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Day 80: MHT-CET Maths

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

  1. Question 1

    Vectors. This type asked 3 times: 13 Apr 2026 S1, 15 Apr 2026 S1, 19 May 2026 S1. This one: 19 May 2026 S1 See all 3 of this type

    97
    The position vector of a point PP, such that OPOP inclined to the X axis at 45∘45^\circ and to the Y axis at 60∘60^\circ and ∣OP∣=12|OP| = 12 units is:

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  2. Question 2

    Circle. This type asked 3 times: 21 Apr 2025 S2, 15 Apr 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 3 of this type

    60
    The angle between the tangents drawn from the point (1,1)(1, 1) to the circle 2x2+2y2−8x+4y+5=02x^2 + 2y^2 - 8x + 4y + 5 = 0 is …\ldots

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  3. Question 3

    Definite Integration. This type asked 3 times: 19 Apr 2025 S1, 11 Apr 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 3 of this type

    84
    The value of I=∫13ex(x+2)2(x+4)2 dxI = \int_1^3 e^x\dfrac{(x + 2)^2}{(x + 4)^2}\, dx is:

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  4. Question 4

    Straight Line. This type asked 3 times: May 2022 S1, 11 May 2023 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 3 of this type

    61
    The equations of the lines passing through the center of circle x2+y2−4x−10y−7=0x^2 + y^2 - 4x - 10y - 7 = 0 and intersecting the line 3x−y−1=03x - y - 1 = 0 at an angle π4\dfrac{\pi}{4} is...

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  5. Question 5

    Complex Numbers. 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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