PYQ Vault

Angles in A.P. (B = 60 degrees): find a side, angle or area

This type of question, asked 9 times: 9 May 2023 S1, 11 May 2023 S1, 14 May 2024 S2, 23 Apr 2025 S1, 11 Apr 2026 S2, 20 Apr 2026 S1, 20 Apr 2026 S2, 14 May 2026 S1, 15 May 2026 S2. All 9 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    9 May 2023 S1

    148
    For the triangle ABC, with usual notations, if the angles A, B, C are in A.P. and m∠A=30∘m\angle A=30^\circ, c=3c=3, then the values of a and b are respectively

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  2. Question 2

    11 May 2023 S1

    133
    If in a triangle ABC, with usual notations, the angles are in A.P. and b:c=3:2b:c = \sqrt{3}:\sqrt{2}, then angle A =

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  3. Question 3

    14 May 2024 S2

    115
    In triangle ABC, ∠A,∠B,∠C\angle A, \angle B, \angle C are in A.P. and lengths of two larger sides are 10 and 9 units, then the length of the third side is

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  4. Question 4

    23 Apr 2025 S1

    124
    With usual notations, in △ABC\bigtriangleup ABC, the lengths of two sides are 10 cm and 9 cm respectively. If angles A,B,CA,B,C are in A.P. then perimeter of △ABC\bigtriangleup ABC is

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  5. Question 5

    11 Apr 2026 S2

    64
    In triangle ABC, with usual notations, if the angles are in Arithmetic Progression and 3c2=2b23c^2 = 2b^2, then the measure of angle A is

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  6. Question 6

    20 Apr 2026 S1

    53
    In a right-angled △ABC\triangle ABC, the measures of the angles are in an Arithmetic Progression (A.P.) If its smallest side is 44 units, then the area of △ABC\triangle ABC is.....

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  7. Question 7

    20 Apr 2026 S2

    62
    The angles of △ABC\triangle ABC are in A.P. and b:c=3:2b : c = \sqrt{3} : \sqrt{2} then ∠A=\angle A =

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  8. Question 8

    14 May 2026 S1

    54
    In ΔABC\Delta ABC with the usual notations, angles A,B,CA, B, C of are in A.P. and b:c=3:2b : c = \sqrt{3} : \sqrt{2}. The ratio of the largest and the smallest angle of the triangle will be

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  9. Question 9

    15 May 2026 S2

    55
    In a triangle, the lengths of the two largest sides are 1010 cm. and 99 cm. If the angles of the triangle are in arithmatic progression (A. P.), then the length of the third side (in cm.) is...

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