A straight line parallel to the line 2x - y + 5 = 0 is also a tan

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101.

A straight line parallel to the line 2x - y + 5 = 0 is also a tangent to the curve y2 = 4x + 5. Then, the point of contact is

  • (2, 1)

  • (- 1, 1)

  • (1, 3)

  • (3, 4)


B.

(- 1, 1)

Given equation of curve is y2 = 4x + 5.

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

2ydydx = 4At point x1, y1,    dydx = 2y1 = m1

Also, given straight line is 2x - y + 5 = 0.

So, the slope of this line is m, = 2

Since, the line is parallel to the tangent of the curve.

 m1 = m2  2y1  y1 = 1As the point (x1, y1) lies on the given curve. y12 = 4x1 + 5Put y1 = 1, we get       12 = 4x1 + 5 4x1 = - 4  x1 = - 1

Hence, the point of contact is (- 1 1).


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102.

The function f(x) = 2x3 - 15x2 + 36x + 6 is strictly decreasing in the interval

  • (2, 3)

  • - , 2

  • (3, 4)

  • - , 3  4, 


103.

The slope of the tangent to the curve y2exy = 9e- 3x2 at (- 1, 3) is

  • - 152

  • - 92

  • 15

  • 152


104.

The radius of a cylinder is increasing at the rate of 5 cm/min so that its volume is constant. When its radius is 5 cm and height is 3 cm, then the rate of decreasing of its height is

  • 6 cm/min

  • 3 cm/min

  • 4 cm/min

  • 5 cm/min


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105.

The slope of the normal to the curve y = x21x2 at (- 1, 0) is

  • 14

  • - 14

  • 4

  • - 4


106.

The minimum value of sin(x) + cos(x) is

  • 2

  • - 2

  • 12

  • - 12


107.

The slope of the tangent to the curve y = 3x2 - 5x + 6 at (1, 4) is

  • - 2

  • 1

  • 0

  • - 1


108.

The chord joining the points (5, 5) and (11, 227) on the curve y = 3x2 - 11x - 15 is parallel to tangent at a point on the curve. Then, the abscissa of the point is

  • - 4

  • 4

  • - 8

  • 8


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109.

The function f(x) = sin(x) - kx - c, where k and c are constants, decreases always when

  • k > 1

  • k  1

  • k < 1

  • k  1


110.

If y = mlog(x) + nx2 + x has its extreme values at x = 2 and x = 1, then 2m + 10n is equal to

  • - 1

  • - 4

  • - 2

  • - 3


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