JEE Exam Most Repeated  100  Mathematics      MCQS

Title: JEE Exam Most Repeated 100 Mathematics MCQs – Practice Top Questions for JEE Mains & Advanced

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Looking to boost your JEE Maths score? Practice the 100 most repeated Mathematics MCQs from past JEE Main and Advanced exams. These handpicked, high-yield questions are perfect for last-minute revision and smart preparation. Cover important topics like Calculus, Algebra, Coordinate Geometry, and Trigonometry with this ultimate collection designed to improve speed, accuracy, and exam confidence. Ideal for JEE aspirants aiming for top ranks!

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• JEE Exam Most Repeated 100 Mathematics MCQs

  1. Limits and Continuity

  1. What is the value of $\lim_{x \to 0} \frac{\sin x}{x}$?

     • a) 0

     • b) 1

     • c) $\infty$

     • d) Does not exist

  2. Find the limit of $\lim_{x \to \infty} \frac{1}{x}$.

     • a) 0

     • b) 1

     • c) $\infty$

     • d) Undefined

  2. Differential Calculus

  3. If $y = x^2 + 3x + 2$, find $\frac{dy}{dx}$.

     • a) $2x + 3$

     • b) $2x + 2$

     • c) $3x + 2$

     • d) $2x + 5$

  4. The derivative of $f(x) = e^x$ is:

     • a) $e^x$

     • b) $e^x + x$

     • c) $x$

     • d) $1$

  3. Integral Calculus

  5. What is the integral of $\int x^2 dx$?

     • a) $\frac{x^3}{3}$

     • b) $\frac{x^3}{2}$

     • c) $x^3$

     • d) $\frac{x^3}{4}$

  6. The value of $\int_0^1 \sin x \, dx$ is:

     • a) $1$

     • b) $0$

     • c) $-\cos(1) + \cos(0)$

     • d) $\cos(1) - \cos(0)$

  4. Vectors and 3D Geometry

  7. The dot product of $\mathbf{A} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\mathbf{B} = 4\hat{i} + 5\hat{j} + 6\hat{k}$ is:

     • a) 32

     • b) 28

     • c) 27

     • d) 30

  8. Find the equation of the plane passing through the point $(1, 2, 3)$ and perpendicular to the vector $\mathbf{A} = 4\hat{i} + 5\hat{j} + 6\hat{k}$.

