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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 15 times: May 2022 S1, 2 May 2023 S2, 3 May 2023 S1, 9 May 2023 S2, 15 May 2023 S1, 10 May 2024 S1, 10 May 2024 S2, 12 May 2024 S2, 20 Apr 2025 S1, 22 Apr 2025 S1, 23 Apr 2025 S1, 15 Apr 2026 S2, 18 Apr 2026 S1, 12 May 2026 S1, 15 May 2026 S2. This one: 15 May 2026 S2 See all 15 of this type

    90
    Let aˉ=2i^−j^+k^\bar{a} = 2\hat{i} - \hat{j} + \hat{k} and bˉ=i^+2j^−2k^\bar{b} = \hat{i} + 2\hat{j} - 2\hat{k}. If a third vector cˉ=xi^+yj^+zk^\bar{c} = x\hat{i} + y\hat{j} + z\hat{k} is coplanar with aˉ\bar{a} and bˉ\bar{b}, is perpendicular to aˉ\bar{a}, and satisfies ∣cˉ∣=45|\bar{c}| = \sqrt{45}, then the sum of all possible values of yy is:

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  2. Question 2

    This type asked 12 times: 2 May 2023 S1, 10 May 2023 S1, 11 May 2023 S1, 11 May 2023 S2, 16 May 2023 S1, 10 May 2024 S1, 11 May 2024 S1, 13 May 2024 S2, 25 Apr 2025 S1, 25 Apr 2025 S2, 13 Apr 2026 S2, 14 May 2026 S2. This one: 14 May 2026 S2 See all 12 of this type

    91
    If pˉ,qˉ,rˉ\bar{p}, \bar{q}, \bar{r} are unit vectors such that pˉ×(qˉ×rˉ)=17qˉ\bar{p} \times (\bar{q} \times \bar{r}) = \dfrac{1}{7}\bar{q}, then the angle between pˉ\bar{p} and rˉ\bar{r} is

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  3. Question 3

    This type asked 11 times: 2 May 2023 S1, 3 May 2023 S2, 9 May 2023 S1, 15 May 2023 S1, 16 May 2023 S1, 16 May 2023 S2, 9 May 2024 S1, 9 May 2024 S2, 26 Apr 2025 S1, 19 May 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 11 of this type

    92
    If three coterminous edges of a parallelopiped are represented by a⃗−b⃗,b⃗−c⃗\vec{a} - \vec{b}, \vec{b} - \vec{c} and c⃗−a⃗\vec{c} - \vec{a} then its volume is

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  4. Question 4

    This type asked 10 times: 2 May 2023 S1, 3 May 2023 S1, 4 May 2023 S2, 9 May 2023 S1, 15 May 2023 S1, 10 May 2024 S1, 11 May 2024 S1, 11 May 2024 S2, 14 May 2024 S2, 15 Apr 2026 S2. This one: 15 Apr 2026 S2 See all 10 of this type

    91
    Let a⃗=i^+2j^−2k^\vec{a} = \hat{i} + 2\hat{j} - 2\hat{k} and b⃗=i^−j^+k^\vec{b} = \hat{i} - \hat{j} + \hat{k}. If c⃗\vec{c} is a vector such that a⃗⋅c⃗=∣c⃗∣,∣c⃗−a⃗∣=22\vec{a}\cdot\vec{c} = |\vec{c}|, |\vec{c} - \vec{a}| = 2\sqrt{2} and the angle between a⃗×b⃗\vec{a} \times \vec{b} and c⃗\vec{c} is 60∘60^\circ, then ∣(a⃗×b⃗)×c⃗∣|(\vec{a} \times \vec{b}) \times \vec{c}| is equal to

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  5. Question 5

    This type asked 9 times: 2 May 2023 S2, 3 May 2023 S2, 9 May 2023 S1, 10 May 2023 S2, 9 May 2024 S2, 13 May 2024 S2, 25 Apr 2025 S1, 16 Apr 2026 S1, 18 Apr 2026 S2. This one: 18 Apr 2026 S2 See all 9 of this type

