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Consider f(x)={{:(cosx,0lexlt(pi)/(2)),(...

Consider `f(x)={{:(cosx,0lexlt(pi)/(2)),(((pi)/(2)-x)^(2),(pi)/(2)lexltpi):}` such that f is periodic with period `pi`. Then which of the following is not true?

A

the range of f is `[0,pi^(2)/4)`

B

f is discontinuous for x

C

f is continuous fo all real x

D

the area bounded by `y=f(x)` and the X-axis for `x=npi` to `x=npi` is n(1+(pi^3)/(24))` for a given `n in N`

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The correct Answer is:
A, D
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ARIHANT MATHS-AREA OF BOUNDED REGIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Consider f(x)={{:(cosx,0lexlt(pi)/(2)),(((pi)/(2)-x)^(2),(pi)/(2)lexlt...

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  2. Area of the region {(x,y) in R^(2):ygesqrt(|x+3|),5ylex+9le15} is eq...

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  3. Let F(x)=int(x)^(x^2+pi/2) 2 cos^(2)dt for all x in R and f:[0,1/2] to...

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  4. The common tangents to the circle x^2=y^2=2 and the parabola y^(2)=8x ...

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  5. The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...

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  6. In Δ PQR, right-angled at Q, PR + QR = 30 cm and PQ = 10 cm. Determine...

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  7. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)for...

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  8. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

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  9. The area of the region bounded by the curve y=e^x and lines x=0a n dy=...

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  10. The area of the region bounded by the curves y=sqrt[[1+sinx]/cosx] and...

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  11. Find the product of (x - 4)(x - 7)

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  12. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

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  13. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

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  14. The area (in sqaure units) of the region {(x,y):x ge 0, x + y le 3, x^...

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  15. The area (in sq. units) of the region {(x,y):y^(2)ge2x and x^(2)+y^(2)...

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  16. The area (in sq units) of the region described by {(x,y):y^(2)le2x and...

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  17. The area (in sq. units) of the quadrilateral formed by the tangents ...

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  18. The area of the region described by A={(x,y):x^(2)+y^(2)le1 and y^(2)l...

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  19. The area bounded by the curves y=sqrt(x),2y+3=x , and x-axis in the 1s...

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  20. The area bounded between the parabolas x^(2)=(y)/(4) and x^(2)=9y and ...

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  21. The area of the region enclosed by the curves y=x, x=e,y=(1)/(x) and t...

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