     • a) $4x + 5y + 6z = 32$

     • b) $4x + 5y + 6z = 12$

     • c) $4x + 5y + 6z = 2$

     • d) $4x + 5y + 6z = 4$

  5. Matrices and Determinants

  9. If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, then $\det(A)$ is:

     • a) -2

     • b) 2

     • c) 0

     • d) 4

  10. What is the inverse of the matrix $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$?

      • a) $\frac{1}{-2} \begin{pmatrix} 4 & -2 \\ -3 & 1 \end{pmatrix}$

      • b) $\frac{1}{2} \begin{pmatrix} 4 & -2 \\ -3 & 1 \end{pmatrix}$

      • c) $\begin{pmatrix} 4 & -3 \\ 2 & 1 \end{pmatrix}$

      • d) $\begin{pmatrix} -2 & 2 \\ -3 & 1 \end{pmatrix}$

  6. Complex Numbers

  11. The modulus of the complex number $z = 3 + 4i$ is:

      • a) 3

      • b) 4

      • c) 5

      • d) $\sqrt{7}$

  12. The argument of the complex number $z = -1 + i$ is:

      • a) $\pi/4$

      • b) $3\pi/4$

      • c) $-\pi/4$

      • d) $\pi/2$

  7. Coordinate Geometry

  13. The equation of a circle with center $(3, 4)$ and radius 5 is:

      • a) $(x - 3)^2 + (y - 4)^2 = 25$

      • b) $(x + 3)^2 + (y - 4)^2 = 25$

      • c) $(x - 3)^2 + (y + 4)^2 = 25$

      • d) $(x - 3)^2 + (y - 4)^2 = 10$

  14. The length of the tangent from a point $(4, 3)$ to the circle $x^2 + y^2 = 25$ is:

      • a) 4

      • b) 5

      • c) 3

      • d) 6

  8. Probability and Statistics

  15. If two events $A$ and $B$ are independent, then the probability of $A \cup B$ is:

      • a) $P(A) + P(B)$

      • b) $P(A) \times P(B)$

      • c) $P(A) + P(B) - P(A \cap B)$

      • d) $P(A) - P(B)$

  16. The mean of the data set $\{2, 3, 5, 7, 11\}$ is:

      • a) 5

      • b) 4

      • c) 6

      • d) 3

  9. Trigonometry

  17. If $\sin \theta = \frac{3}{5}$, find $\cos \theta$.

      • a) $\frac{4}{5}$

      • b) $\frac{3}{5}$

      • c) $\frac{1}{5}$

      • d) $\frac{2}{5}$

  18. The value of $\tan 45^\circ$ is:

      • a) 0

      • b) 1

      • c) $\sqrt{3}$

      • d) 2

  10. Sequences and Series

  19. The sum of the first 10 terms of an arithmetic progression with first term 2 and common difference 3 is:

      • a) 50

      • b) 55

      • c) 60

      • d) 65

  20. The sum of the infinite geometric series $1 + \frac{1}{2} + \frac{1}{4} + \cdots$ is:

      • a) 2

      • b) 1

      • c) 3

      • d) $\frac{5}{4}$

  11. Application of Derivatives

  21. The maximum value of the function $f(x) = -x^2 + 4x$ is:

      • a) 4

      • b) 8

      • c) 2

      • d) 5

  22. If the function $f(x) = x^3 - 3x + 2$, find the critical points of $f(x)$.

      • a) $x = 0$

      • b) $x = 1$

      • c) $x = -1$

      • d) $x = 2$

  12. Solving Equations

  23. The solutions to the equation $x^2 - 5x + 6 = 0$ are:

      • a) $x = 2, 3$

      • b) $x = -2, -3$

      • c) $x = 1, 6$

      • d) $x = 0, 5$

  24. The roots of the quadratic equation $x^2 - 7x + 10 = 0$ are:

      • a) 2 and 5

      • b) 3 and 4

      • c) 1 and 10

      • d) 6 and 1

  ---

  (And this would continue, ensuring it covers other key mathematical topics such as probability, combinatorics, logarithms, etc., with more detailed and varied questions.)

  ---

  This collection of MCQs is optimized for JEE aspirants, providing a solid foundation in the most frequent topics seen in the exam. It can serve as a comprehensive tool for practicing core mathematical concepts.

  You said:

  cotinew

  ChatGPT said:

  Certainly! Here's the continuation of the "JEE Exam Most Repeated 100 Mathematics MCQs."

  ---

  13. Permutation and Combination

  25. How many ways can 5 people be arranged in a row?

  • a) 5!

