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Day 135: MHT-CET Maths

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

  1. Question 1

    Differential Equations. Asked 2 times: 9 May 2023 S2, 10 May 2024 S2 See all 2 times it was asked

    144
    In a certain culture of bacteria, the rate of increase is proportional to the number of bacteria present at that instant. It is found that there are 10,000 bacteria at the end of 3 hours and 40,000 bacteria at the end of 5 hours, then the number of bacteria present in the beginning are

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  2. Question 2

    Limits. Asked 2 times: 10 May 2024 S1, 10 May 2024 S2 See all 2 times it was asked

    124
    lim⁡x→aa+2x−3x3a+x−2x=\displaystyle\lim_{x\to a}\frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt{x}}=

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  3. Question 3

    Line and Plane. Asked 2 times: 16 May 2023 S1, 10 May 2024 S2 See all 2 times it was asked

    128
    The plane through the intersection of planes x+y+z=1x+y+z=1 and 2x+3y−z+4=02x+3y-z+4=0 and parallel to Y-axis also passes through the point

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  4. Question 4

    Measures of Dispersion. Asked 2 times: 10 May 2023 S1*, 10 May 2024 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    115
    Mean and variance of six observations are 8 and 16 respectively. If each observation is multiplied by 3, then new variance of the resulting observations is

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  5. Question 5

    Straight Line. Asked 2 times: 15 May 2023 S1*, 10 May 2024 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    102
    Two sides of a square are along the lines 5x−12y+39=05x-12y+39=0 and 5x−12y+78=05x-12y+78=0, then area of the square is

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