Continuity and Differentiability

CBSE Class 12 · Mathematics · 41 past questions

18 of 41 · show all

1. Q1 2026

   Check whether function $f(x)$ defined as…

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2. Q3 2026

   For f(x) = x + $\frac{1}{x}$ (x ≠ 0)

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3. Q5 2026

   Find the absolute maximum value of $f(x) = \cos x + \sin^2 x,\ x \in [0, \pi]$

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4. Q8 2026

   The rate of change of volume of a sphere with respect to its diameter, when its radius is 5 cm, is…

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5. Q10 2026

   If $(\sin x)^y=y^{\cos x}$, then find $\frac{dy}{dx}$.

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6. Q11 2025

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

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7. 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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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. Q27 2024

    A function $f(x) = |1 - x + |x||$ is…

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11. Q29 2024

    The derivative of $2^x$ w.r.t. $3^x$ is…

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12. Q30 2024

    If $x\cos(p+y)+\cos p\sin(p+y)=0$, prove that $\cos p\,\frac{dy}{dx} = -\cos^2(p+y)$, where p is a constant.

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13. Q31 2024

    The number of points of discontinuity of…

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14. Q33 2024

    If $f(x) = |\tan 2x|$, then find the value of $f'(x)$ at $x = \dfrac{\pi}{3}$.

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15. Q34 2024

    If $x = e^{\cos 3t}$ and $y = e^{\sin 3t}$, prove that $\frac{dy}{dx} = -\frac{y\log x}{x\log y}$.

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16. Q37 2023

    If $y = x^{\frac{1}{x}}$, then find $\frac{dy}{dx}$ at $x = 1$.

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17. Q39 2023

    If $y = (x + \sqrt{x^2 - 1})^2$, then show that $(x^2 - 1)\left(\frac{dy}{dx}\right)^2 = 4y^2$.

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18. Q41 2023

    If $\tan\left(\frac{x+y}{x-y}\right) = k$, then $\frac{dy}{dx}$ is equal to

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