JEE Exam Most Repeated 100 Mathematics

   JEE  Exam  Most Repeated  100  Mathematics

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Are you preparing for the JEE Main or JEE Advanced exams? Boost your score with our curated list of the 100 most repeated Mathematics questions in JEE history. This essential resource is based on past papers, expert analysis, and question trends from the last 10+ years. Whether you're aiming for IITs or top NITs, these frequently asked questions will help you master key topics like Calculus, Algebra, Coordinate Geometry, and Trigonometry. Perfect for last-minute revision or focused practice, this guide is your shortcut to cracking the toughest math problems.

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🧮 JEE Exam Most Repeated 100 Mathematics Questions | Important JEE Maths Topics PDF

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📘 Introduction:

Mathematics in JEE (Main & Advanced) is a scoring yet challenging subject. Every year, several questions repeat either directly or with slight variations. Here is a carefully curated list of the 100 most repeated and important mathematics questions for JEE aspirants. These questions are based on pattern recognition and topic frequency from the last 10–15 years of JEE papers.

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🔢 Most Repeated 100 JEE Mathematics Questions

🧩 Algebra (20 Questions)

1. Solve for $x$ if $x^4 - 10x^2 + 9 = 0$

2. Find the roots of the equation $z^3 = 1$

3. If $A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$, find $A^{-1}$

4. Find the value of $\sum_{k=1}^{n} k^2$

5. If $f(x) = x^3 + 3x + 1$, find $f^{-1}(x)$ at $x = 2$

6. Let $z = x + iy$, find the modulus of $z = 3 - 4i$

7. Use De Moivre’s theorem to evaluate $(1 + i)^{10}$

8. Find the determinant of a 3x3 matrix with rows [1 2 3], [4 5 6], [7 8 9]

9. Solve $|x - 2| + |x + 3| = 7$

10. Let $a_n = 3^n + 4^n$, find a recurrence relation

11. Probability of getting exactly 2 heads in 3 tosses of a coin

12. Binomial expansion of $(1 + 2x)^5$

13. Find the sum of an infinite GP with $a = 3, r = 1/2$

14. Find the condition for consistency in a system of linear equations

15. Find the rank of matrix $A = \begin{bmatrix} 1 & 2 \\ 2 & 4 \end{bmatrix}$

16. Roots of cubic equation $x^3 - 6x^2 + 11x - 6 = 0$

17. Evaluate the determinant $\begin{vmatrix} 1 & 0 & 2 \\ 0 & 3 & 0 \\ 4 & 0 & 1 \end{vmatrix}$

18. Find the number of real solutions of $\log(x^2 + 1) = 0$

19. Find $n$ such that $\binom{n}{2} = 28$

20. Find the inverse of a 2x2 matrix using adjoint method

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📐 Calculus (25 Questions)

21. Differentiate $y = \sin^{-1}(x) + \cos^{-1}(x)$

22. Evaluate $\lim_{x \to 0} \frac{\sin x}{x}$

23. Find the derivative of $e^{x^2}$

24. Find $\frac{dy}{dx}$ if $y = x^x$

25. Evaluate $\int_{0}^{\pi/2} \sin x \, dx$

26. Find the area between curves $y = x^2$ and $y = x$

27. Test the continuity of $f(x) = \frac{|x|}{x}$

28. Find the slope of tangent to $y = \ln x$ at $x = 1$

29. Evaluate $\int x \ln x \, dx$

30. Find maxima and minima of $f(x) = x^3 - 3x$

31. Apply L’Hôpital’s Rule to evaluate $\lim_{x \to 0} \frac{e^x - 1}{x}$

32. Evaluate $\int \frac{dx}{\sqrt{1 - x^2}}$

33. Find $\frac{d^2y}{dx^2}$ if $y = \tan^{-1}(x)$

34. Evaluate definite integral $\int_{1}^{e} \frac{1}{x} dx$

35. Solve the differential equation $\frac{dy}{dx} = x + y$

36. If $f(x)$ is differentiable, prove $f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$

37. Find the derivative of $\tan^{-1} \left( \frac{2x}{1 - x^2} \right)$

38. Evaluate $\int_0^{\pi} |\sin x| dx$

39. Find point of inflection for $y = x^3$

40. Find $\int \frac{1}{x^2 + 1} dx$

41. Evaluate $\int \frac{dx}{x^2 - 1}$

42. Solve $\frac{dy}{dx} + y = e^x$

43. Prove Rolle’s theorem for $f(x) = x(x-1)(x-2)$ on [0,2]

44. Find length of curve $y = x^2$ from 0 to 1

45. Apply Mean Value Theorem to $f(x) = x^2$ on [1,3]

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📏 Coordinate Geometry (20 Questions)

46. Find the equation of a line with slope 2 passing through (1,3)

47. Equation of circle with center (2, -1) and radius 3

48. Find the intersection point of lines $y = 2x + 1$ and $y = -x + 4$

49. Find angle between lines $y = m_1x + c_1$ and $y = m_2x + c_2$

50. Locus of a point equidistant from point and line

51. Find the coordinates of centroid of triangle with vertices A(1,2), B(3,4), C(5,0)

52. Equation of ellipse with major axis along x-axis

53. Find the focus and directrix of parabola $y^2 = 4ax$

54. Find the eccentricity of the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$

55. Distance from point to line

56. Tangent to a parabola $y^2 = 4ax$ at a point

57. Equation of hyperbola centered at origin

58. Circle passing through 3 given points

59. Reflection of a point across a line

60. Equation of pair of straight lines passing through origin

61. Find foot of perpendicular from a point to a line

62. Length of chord in a circle cut by a line

63. Condition for tangency of line to a circle

64. Director circle of a hyperbola

65. Angle between radius and tangent in a circle

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📊 Vectors & 3D Geometry (15 Questions)

66. Dot product of vectors $\vec{a} \cdot \vec{b}$

67. Find cross product of $\vec{i} + \vec{j}$ and $\vec{j} + \vec{k}$

68. Find angle between two vectors

69. Scalar triple product of three vectors

70. Vector projection of one vector onto another

71. Find unit vector perpendicular to two given vectors

72. Find equation of a plane passing through a point and normal to a vector

73. Distance between two skew lines

74. Equation of line passing through two points

75. Find shortest distance between two lines

76. Direction cosines of a line

77. Angle between line and plane

78. Find image of a point in a plane

79. Intersection of line and plane

80. Equation of sphere with given center and radius

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🔢 Trigonometry, Statistics & Misc (20 Questions)

81. Find general solution of $\sin x = 1/2$

82. Prove $\cos(A + B) = \cos A \cos B - \sin A \sin B$

83. Convert from degrees to radians

84. Find the value of $\tan^{-1}(1) + \cot^{-1}(1)$

85. If $\sin A = 3/5$, find $\cos A$

86. Height and distance problem involving angle of elevation

87. Find mean and standard deviation of given data

88. Use sine rule to find unknown side of triangle

89. Use cosine rule to find angle of triangle

90. Find maximum value of $\sin x + \cos x$

91. Solve triangle given 3 sides

92. Express $a \sin x + b \cos x$ in the form $R \sin(x + \alpha)$

93. Find median of data set

94. Use Bayes’ Theorem to find conditional probability

95. Circular permutations of 5 people

96. Find number of ways to arrange letters of “SUCCESS”

97. Use binomial probability to solve coin problem

98. Determine angle between two sides using vector approach

99. Logarithmic identity question: $\log(ab) = \log a + \log b$

100. Application of AM ≥ GM inequality

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