Class 12 Math Ch-8 Application of Integrals MCQs Exam 2027

Topic 1: Area of Standard Circles and Ellipses

1. Area of the circle $x^2 + y^2 = a^2$ is: (2021)

   (A) $\pi a^2$

   (B) $2\pi a$

   (C) $\pi a$

   (D) $\pi a^2/4$

2. Area of the circle $x^2 + y^2 = 16$ is: (2024)

   (A) $4\pi$

   (B) $16\pi$

   (C) $8\pi$

   (D) $32\pi$

3. Area of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is: (2019)

   (A) $\pi ab$

   (B) $2\pi ab$

   (C) $\pi a^2b$

   (D) $\pi ab^2$

4. Area of the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$ is: (2024)

   (A) $12\pi$

   (B) $7\pi$

   (C) $144\pi$

   (D) $25\pi$

5. Area of the circle $x^2 + y^2 = 25$ in the first quadrant is: (2023)

   (A) $25\pi/4$

   (B) $25\pi$

   (C) $5\pi$

   (D) $25\pi/2$

6. Area of the circle $x^2 + y^2 = 1$ is: (2022)

   (A) $\pi$

   (B) $2\pi$

   (C) $\pi/4$

   (D) 1

7. Area of the ellipse $x^2/4 + y^2/1 = 1$: (2023)

   (A) $2\pi$

   (B) $4\pi$

   (C) $\pi$

   (D) $16\pi$

8. Area of the region bounded by $x^2 + y^2 = 4$ and $x = 0, x = 2$: (2021)

   (A) $\pi$

   (B) $2\pi$

   (C) $4\pi$

   (D) $\pi/2$

9. Area of the region bounded by $y = \sqrt{a^2 – x^2}$ and x-axis is: (2021)

   (A) $\pi a^2/2$

   (B) $\pi a^2$

   (C) $\pi a^2/4$

   (D) $a^2$

10. Area of the ellipse $9x^2 + 16y^2 = 144$: (2018)

    (A) $12\pi$

    (B) $144\pi$

    (C) $7\pi$

    (D) $25\pi$

11. Area of the circle $x^2 + y^2 = 9$ in the first quadrant: (2024)

    (A) $9\pi/4$

    (B) $9\pi/2$

    (C) $3\pi$

    (D) $9\pi$

12. Area of the circle $x^2 + y^2 = r^2$: (2017)

    (A) $\pi r^2$

    (B) $2\pi r$

    (C) $\pi r^2/2$

    (D) $4\pi r^2$

13. Area of the ellipse $x^2/25 + y^2/16 = 1$: (2020)

    (A) $20\pi$

    (B) $40\pi$

    (C) $10\pi$

    (D) $5\pi$

14. Area of the region bounded by $y = \sqrt{16-x^2}$ and x-axis: (2021)

    (A) $8\pi$

    (B) $4\pi$

    (C) $16\pi$

    (D) $2\pi$

15. Area of the ellipse $x^2/a^2 + y^2/b^2 = 1$ in the first quadrant: (2023)

    (A) $\pi ab/4$

    (B) $\pi ab/2$

    (C) $\pi ab$

    (D) $ab$

16. Area of the circle $x^2 + y^2 = 49$: (2024)

    (A) $49\pi$

    (B) $7\pi$

    (C) $14\pi$

    (D) $21\pi$

17. Area of the ellipse $4x^2 + 9y^2 = 36$: (2019)

    (A) $6\pi$

    (B) $36\pi$

    (C) $13\pi$

    (D) $5\pi$

18. Area of the region bounded by $y = \sqrt{4-x^2}$, x-axis and $x=0$: (2022)

    (A) $\pi$

    (B) $2\pi$

    (C) $4\pi$

    (D) 1

19. Area of the circle $x^2 + y^2 = 100$: (2024)

    (A) $100\pi$

    (B) $10\pi$

    (C) $20\pi$

    (D) $50\pi$

20. Area of the ellipse $x^2 + 4y^2 = 4$: (2023)

    (A) $2\pi$

    (B) $4\pi$

    (C) $\pi$

    (D) $8\pi$

Topic 2: Area Bounded by Parabolas

21. Area of the region bounded by $y^2 = x$, y-axis and $y = 1$ is: (2024)

