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Day 167: MHT-CET Maths

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

  1. Question 1

    Measures of Dispersion. This type asked 2 times: 16 May 2023 S1, 12 May 2024 S2. This one: 12 May 2024 S2 See all 2 of this type

    149
    For 20 observations of variable xx, if ∑(xi−2)=20\sum(x_i-2)=20 and ∑(xi−2)2=100\sum(x_i-2)^2=100, then the standard deviation of variable xx is

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  2. Question 2

    Straight Line. This type asked 2 times: May 2021 S1, 12 May 2024 S2. This one: 12 May 2024 S2 See all 2 of this type

    112
    If kik_i are possible values of kk for which lines kx+2y+2=0,  2x+ky+3=0kx+2y+2=0,\; 2x+ky+3=0 and 3x+3y+k=03x+3y+k=0 are concurrent, then ∑ki\sum k_i has the value

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  3. Question 3

    Line and Plane. This type asked 2 times: 9 May 2024 S1, 12 May 2024 S1. This one: 12 May 2024 S1 See all 2 of this type

    126
    The equation of the plane through (−1,1,2)(-1,1,2) whose normal makes equal acute angles with coordinate axes is

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  4. Question 4

    Indefinite Integration. This type asked 2 times: 4 May 2023 S2, 10 May 2024 S2. This one: 10 May 2024 S2 See all 2 of this type

    111
    ∫5tan⁡xtan⁡x−2 dx=x+alog⁡∣sin⁡x−2cos⁡x∣+c\displaystyle\int\frac{5\tan x}{\tan x - 2}\,dx = x + a\log|\sin x - 2\cos x| + c, then the value of aa is

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  5. Question 5

    Indefinite Integration. This type asked 2 times: 11 May 2023 S2, 10 May 2024 S1. This one: 10 May 2024 S1 See all 2 of this type

    112
    ∫x−7x2−16x+63 dx=Ax2−16x+63+log⁡∣(x−8)+x2−16x+63∣+c\int\frac{x-7}{\sqrt{x^2-16x+63}}\,dx=A\sqrt{x^2-16x+63}+\log|(x-8)+\sqrt{x^2-16x+63}|+c. Value of A is

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