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Day 54: MHT-CET Maths

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

  1. Question 1

    Vectors. This type asked 4 times: 16 May 2023 S1, 16 Apr 2026 S2, 14 May 2026 S1, 14 May 2026 S2. This one: 14 May 2026 S2 See all 4 of this type

    90
    If the volume of tetrahedron with its coterminous edges aˉ,bˉ,cˉ\bar{a}, \bar{b}, \bar{c} is 66 cu. units then the volume of a tetrahedron with coterminous edges (aˉ×bˉ),(bˉ×cˉ),(cˉ×aˉ)(\bar{a} \times \bar{b}), (\bar{b} \times \bar{c}), (\bar{c} \times \bar{a}) is

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  2. Question 2

    Permutations and Combinations. This type asked 4 times: 12 May 2024 S1, 14 May 2024 S2, 20 Apr 2025 S1, 14 May 2026 S1. This one: 14 May 2026 S1 See all 4 of this type

    56
    In a polygon, the number of diagonals is 5454. Then the number of sides of the polygon is

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  3. Question 3

    Circle. This type asked 4 times: 3 May 2023 S2, 19 Apr 2025 S2, 18 Apr 2026 S1, 13 May 2026 S2. This one: 13 May 2026 S2 See all 4 of this type

    63
    If the tangent to the circle x2+y2=5x^2 + y^2 = 5 at point (1,−2)(1, -2) also touches the circle x2+y2−8x+6y+k=0x^2 + y^2 - 8x + 6y + k = 0, then k5=⋯⋯⋯\dfrac{k}{5} = \cdots\cdots\cdots

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  4. Question 4

    Indefinite Integration. This type asked 4 times: 10 May 2023 S2, 9 May 2024 S2, 17 Apr 2026 S1, 13 May 2026 S2. This one: 13 May 2026 S2 See all 4 of this type

    79
    If f′(x)=k(cos⁡x−sin⁡x),f′(0)=5,f(π2)=19f'(x) = k(\cos x - \sin x), f'(0) = 5, f\left(\dfrac{\pi}{2}\right) = 19, Then f(x)=f(x) =

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  5. Question 5

    Mathematical Logic. This type asked 4 times: 15 Apr 2026 S2, 12 May 2026 S1, 13 May 2026 S1, 13 May 2026 S2. This one: 13 May 2026 S2 See all 4 of this type

    68
    The dual of the statement pattern (p∧q)∧∼(p∨q)(p \wedge q) \wedge \sim(p \vee q) is a:

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