    (A) 1/3

    (B) 2/3

    (C) 1

    (D) 4/3

22. Area of the region bounded by $y^2 = 4x$ and $x = 3$ is: (2023)

    (A) $8\sqrt{3}$

    (B) $4\sqrt{3}$

    (C) $12\sqrt{3}$

    (D) $16\sqrt{3}$

23. Area of the region bounded by $y^2 = 4ax$ and its latus rectum $x = a$ is: (2021)

    (A) $8a^2/3$

    (B) $4a^2/3$

    (C) $2a^2/3$

    (D) $16a^2/3$

24. Area bounded by $x^2 = 4y, y=2, y=4$ and y-axis in 1st quadrant: (2023)

    (A) $\frac{16\sqrt{2}-8}{3}$

    (B) $8\sqrt{2}/3$

    (C) $16/3$

    (D) $4\sqrt{2}$

25. Area of the region bounded by $x^2 = 16y, y = 1, y = 4$ and y-axis: (2022)

    (A) 56/3

    (B) 64/3

    (C) 32/3

    (D) 16/3

26. Area bounded by $y^2 = 4x$ and $y = x$: (2020)

    (A) 8/3

    (B) 4/3

    (C) 2/3

    (D) 1/3

27. Area between $y^2 = 4x$ and $x^2 = 4y$: (2019)

    (A) 16/3

    (B) 8/3

    (C) 4/3

    (D) 32/3

28. Area of the region bounded by $y^2 = 9x$ and $x = 2, x = 4$: (2021)

    (A) $16\sqrt{2}-8$

    (B) $32-8\sqrt{2}$

    (C) $16-4\sqrt{2}$

    (D) 4

29. Area of the region bounded by $x = y^2$ and $x = 4$: (2021)

    (A) 32/3

    (B) 16/3

    (C) 8/3

    (D) 64/3

30. Area of the region bounded by $y = x^2$ and $y = 4$: (2021)

    (A) 32/3

    (B) 16/3

    (C) 8/3

    (D) 4

31. Area of the region bounded by $y^2 = 4ax$ and $y = mx$: (2017)

    (A) $8a^2/3m^3$

    (B) $4a^2/3m^3$

    (C) $16a^2/3m^3$

    (D) $a^2/m^2$

32. Area of the region bounded by $y^2 = 8x$ and $y = x$: (2020)

    (A) 32/3

    (B) 16/3

    (C) 8/3

    (D) 4/3

33. Area of the region bounded by $y^2 = 2x$ and $y = x$: (2019)

    (A) 2/3

    (B) 1/3

    (C) 4/3

    (D) 1/6

34. Area of the region bounded by $y = x^2$ and $y = |x|$: (2018)

    (A) 1/3

    (B) 2/3

    (C) 1/6

    (D) 1

35. Area of the region bounded by $x^2 = y$ and $y = 1$: (2022)

    (A) 4/3

    (B) 2/3

    (C) 1/3

    (D) 8/3

36. Area of the region bounded by $y^2 = 4x$ and $y = 4$: (2022)

    (A) 16/3

    (B) 8/3

    (C) 32/3

    (D) 4

37. Area of the region bounded by $x^2 = 4y$ and $x = 2$: (2021)

    (A) 2/3

    (B) 4/3

    (C) 1/3

    (D) 1

38. Area of the region bounded by $y^2 = x$ and $x = 1$: (2023)

    (A) 4/3

    (B) 2/3

    (C) 1/3

    (D) 1

39. Area of the region bounded by $y^2 = 4ax, x = 0, y = b$: (2017)

    (A) $b^3/12a$

    (B) $b^3/4a$

    (C) $b^2/4a$

    (D) $b^3/6a$

40. Area of the region bounded by $y = x^2$ and $y = x$: (2023)

    (A) 1/6

    (B) 1/3

    (C) 1/2

    (D) 2/3

Topic 3: Area of Trigonometric Functions

41. Area bounded by $y = \sin x$ between $x = 0$ and $x = \pi$ is: (2020)

    (A) 2

    (B) 1

    (C) 0

    (D) 4

42. Area bounded by $y = \cos x$ between $x = 0$ and $x = \pi/2$ is: (2022)

