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Day 177: MHT-CET Maths

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

  1. Question 1

    Limits. Asked once: 20 Apr 2026 S2 (same type asked 9 times) See all 9 of this type

    69
    If the function f(x)f(x) defined by f(x)={ax+1if x≤3bx+3if x>3f(x) = \begin{cases} ax + 1 & \text{if } x \le 3 \\ bx + 3 & \text{if } x > 3 \end{cases} is continuous at x=3x = 3, then (a−b)=(a - b) = ..........

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  2. Question 2

    Linear Programming. Asked once: 15 May 2026 S1 (same type asked 9 times) See all 9 of this type

    97
    The L.P.P. Maximize Z=0.75x+0.5yZ = 0.75x + 0.5y subject to 3x+2y≤63x + 2y \le 6, x+4y≤4x + 4y \le 4, x≥0,y≥0x \ge 0, y \ge 0 has

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  3. Question 3

    Trigonometric Functions. Asked once: 14 May 2026 S1 (same type asked 9 times) See all 9 of this type

    54
    In ΔABC\Delta ABC with the usual notations, angles A,B,CA, B, C of are in A.P. and b:c=3:2b : c = \sqrt{3} : \sqrt{2}. The ratio of the largest and the smallest angle of the triangle will be

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  4. Question 4

    Differentiation. Asked once: 14 May 2026 S1 (same type asked 9 times) See all 9 of this type

    72
    If y=xxy = x^{\sqrt{x}}, then dydx=\dfrac{dy}{dx} =

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  5. Question 5

    Applications of Derivative. Asked once: 18 Apr 2026 S2 (same type asked 9 times) See all 9 of this type

    76
    If the function f(x)=ax2+bx+sin⁡xf(x) = ax^2 + bx + \sin x satisfies all the conditions of Rolle's theorem on [0,π][0, \pi] and the slope of the tangent to the curve y=f(x)y = f(x) at x=π4x = \dfrac{\pi}{4} is zero, then a−b=a - b =

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