Continuity and Differentiability

Bihar Board Class 12 · Mathematics · 139 past questions

17 of 139 · show all

1. Q4 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I

   $\frac{d}{dx}\left\{\lim_{x\to 0}\frac{x^5-a^5}{x-a}\right\} =$

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2. Q31 2025

   $\dfrac{d}{dx}\log\sin(\sec^{-1}x + \text{cosec}^{-1}x) =$

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3. Q40 2025

   $\dfrac{d\left(e^{\log x^2}\right)}{dx} =$

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4. Q43 2025

   If $y = \log\left|\dfrac{1-x^2}{1+x^2}\right|$, then find $\dfrac{dy}{dx}$.

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5. Q46 2025 Set A2025 Set E

   $\dfrac{d}{dx}\left\{\lim_{n\to 1}\dfrac{x^n - 1}{n+1}\right\} =$

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6. Q47 2025 Set A2025 Set E

   $\dfrac{d}{dx}\{\log_3 x \times \log_x 3\} =$

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7. Q48 2025 Set A2025 Set E

   $\frac{d}{dx}(\sec^2 x - \tan^2 x) =$

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8. Q50 2025 Set A

   $\frac{d}{dx}\left[\lim_{x\to a}\frac{x^n + a^n}{x + a}\right] =$

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9. Q52 2025 Set A2025 Set E

   $\frac{d}{dx}\left[\frac{(x+2)(x^2-2x+4)}{x^3+8}\right]=$

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10. Q54 2025 Set A2025 Set E

    $\frac{d}{dx}\left[(1-\cos 2x)+2\cos^2 x\right]=$

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11. Q57 2025 Set A2025 Set E

    $\frac{d}{dx}\{\cos(\pi x+\sin \pi)\} =$

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12. Q62 2025 Set E

    $\frac{d}{dx}\left[\lim_{x\to a}\frac{x^n+a^n}{x+a}\right]=$

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13. Q70 2024 Set D2024 Set J

    If $y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots\text{ to }\infty}}}$ then $\frac{dy}{dx} =$

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14. Q98 2021 Set I

    $\dfrac{d}{dx}\left[\lim_{x\to 0}\cos 3x\right] =$

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15. Q111 2021 Set J

    $\frac{d}{dx}\left[\lim_{x\to 0}\cos 3x\right] =$

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16. Q119 2018

    $\frac{d}{dx}\left[\log(\sec x + \tan x)\right] =$

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17. Q124 2018

    $\dfrac{d}{dx}\left[\lim_{x\to a}\dfrac{x^{5}-a^{5}}{x-a}\right]=$

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