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Day 319: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked once: 9 May 2023 S1 (same type asked 3 times) See all 3 of this type

    123
    The maximum value of log⁡xx\frac{\log x}{x} is

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  2. Question 2

    Line and Plane. Asked once: 25 Apr 2025 S2 (same type asked 3 times) See all 3 of this type

    131
    The lines rˉ=(i^+j^−k^)+λ(3i^−j^)\bar{r}= (\widehat{i}+\widehat{j}-\widehat{k}) +\lambda(3\widehat{i}-\widehat{j}) and r‾=(4i^−k^)+μ(2i^+3k^)\overline{r}= (4\widehat{i}-\widehat{k}) +\mu(2\widehat{i}+ 3\widehat{k}) are

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  3. Question 3

    Sets, Relations and Functions. Asked once: 2 May 2023 S1 (same type asked 3 times) See all 3 of this type

    128
    For a suitable chosen real constant aa, let a function f:R∖{−a}→Rf: \mathbb{R} \setminus \{-a\} \to \mathbb{R} be defined by f(x)=a−xa+xf(x) = \dfrac{a-x}{a+x}. Further suppose that for any real number x≠−ax \ne -a and f(x)≠−af(x) \ne -a, (f∘f)(x)=x(f \circ f)(x) = x. Then f(−15)f\left(-\dfrac{1}{5}\right) is equal to

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  4. Question 4

    Pair of Straight Lines. Asked once: 10 May 2023 S1 (same type asked 3 times) See all 3 of this type

    150
    △OAB\triangle OAB is formed by the lines x2−4xy+y2=0x^2-4xy+y^2=0 and the line AB. The equation of line AB is 2x+3y−1=02x+3y-1=0. Then the equation of the median of the triangle drawn from the origin is

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  5. Question 5

    Probability Distribution. Asked once: 11 May 2024 S2 (same type asked 3 times) See all 3 of this type

    119
    If A and B are two events such that P(A)=13P(A)=\frac{1}{3}, P(B)=15P(B)=\frac{1}{5}, P(A∪B)=13P(A\cup B)=\frac{1}{3}, then the value of P(A′/B′)+P(B′/A′)P(A'/B')+P(B'/A') is:

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