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Day 315: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 19 Apr 2025 S1 (same type asked 3 times) See all 3 of this type

    112
    ∫e2030log⁡x−e2029log⁡xe2028log⁡x−e2027log⁡xdx=…\int\frac{e^{2030\log x}-e^{2029\log x}}{e^{2028\log x}-e^{2027\log x}}dx = \ldots.

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  2. Question 2

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

    146
    A manufacturing company produces two items, A and B. Each toy should be processed by two machines, I and II. Machine I can be operated for maximum 10 hours 40 minutes. It takes 20 minutes for an item of A and 15 minutes for B. Machine II can be operated for a total time at 8 hours 20 minutes. It takes 5 minutes for an item A and 8 minutes for B . The profit per item of AA is ₹ 25 and per item of BB is ₹ 18 . The formulation of an L.P.P. to maximize the profit (where xx is number of items A and yy is the number of item BB ) is

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  3. Question 3

    Permutations and Combinations. Asked once: 21 Apr 2025 S2 (same type asked 3 times) See all 3 of this type

    133
    If  n+4Cn+1− n+3Cn=15(n+2)\ ^{n+ 4}C_{n+ 1}-\ ^{n+ 3}C_{n}= 15(n+ 2), then n=n=

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  4. Question 4

    Line and Plane. Asked once: 12 May 2024 S2 (same type asked 3 times) See all 3 of this type

    135
    If the volume of tetrahedron, whose vertices are A(1,2,3), B(−3,−1,1), C(2,1,3)A(1,2,3),\, B(-3,-1,1),\, C(2,1,3) and D(−1,2,x)D(-1,2,x) is 116\frac{11}{6} cubic units, then the value of xx is

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  5. Question 5

    Line and Plane. Asked once: 11 May 2023 S1 (same type asked 3 times) See all 3 of this type

    120
    The plane 2x+3y+4z=12x + 3y + 4z = 1 meets X-axis in A, Y-axis in B and Z-axis in C. Then the centroid of △ABC\triangle ABC is

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