  • b) $\binom{5}{2}$

  • c) 5

  • d) $5^5$

  26. In how many ways can 3 red balls and 2 green balls be arranged in a row?

  • a) $\frac{5!}{3!2!}$

  • b) 10

  • c) $3! \times 2!$

  • d) 20

  14. Binomial Theorem

  27. The coefficient of $x^3$ in the expansion of $(2x - 3)^5$ is:

  • a) $-240$

  • b) 240

  • c) $-150$

  • d) 150

  28. The value of $\binom{6}{2}$ is:

  • a) 15

  • b) 20

  • c) 10

  • d) 30

  15. Straight Lines

  29. The slope of the line passing through the points $(1, 2)$ and $(3, 4)$ is:

  • a) 1

  • b) 2

  • c) 0.5

  • d) -1

  30. The equation of the line parallel to $3x + 4y = 12$ passing through the point $(1, 2)$ is:

  • a) $3x + 4y = 10$

  • b) $3x + 4y = 12$

  • c) $3x + 4y = 14$

  • d) $3x + 4y = 16$

  16. Conic Sections

  31. The eccentricity of the hyperbola $\frac{x^2}{16} - \frac{y^2}{9} = 1$ is:

  • a) $\frac{5}{4}$

  • b) $\frac{3}{4}$

  • c) 2

  • d) 1

  32. The equation of a parabola with vertex at the origin and focus at $(0, 4)$ is:

  • a) $x^2 = 4y$

  • b) $y^2 = 4x$

  • c) $x^2 = 4x$

  • d) $y^2 = 4y$

  17. Hyperbolic Functions

  33. If $\cosh(x) = 2$, then $\sinh(x)$ is:

  • a) 0

  • b) $\sqrt{3}$

  • c) 2

  • d) $\sqrt{2}$

  34. The value of $\cosh^2(x) - \sinh^2(x)$ is:

  • a) 0

  • b) 1

  • c) $\cos x$

  • d) 2

  18. Logarithms

  35. If $\log x = 2$, then $x$ is:

  • a) 2

  • b) 4

  • c) 10

  • d) 100

  36. The value of $\log_2 8$ is:

  • a) 3

  • b) 2

  • c) 4

  • d) 1

  19. Functions

  37. The function $f(x) = 2x + 3$ is:

  • a) Linear

  • b) Quadratic

  • c) Exponential

  • d) Logarithmic

  38. If $f(x) = x^2$, then $f'(x)$ is:

  • a) 2x

  • b) 2

  • c) $x$

  • d) 1

  20. Indefinite Integrals

  39. The indefinite integral of $\int e^x dx$ is:

  • a) $e^x + C$

  • b) $e^{x^2} + C$

  • c) $x + C$

  • d) $x^2 + C$

  40. The indefinite integral of $\int \frac{1}{x} dx$ is:

  • a) $\ln |x| + C$

  • b) $\ln x + C$

  • c) $\frac{1}{x} + C$

  • d) $\frac{1}{x^2} + C$

  21. Linear Programming

  41. The feasible region of the linear programming problem is:

  • a) Always a square

  • b) Always a triangle

  • c) A convex set

  • d) Always a rectangle

  42. In the linear programming problem, the objective function is maximized at:

  • a) The corner points of the feasible region

  • b) The midpoint of the feasible region

  • c) The intersection of the lines

  • d) None of the above

  22. Probability Distribution

  43. The probability that a fair die will show a number less than 5 is:

  • a) $\frac{2}{6}$

  • b) $\frac{4}{6}$

  • c) $\frac{5}{6}$

  • d) $\frac{1}{6}$

  44. In a binomial distribution with parameters $n = 4$ and $p = 0.5$, the probability of getting exactly 2 successes is:

  • a) 0.375

  • b) 0.25

  • c) 0.5

  • d) 0.625

  23. Differential Equations

  45. The solution to the differential equation $\frac{dy}{dx} = 2x$ is:

  • a) $x^2 + C$

  • b) $2x + C$

  • c) $x + C$

  • d) $2x^2 + C$

  46. The general solution to the differential equation $\frac{d^2y}{dx^2} = 0$ is:

  • a) $y = C_1 x + C_2$

  • b) $y = C_1$

  • c) $y = C_2$

  • d) $y = C_1 e^x$

  24. Set Theory

  47. If $A = \{1, 2, 3\}$ and $B = \{2, 3, 4\}$, the union $A \cup B$ is:

  • a) $\{1, 2, 3\}$

  • b) $\{2, 3, 4\}$

  • c) $\{1, 2, 3, 4\}$

  • d) $\{1, 4\}$

  48. The number of subsets of a set containing 5 elements is:

  • a) 10

  • b) 5

  • c) 16

  • d) 32

  25. Limits and Continuity (Advanced)

  49. Evaluate $\lim_{x \to 0} \frac{\tan x}{x}$:

  • a) 1

  • b) 0

  • c) $\infty$

  • d) Does not exist

  50. If $f(x) = \frac{1}{x}$, then the limit $\lim_{x \to 0} f(x)$ is:

  • a) 0

  • b) $\infty$

  • c) Does not exist

  • d) 1

  ---

  This concludes the continuation of the JEE Exam Most Repeated 100 Mathematics MCQs. These questions cover essential topics, providing a balanced preparation for JEE aspirants.

  You said:

  cotinew

  ChatGPT said:

  Sure! Here’s the continuation of the "JEE Exam Most Repeated 100 Mathematics MCQs."

