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A point P lying inside the curve y = sqr...

A point P lying inside the curve `y = sqrt(2ax-x^2)` is moving such that its shortest distance from the curve at any position is greater than its distance from X-axis. The point P enclose a region whose area is equal to

A

(a)`(pi a^2)/2`

B

(b)`(a^2)/(3)`

C

(c)`(2a^2)/(3)`

D

(d)`((3pi-4)/(6))a^2`

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-AREA OF BOUNDED REGIONS-Exercise (Single Option Correct Type Questions)
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  3. Let 'a' be a positive constant number. Consider two curves C1: y=e^x...

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  4. 3 point O(0,0),P(a,a^2),Q(-b,b^2)(agt0,bgt0) are on the parabola y=x^2...

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  5. Area enclosed by the graph of the function y= In^2x-1 lying in the 4...

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  6. The area bounded by y = 2-|2-x| and y=3/|x| is:

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  7. Suppose g(x)=2x+1 and h(x)=4x^(2)+4x+5 and h(x)=(fog)(x). The area enc...

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  8. The area bounded by the curves y=-sqrt(-x) and x=-sqrt(-y) where x,yle...

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  9. y=f(x) is a function which satisfies f(0)=0, f"''(x)=f'(x) and f'(0)=1...

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  10. The area of the region enclosed between the curves x=y^(2)-1 and x=|x|...

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  11. The area bounded by the curve y=xe^(-x),y=0 and x=c, where c is the x-...

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  12. If (a,0), agt 0, is the point where the curve y=sin 2x-sqrt3 sin x cut...

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  13. The curve y=ax^2+bx +c passes through the point (1,2) and its tangent ...

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  14. A function y=f(x) satisfies the differential equation (dy)/(dx)-y= co...

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  15. If the area bounded between X-axis and the graph of y=6x-3x^2 between ...

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  16. Area bounded by y=f^(-1)(x) and tangent and normal drawn to it at poin...

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  17. If f(x)=x-1 and g(x)=|f|(x)|-2|, then the area bounded by y=g(x) and t...

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  18. Let S = {(x,y): (y(3x-1))/(x(3x-2))<0}, S'= {(x,y) in AxxB: -1 leqAleq...

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  19. The area of the region bounded between the curves y=e||x|In|x||,x^2+y...

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  20. A point P lying inside the curve y = sqrt(2ax-x^2) is moving such that...

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