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Day 267: MHT-CET Maths

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

  1. Question 1

    Differential Equations. Asked once: 13 Apr 2026 S2 (same type asked 11 times) See all 11 of this type

    85
    The differential equation of 3y=x+c33y = \sqrt[3]{x + c} is

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  2. Question 2

    Vectors. Asked once: 26 Apr 2025 S1 (same type asked 11 times) See all 11 of this type

    150
    The volume of tetrahedron with co-terminus edges aˉ,bˉ,cˉ\bar{a},\bar{b},\bar{c} is 643\frac{64}{3} cubic units, then volume of parallelopiped considering co-terminus edges given by the vectors aˉ+bˉ,bˉ+cˉ,cˉ+aˉ\bar{a}+\bar{b},\bar{b}+\bar{c},\bar{c}+\bar{a} is ____\_\_\_\_ cubic units.

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  3. Question 3

    Determinants and Matrices. Asked once: 17 Apr 2026 S1 (same type asked 11 times) See all 11 of this type

    66
    If AA is a non-singular matrix and A2−A+I=0A^2 - A + I = 0, then A−1=…A^{-1} = \ldots

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  4. Question 4

    Differential Equations. Asked once: 19 Apr 2026 S2 (same type asked 11 times) See all 11 of this type

    85
    If the solution of the differential equation (1+x3)dydx+6x2y=1+x2(1 + x^3)\dfrac{dy}{dx} + 6x^2y = 1 + x^2 is y=1(1+x3)s[x+xpp+xqq+xrr+c]y = \dfrac{1}{(1 + x^3)^s}\left[x + \dfrac{x^p}{p} + \dfrac{x^q}{q} + \dfrac{x^r}{r} + c\right], then the LCM of p,q,rp, q, r and ss is...

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  5. Question 5

    Differential Equations. Asked once: 12 May 2024 S1 (same type asked 11 times) See all 11 of this type

    108
    The decay rate of radioactive material at any time tt is proportional to its mass at that time. The mass is 27 grams when t=0t=0. After three hours it was found that 8 grams are left. Then the substance left after one more hour is

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