    93
    If aˉ⋅bˉ=β\bar{a}\cdot\bar{b} = \beta and aˉ×bˉ=cˉ\bar{a} \times \bar{b} = \bar{c} then aˉ=\bar{a} =

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  6. Question 6

    Asked 8 times: 9 May 2023 S2*, 10 May 2023 S1*, 11 May 2024 S1, 22 Apr 2025 S2*, 26 Apr 2025 S1*, 19 Apr 2026 S1*, 19 Apr 2026 S2*, 12 May 2026 S2 (* = numbers or wording changed that year) See all 8 times it was asked

    89
    If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are three vectors such that a⃗⋅(b⃗+c⃗)+b⃗⋅(c⃗+a⃗)+c⃗⋅(a⃗+b⃗)=0\vec{a}\cdot(\vec{b} + \vec{c}) + \vec{b}\cdot(\vec{c} + \vec{a}) + \vec{c}\cdot(\vec{a} + \vec{b}) = 0 and ∣a⃗∣=8,∣b⃗∣=1,∣c⃗∣=4|\vec{a}| = 8, |\vec{b}| = 1, |\vec{c}| = 4, then ∣a⃗+b⃗+c⃗∣=…|\vec{a} + \vec{b} + \vec{c}| = \ldots

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  7. Question 7

    This type asked 8 times: May 2022 S1, 2 May 2023 S2, 3 May 2023 S2, 14 May 2024 S2, 22 Apr 2025 S2, 20 Apr 2026 S1, 20 Apr 2026 S2, 15 May 2026 S1. This one: 15 May 2026 S1 See all 8 of this type

    88
    Let aˉ=2i^+k^\bar{a} = 2\hat{i} + \hat{k}, bˉ=i^+j^+k^\bar{b} = \hat{i} + \hat{j} + \hat{k}, and cˉ=4i^−3j^+7k^\bar{c} = 4\hat{i} - 3\hat{j} + 7\hat{k}. If rˉ\bar{r} is a vector such that rˉ×bˉ=cˉ×bˉ\bar{r} \times \bar{b} = \bar{c} \times \bar{b} and rˉ⋅aˉ=0\bar{r} \cdot \bar{a} = 0, then the value of the scalar product rˉ⋅i^\bar{r} \cdot \hat{i} is:

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  8. Question 8

    This type asked 8 times: 2 May 2023 S1, 4 May 2023 S1, 9 May 2024 S1, 10 May 2024 S2, 14 May 2024 S2, 11 Apr 2026 S2, 19 Apr 2026 S1, 19 Apr 2026 S2. This one: 19 Apr 2026 S2 See all 8 of this type

    89
    The maximum volume of a parallelopiped (in cubic units) with vectors (2ai^+k^),(aj^−ak^)(2a\hat{i} + \hat{k}), (a\hat{j} - a\hat{k}), and (3i^+aj^)(3\hat{i} + a\hat{j}), where a∈[0,1]a \in [0, 1], as its coterminous edges is...

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  9. Question 9

    Asked 7 times: 3 May 2023 S1*, 16 May 2023 S1*, 12 May 2024 S1, 14 May 2024 S2, 19 Apr 2025 S2, 26 Apr 2025 S2*, 18 Apr 2026 S1 (* = numbers or wording changed that year) See all 7 times it was asked

    89
    Let uˉ,vˉ,wˉ\bar{u}, \bar{v}, \bar{w} be three vectors such that ∣uˉ∣=1,∣vˉ∣=2,∣wˉ∣=3|\bar{u}| = 1, |\bar{v}| = 2, |\bar{w}| = 3. If the projection of vˉ\bar{v} along uˉ\bar{u} is equal to the projection of wˉ\bar{w} along uˉ\bar{u} and vˉ,wˉ\bar{v}, \bar{w} are perpendicular to each other, then ∣uˉ−vˉ+wˉ∣=|\bar{u} - \bar{v} + \bar{w}| =...

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  10. Question 10

    This type asked 7 times: 4 May 2023 S1, 15 May 2023 S2, 11 May 2024 S2, 22 Apr 2025 S2, 11 Apr 2026 S2, 13 Apr 2026 S2, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 7 of this type

    91
    The sum of all real values of λ\lambda for which the vectors a⃗=λi^+j^+k^,b⃗=i^+λj^+2k^,c⃗=2i^+3j^+λk^\vec{a} = \lambda\hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{i} + \lambda\hat{j} + 2\hat{k}, \vec{c} = 2\hat{i} + 3\hat{j} + \lambda\hat{k} are coplanar is...

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