If the slope of y = 3x2 + ax3 is maximum at x = 12, then the

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 Multiple Choice QuestionsMultiple Choice Questions

91.

If the straight line y - 2x+ 1 = 0 is the tangent to the curve xy + ax + by = 0 at x = i, then the values of a and b are respectively

  • 1 and 2

  • 1 and - 1

  • - 1 and 2

  • 1 and - 2


92.

If the angle between the curves y = 2x and y = 3x is α, then the value of tan(α) is equal to

  • log321 + log2log3

  • 67

  • 17

  • log61 + log2log3


93.

The function f(x) = 3x3 - 36x + 99 is increasing for

  • -  < x < 2

  • - 2 < x < 

  • - 2 < x < 2

  • x < - 2 or x > 2


94.

The minimum value of the function fx = 1sinx + cosx in the interval 0, π2 is

  • 22

  • - 22

  • 23 + 1

  • -23 + 1


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95.

The equation of the tangent to the curve xa + yb = 1 at the point (x1, y1) is xax1 + yby1 = k. Then, the value of k is

  • 2

  • 1

  • 3

  • 3


96.

The slope of the normal to the curve x = t2 + 3t - 8 and y = 2t2 - 2t - 5 at the point (2, - 1) is

  • 67

  • - 67

  • 76

  • 76


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97.

If the slope of y = 3x2 + ax3 is maximum at x = 12, then the value of a is

  • 2

  • 1

  • - 1

  • - 2


D.

- 2

Given curve is

y = 3x2 + ax3

On differentiating w.r.t. x, we get

dydx = 6x + 3ax2 = mNow, differentiating Eq. (i) w.r.t. x, we getdmdx = 6 +6axand d2mdx2 = 6aFor maximum or minimum of m,put dmdx = 0  6 + 6ax = 0 x = - 1a < 0But given m is maximum at x = 12. - 1a = 12  a =  -2


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98.

If y = 4x - 5 is a tangent to the curve y = px3 + q at (2, 3), then (p + q) is equal to

  • - 5

  • 5

  • - 9

  • 9


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99.

The point on the curve y = 5 + x - x2 at which the normal makes equal intercepts is

  • (1, 5)

  • (0, - 1)

  • (- 1, 3)

  • (0, 5)


100.

If the point (a, b) on the curve y = x is close to the point (1, 0), then the value of ab is

  • 12

  • 22

  • 14

  • 24


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