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Day 42: MHT-CET Maths

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

  1. Question 1

    Differentiation. This type asked 5 times: 2 May 2023 S2, 11 May 2023 S2, 11 May 2024 S1, 25 Apr 2025 S1, 16 Apr 2026 S1. This one: 16 Apr 2026 S1 See all 5 of this type

    71
    The derivative of log⁡8(log⁡5x)\log_8(\log_5 x) w. r. t. xx is

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  2. Question 2

    Circle. This type asked 5 times: 3 May 2023 S1, 4 May 2023 S2, 9 May 2023 S2, 16 May 2023 S1, 13 Apr 2026 S2. This one: 13 Apr 2026 S2 See all 5 of this type

    59
    The equation of the circle concentric with circle x2+y2−6x+7=0x^2 + y^2 - 6x + 7 = 0 and which touches the line x+y+3=0x + y + 3 = 0 is ....

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  3. Question 3

    Line and Plane. This type asked 5 times: 3 May 2023 S2, 15 May 2023 S1, 9 May 2024 S1, 12 May 2024 S1, 11 Apr 2026 S2. This one: 11 Apr 2026 S2 See all 5 of this type

    94
    If the centroid of a tetrahedron OABCOABC is (1,2,−1)(1, 2, -1), where O is the origin, A(a,2,3),B(1,b,2),C(2,1,c)A(a, 2, 3), B(1, b, 2), C(2, 1, c) are the other vertices, then the distance of the point P(a,b,c)P(a, b, c) from the origin is...

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  4. Question 4

    Vectors. This type asked 5 times: 9 May 2023 S1, 13 May 2024 S2, 19 Apr 2025 S1, 22 Apr 2025 S1, 11 Apr 2026 S1. This one: 11 Apr 2026 S1 See all 5 of this type

    90
    If a,b,ca, b, c are distinct non-negative numbers and the vectors ai^+aj^+ck^,i^+k^,ci^+cj^+bk^a\hat{i} + a\hat{j} + c\hat{k}, \hat{i} + \hat{k}, c\hat{i} + c\hat{j} + b\hat{k} lie in the same plane, then the value of cc is...

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  5. Question 5

    Differential Equations. This type asked 5 times: 10 May 2023 S2, 15 May 2023 S2, 14 May 2024 S2, 19 Apr 2025 S1, 25 Apr 2025 S2. This one: 25 Apr 2025 S2 See all 5 of this type

    117
    The order of the differential equation whose general solution is given by y=(C1+C2)sin⁡(x+C3)−C4ex+C5y=\left( C_{1}+C_{2} \right)\sin\left( x+C_{3} \right)-C_{4}e^{x+C_{5}} is (where C1,C2,C3,C4,C5C_{1},C_{2},C_{3},C_{4},C_{5} are arbitrary constants)

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