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NDA I 2025 Mathematics Test - 9
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NDA I 2025 Mathematics Test - 9
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  • Question 1/10
    2.5 / -0.83

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  • Question 2/10
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    Let A and B be two events such that where A̅ stands for the complement of the event A. Then the events A and B are:

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  • Question 3/10
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    If x satisfies |3x - 2| + |3x - 4| + |3x - 6| ≥ 12, then

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    Concept:

    Modulus function: It gives the absolute value of a variable (x). It is denoted by |x|

    ⇒ 12 - 9x ≥ 12

    ⇒ - 9x ≥ 0

    ⇒ 9x ≤ 0

    ⇒ x ≤ 0 ⋯ (ii)

    Taking intersection of (i) and (ii), we get x ≤ 0 ⋯ (iii)

  • Question 4/10
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    The equation of the pair of the angle bisectors of the lines x2 + 6xy – 3y2 = 0 is:

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  • Question 5/10
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    The area (in sq. units) of the region described by {(x, y) : y2 ≤ 2x, and y ≥ 4x –1} is

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    Explanation -

  • Question 6/10
    2.5 / -0.83

    Solutions

    Concept:

    Greatest Integer Function:

    The greatest integer function is denoted by [x], for any real function. The function rounds off the real number down to the integer less than the number.

    Properties of the greatest integer function

    • [x] = x, where x is an integer
    • [x + n] = [x] + n, where n ∈ Z
    • [ - x] = - [x], if x ∈ Z
    • [ - x] = - [x] - 1, if x ∉ Z

    Fractional Part:

    It is defined as difference between a number and its integral value. {x} = x - [x]

    Calculation:

  • Question 7/10
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  • Question 8/10
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    The slopes of the common tangents of the ellipse  and the circle x2 + y2 = 3 are

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  • Question 9/10
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    Solutions

    Hence, Statement I is correct.

    ⇒ r = 1 + 1

    ⇒ r = 2 

    From eq. (1) n = 3

    Hence, (n, r) = (3, 2)

    ∴ Statement II is incorrect.

    So, the correct option is (1)

  • Question 10/10
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    Solutions

    5β - 4α =15 - 3 = 12 

    Hence option (2) is correct

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