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← Bihar Board Class 12 PYQ

Continuity and Differentiability

Bihar Board Class 12 · Mathematics · 139 past questions

  1. Q1 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set D2026 Set J2026 Set B
    $\frac{d}{dx}\sqrt{x^2+ax+1} =$
  2. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set B2026 Set F2026 Set D2021 Set I
    $\frac{d}{dx}(\sin x^2) =$
  3. Q3 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\frac{d}{dx}\sqrt{\cot x} =$
  4. Q4 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\frac{d}{dx}\left\{\lim_{x\to 0}\frac{x^5-a^5}{x-a}\right\} =$
  5. Q5 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set B2021 Set J2021 Set I
    $\frac{d}{dx}(e^{x-a}) =$
  6. 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
    $\frac{d}{dx}(\log x^n) =$
  7. Q7 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\frac{d^2}{dx^2}(\sin 2x) =$
  8. Q8 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set J2026 Set B
    Find $\frac{dy}{dx}$ when $x=at^2,\ y=2at$.
  9. 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 $\dfrac{dy}{dx}=$
  10. Q10 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\frac{d}{dx}(\cos x^3) =$
  11. 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 $\frac{dy}{dx} =$
  12. Q12 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    If $y = x^x$ then $\frac{dy}{dx} =$
  13. Q13 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\frac{d}{dx}\sin^{-1}(3x - 4x^3) =$
  14. Q14 2026 Set A2026 Set E2026 Set J2025 Set A2025 Set E
    $\frac{d}{dx}\left[2\tan^{-1}x\right]=$
  15. Q15 2026 Set C
    $\frac{d}{dx}(\sin3x\cos5x)=$
  16. Q16 2026 Set C
    $\frac{d}{dx}\sqrt{x^2 + ax + 1} =$
  17. Q17 2026 Set E2026 Set B2026 Set F
    $\frac{d}{dx}(\sin3x\cdot\cos5x)=$
  18. Q18 2026 Set F2026 Set H2026 Set B2026 Set D
    $\frac{d}{dx}(\tan^{-1}\sqrt{x} + \cot^{-1}\sqrt{x}) =$
  19. Q19 2026 Set H2026 Set B2026 Set F2026 Set D2021 Set J2021 Set I
    $\frac{d}{dx}(2\tan^{-1}x) =$
  20. Q20 2026 Set H2026 Set C2026 Set F2026 Set D2026 Set B2021 Set J2021 Set I
    $\frac{d}{dx}(\log\sqrt{x}) =$
  21. Q21 2026 Set H
    The equation of the tangent to the curve $y=x^2+4x+1$ at the point $x=3$ is
  22. Q22 2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set B
    If $x^n+y^n=a^n$ then $\dfrac{dy}{dx}=$
  23. Q23 2026 Set H2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\frac{d}{dx}(\cot^{-1} x) =$
  24. Q24 2026 Set J2026 Set A2026 Set E2021 Set I
    $\frac{d}{dx}\left(\tan^{-1}\sqrt{x} + \cot^{-1}\sqrt{x}\right) =$
  25. Q25 2026 Set J2026 Set A2026 Set E
    $\frac{d}{dx}\left(\cos\sqrt{x}\right) =$
  26. Q26 2026 Set J2025 Set A2025 Set E2023 Set E2021 Set J2021 Set I
    $\dfrac{d}{dx}\left(e^{x^3}\right) =$
  27. Q27 2026 Set J2026 Set A2026 Set D2026 Set H
    $\frac{d}{dx}(\sin 3x \cdot \cos 5x) =$
  28. Q28 2026 Set J2026 Set A
    If $x^n + y^n = a^n$ then $\frac{dy}{dx} =$
  29. Q29 2026 Set J
    $\dfrac{d}{dx}\left(\sin x^2\right)=$
  30. Q30 2025
    $\dfrac{d(\sin x)}{dx} =$
  31. Q31 2025
    $\dfrac{d}{dx}\log\sin(\sec^{-1}x + \text{cosec}^{-1}x) =$
  32. Q32 2025
    If $y = t^{21}$ then $\dfrac{d^2y}{dt^2} =$
  33. Q33 2025
    If $x = 4t, y = \dfrac{4}{t}$ then $\dfrac{dy}{dx} =$
  34. Q34 2025
    $\dfrac{d\cos^{-1}(\sin x)}{dx} =$
  35. Q35 2025
    $\dfrac{d\ \sin(\sqrt{x})}{dx} =$
  36. Q36 2025
    $\dfrac{d\ (2+\cos 2x)}{dx} =$
  37. Q37 2025
    $\dfrac{d(\text{cosec}^{-1}x)}{dx} =$
  38. Q38 2025
    $\dfrac{d(\log(\sec x))}{dx} =$
  39. Q39 2025
    $\dfrac{d(3x^2-\cos x+2)}{dx} =$
  40. Q40 2025
    $\dfrac{d\left(e^{\log x^2}\right)}{dx} =$
  41. Q41 2025
    If $x = 3\cos\theta - 2\cos^3\theta$, $y = 3\sin\theta - 2\sin^3\theta$ then find $\dfrac{dy}{dx}$.
