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Day 269: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked once: May 2022 S1 (same type asked 10 times) See all 10 of this type

    120
    If y=sin⁡ ⁣(2tan⁡−1 ⁣1+x1−x)y = \sin\!\left(2\tan^{-1}\!\sqrt{\frac{1+x}{1-x}}\right) then dydx\frac{dy}{dx} is equal to

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  2. Question 2

    Linear Programming. Asked once: 18 Apr 2026 S1 (same type asked 10 times) See all 10 of this type

    97
    The maximum value of Z=4x+5yZ = 4x + 5y, subject to the constraints 3x+y≤15,3x+4y≤24,x≥0,y≥03x + y \le 15, 3x + 4y \le 24, x \ge 0, y \ge 0 is

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  3. Question 3

    Applications of Definite Integral. Asked once: 19 Apr 2025 S2 (same type asked 10 times) See all 10 of this type

    111
    The area enclosed between the curves y2=4xy^{2}= 4x and y=∣x∣y= |x| is

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  4. Question 4

    Limits. Asked once: 11 May 2024 S1 (same type asked 10 times) See all 10 of this type

    128
    If f(x)={1+mx−1−mxx,−1≤x<02x+1x−2,0≤x≤1f(x)=\begin{cases}\dfrac{\sqrt{1+mx}-\sqrt{1-mx}}{x}, & -1\leq x<0\\ \dfrac{2x+1}{x-2}, & 0\leq x\leq1\end{cases} is continuous in the interval [−1,1][-1,1], then m is equal to

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  5. Question 5

    Limits. Asked once: 15 Apr 2026 S1 (same type asked 10 times) See all 10 of this type

    61
    If lim⁡x→0(4x−1)3tan⁡(x4)log⁡(1+x23)=96(log⁡a)b\displaystyle\lim_{x \to 0}\dfrac{(4^x - 1)^3}{\tan\left(\dfrac{x}{4}\right)\log\left(1 + \dfrac{x^2}{3}\right)} = 96(\log a)^b, then (a+b)=(a + b) =

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