PYQ Vault

Day 225: MHT-CET Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Vectors. Asked once: 15 Apr 2026 S1 (same type asked 3 times) See all 3 of this type

    96
    If a unit vector makes angles π4\dfrac{\pi}{4} with i^\hat{i}, π3\dfrac{\pi}{3} with j^\hat{j} and θ∈(0,π)\theta \in (0, \pi) with k^\hat{k}, then a value of θ\theta is equal to...

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  2. Question 2

    Circle. Asked once: 21 Apr 2025 S2 (same type asked 3 times) See all 3 of this type

    118
    The locus of point of intersection of the tangents to the circle x2+y2=16x^{2}+y^{2}= 16, such that the angle between them is 60∘60^{\circ}, is

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  3. Question 3

    Definite Integration. Asked once: 11 Apr 2026 S2 (same type asked 3 times) See all 3 of this type

    81
    If ∫2e[1log⁡x−1(log⁡x)2]dx=a+blog⁡2\displaystyle\int_2^e\left[\dfrac{1}{\log x} - \dfrac{1}{(\log x)^2}\right]dx = a + \dfrac{b}{\log 2}, then values of aa and bb are

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  4. Question 4

    Straight Line. Asked once: 11 May 2023 S2 (same type asked 3 times) See all 3 of this type

    137
    A straight line L through the point (3,−2)(3,-2) is inclined at an angle of 60°60° to the line 3x+y=1\sqrt{3}x+y=1. If L also intersects the X-axis, then the equation of L is

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  5. Question 5

    Complex Numbers. Asked once: 12 May 2026 S1 (same type asked 3 times) See all 3 of this type

    56
    If n∈Zn \in Z, then the expression 2n(1−i)2n+(1+i)2n2n\dfrac{2^n}{(1 - i)^{2n}} + \dfrac{(1 + i)^{2n}}{2^n} is equal to ...

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