    (A) 1

    (B) 2

    (C) 0

    (D) -1

43. Area bounded by $y = \sin x$ from $x = 0$ to $x = 2\pi$ is: (2021)

    (A) 4

    (B) 0

    (C) 2

    (D) 1

44. Area bounded by $y = \cos x$ from $x = 0$ to $x = \pi$ is: (2018)

    (A) 2

    (B) 0

    (C) 1

    (D) 4

45. Area of the region bounded by $y = \sin 2x, x=0, x=\pi/4$: (2022)

    (A) 1/2

    (B) 1

    (C) 2

    (D) 1/4

46. Area of the region bounded by $y = \cos 2x, x=0, x=\pi/4$: (2021)

    (A) 1/2

    (B) 1

    (C) 1/4

    (D) 0

47. Area bounded by $y = \tan x$, x-axis and $x=0, x=\pi/4$: (2017)

    (A) $\log \sqrt{2}$

    (B) $\log 2$

    (C) 1/2

    (D) $\pi/4$

48. Area of the region bounded by $y = \sec^2 x, x=0, x=\pi/4$: (2019)

    (A) 1

    (B) $\pi/4$

    (C) 0

    (D) $\sqrt{2}$

49. Area bounded by $y = \sin x$ and $y = \cos x$ from $x=0$ to $x=\pi/4$: (2020)

    (A) $\sqrt{2}-1$

    (B) 1

    (C) $2-\sqrt{2}$

    (D) 1/2

50. Area of the region bounded by $y = \sin x$ from $x = \pi/2$ to $x = \pi$: (2022)

    (A) 1

    (B) 2

    (C) 0

    (D) 1/2

51. Area of the region bounded by $y = \cos x$ from $x = -\pi/2$ to $x = \pi/2$: (2021)

    (A) 2

    (B) 1

    (C) 0

    (D) 4

52. Area of the region bounded by $y = \sin^2 x$ from $x=0$ to $x=\pi$: (2019)

    (A) $\pi/2$

    (B) $\pi$

    (C) $2\pi$

    (D) $\pi/4$

53. Area of the region bounded by $y = \cos^2 x$ from $x=0$ to $x=\pi$: (2019)

    (A) $\pi/2$

    (B) $\pi$

    (C) $2\pi$

    (D) $\pi/4$

54. Area of the region bounded by $y = \tan^2 x, x=0, x=\pi/4$: (2015)

    (A) $1 – \pi/4$

    (B) $\pi/4 – 1$

    (C) $1 + \pi/4$

    (D) $\pi/2$

55. Area of the region bounded by $y = \sin x + \cos x, x=0, x=\pi/2$: (2021)

    (A) 2

    (B) 1

    (C) $\sqrt{2}$

    (D) 0

56. Area of the region bounded by $y = \sin 3x, x=0, x=\pi/6$: (2023)

    (A) 1/3

    (B) 1

    (C) 3

    (D) 0

57. Area of the region bounded by $y = \cos x$ from $x=0$ to $x=2\pi$: (2020)

    (A) 4

    (B) 0

    (C) 2

    (D) 1

58. Area of the region bounded by $y = \sin x, y = \cos x$ and y-axis: (2023)

    (A) $\sqrt{2}-1$

    (B) $\sqrt{2}+1$

    (C) 1

    (D) 2

59. Area of the region bounded by $y = \sin 2x, x=0, x=\pi/2$: (2024)

    (A) 1

    (B) 2

    (C) 0

    (D) 1/2

60. Area of the region bounded by $y = |\sin x|$ from $x=0$ to $x=2\pi$: (2021)

    (A) 4

    (B) 0

    (C) 2

    (D) 1

Topic 4: Area of Polynomials and Linear Equations

61. Area of the region bounded by $y = x^2, x=1, x=2$ and x-axis: (2021)

    (A) 7/3

    (B) 8/3

    (C) 5/3

    (D) 2/3

62. Area of the region bounded by $y = x^3, x=1, x=2$ and x-axis: (2024)

    (A) 15/4

    (B) 17/4

    (C) 19/4

    (D) 13/4

63. Area of the region bounded by $y = 3x+2, x=0, x=2$ and x-axis: (2024)

