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For a > 0, let the curves C(1) : y^(2) =...

For a > 0, let the curves `C_(1) : y^(2) = ax` and `C_(2) : x^(2) = ay` intersect at origin O and a point P. Let the line `x = b(0 lt b lt a)` intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, `C_(1)` and `C_2`, and the area of `triangleOQR = 1//2`, then 'a' satisfies the equation:

A

`x^(6) - 12x^(3) + 4=0`

B

`x^(6) - 12x^(3) - 4=0`

C

`x^(6) + 6x^(3) -4=0`

D

`x^(6) - 6x^(2) + 4=0`

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A
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MCGROW HILL PUBLICATION-JEE (MAIN) 2020 QUESTION PAPER MATHEMATICS (8TH JAN - MORNING) -QUESTIONS
  1. Let FIGURE:R to R be such that FIGUREor all x in R (2^(1+x)+2^(1-x)), ...

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  2. The locus of a point which divides the line segment joining the point ...

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  3. For a > 0, let the curves C(1) : y^(2) = ax and C(2) : x^(2) = ay int...

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  4. f(x) = (8^(2x) - 8^(-2x))/(8^(2x) + 8^(-2x) find the inverse of the fu...

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  5. lim(xrarr0) ((3x^2 + 2)/ (7x^2 +2))^(1/x^2) is equal to

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  6. Let f(x) = {(sin (tan^(-1) x) + sin (cot^(-1) x)}^2 - 1, where |x| gt ...

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  7. Roots of the equation x^2 + bx + 45 = 0, b in R lie on the curve |z + ...

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  8. Mean and standard deviations of 10 observations are 20 and 2 respectiv...

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  9. Let int (cos x dx)/(sin^3 x (1 + sin^6 x))^(2/3) = f(x), (1 + sin^6 x ...

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  10. Let A and B be two independent events such that P(A) = 1/3 and P(B) = ...

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  11. Let the volume of a parallelopiped whose coterminus edges are given by...

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  12. Let two points be A(1,-1) and B(0, 2). If a point P(x', y') be such t...

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  13. If the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3)/...

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  14. Let the line y=mx and the ellipse 2x^(2)+y^(2)=1 intersect at a point ...

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  15. If c is a point at which Roll's theorem holds for the function, f(x) =...

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  16. Let f(x) = x cos^(-1)(sin-|x|), x in (-pi/2,pi/2)

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  17. An urn contains 5 read marbels,4 black marbels and 3 white marbles. Th...

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  18. If normal at P on the curve y^2 - 3x^2 + y + 10 = 0 passes through the...

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  19. The equation 2x^2 + (a - 10)x + 33/2 = 2a has real roots. Find least p...

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  20. Find the sum, sum(k=1) ^(20) (1+2+3+.....+k)

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