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Day 4: MHT-CET Maths

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

  1. Question 1

    Vectors. This type asked 11 times: 2 May 2023 S1, 3 May 2023 S2, 9 May 2023 S1, 15 May 2023 S1, 16 May 2023 S1, 16 May 2023 S2, 9 May 2024 S1, 9 May 2024 S2, 26 Apr 2025 S1, 19 May 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 11 of this type

    92
    If three coterminous edges of a parallelopiped are represented by a⃗−b⃗,b⃗−c⃗\vec{a} - \vec{b}, \vec{b} - \vec{c} and c⃗−a⃗\vec{c} - \vec{a} then its volume is

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  2. Question 2

    Determinants and Matrices. This type asked 11 times: 4 May 2023 S1, 4 May 2023 S2, 16 May 2023 S2, 12 May 2024 S1, 19 Apr 2025 S2, 26 Apr 2025 S1, 26 Apr 2025 S2, 17 Apr 2026 S1, 12 May 2026 S2, 14 May 2026 S1, 19 May 2026 S1. This one: 19 May 2026 S1 See all 11 of this type

    69
    Let A=[12−51]A = \begin{bmatrix} 1 & 2 \\ -5 & 1 \end{bmatrix} and A−1=xA+yIA^{-1} = xA + yI, then the pair (x,y)=⋯(x, y) = \cdots

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  3. Question 3

    Differential Equations. This type asked 11 times: 10 May 2023 S1, 10 May 2024 S2, 11 May 2024 S2, 20 Apr 2025 S1, 22 Apr 2025 S1, 26 Apr 2025 S2, 15 Apr 2026 S1, 18 Apr 2026 S1, 19 Apr 2026 S2, 20 Apr 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 11 of this type

    87
    The general solution of the differential equation (x+1)dydx−y=ex(x+1)2(x + 1)\dfrac{dy}{dx} - y = e^x(x + 1)^2 is given by:

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  4. Question 4

    Differential Equations. This type asked 11 times: 9 May 2023 S1, 9 May 2023 S2, 11 May 2023 S1, 16 May 2023 S2, 10 May 2024 S2, 12 May 2024 S1, 21 Apr 2025 S2, 22 Apr 2025 S1, 25 Apr 2025 S1, 25 Apr 2025 S2, 26 Apr 2025 S2. This one: 26 Apr 2025 S2 See all 11 of this type

    128
    The population of towns A and B increase at the rate proportional to their population present at that time. At the end of the year 1984, the population of both the towns was 20,000. At the end of the year 1989, the population of town A was 25,000 and that of town B was 28,000. The difference of populations of towns A and B at the end of 1994 was

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  5. Question 5

    Pair of Straight Lines. This type asked 10 times: 2 May 2023 S1, 4 May 2023 S1, 11 May 2023 S1, 15 May 2023 S1, 16 May 2023 S1, 19 Apr 2025 S1, 25 Apr 2025 S2, 11 Apr 2026 S2, 16 Apr 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 10 of this type

    54
    If the slopes of the lines given by ax2+2hxy+by2=0ax^2 + 2hxy + by^2 = 0 are in the ratio 2:32 : 3, then h2=h^2 =

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