If the tangent to the curve, y = x3 + ax - b at the point (-

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 Multiple Choice QuestionsMultiple Choice Questions

141.

The point on the curve y = 2x2 - 6x - 4 at which the tangent is parallel to the x-axis, is :

  • 32, 132

  • - 52, - 172

  • 32, 172

  • 32, - 172


142.

The minimum value of 2cosθ + 1sinθ + 2tanθ in the interval 0, π2 is :

  • 2 + 2

  • 32

  • 23

  • 3 + 2


143.

If S1 and S2 are respectively the sets of local minimum and local maximum points of the function, f(x) = 9x4 + 12x3 - 36x2 - 25, x  R, then:

  • S1 = { - 1}; S2 = {0, 2}

  • S1 = { - 2, 1}, S2 = {0}

  • S1 = { - 2}; S2 = {0, 1}

  • S1 = { - 2, 0}; S2 = {1}


144.

Let f : [0, 2]  R be a twice differentiable function such that f’’(x) > 0, for all  x  0, 2. If ϕx = f(x) + f(2 - x), then ϕ is :

  • Increasing on (0, 1) and decreasing on (1, 2)

  • Decreasing on (0, 1) and increasing on (1, 2)

  • Decreasing on (0, 2)

  • Increasing on (0, 2)


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145.

The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is :

  • 233

  • 3

  • 23

  • 6


146.

Given that the slope of the tangent to a curve y = y(x) at any point (x, y) is 2yx2. If the curve passes through the centre of the circle x2 + y2 - 2x - 2y = 0, then its equation is :

  • xlogey = 2x - 1

  • xlogey = - 2x - 1

  • x2logey = - 2x - 1

  • xlogey = x - 1


147.

A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is tan-112. Water is poured into it at a constant rate of 5 cubic meter per minute. Then the rate (in m/min), at which the level of water is rising at the instant when the depth of water in the tank is 10m; is :

  • 110π

  • 115π

  • 15π

  • 2π


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148.

If the tangent to the curve, y = x3 + ax - b at the point (- 1, - 5) is perpendicular to the line, - x + y + 4 = 0, then which one of the following points lies on the curve ?

  • (2, - 1)

  • (- 2, 2)

  • (2, - 2)

  • (- 2, 1)


C.

(2, - 2)

f1 = - 5  1 + a - b = - 5  a - b = - 6    ...(i)f1x = 3x2 + a  f11 = 3 +a = - 1  a = - 4b = a +6 = 2f(x) = x3 - 4x - 2 check options ((2, - 2) satisfies)


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149.

Let f(x) = ex - x and g(x) = x2 - x,  x  R. Then the set of all x  R, where the function h(x) = (fog)(x) is increasing, is :

  • [- 12, 0]  [1, )

  • [- 1, - 12]  [12, )

  • [0, )

  • [0,  12]  [1, )


150.

The tangent and normal to the ellipse 3x2 + 5y2 = 32 at the point P(2, 2) meet the x-axis at Q and R, respectively .Then the area (in sq. units) of the triangle PQR is :

  • 6815

  • 163

  • 143

  • 3415


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