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CDS I 2026 Mathematics Test - 7
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CDS I 2026 Mathematics Test - 7
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  • Question 1/10
    1 / -0.33

    The value of (1+ sin4A - cos4A) cosec2A is:

    Solutions

    The correct answer is option 2 i.e. 2.

    Formula used:

    a2 - b2 = (a + b)(a - b)

    sin2A + cos2A = 1

    Calculations:

    ⇒ (1+ sin4A - cos4A) cosec2A

    ⇒ (1 + (sin2A + cos2A)(sin2A - cos2A)) cosec2A

    ⇒ (1 + sin2A - cos2A) cosec2A

    ⇒ 2 × sin2A × cosec2A

    ⇒ 2

  • Question 2/10
    1 / -0.33

    Pie-chart represent the modes of transport used by different employees in a university.

    The central angle of the sector for officers using two-wheelers is:

    Solutions

    The correct answer is option 4 i.e. 54˚.

    Percentage of two wheelers = 15%

    Total central angle = 360º

    According to the question

    The central angle of the sector for officers using two-wheelers = (360/100) × 15 = 54º

  • Question 3/10
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    Solutions

    The correct answer is Option 2 i.e. 198.

    x = 3 + √8

    ⇒ 1/x = (3 - √8)/[(3 + √8)(3 - √8)] = 3 - √8

    ⇒ x + 1/x = (3 + √8) + (3 - √8) = 6

    So, x3 + 1/x3 = (x + 1/x)3 - 3(x + 1/x)

    = 63 - 3 × 6

    = 216 - 18

    = 198

  • Question 4/10
    1 / -0.33

    If (3x + 4y)(5x - 6y) = ax2 + 2hxy + by2 then what is the value of (4a - h + 2b)?

    Solutions

    The correct answer is option 3 i.e. 11.

    (3x + 4y)(5x - 6y) = ax2 + 2hxy + by2

    ⇒ 15x2 + 2xy - 24y2 = ax2 + 2hxy + by2

    Comparing the expanded form with the given form, we get,

    a = 15

    2h = 2 ⇒ h = 1

    b = -24

    Now, 4a - h + 2b = 4(15) - 1 + 2(-24) = 60 - 1 - 48 = 11

    Therefore, the value of 4a - h + 2b is 11.

  • Question 5/10
    1 / -0.33

    A can complete a task in 18 days, and B can complete the same task in 32 days. They start working together, but B works only for 8 days. Thereafter, the work is completed by A. If they received Rs. 8,800 after completion of the work, then what is A's share (in Rs.)?

    Solutions

    The correct answer is Option 2 i.e. 6600.

    Combined work rate = (1/18 + 1/32) = 25/288

    Work in 8 days = 8 × 25/288 = 25/36

    Remaining work = 1 - 25/36 = 11/36

    Time taken by A Alone for remaining = (11/36)/(1/18) = 5.5 days

    Total time worked by A = 5.5 + 8 = 13.5 days

    A’s total work = 13.5 × 1/18 = 0.75

    B’s total work = 8 × 1/32 = 0.25

    Ratio = 0.75 : 0.25 = 3 : 1

    A’s Share = (3/4) × 8800 = 6600

  • Question 6/10
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    Solutions

  • Question 7/10
    1 / -0.33

    The difference between two numbers is 3820. The quotient and remainder are respectively 32 and 7 when the larger number is divided by the smaller one. Find the larger number.

    Solutions

    The correct answer is option 3 i.e. 3943.

    Let the smaller number = x

    Larger number = 32x + 7

    (32x + 7) - x = 3820

    ⇒ 31x = 3813

    ⇒ x = 123

    Larger number = 32 × 123 + 7 = 3936 + 7 = 3943

  • Question 8/10
    1 / -0.33

    Consider the following for thenext two(02) items that follow:

    The diameters of the two circular ends of a frustum of a cone are 6m and 10m. If the height of the frustum is 4m, find:

    (i) the total surface area of the frustum.

    Solutions

  • Question 9/10
    1 / -0.33

    Consider the following for the next two(02) items that follow:

    The diameters of the two circular ends of a frustum of a cone are 6m and 10m. If the height of the frustum is 4m, find:

    (ii) the ratio of the areas of the two circular ends:

    Solutions

  • Question 10/10
    1 / -0.33

    Consider the following for the next two(02) items that follow:

    In triangle DEF, right-angled at E, the perimeter of the triangle is 36 cm, and the difference between the sum of the perpendicular sides and the hypotenuse is 6 cm.

    (i) Find the area of triangle DEF.

    Solutions

    The correct answer is Option 3 i.e. 54 cm2.

    DE + EF + DF = 36.......(1)

    (DE + EF) - DF = 6......(2)

    Subtract equation 2 from equation 1

    ⇒ 2DF = 30

    ⇒ DF(hypotaneous) = 15 cm

    Remember: (9, 12, 15) is a triplet

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