Continuity and Differentiability

CBSE Class 12 · Mathematics · 41 past questions

13 of 41 · show all

1. Q11 2025

   If $f(x) = |x| + |x - 1|$, then which of the following is correct ?

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2. Q12 2025

   The absolute maximum value of function $f(x) = x^3 - 3x + 2$ in $[0, 2]$ is…

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3. Q13 2025

   Assertion (A) : $f(x)=\begin{cases}3x-8, & x\le 5\\ 2k, & x>5\end{cases}$ is continuous at $x = 5$ for…

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4. Q14 2025

   Differentiate $2^{\cos^2 x}$ w.r.t. $\cos^2 x$.

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5. Q15 2025

   The side of an equilateral triangle is increasing at the rate of 3 cm/s. At what rate its area increasing…

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6. Q16 2025

   Find the absolute maximum and absolute minimum of function $f(x)=2x^3-15x^2+36x+1$ on $[1,5]$.

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7. Q17 2025

   If A denotes the set of continuous functions and B denotes set of differentiable functions, then which of the… (with a figure)

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8. Q18 2025

   If $x = e^{x/y}$, then prove that $\frac{dy}{dx} = \frac{x - y}{x \log x}$.

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9. Q19 2025

   If $y = \sin^{-1} x$, then $(1 - x^2)\dfrac{d^2y}{dx^2}$ is equal to…

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10. Q20 2025

    If $f(x) = \begin{cases} 3x - 2, & 0 < x \le 1 \\ 2x^2 + ax, & 1 < x < 2 \end{cases}$ is continuous for…

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11. Q21 2025

    The function f defined by…

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12. Q22 2025

    If $f(x) = 2x + \cos x$, then $f(x)$…

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13. Q23 2025

    Find k so that…

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