/sec. How fas...

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  6. Evaluate: int(2x)/((x^2+1)(x^2+2))dx

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  7. Evaluate: int0^pi(xsinx)/(1+cos^2x)\ dx

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  8. Prove that x^2-y^2=c(x^2+y^2)^2 is the general solution of differe...

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  9. Show that the function f(x) = x^3– 3x^2 + 6x – 100 is increasing on R

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  10. The x-coordinates of a point on t line joining the points Q(2,2,1)a...

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  11. The random variable X can the values 0, 1, 2, 3, Give P(X = 0) = P(X =...

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  12. A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be ...

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  13. Often it is taken that a truthful person commands, more respect in ...

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  14. Two tailors, A and B, earn 300 and 400 per day respectively. A can st...

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  15. Find : int (dx)/(5-8x-x^2)

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  16. Discuss the commutativity and associativity of binary operation * d...

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  17. If the sum of lengths of hypotenuse and a side of a right angled tri...

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  18. Using integration, find the area of region bounded by the triangle who...

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  19. If tan^-1 ((x-3)/(x-4))+tan^-1((x+3)/(x+4))=pi/4, find x

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  20. If x^y+y^x=a^b , then find dy/dx.

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