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Trigonometric Functions

MHT-CET Maths. Try each one first, then open its answer.

Top 10 MHT-CET PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 14 times: 4 May 2023 S2, 9 May 2023 S2, 15 May 2023 S1, 11 May 2024 S1, 11 May 2024 S2, 14 May 2024 S2, 21 Apr 2025 S1, 11 Apr 2026 S1, 16 Apr 2026 S1, 17 Apr 2026 S1, 19 Apr 2026 S2, 12 May 2026 S2, 14 May 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 14 of this type

    63
    If tan⁡−1(13)+tan⁡−1(15)+tan⁡−1(17)=π4−tan⁡−1(1k)\tan^{-1}\left(\dfrac{1}{3}\right) + \tan^{-1}\left(\dfrac{1}{5}\right) + \tan^{-1}\left(\dfrac{1}{7}\right) = \dfrac{\pi}{4} - \tan^{-1}\left(\dfrac{1}{k}\right) then the value of kk is

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  2. Question 2

    This type asked 12 times: 2 May 2023 S1, 4 May 2023 S1, 10 May 2023 S1, 10 May 2023 S2, 11 May 2023 S1, 11 May 2023 S2, 16 May 2023 S2, 13 May 2024 S2, 22 Apr 2025 S2, 26 Apr 2025 S2, 16 Apr 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 12 of this type

    64
    The value of cot⁡(csc⁡−153+tan⁡−123)\cot\left(\mathrm{\csc}^{-1}\dfrac{5}{3} + \tan^{-1}\dfrac{2}{3}\right) is ...

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  3. Question 3

    This type 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. This one: 15 May 2026 S2 See all 9 of this type

    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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  4. Question 4

    This type asked 8 times: 19 Apr 2025 S1, 20 Apr 2025 S2, 13 Apr 2026 S1, 17 Apr 2026 S1, 18 Apr 2026 S1, 19 Apr 2026 S1, 19 Apr 2026 S2, 12 May 2026 S2. This one: 12 May 2026 S2 See all 8 of this type

    55
    In △ABC\triangle ABC, if l(AB)=8,l(BC)=5,l(AC)=7l(AB) = 8, l(BC) = 5, l(AC) = 7, then cot⁡A2+cot⁡B2+cot⁡C2\cot\dfrac{A}{2} + \cot\dfrac{B}{2} + \cot\dfrac{C}{2} is equal to......

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  5. Question 5

    This type asked 8 times: 2 May 2023 S1, 4 May 2023 S1, 10 May 2023 S2, 16 May 2023 S2, 10 May 2024 S1, 22 Apr 2025 S2, 25 Apr 2025 S2, 18 Apr 2026 S2. This one: 18 Apr 2026 S2 See all 8 of this type

    67
    If tan⁡−1ax+tan⁡−13x=π4\tan^{-1}ax + \tan^{-1}3x = \dfrac{\pi}{4}, where 3ax2<13ax^2 < 1, then value of aa for x=16x = \dfrac{1}{6} is …\ldots

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  6. Question 6

    This type asked 7 times: 9 May 2024 S1, 14 May 2024 S2, 19 Apr 2025 S1, 26 Apr 2025 S2, 18 Apr 2026 S1, 20 Apr 2026 S1, 14 May 2026 S2. This one: 14 May 2026 S2 See all 7 of this type

    70
    The value of cot⁡−1(ab+1a−b)+tan⁡−1(b−cbc+1)+cot⁡−1(ac+1c−a)\cot^{-1}\left(\dfrac{ab + 1}{a - b}\right) + \tan^{-1}\left(\dfrac{b - c}{bc + 1}\right) + \cot^{-1}\left(\dfrac{ac + 1}{c - a}\right) is

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  7. Question 7

    This type asked 7 times: 3 May 2023 S1, 11 May 2024 S2, 20 Apr 2025 S1, 11 Apr 2026 S2, 16 Apr 2026 S2, 12 May 2026 S1, 14 May 2026 S2. This one: 14 May 2026 S2 See all 7 of this type

    53
    The number of solutions of cos⁡2x=cos⁡x\cos 2x = \cos x in the interval [0,2π][0, 2\pi] is

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  8. Question 8

    This type asked 7 times: 9 May 2023 S1, 10 May 2024 S1, 13 May 2024 S2, 20 Apr 2025 S2, 15 Apr 2026 S1, 16 Apr 2026 S1, 20 Apr 2026 S1. This one: 20 Apr 2026 S1 See all 7 of this type

    56
    The general solution of cos⁡x+sin⁡x=cos⁡2x+sin⁡2x\cos x + \sin x = \cos 2x + \sin 2x is x=npπx = np\pi or x=nqπ3+π6x = \dfrac{nq\pi}{3} + \dfrac{\pi}{6} for n∈Zn \in Z then p:q=p : q =

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  9. Question 9

    This type asked 7 times: 4 May 2023 S1, 10 May 2023 S1, 10 May 2023 S2, 11 May 2023 S2, 11 May 2024 S2, 12 May 2024 S2, 11 Apr 2026 S1. This one: 11 Apr 2026 S1 See all 7 of this type

    62
    In △ABC\triangle ABC, with usual notations, if cos⁡A=12,a=3,∠B=πc6\cos A = \dfrac{1}{2}, a = 3, \angle B = \dfrac{\pi^c}{6}, then the values of bb and cc are.....

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  10. Question 10

    This type asked 6 times: 9 May 2023 S1, 11 May 2023 S2, 15 May 2023 S2, 10 May 2024 S1, 14 May 2024 S1, 14 May 2026 S1. This one: 14 May 2026 S1 See all 6 of this type

    53
    The general solution of the equation tan⁡x+sec⁡x=2cos⁡x\tan x + \sec x = 2\cos x is

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