The equation of the tangent to the curve xa + yb&n

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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


B.

1

Given curve is,

xa + yb = 1       ...iOn differentiating w.r.t. to x, we get1a . 12x + 1b . 12ydydx = 0 dydx = - byax  dydxx1, y1 = - by1ax1 Equation of tangent passing through the point (x1, y1) isy - y1 = - by1ax1x - x1     yby1 - y1by1 = - xax1 + x1ax1 xax1 + yby1 = x1ax1 + y1by1 = x1a + y1b xax1 + yby1 = 1  from Eq. (i)         at x1, y1, x1a + y1b = 1But, xax1 + yby1 = k                            k = 1


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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


97.

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

  • 2

  • 1

  • - 1

  • - 2


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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