    (A) 10

    (B) 12

    (C) 8

    (D) 14

64. Area of the region bounded by $y = x, y=0, x=5$: (2024)

    (A) 12.5

    (B) 25

    (C) 10

    (D) 5

65. Area of the region bounded by $y = 2x, x=0, x=3$: (2023)

    (A) 9

    (B) 18

    (C) 6

    (D) 12

66. Area of the region bounded by $y = x^4, x=1, x=2$: (2021)

    (A) 31/5

    (B) 32/5

    (C) 63/5

    (D) 7/5

67. Area of the region bounded by $y = |x|, x=-1, x=1$: (2021)

    (A) 1

    (B) 2

    (C) 1/2

    (D) 0

68. Area of the region bounded by $y = x^2$ and $y=x$: (2023)

    (A) 1/6

    (B) 1/3

    (C) 1/2

    (D) 2/3

69. Area of the region bounded by $y = x^3, x=-2, x=1$: (2018)

    (A) 17/4

    (B) 15/4

    (C) 19/4

    (D) 1

70. Area of the region bounded by $y = \sqrt{x}, x=1, x=4$: (2022)

    (A) 14/3

    (B) 7/3

    (C) 28/3

    (D) 16/3

71. Area of the region bounded by $y = 4-x^2, x=0, x=2$: (2024)

    (A) 16/3

    (B) 8/3

    (C) 4/3

    (D) 20/3

72. Area of the region bounded by $y = x, y=0, x=2, x=4$: (2024)

    (A) 6

    (B) 8

    (C) 4

    (D) 12

73. Area of the region bounded by $y = 3x^2, x=1, x=2$: (2024)

    (A) 7

    (B) 14

    (C) 21

    (D) 9

74. Area of the region bounded by $y = 2\sqrt{x}, x=0, x=1$: (2024)

    (A) 4/3

    (B) 2/3

    (C) 8/3

    (D) 1

75. Area of the region bounded by $y = x|x|, x=-1, x=1$: (2022)

    (A) 2/3

    (B) 1/3

    (C) 1

    (D) 0

76. Area of the region bounded by $y = x^2+1, x=0, x=1$: (2024)

    (A) 4/3

    (B) 2/3

    (C) 5/3

    (D) 1

77. Area of the region bounded by $y = 5x, x=1, x=3$: (2021)

    (A) 20

    (B) 10

    (C) 40

    (D) 15

78. Area of the region bounded by $y = \sqrt{x}$ and $y = x$: (2017)

    (A) 1/6

    (B) 1/3

    (C) 2/3

    (D) 1

79. Area of the region bounded by $y = 1/x^2, x=1, x=2$: (2024)

    (A) 1/2

    (B) 1/3

    (C) 1/4

    (D) 1

80. Area of the region bounded by $y = x^2, y=0, x=1, x=3$: (2023)

    (A) 26/3

    (B) 28/3

    (C) 9

    (D) 8

Topic 5: Exponential and Logarithmic Areas

81. Area of the region bounded by $y = e^x, x=0, x=1$: (2024)

    (A) $e-1$

    (B) $e$

    (C) $e+1$

    (D) 1

82. Area of the region bounded by $y = \log x, x=1, x=e$: (2021)

    (A) 1

    (B) $e$

    (C) $e-1$

    (D) $1/e$

83. Area of the region bounded by $y = 1/x, x=1, x=e$: (2024)

    (A) 1

    (B) $e$

    (C) $1/e$

    (D) $\log e$

84. Area of the region bounded by $y = e^{2x}, x=0, x=1$: (2024)

    (A) $(e^2-1)/2$

    (B) $e^2-1$

    (C) $e^2/2$

    (D) 1

85. Area of the region bounded by $y = e^{-x}, x=0, x=1$: (2022)

    (A) $1 – 1/e$

    (B) $1/e$

    (C) $e-1$

    (D) 1

86. Area of the region bounded by $y = 2^x, x=0, x=1$: (2024)

    (A) $1/\log 2$

