PYQ Vault

Complex Numbers

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 6 times: 3 May 2023 S2, 11 Apr 2026 S2, 15 Apr 2026 S2, 17 Apr 2026 S1, 18 Apr 2026 S1, 20 Apr 2026 S1. This one: 20 Apr 2026 S1 See all 6 of this type

    51
    If ww is a complex cube root of unity , then the value of w10−w7+w5−w2+1w^{10} - w^7 + w^5 - w^2 + 1 is.

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  2. Question 2

    Asked 4 times: May 2022 S1, 11 May 2023 S1*, 15 May 2023 S1*, 26 Apr 2025 S2 (* = numbers or wording changed that year) See all 4 times it was asked

    119
    Let zz be the complex number such that ∣z∣+z=3+i|z| +z= 3 +i where i=−1i=\sqrt{- 1}, then ∣z∣=|z| =

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  3. Question 3

    This type asked 4 times: 2 May 2023 S2, 10 May 2024 S1, 20 Apr 2025 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 4 of this type

    52
    If ∣z−5i∣=∣z+3∣|z - 5i| = |z + 3|, where zz is a complex number, then the equation of the locus of zz in Cartesian coordinates is ...

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  4. Question 4

    This type asked 4 times: 9 May 2024 S1, 19 Apr 2026 S2, 20 Apr 2026 S2, 14 May 2026 S2. This one: 14 May 2026 S2 See all 4 of this type

    54
    The value of ∑n=14(in+in+1)\displaystyle\sum_{n=1}^{4}\left(i^n + i^{n+1}\right) is

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  5. Question 5

    This type asked 4 times: 9 May 2023 S1, 16 May 2023 S2, 10 May 2024 S2, 11 Apr 2026 S1. This one: 11 Apr 2026 S1 See all 4 of this type

    52
    If −1+−3=reiθ-1 + \sqrt{-3} = re^{i\theta}, then the value of θ\theta is

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  6. Question 6

    Asked 3 times: 2 May 2023 S1*, 12 May 2024 S1*, 14 May 2024 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    136
    If a>0a>0 and z=(1+i)2a−iz=\dfrac{(1+i)^2}{a-i}, i=−1i=\sqrt{-1}, has magnitude 25\dfrac{2}{\sqrt{5}}, then zz is

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  7. Question 7

    This type asked 3 times: 19 Apr 2026 S1, 12 May 2026 S1, 15 May 2026 S1. This one: 15 May 2026 S1 See all 3 of this type

    54
    If n∈Zn \in Z, then the value of 2n(1+i)2n+2n(1−i)2n+(1+i)2n+(1−i)2n2n\dfrac{2^n}{(1+i)^{2n}} + \dfrac{2^n}{(1-i)^{2n}} + \dfrac{(1+i)^{2n} + (1-i)^{2n}}{2^n} is equal to

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  8. Question 8

    This type asked 3 times: 11 May 2024 S2, 23 Apr 2025 S1, 14 May 2026 S1. This one: 14 May 2026 S1 See all 3 of this type

    55
    If x=253−4ix = \dfrac{25}{3 - 4i} then 2x3−11x2+44x+27=2x^3 - 11x^2 + 44x + 27 =

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  9. Question 9

    This type asked 3 times: 16 Apr 2026 S2, 12 May 2026 S2, 13 May 2026 S1. This one: 13 May 2026 S1 See all 3 of this type

    54
    If z=3+i2z = \dfrac{\sqrt{3} + i}{2}, then the value of z69z^{69} is

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  10. Question 10

    This type asked 3 times: 4 May 2023 S2, 15 May 2023 S2, 22 Apr 2025 S1. This one: 22 Apr 2025 S1 See all 3 of this type

    136
    If z=x+iyz =x+ iy is a complex number, then the equation ∣z+iz−i∣=3\left| \frac{z+i}{z-i} \right|=\sqrt{3} represents the

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