Continuity and Differentiability

Bihar Board Class 12 · Mathematics · 139 past questions

33 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. Q9 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   If $y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots}}}$ then $\dfrac{dy}{dx}=$

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3. Q11 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set B2026 Set F2026 Set D2026 Set J2023 Set E

   If $x = a(1-\cos\theta)$, $y = a(\theta + \sin\theta)$, then $\frac{dy}{dx} =$

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4. Q13 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $\frac{d}{dx}\sin^{-1}(3x - 4x^3) =$

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5. Q15 2026 Set C

   $\frac{d}{dx}(\sin3x\cos5x)=$

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6. Q17 2026 Set E2026 Set B2026 Set F

   $\frac{d}{dx}(\sin3x\cdot\cos5x)=$

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7. Q21 2026 Set H

   The equation of the tangent to the curve $y=x^2+4x+1$ at the point $x=3$ is

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8. Q27 2026 Set J2026 Set A2026 Set D2026 Set H

   $\frac{d}{dx}(\sin 3x \cdot \cos 5x) =$

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9. Q31 2025

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

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10. Q34 2025

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

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11. 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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12. Q43 2025

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

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13. 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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14. Q45 2025

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

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15. 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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16. Q57 2025 Set A2025 Set E

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

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17. Q59 2025 Set A2025 Set E

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

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18. Q68 2024 Set D2024 Set J

    If $y=\tan^{-1}\left(\dfrac{1-\cos x}{\sin x}\right)$ then $\dfrac{dy}{dx}=$

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19. 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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20. Q92 2023 Set E

    If $x=a\cos^2\theta,\ y=b\sin^2\theta$ then the value of $\frac{dy}{dx}$ is

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21. Q97 2021 Set I

    $\frac{d}{dx}\{\sin^{-1}(3x-4x^3)\}$ ; ................ $-\frac{1}{2}\le x\le\frac{1}{2}$

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22. Q106 2021 Set J

    $\dfrac{d}{dx}\{\sin^{-1}(3x-4x^3)\}=\ldots\ldots,\ -\frac{1}{2}\le x\le\frac{1}{2}$

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23. Q118 2019 Set F

    The slope of the tangent to the curve $x = t^2 + 3t - 8,\ y = 2t^2 - 2t - 5$ at the point $(2,-1)$ is -

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24. Q120 2018

    If $x^2 y^3 = (x+y)^5$ then, $\frac{dy}{dx}$

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25. Q121 2018

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

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26. Q122 2018

    $\frac{d(2^x)}{d(3^x)} =$

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27. Q123 2018

    If $y=\log\cos x^{2}$ then $\dfrac{dy}{dx}$ at $x=\sqrt{x}$ has the value

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28. Q124 2018

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

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29. Q125 2018

    Find $\frac{dy}{dx}$ if $x=y\log(xy)$

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30. Q126 2018

    If $y = \tan^{-1}\left(\dfrac{\cos x}{1+\sin x}\right)$ then find $\dfrac{dy}{dx}$.

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31. Q127 2018

    If $y = \sqrt{x+\sqrt{x+\sqrt{x+\cdots\text{ to }\infty}}}$ then find $\dfrac{dy}{dx}$.

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32. Q133 2017

    If $y = \sin\left[\cos\{\tan(\cot x)\}\right]$ then find $\frac{dy}{dx}$

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33. Q139 2015

    If $y = \tan^{-1} x$, then find $\frac{dy}{dx}$ by first principle.

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