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Day 58: MHT-CET Maths

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

  1. Question 1

    Applications of Definite Integral. This type asked 4 times: 11 May 2023 S1, 13 Apr 2026 S2, 15 Apr 2026 S1, 20 Apr 2026 S1. This one: 20 Apr 2026 S1 See all 4 of this type

    83
    The area of the region lying in the first quadrant and bounded by the curve y=4x2y = 4x^2, the Y-axis, and the lines y=2,y=4y = 2, y = 4 is...

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  2. Question 2

    Limits. This type asked 4 times: May 2022 S1, 4 May 2023 S2, 17 Apr 2026 S1, 19 Apr 2026 S2. This one: 19 Apr 2026 S2 See all 4 of this type

    59
    If lim⁡x→1x3+ax2+bx+cx2−2x+1=2026\lim_{x \to 1}\dfrac{x^3 + ax^2 + bx + c}{x^2 - 2x + 1} = 2026 then the value of a−ca - c is...

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  3. Question 3

    Line and Plane. This type asked 4 times: 3 May 2023 S1, 11 May 2023 S2, 15 May 2023 S1, 19 Apr 2026 S2. This one: 19 Apr 2026 S2 See all 4 of this type

    94
    Let r⃗⋅(3i^−2j^+7k^)=32\vec{r}\cdot(3\hat{i} - 2\hat{j} + 7\hat{k}) = 32 is the equation of a plane and the line having direction ratios (5,b,3)(5, b, 3) is parallel to the plane, then the value of b is...

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  4. Question 4

    Conic Sections. This type asked 4 times: 22 Apr 2025 S1, 26 Apr 2025 S2, 17 Apr 2026 S1, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 4 of this type

    59
    A tangent having slope −12-\dfrac{1}{2} to the ellipse 3x2+4y2=123x^2 + 4y^2 = 12 intersects the X-axis and Y-axis at the points A and B respectively. if O is the origin, then the area of △AOB\triangle AOB is ...

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  5. Question 5

    Sets, Relations and Functions. This type asked 4 times: 9 May 2024 S1, 12 May 2024 S2, 17 Apr 2026 S1, 19 Apr 2026 S1. This one: 19 Apr 2026 S1 See all 4 of this type

    70
    If f(x)=x2f(x) = x^2 and g(x)=[x2]g(x) = [x^2] where [⋅][\cdot] represents the greatest integer function then, (f∘g)(32)+(g∘f)(32)(f \circ g)\left(\dfrac{3}{2}\right) + (g \circ f)\left(\dfrac{3}{2}\right) is equal to ...

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