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Day 241: MHT-CET Maths

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

  1. Question 1

    Conic Sections. Asked once: 21 Apr 2025 S1 (same type asked 2 times) See all 2 of this type

    145
    The Y-intercept of the common tangent to the parabolas y2=32xy^{2}= 32x and x2=108yx^{2}= 108y is

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  2. Question 2

    Line and Plane. Asked once: 22 Apr 2025 S1 (same type asked 2 times) See all 2 of this type

    109
    If the planes rˉ⋅(2i^−λj^+k^)=3\bar{r}\cdot (2\widehat{i}-\lambda\widehat{j}+\widehat{k}) = 3 and r‾⋅(4i^−j^+μk^)=5\overline{r}\cdot (4\widehat{i}-\widehat{j}+\mu\widehat{k}) = 5 are parallel, then λ+μ=\lambda+\mu=

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  3. Question 3

    Definite Integration. Asked once: 14 May 2026 S1 (same type asked 2 times) See all 2 of this type

    82
    If ∫0xf(t) dt=x+∫x0t⋅f(t) dt\int_0^x f(t)\,dt = x + \int_x^0 t \cdot f(t)\,dt then the value of f(1)=f(1) =

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  4. Question 4

    Differentiation. Asked once: 4 May 2023 S1 (same type asked 2 times) See all 2 of this type

    105
    If 8f(x)+6f ⁣(1x)=x+58f(x)+6f\!\left(\frac{1}{x}\right)=x+5 and y=x2f(x)y=x^2 f(x), then dydx\frac{dy}{dx} at x=−1x=-1 is

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  5. Question 5

    Complex Numbers. Asked once: 10 May 2023 S1 (same type asked 2 times) See all 2 of this type

    134
    If w=−1+i32w=\frac{-1+i\sqrt{3}}{2}, where i=−1i=\sqrt{-1}, then the value of (3+w+3w2)4(3+w+3w^2)^4 is

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