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IAF Group X 2020 Mathematics Test - 15
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IAF Group X 2020 Mathematics Test - 15

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  • Question 1/10
    1 / -0

    The points A (1, 2), B (2, 5) and C (5, 6) are the vertices of

    Solutions

    ∴ AB2 = (2 − 1)2 + (5 − 2)2 = 10 ⇒ AB = √10

    AC2 = (5 − 1)2 + (6 − 2)2 = 32 ⇒ AC = √32

    BC2 = (5 − 2)2 + (6 − 5)2 = 10 ⇒ BC = √10

    BC2 = (5 − 2)2 + (6 − 5)2 = 10 ⇒ BC = √10

    But AC2 ≠ AB2 + BC2                         (∵ 32 ≠ 10 + 10)

    Hence, it is not right angled.

     

  • Question 2/10
    1 / -0

    If α = cos−1(3/5),β = tan−1(1/3), where 0 < α,β < π/2, then α – β is equal to:

    Solutions

    .

     

  • Question 3/10
    1 / -0

    6th term in expansion of (2x2 − 1/3x2)10 is

    Solutions

     

  • Question 4/10
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    Compute real values of x and y if

    Solutions

     

  • Question 5/10
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    Solutions

    Order of a differential equation is defined as the order of the highest order derivative and the degree of a differential equation, when it is a polynomial equation in derivatives, is defined as the highest power (positive integral index) of the highest order derivative.

    The highest order derivative present in the given differential equation is d2y/dx2, so its order is two. It is a polynomial equation in d2y/dx2 and dy/dx and the highest power raised to d2y/dx2 is one, so its degree is one.

     

  • Question 6/10
    1 / -0

    If A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5}, then A – B is {where,  means complement of A}

    Solutions

     

  • Question 7/10
    1 / -0

    Solutions

    Given, A is a symmetric matrix and B is a skew-symmetric matrix.

     

  • Question 8/10
    1 / -0

    If the standard Deviation of a set of data is 8.5%, what is its variance?

    Solutions

    We know,

    Variance = (S.D)2

    = (8.5)2 = 72.25

     

  • Question 9/10
    1 / -0

    If Sn = nP + 1/2n(n − 1)Q where Sn denotes the sum of the first n terms of an A.P. then the common difference is

    Solutions

    Short-trick:

    Sn = n/2{2P + (n − 1)Q}-----------(1)

    The standard formula of Sn = n/2 × {2a + (n − 1)d}, where a is the first term and d is the common difference.

    By, comparing the equation (1), with the standard formula of Sn , we get  d = Q.

     

  • Question 10/10
    1 / -0

    The radius of a cylinder is increasing at the rate of 2 cm/sec and its altitude is decreasing at the rate of 3 cm/sec. the rate of change of volume when the radius is 3 cm and the altitude is 5 cm is 

    Solutions

     

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