    (B) $\log 2$

    (C) $2/\log 2$

    (D) $2 \log 2$

87. Area of the region bounded by $y = 1/x, x=e, x=e^2$: (2023)

    (A) 1

    (B) 2

    (C) $e$

    (D) $\log 2$

88. Area of the region bounded by $y = e^x, y = e^{-x}$ and $x = 1$: (2024)

    (A) $e + 1/e – 2$

    (B) $e – 1/e$

    (C) $e + 1/e$

    (D) 2

89. Area of the region bounded by $y = \log x$ and $x = e$ and x-axis: (2021)

    (A) 1

    (B) $e-1$

    (C) $e$

    (D) $1/e$

90. Area of the region bounded by $y = e^{x/2}, x=0, x=2$: (2024)

    (A) $2(e-1)$

    (B) $e-1$

    (C) $2e$

    (D) 1

Topic 6: Area of Modulus and Intersection Curves

91. Area of the region bounded by $y = |x-1|, x=0, x=2$: (2022)

    (A) 1

    (B) 2

    (C) 1/2

    (D) 4

92. Area of the region bounded by $y = |x-2|, x=1, x=3$: (2022)

    (A) 1

    (B) 2

    (C) 1/2

    (D) 0

93. Area of the region bounded by $y = |x+3|, x=-6, x=0$: (2023)

    (A) 9

    (B) 18

    (C) 4.5

    (D) 0

94. Area of the region bounded by $y = x^2$ and $y = |x|$: (2018)

    (A) 1/3

    (B) 2/3

    (C) 1/6

    (D) 1

95. Area of the region bounded by $y = x^2$ and $y=x^3$: (2019)

    (A) 1/12

    (B) 1/6

    (C) 1/3

    (D) 1/4

96. Area of the region bounded by $y = x$ and $y=x^2$: (2023)

    (A) 1/6

    (B) 1/3

    (C) 1/2

    (D) 2/3

97. Area of the region bounded by $y = \sqrt{x}$ and $y=x$: (2017)

    (A) 1/6

    (B) 1/3

    (C) 2/3

    (D) 1

98. Area of the region bounded by $y^2=x$ and $y=x$: (2019)

    (A) 1/6

    (B) 1/3

    (C) 2/3

    (D) 1/2

99. Area of the region bounded by $y^2=4x$ and $y=x$: (2020)

    (A) 8/3

    (B) 4/3

    (C) 16/3

    (D) 2/3

100. Area of the region bounded by $y = x^2+2, y=x, x=0, x=3$: (2021)

     (A) 21/2

     (B) 15/2

     (C) 33/2

     (D) 12

Topic 7: Area Bounded by Coordinate Axes and Random Curves

101. Area of the region bounded by $x = 2y – y^2$ and y-axis: (2014)

     (A) 4/3

     (B) 2/3

     (C) 1/3

     (D) 1

102. Area of the region bounded by $y = 2x – x^2$ and x-axis: (2013)

     (A) 4/3

     (B) 2/3

     (C) 1/3

     (D) 1

103. Area of the triangle with vertices $(0,0), (4,0), (0,3)$: (2012)

     (A) 6

     (B) 12

     (C) 4

     (D) 3

104. Area of the region bounded by $y = \sqrt{x-1}, x=5, y=0$: (2023)

     (A) 16/3

     (B) 8/3

     (C) 4/3

     (D) 32/3

105. Area of the region bounded by $x = y^2, y=1, y=2$: (2023)

     (A) 7/3

     (B) 14/3

     (C) 8/3

     (D) 5/3

106. Area of the region bounded by $y = x^3$ and $y = x$: (2020)

     (A) 1/2

     (B) 1/4

     (C) 1

     (D) 0

107. Area of the region bounded by $y = 4x-x^2$ and x-axis: (2018)

     (A) 32/3

     (B) 16/3

     (C) 64/3

     (D) 8/3

108. Area of the region bounded by $y = x^2 – 4$ and x-axis: (2016)

