The angle of intersection between the curves y2 + x2 = a22 and x2

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 Multiple Choice QuestionsMultiple Choice Questions

441.

If ddxx + 1x2 + 1x4 + 1x8 + 1= 15xp - 16xq + 1x - 1 - 2, then p, q = ?

  • (12, 11)

  • (15, 14)

  • (16, 14)

  • (16, 15)


442.

limx01 + x2 - 1 - x + x23x - 1 = ?

  • 1loge3

  • loge9

  • 1loge9

  • loge3


443.

If y = tan-11 +a2x2 - 1ax, then 1 + a2x2y'' +2a2y' = ?

  • - 2a2

  • a2

  • 2a2

  • 0


444.

If x2 + y2 = t +1t and x4 + y4 = t2 +1t2, then dydx = ?

  • -xy

  • -yx

  • x2y2

  • y2x2


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445.

If x = at2 and y = 2at, then d2ydx2 at t = 12 is

  • - 2a

  • 4a

  • 8a

  • - 4a


446.

The equations x - y + 2z = 43x + y + 4z = 6x + y + z = 1 have

  • unique solution

  • infinitely many solutions

  • no solution

  • two solutions


447.

The value (s) of x for which the function

f(x) = 1 - x, x < 1=1 - x2 - x, 1  x  23 - x, x > 2fails to be continuous is (are)

  • 1

  • 2

  • 3

  • all real numbers


448.

If y = log2log2x, then dydx = ?

  • loge2xlogex

  • 1loge2xx

  • 1xlogexloge2

  • 1xlog2x2


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449.

The angle of intersection between the curves y2 + x2 = a22 and x2 - y2 = a2 is

  • π3

  • π4

  • π6

  • π12


B.

π4

Given, y2 + x2 = a22          ...iand x2 - y2  = a2                    ...iiOn solving eqs i and ii, we getx = a2 + 12, y = a2 - 12Now, y2 + x2 = a222ydydx1 + 2x = 0  dydx1 = - xy dydx1 =  - a2 + 12 a2 - 12= - 2 + 12 - 1and x2 - y2 = a2On differentiating

dydx2 = xy = 2 + 12 - 1Then, tanθ = dydx1 - dydx21 + dydx1 dydx2= - 2 + 12 - 1 - 2 + 12 - 11 + - 2 + 12 - 1 2 + 12 - 1 =  - 22 + 12 - 11 - 2 + 12 - 1= - 22 + 12 - 12 - 1 - 2 - 1=  - 22 - 1 - 2 = 1θ = tan-11 = π4


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450.

If the function fx = k1x - π2, x  πk2cosx, x > π is twice differentiable, then the ordered pair (k1, k2) is equal to 

  • 12, - 1

  • 12, 1

  • (1, 0)

  • (1, 1)


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