Continuity and Differentiability

Bihar Board Class 12 · Mathematics · 139 past questions

37 of 139 · show all

1. Q6 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2025 Set A2025 Set E2021 Set J2021 Set I

   $\frac{d}{dx}(\log x^n) =$

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2. Q14 2026 Set A2026 Set E2026 Set J2025 Set A2025 Set E

   $\frac{d}{dx}\left[2\tan^{-1}x\right]=$

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3. Q26 2026 Set J2025 Set A2025 Set E2023 Set E2021 Set J2021 Set I

   $\dfrac{d}{dx}\left(e^{x^3}\right) =$

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4. Q30 2025

   $\dfrac{d(\sin x)}{dx} =$

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5. Q31 2025

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

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6. Q32 2025

   If $y = t^{21}$ then $\dfrac{d^2y}{dt^2} =$

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7. Q33 2025

   If $x = 4t, y = \dfrac{4}{t}$ then $\dfrac{dy}{dx} =$

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8. Q34 2025

   $\dfrac{d\cos^{-1}(\sin x)}{dx} =$

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9. Q35 2025

   $\dfrac{d\ \sin(\sqrt{x})}{dx} =$

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10. Q36 2025

    $\dfrac{d\ (2+\cos 2x)}{dx} =$

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11. Q37 2025

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

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12. Q38 2025

    $\dfrac{d(\log(\sec x))}{dx} =$

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13. Q39 2025

    $\dfrac{d(3x^2-\cos x+2)}{dx} =$

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14. Q40 2025

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

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15. Q41 2025

    If $x = 3\cos\theta - 2\cos^3\theta$, $y = 3\sin\theta - 2\sin^3\theta$ then find $\dfrac{dy}{dx}$.

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16. Q42 2025

    If $\tan^{-1}(x^2+y^2) = K$ then find $\dfrac{dy}{dx}$.

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17. Q43 2025

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

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18. Q44 2025

    If $\sqrt{x}+\sqrt{y}=1$ then find the value of $\dfrac{dy}{dx}$ at point $\left(\dfrac14,\dfrac14\right)$.

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19. Q45 2025

    If the curves $ay+x^2=7$ and $x^3=y$ cut each other orthogonally at $(1,1)$.

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20. 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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21. Q47 2025 Set A2025 Set E

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

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22. Q48 2025 Set A2025 Set E

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

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23. Q49 2025 Set A

    $\frac{d}{dx}[e^2 + 2ex] =$

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24. Q50 2025 Set A

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

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25. Q51 2025 Set A

    $\frac{d}{dx}\left[\sin^{-1}2x\right]=$

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26. 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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27. Q53 2025 Set A2025 Set E

    $\frac{d}{dx}\left[2\sqrt{x}\right]=$

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28. Q54 2025 Set A2025 Set E

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

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29. Q55 2025 Set A2025 Set E

    $\frac{d}{dx}\left[\log x^2+\log a^2\right]=$

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30. Q56 2025 Set A2025 Set E

    $\frac{d}{dx}\left[e^{x^2}\right]=$

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31. Q57 2025 Set A2025 Set E

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

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32. Q58 2025 Set A

    $\dfrac{d}{dx}(\log x^{100}) =$

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33. Q59 2025 Set A2025 Set E

    $\dfrac{d}{dx}\left[\sin^{-1}\left(2x\sqrt{1-x^2}\right)\right] =$

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34. Q60 2025 Set E

    $\dfrac{d}{dx}\left(\log x^{100}\right) =$

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35. Q61 2025 Set E

    $\frac{d}{dx}[e^2+2ex] =$

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36. Q62 2025 Set E

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

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37. Q63 2025 Set E

    $\frac{d}{dx}(\sin^{-1}2x)=$

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