     (A) 32/3

     (B) 16/3

     (C) 8/3

     (D) 64/3

109. Area of the region bounded by $y = 3\sqrt{x}, x=1, x=4$: (2023)

     (A) 14

     (B) 7

     (C) 21

     (D) 28

110. Area of the region bounded by $y = \sin x, y = \cos x, x=0, x=\pi/2$: (2021)

     (A) $2\sqrt{2}-2$

     (B) $\sqrt{2}$

     (C) 2

     (D) 1

111. Area of the region bounded by $y = x^2, y=x+2$: (2018)

     (A) 9/2

     (B) 4/3

     (C) 7/2

     (D) 1/6

112. Area of the region bounded by $x^2 = 16y, y=4$: (2022)

     (A) 128/3

     (B) 64/3

     (C) 256/3

     (D) 32/3

113. Area of the region bounded by $y^2 = 8x, y=2x$: (2020)

     (A) 4/3

     (B) 2/3

     (C) 1/3

     (D) 8/3

114. Area of the region bounded by $y = e^x, y=0, x=0, x=\log 2$: (2024)

     (A) 1

     (B) 2

     (C) $e-1$

     (D) $\log 2$

115. Area of the region bounded by $y = x, y=0, x=3$: (2024)

     (A) 4.5

     (B) 9

     (C) 3

     (D) 6

116. Area of the region bounded by $y = x^2, y=1$: (2021)

     (A) 4/3

     (B) 2/3

     (C) 1/3

     (D) 8/3

117. Area of the region bounded by $y = x^3-x$ and x-axis: (2018)

     (A) 1/2

     (B) 1/4

     (C) 1

     (D) 0

118. Area of the region bounded by $y^2 = 4x, y = 4$: (2022)

     (A) 16/3

     (B) 8/3

     (C) 32/3

     (D) 4

119. Area of the region bounded by $x^2 = 4y, y=1$: (2022)

     (A) 8/3

     (B) 4/3

     (C) 16/3

     (D) 2/3

120. Area of the region bounded by $y = |x|, y=1$: (2022)

     (A) 1

     (B) 2

     (C) 1/2

     (D) 0

Topic 8: Mixed Advanced/Revision MCQs

121. Area of the region bounded by $y = 3x^2+1, x=0, x=2$: (2023)

     (A) 10

     (B) 8

     (C) 12

     (D) 9

122. Area of the region bounded by $y = \cos x, x=0, x=2\pi$: (2020)

     (A) 4

     (B) 0

     (C) 2

     (D) 1

123. Area of the region bounded by $y^2=x^3, x=1$: (2017)

     (A) 4/5

     (B) 2/5

     (C) 8/5

     (D) 1

124. Area of the region bounded by $y = 4x^3, x=1, x=2$: (2023)

     (A) 15

     (B) 16

     (C) 14

     (D) 20

125. Area of the region bounded by $y = \sec^2 x, x=0, x=\pi/3$: (2019)

     (A) $\sqrt{3}$

     (B) 1

     (C) $1/\sqrt{3}$

     (D) $\sqrt{3}/2$

126. Area of the region bounded by $y = 1/x, x=1, x=2$: (2021)

     (A) $\log 2$

     (B) $\log 1$

     (C) $1/2$

     (D) 2

127. Area of the region bounded by $y = \sin 2x, x=0, x=\pi/2$: (2024)

     (A) 1

     (B) 2

     (C) 0

     (D) 1/2

128. Area of the region bounded by $y = x, x=2, x=4$: (2024)

     (A) 6

     (B) 12

     (C) 8

     (D) 4

129. Area of the region bounded by $y = \cos x, x=\pi/2, x=\pi$: (2018)

     (A) 1

     (B) 2

     (C) 0

     (D) 1/2

130. Area of the ellipse $x^2/16 + y^2/9 = 1$: (2024)

     (A) $12\pi$

     (B) $144\pi$

