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Mathematics Test 147

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Mathematics Test 147
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Weekly Quiz Competition
  • Question 1
    4 / -1

    There are 3 common tangents of parabola y2 = 4x and circle x2 + y2 – 6x = 0  forming a triangle T. Identify correct facts about triangle 'T'

    Solution

     

  • Question 2
    4 / -1

    If length of perpendicular drawn from origin to any normal of the ellipse  is ℓ, then ℓ cannot be –

    Solution

    Equation of normal is

    4xsecθ – 5y.cosecθ = –9

     

  • Question 3
    4 / -1

    Points on the ellipse x2 + 3y= 37, where normal is parallel to the line 6x – 5y = 2, is -

    Solution

    ∴  x= 5,  x= –5

        y1 = 2,  y= –2

     

  • Question 4
    4 / -1

    The equation  represents

    Solution

    It is obvious.

     

  • Question 5
    4 / -1

    Tangents are drawn to the hyperbola x2/9 - y2/4 = 1, parallel to the straight line 2x – y = 1. The points of contact of the tangents on the hyperbola are

    Solution

    Let parametric coordinates be P(3secθ, 2tanθ)

    Equation of tangent at point P will be

     

  • Question 6
    4 / -1

    If the maximum area bounded by the curves x2 = 4ay, y = ax, y = x/a , 1 < a < 2 is α, then

    Solution

    ⇒  maximum value of area occures of 

        α = 2

    ⇒ α = 84

     

  • Question 7
    4 / -1

    y = ƒ(x) is differentiable function ∀ x ∈ R and satisfies dy / dx = |y| + 1 and ƒ(0) = 0. 

    If a1, a2, a3, a4, ........., an are the solution(s) of equation ƒ(x) = sin2x, then the value of |[a1] + [a2] + [a3] +....... + [an]| is not equal to (where [.] denotes greatest integer function)

    Solution

    There are 3 solutions.

    a1 ∈ (–1,0)

    a2 = 0

    a3 ∈ (0,1)

     

  • Question 8
    4 / -1

    y = ƒ(x) is differentiable function ∀ x ∈ R and satisfies dy/dx = |y| + 1 and ƒ(0) = 0. 

    Which of the following statement is False ?

    Solution

    we get ƒ(x) = –ƒ(–x) ⇒ ƒ(x) is odd function

     

  • Question 9
    4 / -1

    Directions For Questions

    Consider an ellipse  (where α is a positive parameter) and parabola y2 = 8x. If a tangent to the parabola meet the co-ordinate axes at A and B

    On the basis of above information, answer the following questions :

    ...view full instructions

    If locus of the mid point of line segment AB is a conic, then its length of latus rectum is less than

    Solution

    Eliminating, m

    y2 = –x

    ∴ Length of latus rectum = 1

     

  • Question 10
    4 / -1

    Directions For Questions

    Consider an ellipse  (where α is a positive parameter) and parabola y2 = 8x. If a tangent to the parabola meet the co-ordinate axes at A and B

    On the basis of above information, answer the following questions :

    ...view full instructions

    If α = 8, then the equation of line which touches both parabola and ellipse is -

    Solution

    If a = 8, then tangent to parabola is

     

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