  42. Q42 2025
    If $\tan^{-1}(x^2+y^2) = K$ then find $\dfrac{dy}{dx}$.
  43. Q43 2025
    If $y = \log\left|\dfrac{1-x^2}{1+x^2}\right|$, then find $\dfrac{dy}{dx}$.
  44. Q44 2025
    If $\sqrt{x}+\sqrt{y}=1$ then find the value of $\dfrac{dy}{dx}$ at point $\left(\dfrac14,\dfrac14\right)$.
  45. Q45 2025
    If the curves $ay+x^2=7$ and $x^3=y$ cut each other orthogonally at $(1,1)$.
  46. Q46 2025 Set A2025 Set E
    $\dfrac{d}{dx}\left\{\lim_{n\to 1}\dfrac{x^n - 1}{n+1}\right\} =$
  47. Q47 2025 Set A2025 Set E
    $\dfrac{d}{dx}\{\log_3 x \times \log_x 3\} =$
  48. Q48 2025 Set A2025 Set E
    $\frac{d}{dx}(\sec^2 x - \tan^2 x) =$
  49. Q49 2025 Set A
    $\frac{d}{dx}[e^2 + 2ex] =$
  50. Q50 2025 Set A
    $\frac{d}{dx}\left[\lim_{x\to a}\frac{x^n + a^n}{x + a}\right] =$
  51. Q51 2025 Set A
    $\frac{d}{dx}\left[\sin^{-1}2x\right]=$
  52. Q52 2025 Set A2025 Set E
    $\frac{d}{dx}\left[\frac{(x+2)(x^2-2x+4)}{x^3+8}\right]=$
  53. Q53 2025 Set A2025 Set E
    $\frac{d}{dx}\left[2\sqrt{x}\right]=$
  54. Q54 2025 Set A2025 Set E
    $\frac{d}{dx}\left[(1-\cos 2x)+2\cos^2 x\right]=$
  55. Q55 2025 Set A2025 Set E
    $\frac{d}{dx}\left[\log x^2+\log a^2\right]=$
  56. Q56 2025 Set A2025 Set E
    $\frac{d}{dx}\left[e^{x^2}\right]=$
  57. Q57 2025 Set A2025 Set E
    $\frac{d}{dx}\{\cos(\pi x+\sin \pi)\} =$
  58. Q58 2025 Set A
    $\dfrac{d}{dx}(\log x^{100}) =$
  59. Q59 2025 Set A2025 Set E
    $\dfrac{d}{dx}\left[\sin^{-1}\left(2x\sqrt{1-x^2}\right)\right] =$
  60. Q60 2025 Set E
    $\dfrac{d}{dx}\left(\log x^{100}\right) =$
  61. Q61 2025 Set E
    $\frac{d}{dx}[e^2+2ex] =$
  62. Q62 2025 Set E
    $\frac{d}{dx}\left[\lim_{x\to a}\frac{x^n+a^n}{x+a}\right]=$
  63. Q63 2025 Set E
    $\frac{d}{dx}(\sin^{-1}2x)=$
  64. Q64 2024 Set D2024 Set J
    $\frac{d}{dx}(x^5+\cos 2x)=$
  65. Q65 2024 Set D2024 Set J
    $\frac{d}{dx}\log(\cos x)=$
  66. Q66 2024 Set D2024 Set J
    $\dfrac{d}{dx}\log(\sec x+\tan x)=$
  67. Q67 2024 Set D
    $\dfrac{d}{dx}(\sec^{-1}x+\operatorname{cosec}^{-1}x)=$
  68. Q68 2024 Set D2024 Set J
    If $y=\tan^{-1}\left(\dfrac{1-\cos x}{\sin x}\right)$ then $\dfrac{dy}{dx}=$
  69. Q69 2024 Set D
    If $x = a\sec\theta,\ y = b\tan\theta$ then $\frac{dy}{dx} =$
  70. Q70 2024 Set D2024 Set J
    If $y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots\text{ to }\infty}}}$ then $\frac{dy}{dx} =$
  71. Q71 2024 Set D2024 Set J
    If $y=x^{20}$ then $\frac{d^2y}{dx^2}=$