     (C) $25\pi$

     (D) $7\pi$

131. Area of the region bounded by $y^2 = 4ax$ and $x = a$: (2019)

     (A) $8a^2/3$

     (B) $4a^2/3$

     (C) $16a^2/3$

     (D) $2a^2/3$

132. Area of the region bounded by $y = |x|, x=-2, x=2$: (2021)

     (A) 4

     (B) 2

     (C) 8

     (D) 0

133. Area of the region bounded by $y = x^2, y=4x$: (2019)

     (A) 32/3

     (B) 16/3

     (C) 8/3

     (D) 64/3

134. Area of the region bounded by $y = \sin x, x=0, x=\pi/4$: (2024)

     (A) $1 – 1/\sqrt{2}$

     (B) $1/\sqrt{2}$

     (C) 1

     (D) 1/2

135. Area of the region bounded by $y = 1+x^2, x=0, x=1$: (2024)

     (A) 4/3

     (B) 2/3

     (C) 5/3

     (D) 1

136. Area of the region bounded by $y = \log x, x=1, x=2$: (2022)

     (A) $2\log 2 – 1$

     (B) $\log 2$

     (C) $2\log 2 + 1$

     (D) 1

137. Area of the region bounded by $y = x^2, y=x^3$ in 1st quadrant: (2019)

     (A) 1/12

     (B) 1/6

     (C) 1/3

     (D) 1/4

138. Area of the region bounded by $y = x^2$ and $x = y^2$: (2018)

     (A) 1/3

     (B) 2/3

     (C) 1/6

     (D) 1

139. Area of the region bounded by $y = \cos 2x, x=0, x=\pi/2$: (2024)

     (A) 0

     (B) 1

     (C) 2

     (D) 1/2

140. Area of the region bounded by $y = 4x^2, y=1, y=4$: (2022)

     (A) 7/3

     (B) 14/3

     (C) 28/3

     (D) 4/3

141. Area of the region bounded by $y = |x-1|, y=0, x=0, x=2$: (2022)

     (A) 1

     (B) 2

     (C) 1/2

     (D) 4

142. Area of the region bounded by $y = \sin x + \cos x, x=0, x=\pi/2$: (2024)

     (A) 2

     (B) 1

     (C) $\sqrt{2}$

     (D) 0

143. Area of the region bounded by $y = 2x, x=0, x=5$: (2024)

     (A) 25

     (B) 50

     (C) 10

     (D) 15

144. Area of the region bounded by $y = \cos x, y = \sin x, x=\pi/4, x=\pi/2$: (2023)

     (A) $\sqrt{2}-1$

     (B) $\sqrt{2}+1$

     (C) 1

     (D) $\sqrt{2}$

145. Area of the region bounded by $y = \sqrt{a^2-x^2}$ from $x = a/\sqrt{2}$ to $x = a$: (2021)

     (A) $\frac{a^2}{4}(\pi/2 – 1)$

     (B) $\pi a^2/4$

     (C) $a^2/2$

     (D) $a^2$

146. Area of the region bounded by $y = x^2, x = 0, y = 4$: (2023)

     (A) 16/3

     (B) 8/3

     (C) 4/3

     (D) 32/3

147. Area of the region bounded by $y = \log_e x, y = 0, x = e$: (2021)

     (A) 1

     (B) $e$

     (C) $e-1$

     (D) $1/e$

148. Area of the region bounded by $y = \sin x$ from $x = 0$ to $x = \pi/4$: (2024)

     (A) $1 – 1/\sqrt{2}$

     (B) $1/\sqrt{2}$

     (C) 1

     (D) 1/2

149. Area of the region bounded by $y^2 = 4ax$ and $y = mx$: (2017)

     (A) $8a^2/3m^3$

     (B) $4a^2/3m^2$

     (C) $8a^2/m^3$

     (D) $16a^2/3m^3$

150. Area of the region bounded by $x^2/9 + y^2/4 = 1$: (2024)

     (A) $6\pi$

     (B) $36\pi$

     (C) $13\pi$

     (D) $5\pi$