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Day 223: MHT-CET Maths

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

  1. Question 1

    Probability Distribution. Asked once: 13 May 2024 S2 (same type asked 3 times) See all 3 of this type

    137
    Two dice are rolled. If both dice have six faces numbered 1,2,3,5,7,111,2,3,5,7,11, then the probability that the sum of the numbers on upper most face is prime is

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  2. Question 2

    Vectors. Asked once: 15 Apr 2026 S2 (same type asked 3 times) See all 3 of this type

    89
    The altitude of the parallelopiped, whose coterminous edges are the vectors a⃗=i^+j^+k^\vec{a} = \hat{i} + \hat{j} + \hat{k}, b⃗=2i^+4j^−k^\vec{b} = 2\hat{i} + 4\hat{j} - \hat{k}, c⃗=i^+j^+3k^\vec{c} = \hat{i} + \hat{j} + 3\hat{k}, where a⃗,b⃗\vec{a}, \vec{b} are the sides of the base of parallelopiped, is

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  3. Question 3

    Vectors. Asked once: 26 Apr 2025 S2 (same type asked 3 times) See all 3 of this type

    140
    In this question figure, PP divides ACAC in the ratio 3:43:4 and Q divides BC in the ratio 4:34:3. Then M divides AQ in the ratio

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  4. Question 4

    Applications of Derivative. Asked once: 13 Apr 2026 S2 (same type asked 3 times) See all 3 of this type

    75
    If the tangent to the curve 2y3=x3+ax22y^3 = x^3 + ax^2 at the point (a,a)(a, a) cuts off intercepts α\alpha and β\beta on the coordinate axes such that α2+β2=61\alpha^2 + \beta^2 = 61, then the value of aa is

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  5. Question 5

    Determinants and Matrices. Asked once: 15 May 2026 S1 (same type asked 3 times) See all 3 of this type

    69
    If A=[1−1102−3210]A = \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \end{bmatrix}, B=adj AB = \mathrm{adj}\ A and C=5AC = 5A, then the value of ∣adj B∣∣C∣\dfrac{|\mathrm{adj}\ B|}{|C|} is:

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