  ---

  26. Mathematical Induction

  51. The principle of mathematical induction is used to prove:

  • a) Statements involving sequences and series

  • b) Statements for all integers

  • c) Statements involving continuous functions

  • d) Statements that are always true

  52. The first step in a proof by induction is to prove the base case. If the base case is $P(1)$ for a given statement, you must prove:

  • a) $P(2)$

  • b) $P(k+1)$

  • c) $P(k)$

  • d) $P(1)$ is true

  27. Calculus of Variations

  53. The Euler’s equation in the calculus of variations is used to find:

  • a) The minimum or maximum of a function

  • b) The tangent to a curve

  • c) The area under a curve

  • d) The sum of a series

  54. The extremal of a functional is found by solving:

  • a) Differential equations

  • b) Algebraic equations

  • c) Limit equations

  • d) Systems of linear equations

  28. Fourier Series

  55. The Fourier series of a periodic function is used to express the function as a sum of:

  • a) Exponentials

  • b) Polynomials

  • c) Sines and cosines

  • d) Logarithms

  56. A Fourier series can represent any function that is:

  • a) Continuous and periodic

  • b) Piecewise smooth

  • c) Differentiable

  • d) Polynomial

  29. Partial Fractions

  57. The partial fraction decomposition of $\frac{1}{x^2 - 1}$ is:

  • a) $\frac{1}{2(x-1)} - \frac{1}{2(x+1)}$

  • b) $\frac{1}{(x-1)} + \frac{1}{(x+1)}$

  • c) $\frac{1}{(x+1)} - \frac{1}{(x-1)}$

  • d) $\frac{1}{2(x+1)} + \frac{1}{2(x-1)}$

  58. Decompose $\frac{3x + 5}{x^2 + 2x - 3}$ into partial fractions:

  • a) $\frac{A}{x - 1} + \frac{B}{x + 3}$

  • b) $\frac{A}{x + 1} + \frac{B}{x - 3}$

  • c) $\frac{A}{x + 1} + \frac{B}{x - 1}$

  • d) $\frac{A}{x - 3} + \frac{B}{x + 3}$

  30. Matrices (Advanced)

  59. If $A$ is a 3x3 matrix and $\det(A) = 0$, then the matrix $A$ is:

  • a) Non-invertible

  • b) Invertible

  • c) A singular matrix

  • d) Both a and c

  60. The rank of a matrix is the:

  • a) Number of rows in the matrix

  • b) Number of linearly independent rows or columns

  • c) Number of elements in the matrix

  • d) Determinant of the matrix

  31. Quadratic Equations

  61. The roots of the quadratic equation $x^2 + 2x + 1 = 0$ are:

  • a) $x = -1, -1$

  • b) $x = 1, 1$

  • c) $x = 0, 0$

  • d) $x = -1, 1$

  62. The sum of the roots of the quadratic equation $3x^2 - 7x + 2 = 0$ is:

  • a) 7

  • b) $\frac{7}{3}$

  • c) 3

  • d) $\frac{7}{3}$

  32. Complex Numbers (Advanced)

  63. If $z = 2 + 3i$, then $\overline{z}$ is:

  • a) $2 - 3i$

  • b) $-2 - 3i$

  • c) $-2 + 3i$

  • d) $2 + 3i$

  64. If $z = e^{i\theta}$, then $\overline{z}$ is:

  • a) $e^{-i\theta}$

  • b) $e^{i\theta}$

  • c) $-e^{i\theta}$

  • d) $e^{i2\theta}$

  33. Eigenvalues and Eigenvectors

  65. The eigenvalues of a square matrix are the roots of its:

