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Mathematical Ability Test-2
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Mathematical Ability Test-2
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  • Question 1/10
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  • Question 2/10
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  • Question 3/10
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    If the parabola has focus is (5, 0) and vertex is (3, 0) find its equation.

    Solutions

    Given:

    vertex= (3,0)

    Therefore, h=3 and k=0.

    For focus =(5,0)

    h + a = 5

    3 + a = 5

    a = 2

    So, equation of parabola:

    (y − k)2 = 4a(x − h)

    (y − 0)2 = 4 × 2(x − 3)

    y2 = 8x − 24

     

  • Question 4/10
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    ABCD is a quadrilateral such that all of its sides touch a circle. If AB = 5 cm., BC = 6.5 cm. and CD = 7 cm., then find the length of AD?

    Solutions

     

  • Question 5/10
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    Running at 7/8 of its usual speed, a train is 20 minutes late. Find its usual time to cover the journey

    Solutions

    New speed : Usual speed = 7 : 8

    So, New time : Usual time = 8 : 7 = 8x : 7x

    According to question,

    8x - 7x = 20 minutes

    ⇒ x = 20 minutes

    ∴ Usual time = 7x = 140 minutes

     

  • Question 6/10
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    Find the middle terms in the expansion of (1 + 3x + 3x2 + x3)2n.

    Solutions

     

  • Question 7/10
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    The mean deviation from the median is:

    Solutions

    Case 1:

    It is a fundamental property.

    Example

    Consider a set of 5 data points

    {1, 2, 3, 4, 5}

    median = 3

    Deviation from mean:

    1 - 3 = -2

    2 - 3 = -1

    3 - 3 = 0

    4 - 3 = 1

    5 - 3 = 2

    Mean of deviations (about mean) = 05 = 0

    Case 2:

    Consider data point 2

    Deviations of data about 2

    1 - 2 = - 1

    2 - 2 = 0

    3 - 2 = 1

    4 - 2 = 2

    5 - 2 = 3

    Mean of deviation of data about median is minimum and this is true for all data.

     

  • Question 8/10
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    If sin⁡ 2θ = cos⁡3θ, where 0 < θ < π/2, then what is sin ⁡θ equal to?

    Solutions

     

  • Question 9/10
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    A and B invest in a business in the ratio of 2 : 1. If 10% of the total profit goes to charity and A's share is Rs. 600, the total profit is :

    Solutions

     

  • Question 10/10
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