  72. Q72 2024 Set D2024 Set J
    $\dfrac{d}{dx}(\sec^{-1}x)=$
  73. Q73 2024 Set J2024 Set D2021 Set J
    $\frac{d}{dx}(\sin^2 x)=$
  74. Q74 2024 Set J2024 Set D2021 Set J
    $\frac{d}{dx}(a^x)=$
  75. Q75 2024 Set J
    The slope of the tangent to the curve $y = 2x^2 + 3\sin x$ at $x = 0$ is
  76. Q76 2024 Set J
    The rate of change of the area of a circle with respect to its radius $r$ ( in cm$^2$/cm) at $r = 6$ cm is
  77. Q77 2024 Set J
    If $x=a\sec\theta,\ y=b\tan\theta$ then $\frac{dy}{dx}=$
  78. Q78 20232023 Set E
    $\dfrac{d}{dx}\left(2\cos\dfrac{3x}{4}\right) =$
  79. Q79 2023
    $\dfrac{d}{dx}(e^{-3x}) =$
  80. Q80 2023
    $\dfrac{d}{dx}(11^x) =$
  81. Q81 20232023 Set E
    $\dfrac{d}{dx}\left(\dfrac{1}{3x-2}\right) =$
  82. Q82 2023
    If $x = a\cos^2\theta$, $y = b\sin^2\theta$, then the value of $\dfrac{dy}{dx}$ is
  83. Q83 2023
    $\dfrac{d}{dx}(e^x + \cos 5x) =$
  84. Q84 2023
    $\dfrac{d}{dx}(\sin 2x + e^x - \cos x) =$
  85. Q85 20232023 Set E
    $\dfrac{d}{dx}\left(\dfrac{1}{4}\sec 4x\right) =$
  86. Q86 2023
    $\dfrac{d}{dx}(\log_e 10x) =$
  87. Q87 20232023 Set E
    $\dfrac{d}{dx}\left(\sin \dfrac{4x}{5}\right) =$
  88. Q88 20232023 Set E
    $\frac{d}{dx}(x^3+e^x) =$
  89. Q89 20232023 Set E
    $\frac{d}{dx}(\tan x + \sin^2 x) =$
  90. Q90 20232023 Set E
    $\frac{d^2}{dx^2}(e^{5x}) =$
  91. Q91 2023 Set E
    $\frac{d}{dx}\left(11^{x}\right) =$
  92. Q92 2023 Set E
    If $x=a\cos^2\theta,\ y=b\sin^2\theta$ then the value of $\frac{dy}{dx}$ is
  93. Q93 2023 Set E
    $\frac{d}{dx}\left(e^x + \cos 5x\right) =$
  94. Q94 2023 Set E
    $\frac{d}{dx}\left(\sin 2x + e^x - \cos x\right) =$
  95. Q95 2023 Set E
    $\frac{d}{dx}\left(\log_e 10x\right) =$
  96. Q96 2021 Set I
    $\frac{d}{dx}(\log 3^x)=$
  97. Q97 2021 Set I
    $\frac{d}{dx}\{\sin^{-1}(3x-4x^3)\}$ ; ................ $-\frac{1}{2}\le x\le\frac{1}{2}$
  98. Q98 2021 Set I
    $\dfrac{d}{dx}\left[\lim_{x\to 0}\cos 3x\right] =$
  99. Q99 2021 Set I
    $\frac{d}{dx}(5^x) =$
  100. Q100 2021 Set J2021 Set I2017
    $\frac{d}{dx}(\tan ax)=$
  101. Q101 2021 Set J2021 Set I
    $\frac{d^3y}{dx^3}(x^4) =$
  102. Q102 2021 Set J2021 Set I
    $\frac{d}{dx}\left(\sqrt{x^2+ax+1}\right) =$
  103. Q103 2021 Set J2021 Set I
    $\frac{d}{dx}(2e^{2x}) =$
  104. Q104 2021 Set J2021 Set I
    $\frac{d}{dx}(\tan x^2) =$
  105. Q105 2021 Set J2021 Set I
    $\frac{d}{dx}\left(\sqrt{\cot x}\right) =$