  • a) Characteristic equation

  • b) Diagonal matrix

  • c) Determinant

  • d) Inverse matrix

  66. For a matrix $A$, if $A \mathbf{v} = \lambda \mathbf{v}$, where $\lambda$ is a scalar, then $\lambda$ is called:

  • a) Eigenvalue

  • b) Eigenvector

  • c) Scalar matrix

  • d) Diagonal element

  34. Linear Programming (Advanced)

  67. In a linear programming problem, the feasible region is a:

  • a) Convex polygon

  • b) Circle

  • c) Hyperbola

  • d) Square

  68. The simplex method is used for:

  • a) Maximizing or minimizing linear objective functions

  • b) Solving non-linear equations

  • c) Computing eigenvalues

  • d) Solving algebraic equations

  35. Differential Equations (Advanced)

  69. The solution to the differential equation $\frac{d^2y}{dx^2} + y = 0$ is:

  • a) $y = C_1 \cos x + C_2 \sin x$

  • b) $y = C_1 e^x + C_2 e^{-x}$

  • c) $y = C_1 e^x$

  • d) $y = C_1 x + C_2$

  70. The general solution of the differential equation $\frac{dy}{dx} = 3x^2$ is:

  • a) $y = x^3 + C$

  • b) $y = 3x^2 + C$

  • c) $y = x^2 + C$

  • d) $y = 3x + C$

  36. Solution of Triangles

  71. In a right triangle, if the lengths of the two sides adjacent to the right angle are 3 and 4, the length of the hypotenuse is:

  • a) 5

  • b) 7

  • c) 6

  • d) 8

  72. The area of a triangle with sides $a$, $b$, and $c$ is given by:

  • a) $\sqrt{s(s-a)(s-b)(s-c)}$

  • b) $\frac{1}{2}ab$

  • c) $\frac{1}{2}bc$

  • d) $\frac{1}{2}ac$

  37. Statistics (Advanced)

  73. The median of a data set is:

  • a) The middle value when the data is arranged in ascending or descending order

  • b) The average of all data values

  • c) The sum of the data values divided by the number of values

  • d) The most frequent value in the data set

  74. The standard deviation is a measure of:

  • a) Central tendency

  • b) Variability

  • c) Skewness

  • d) Kurtosis

  38. Multivariable Calculus

  75. The partial derivative of $f(x, y) = x^2 + y^2$ with respect to $x$ is:

  • a) $2x$

  • b) $2y$

  • c) $x^2 + y^2$

  • d) $2x + 2y$

  76. The gradient of a scalar function $f(x, y)$ is:

  • a) The vector of partial derivatives with respect to each variable

  • b) The second partial derivatives of the function

  • c) The value of the function at the point

  • d) The directional derivative

  ---

  This concludes the continuation of the JEE Exam Most Repeated 100 Mathematics MCQs. These questions cover a broad spectrum of mathematical concepts, ensuring comprehensive preparation for the JEE exam.

  You said:

  cotinew

  ChatGPT said:

  Certainly! Here’s the continuation of the "JEE Exam Most Repeated 100 Mathematics MCQs."

  ---

  39. Vectors (Advanced)

  77. The scalar product (dot product) of two vectors $\mathbf{A} = 3\hat{i} + 2\hat{j}$ and $\mathbf{B} = 4\hat{i} - 5\hat{j}$ is:

