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CDS I 2026 Mathematics Test - 6
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CDS I 2026 Mathematics Test - 6
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  • Question 1/10
    1 / -0.33

    If a2 + a = 13, then find the value of (a + 4)3 – 1/(a + 4)3

    Solutions

    The correct answer is option 1 i.e. 364.

    a2 + a = 13

    a2 + 8a + 16 = 7a + 13 + 16

    (a + 4)2  - 1 = 7 (a + 4)

    (a + 4) – 1/(a + 4)  = 7

    (a + 4)3 – 1/(a + 4)3 = 7 (72 + 3) = 7 × 52 = 364

  • Question 2/10
    1 / -0.33

    If sin A+ sin2 A = 1, then the value of cos4 A + cos6 A is:

    Solutions

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

    Given that

    If sin A+ sin2 A = 1,

    sin A = 1 - sin2 A = cos2 A

    the value of cos4 A + cos6 A

    ⇒ cos4 A + cos6 A

    ⇒ (cos2 A)2 + (cos2 A)3

    ⇒ sin2 A + sin3 A

    ⇒ sin A (sin A + sin2 A)

    ⇒ sin A × 1

    ⇒ sin A

  • Question 3/10
    1 / -0.33

    If the median and mean are 36 and 35 respectively, find the mode.

    Solutions

    The correct answer is option 2 i.e. 38.

    median = 36

    Mean = 35

    Mode = 3(Median) - 2(Mean)

    Mode = 3(36) - 2(35)

    ⇒ Mode = 108 - 70

    ⇒ Mode = 38

  • Question 4/10
    1 / -0.33

    If a - b = 10 and ab = 4, then the value of a3 - b3 + 4(a + b)2 is:

    Solutions

    The correct answer is Option 3 i.e. 1584.

    (a + b)2 = (a - b)2 + 4ab = 102 + 4 × 4 = 116

    a3 - b3 + 4(a + b)2

    = (a - b)[(a - b)2 + 3ab] + 4(a + b)2

    = 10 × (100 + 12) + 4 × 116

    = 1120 + 464

    = 1584

  • Question 5/10
    1 / -0.33

    The circumcentre of a ΔABC is O. If ∠ BAC = 70°  and ∠ BCA = 80°, then the measure of ∠ OAC is equal to:

    Solutions

    The correct answer is Option 3 i.e. 60°.

    ∠ABC = 180° - (70° + 80°) = 30°

    ∠BOC = 2 × ∠BAC = 140° (central angle theorem)

    In ΔBOC (isosceles), ∠OBC = ∠OCB = 20°

    ∠OCA = 80° - 20° = 60°

    In ΔOAC (isosceles), ∠OAC = ∠OCA = 60°

  • Question 6/10
    1 / -0.33

    A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is 60º and the angle of depression of the bottom of the tower is 30º. If the height of the pole is 24m, then find the height of the tower (in m).

    Solutions

    The correct answer is option 4 i.e. 96.

  • Question 7/10
    1 / -0.33

    Two pillars A and B of the same height are on opposite sides of a road which is 40 m wide. The angles of elevation of the tops of the pillars A and B are 30º and 45º, respectively, at a point on the road between the pillars. What is the difference (in m) of the point from the foot of pillar A?

    Solutions

  • Question 8/10
    1 / -0.33

    Solutions

  • Question 9/10
    1 / -0.33

    In the given figure, AD is the angle bisector of ∠CAE, CD = 6 cm, and DE = 8cm. Find the length of BC.

    Solutions

    The correct answer is Option 1 i.e. 18.

    From figure ∠BAD = ∠BDA

    ⇒ AB = BC

    AB = BD = x (let)

    By the tangent secant property

    ⇒ BA2 = BC × BE

    ⇒ x2 = (x - 6)(x + 8)

    ⇒ x2 = x2 + 2x - 48

    ⇒ x = 24

    ⇒ BC = x - 6 = 24 - 6 = 18 cm

  • Question 10/10
    1 / -0.33

    The resistance of a wire is proportional to its length and inversely proportional to the square of its radius. Two wires of the same material have the resistance 2:3 and their radii are in the ratio  8: 7 . If the first wire is 128 cm. Find the length of the other wire?

    Solutions

    The correct answer is  option 2  i.e.  147 cm.

    Let the radius of a wire = r

    length of a wire = l

    R ∝ l / r2

    R1 / R2  = l1 / l2 × (r2 / r1)2

    2/ 3 = 128 / l2 ( 49 / 64 )

    l2 = 147 cm

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