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Day 443: MHT-CET Maths

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

  1. Question 1

    Limits. Asked once: 16 Apr 2026 S1

    70
    If the derivative of the function f(x)={ax2+bif x<−1bx2+ax+4if x≥−1f(x) = \begin{cases} ax^2 + b & \text{if } x < -1 \\ bx^2 + ax + 4 & \text{if } x \ge -1 \end{cases} is continuous everywhere then

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  2. Question 2

    Line and Plane. Asked once: 13 May 2026 S2

    93
    The vector equation of the plane determined by the lines x=y,z=0x = y, z = 0 and x+y=0,z=0x + y = 0, z = 0 is

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  3. Question 3

    Mathematical Logic. Asked once: 19 Apr 2025 S2

    101
    The last column in the truth table of the statement pattern [p→(q∧∼p)]∨[(p∨∼q)∧p]\lbrack p\rightarrow (q\land \sim p)\rbrack \vee \lbrack(p\vee \sim q) \land p\rbrack is

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  4. Question 4

    Measures of Dispersion. Asked once: 9 May 2023 S1

    134
    The mean and the standard deviation of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by pp and then reduced by qq, where p≠0p\neq0 and q≠0q\neq0. If the new mean and new standard deviation (s.d.) become half of the original values, then qq is equal to

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  5. Question 5

    Pair of Straight Lines. Asked once: 21 Apr 2025 S1

    120
    The joint equation of the bisectors of the angles between the lines x=5x= 5 and y=3y= 3 is

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