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Day 428: MHT-CET Maths

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

  1. Question 1

    Limits. Asked once: 18 Apr 2026 S2

    58
    If lim⁡x→kx3−k3x2−k2=lim⁡x→01−cos⁡(2x)xsin⁡x\lim_{x \to k}\dfrac{x^3 - k^3}{x^2 - k^2} = \lim_{x \to 0}\dfrac{1 - \cos(2x)}{x\sin x}, then the value of kk is …\ldots

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  2. Question 2

    Line and Plane. Asked once: 15 May 2026 S2

    95
    If the line x+4a=y−2b=z+1c\dfrac{x + 4}{a} = \dfrac{y - 2}{b} = \dfrac{z + 1}{c} passes through the point (−3,1,−2)(-3, 1, -2) and its direction is chosen such that it makes an acute angle γ\gamma with the positive direction of Z- axis, then value of cos⁡γ\cos\gamma is:

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  3. Question 3

    Mathematical Logic. Asked once: 20 Apr 2026 S1

    63
    Consider the following statements. pp: If 34>433^4 > 4^3, then 33>443^3 > 4^4 qq: The roots of the equation x2−2x+2=0x^2 - 2x + 2 = 0 are real if and only if Mumbai is in Maharashtra. rr: Statement pp is true or statement qq is false. Which of the following has truth value T (true)?

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  4. Question 4

    Measures of Dispersion. Asked once: 9 May 2024 S1

    149
    The standard deviation of the following distribution: C.I.: 0–6, 6–12, 12–18; fif_i: 2, 4, 6

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  5. Question 5

    Pair of Straight Lines. Asked once: 20 Apr 2026 S1

    59
    If the equation 16x2−24xy+9y2−8x+6y−35=016x^2 - 24xy + 9y^2 - 8x + 6y - 35 = 0 represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is..........

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