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Day 365: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked once: 25 Apr 2025 S1 (same type asked 9 times) See all 9 of this type

    110
    If Rolle's theorem holds for the function x3+ax2+bx,1≤x≤2x^{3}+ax^{2}+bx,1 \leq x\leq 2 at the point 43\frac{4}{3}, then the values of aa and bb are respectively

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  2. Question 2

    Applications of Derivative. Asked once: 9 May 2024 S1 (same type asked 9 times) See all 9 of this type

    126
    The value of cc of Lagrange's mean value theorem for f(x)=25−x2f(x)=\sqrt{25-x^2} on [1,5][1,5] is

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  3. Question 3

    Mathematical Logic. Asked once: 26 Apr 2025 S2 (same type asked 9 times) See all 9 of this type

    101
    Which of the following statement is a tautology?

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  4. Question 4

    Definite Integration. Asked once: 12 May 2024 S2 (same type asked 9 times) See all 9 of this type

    106
    The value of ∫0π∣sin⁡x−2xπ∣ dx\int_0^{\pi} \left|\sin x - \frac{2x}{\pi}\right|\,dx is

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  5. Question 5

    Mathematical Logic. Asked once: 19 Apr 2025 S1 (same type asked 9 times) See all 9 of this type

    148
    Consider the three statements p:∀n∈N,10n−3p:\forall n \in\mathbb{N},10n - 3 is a prime number, when n is not divisible by 3 . q:23,−23,−13q:\frac{2}{\sqrt{3}},\frac{- 2}{\sqrt{3}},\frac{- 1}{\sqrt{3}} are the direction cosines of a directed line. r:sin⁡xr:\sin x is an increasing function in the interval [−π2,π2]\left\lbrack \frac{-\pi}{2},\frac{\pi}{2} \right\rbrack. Then which of the following statement pattern has truth value true?

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