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Day 128: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked 2 times: 13 May 2024 S2, 14 May 2024 S1 See all 2 times it was asked

    137
    Let f:R→Rf:R\rightarrow R be a function such that f(x)=x3+x2f′(1)+xf′′(2)+6f(x)=x^3+x^2f'(1)+xf''(2)+6, x∈Rx\in R, then f(2)f(2) equals

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  2. Question 2

    Indefinite Integration. Asked 2 times: 9 May 2024 S1, 14 May 2024 S1 See all 2 times it was asked

    143
    ∫sin⁡x+sin⁡3xcos⁡2x dx=Acos⁡x+Blog⁡∣f(x)∣+c\int\dfrac{\sin x+\sin^3 x}{\cos2x}\,dx=A\cos x+B\log|f(x)|+c (where c is a constant of integration). Then values of A, B and f(x)f(x) are

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  3. Question 3

    Line and Plane. Asked 2 times: 16 May 2023 S1, 14 May 2024 S1 See all 2 times it was asked

    130
    A line with positive direction cosines passes through the point P(2,−1,2)P(2,-1,2) and makes equal angles with the co-ordinate axes. The line meets the plane 2x+y+z=92x+y+z=9 at point QQ. The length of the line segment PQPQ equals

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  4. Question 4

    Probability Distribution. Asked 2 times: 12 May 2024 S1, 14 May 2024 S1 See all 2 times it was asked

    139
    Two cards are drawn successively with replacement from well shuffled pack of 52 cards, then the probability distribution of number of queens is

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  5. Question 5

    Probability Distribution. Asked 2 times: 10 May 2024 S1, 14 May 2024 S1 See all 2 times it was asked

    131
    Three critics review a book. For the three critics the odds in favour of the book are 2:5, 3:4 and 4:3 respectively. The probability that the majority is in favour of the book, is given by

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