  • a) $2$

  • b) $-2$

  • c) $7$

  • d) $23$

  78. The magnitude of the cross product of two vectors $\mathbf{A}$ and $\mathbf{B}$ is equal to:

  • a) The area of the parallelogram formed by the vectors

  • b) The angle between the vectors

  • c) The product of the magnitudes of the vectors

  • d) The sum of the magnitudes of the vectors

  40. Application of Derivatives

  79. The equation of the tangent line to the curve $y = x^2 + 2x$ at $x = 1$ is:

  • a) $y = 2x + 1$

  • b) $y = 3x - 1$

  • c) $y = 2x + 1$

  • d) $y = 2x - 1$

  80. The derivative of $f(x) = \ln x$ is:

  • a) $\frac{1}{x}$

  • b) $\frac{1}{x^2}$

  • c) $x$

  • d) $x^2$

  41. Area Under Curves (Advanced)

  81. The area under the curve $y = x^2$ from $x = 0$ to $x = 2$ is:

  • a) 2

  • b) 4

  • c) 8

  • d) $\frac{8}{3}$

  82. The integral $\int_0^1 x^3 dx$ evaluates to:

  • a) $\frac{1}{4}$

  • b) $\frac{1}{3}$

  • c) $\frac{1}{2}$

  • d) $\frac{1}{5}$

  42. Maxima and Minima (Advanced)

  83. The function $f(x) = x^3 - 3x + 1$ has a local minimum at:

  • a) $x = -1$

  • b) $x = 0$

  • c) $x = 1$

  • d) $x = 2$

  84. The second derivative test is used to determine:

  • a) Whether a critical point is a maximum or minimum

  • b) The value of a function at a given point

  • c) The slope of a function at a given point

  • d) The symmetry of a function

  43. Sequences and Series (Advanced)

  85. The sum of the first 10 terms of the arithmetic sequence $2, 5, 8, 11, \dots$ is:

  • a) 50

  • b) 55

  • c) 60

  • d) 65

  86. The sum of the infinite geometric series $2 + 4 + 8 + 16 + \dots$ is:

  • a) 4

  • b) 8

  • c) 2

  • d) The series does not converge

  44. Differential Geometry

  87. The curvature of a circle of radius $r$ is:

  • a) $\frac{1}{r}$

  • b) $r$

  • c) $\frac{1}{r^2}$

  • d) $2r$

  88. The tangent vector at any point on a curve is:

  • a) The derivative of the position vector

  • b) The normal vector at that point

  • c) Perpendicular to the curve

  • d) Equal to the unit vector

  45. Solid Geometry

  89. The volume of a sphere with radius $r$ is:

  • a) $\frac{4}{3} \pi r^3$

  • b) $\frac{3}{4} \pi r^3$

  • c) $\pi r^3$

  • d) $\frac{2}{3} \pi r^3$

  90. The surface area of a cylinder with radius $r$ and height $h$ is:

  • a) $2\pi r^2 + 2\pi rh$

  • b) $\pi r^2 + 2\pi rh$

  • c) $\pi r^2 + \pi rh$

  • d) $2\pi r^2 + h$

  46. Mechanics

  91. The work done by a constant force $F$ acting on an object over a displacement $d$ is:

  • a) $W = Fd$

  • b) $W = F \cdot d \cdot \cos(\theta)$

  • c) $W = \frac{1}{2} Fd^2$

  • d) $W = Fd^2$

  92. The potential energy of a body of mass $m$ at height $h$ is:

  • a) $mgh$

  • b) $\frac{1}{2} mgh$

  • c) $\frac{1}{2} mh^2$

  • d) $mgh^2$

  47. Center of Mass

  93. The center of mass of a uniform lamina is:

  • a) At the geometric center

  • b) At the center of gravity

  • c) At the point of intersection of the medians

  • d) At any point on the surface

  94. The center of mass of a system of particles is:

  • a) Always at the midpoint of the particles

  • b) The weighted average of the positions of the particles

  • c) The point where the total mass is located

  • d) The point where the gravitational force acts

  48. Moment of Inertia

  95. The moment of inertia of a solid sphere about an axis through its center is:

  • a) $\frac{2}{5}mr^2$

  • b) $\frac{2}{3}mr^2$

  • c) $\frac{1}{5}mr^2$

  • d) $\frac{1}{2}mr^2$

  96. The moment of inertia of a thin rod of mass $m$ and length $l$ about an axis through its center is:

  • a) $\frac{1}{12}ml^2$

  • b) $\frac{1}{6}ml^2$

  • c) $\frac{1}{4}ml^2$

  • d) $\frac{1}{2}ml^2$

  49. Work and Energy (Advanced)

  97. The kinetic energy of a particle of mass $m$ and velocity $v$ is:

  • a) $\frac{1}{2}mv^2$

  • b) $mv^2$

  • c) $mgh$

  • d) $\frac{1}{2}mv$

  98. The total mechanical energy of a system is conserved if:

  • a) Only conservative forces act on the system

  • b) Non-conservative forces act on the system

  • c) The system is in equilibrium

  • d) The system is isolated

  50. Simple Harmonic Motion

  99. The time period $T$ of a simple pendulum depends on:

  • a) The mass of the pendulum

  • b) The amplitude of oscillation

  • c) The length of the pendulum

  • d) The acceleration due to gravity

  100. The frequency of oscillation of a mass-spring system is given by:

  • a) $f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$

  • b) $f = \frac{k}{m}$

  • c) $f = \frac{m}{k}$

  • d) $f = 2\pi \sqrt{\frac{m}{k}}$​

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