  106. Q106 2021 Set J
    $\dfrac{d}{dx}\{\sin^{-1}(3x-4x^3)\}=\ldots\ldots,\ -\frac{1}{2}\le x\le\frac{1}{2}$
  107. Q107 2021 Set J2021 Set I
    $\dfrac{d}{dx}(\sin\sqrt{x})=$
  108. Q108 2021 Set J
    $\dfrac{d}{dx}\{\sin^{-1}\sqrt{x}+\cos^{-1}\sqrt{x}\}=$
  109. Q109 2021 Set J
    $\dfrac{d}{dx}\left(\log 3^x\right) =$
  110. Q110 2021 Set J2021 Set I
    $\dfrac{d}{dx}\left(\dfrac{1}{\sin x}+e^x\right) =$
  111. Q111 2021 Set J
    $\frac{d}{dx}\left[\lim_{x\to 0}\cos 3x\right] =$
  112. Q112 2021 Set J2021 Set I
    $\frac{d}{dx}(\sqrt{x}) =$
  113. Q113 2019 Set F
    $\frac{d}{dx}[\sin^2 x] = ?$
  114. Q114 2019 Set F
    $\frac{d}{dx}[\log x]=?$
  115. Q115 2019 Set F
    $\frac{d}{dx}[\sin^{-1}x+\cos^{-1}x]=?$
  116. Q116 2019 Set F
    $\frac{d}{dx}[\tan x] = ?$
  117. Q117 2019 Set F
    $\frac{d}{dx}[\sin^{-1} x] = ?$
  118. 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 -
  119. Q119 2018
    $\frac{d}{dx}\left[\log(\sec x + \tan x)\right] =$
  120. Q120 2018
    If $x^2 y^3 = (x+y)^5$ then, $\frac{dy}{dx}$
  121. Q121 2018
    $\frac{d}{dx}\left[\tan^{-1}\sqrt{1+x^2} - \cot^{-1}\left(-\sqrt{1+x^2}\right)\right] =$
  122. Q122 2018
    $\frac{d(2^x)}{d(3^x)} =$
  123. Q123 2018
    If $y=\log\cos x^{2}$ then $\dfrac{dy}{dx}$ at $x=\sqrt{x}$ has the value
  124. Q124 2018
    $\dfrac{d}{dx}\left[\lim_{x\to a}\dfrac{x^{5}-a^{5}}{x-a}\right]=$
  125. Q125 2018
    Find $\frac{dy}{dx}$ if $x=y\log(xy)$
  126. Q126 2018
    If $y = \tan^{-1}\left(\dfrac{\cos x}{1+\sin x}\right)$ then find $\dfrac{dy}{dx}$.
  127. Q127 2018
    If $y = \sqrt{x+\sqrt{x+\sqrt{x+\cdots\text{ to }\infty}}}$ then find $\dfrac{dy}{dx}$.
  128. Q128 2017
    $\frac{d}{dx}(\tan ax)=$
  129. Q129 2017
    $\frac{d}{dx}(\sec x)=$
  130. Q130 2017
    $\frac{d}{dx}(\sin^{-1}x)=$
  131. Q131 2017
    If $y = \sin(\log x)$, then $\frac{dy}{dx} = $ ...........
  132. Q132 2017
    If $y = x^5$ then $\frac{dy}{dx} = $ ...........
  133. Q133 2017
    If $y = \sin\left[\cos\{\tan(\cot x)\}\right]$ then find $\frac{dy}{dx}$
  134. Q134 2016
    If $y=\cos(\log x)$, then $\frac{dy}{dx}$
  135. Q135 2016
    If $y=x^3$, then $\frac{d^2y}{dx^2}=$
  136. Q136 2015
    If $y=\sin\left(x^3\right)$
  137. Q137 2015
    $y=\tan^2x$, then $\dfrac{dy}{dx}$
  138. Q138 2015
    If $\sin\{\cos[\tan(\cot x)]\}$, find $\frac{dy}{dx}$ by first principle.
  139. Q139 2015
    If $y = \tan^{-1} x$, then find $\frac{dy}{dx}$ by first principle.