The point on the curve y2 = x where the tangent makes an angle of

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 Multiple Choice QuestionsMultiple Choice Questions

711.

The function f(x) = x2 + 2x - 5 is strictly increasing in the interval

  • (- , 1]

  • (- 1, )


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712.

The point on the curve y2 = x where the tangent makes an angle of π/4 with X-axis is

  • (4, 2)

  • 12, 14

  • 14, 12

  • (1, 1)


C.

14, 12

We have, y2 = x                                    ...i      2ydydx = 1         dydx = 12y Slope of tangent = 12y                    ...iiNow, tangent makes an angle of π/4 wth X-axis Slope of tangent = tanπ4 = 1     ...iiiFrom Eqs (ii) and (iii), we get          12y = 1  y = 12Putting, y =12 in Eq. (i), we get      122 = x       x = 14 Required point is 14, 12.


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713.

The rate of change ofvolume of a sphere with respect to its surface area when the radius is 4 cm is

  • 4 cm3/cm2

  • 6 cm3/cm2

  • 2 cm3/cm2

  • 8 cm3/cm2


714.

The two curves x3 - 3xy2 + 2 = 0 and 3x2y - y3 - 2 = 0

  • cut at right angle

  • touch each other

  • cut at an angle π3

  • cut at an angle π4


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715.

The function f(x) = cot-1(x) + x, increases in the interval

  • 1, 

  • - 1, 

  • - , 

  • 0, 


716.

For all real values of x, increasing function is

  • x- 1

  • x2

  • x3

  • x4


717.

Maximum value of f(x) = sin(x) + cos(x) is

  • 1

  • 2

  • 12

  • 2


718.

The greatest value of f(x) = (x + 1)1/3 - (x - 1)1/3 on [0, 1] is

  • 1

  • 2

  • 3

  • 1/3


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719.

The equation of normal to the circle 2x2 + 2y2 - 2 - 5y + 3 = 0 at (1, 1) is

  • 2x + y = 3

  • x - 2y = 3

  • x + 2y = 3

  • None of these


720.

The minimum value of the function f(x) = 2x3 - 21x2 + 36x - 20 is

  • - 128

  • - 126

  • - 120

  • None of these


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