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#	Question	Subject and topic	Difficulty
1	What is the derivative of x² at x = 3?	Mathematics/Applied Mathematics Second-order derivatives	Easy
2	∫ 2x dx is equal to:	Mathematics/Applied Mathematics Indefinite integrals	Easy
3	Two fair dice are thrown. What is the probability that the sum is 7?	Mathematics/Applied Mathematics Conditional probability	Medium
4	What is the value of the determinant of the matrix [[2, 3], [1, 4]]?	Mathematics/Applied Mathematics Determinants	Easy
5	If f(x) = 2x + 3, what is f⁻¹(7)?	Mathematics/Applied Mathematics Types of functions	Medium
6	How many elements are in the power set of a set with 3 elements?	Mathematics/Applied Mathematics Types of relations	Easy
7	On A = {1, 2, 3}, the relation R = {(1, 1), (2, 2), (3, 3), (1, 2)} is	Mathematics/Applied Mathematics Types of relations	Easy
8	How many relations can be defined on a set with 2 elements?	Mathematics/Applied Mathematics Types of relations	Easy
9	On the set of integers, a R b means 5 divides a − b. Which set is the equivalence class of 2?	Mathematics/Applied Mathematics Types of relations	Medium
10	The relation "line l₁ is perpendicular to line l₂" on the set of all lines in a plane is	Mathematics/Applied Mathematics Types of relations	Medium
11	How many equivalence relations on {1, 2, 3} contain the pair (1, 2)?	Mathematics/Applied Mathematics Types of relations	Hard
12	The function f : R → R given by f(x) = 2x + 3 is	Mathematics/Applied Mathematics Types of functions	Easy
13	The function f : R → R defined by f(x) = x² is	Mathematics/Applied Mathematics Types of functions	Easy
14	If f : R → R is defined by f(x) = 3x − 2, then f⁻¹(x) equals	Mathematics/Applied Mathematics Types of functions	Medium
15	If f(x) = x² and g(x) = x + 1, what is (fog)(2) − (gof)(2)?	Mathematics/Applied Mathematics Types of functions	Medium
16	How many one-one functions are there from {1, 2, 3} to {a, b, c, d}?	Mathematics/Applied Mathematics Types of functions	Hard
17	The principal value of sin⁻¹(−½) is	Mathematics/Applied Mathematics Inverse trigonometric functions	Easy
18	The range of the principal value branch of cos⁻¹x is	Mathematics/Applied Mathematics Inverse trigonometric functions	Easy
19	The value of cos⁻¹(cos 7π/6) is	Mathematics/Applied Mathematics Inverse trigonometric functions	Medium
20	The value of tan⁻¹(1) + cos⁻¹(−½) + sin⁻¹(−½) is	Mathematics/Applied Mathematics Inverse trigonometric functions	Medium
21	The value of tan⁻¹2 + tan⁻¹3 is	Mathematics/Applied Mathematics Inverse trigonometric functions	Hard
22	How many elements does a matrix of order 2 × 3 have?	Mathematics/Applied Mathematics Matrices and their types	Easy
23	The diagonal elements of every skew-symmetric matrix are	Mathematics/Applied Mathematics Matrices and their types	Easy
24	How many different orders are possible for a matrix having 12 elements?	Mathematics/Applied Mathematics Matrices and their types	Medium
25	A 2 × 2 matrix has elements aᵢⱼ = (i + 2j)²/2. What is a₂₁?	Mathematics/Applied Mathematics Matrices and their types	Medium
26	For A = [[1, 5], [3, 2]] (rows listed), the symmetric part ½(A + Aᵀ) is	Mathematics/Applied Mathematics Matrices and their types	Hard
27	If A is of order 2 × 3 and B is of order 3 × 4, the order of AB is	Mathematics/Applied Mathematics Algebra of matrices	Easy
28	If A = [[1, 2], [3, 4]] and I is the 2 × 2 identity matrix, then A + 2I equals	Mathematics/Applied Mathematics Algebra of matrices	Easy
29	If A = [[1, 2], [0, 1]], then A² equals	Mathematics/Applied Mathematics Algebra of matrices	Medium
30	For any two square matrices A and B of the same order, which statement is always true?	Mathematics/Applied Mathematics Algebra of matrices	Medium
31	If A = [[1, 1], [1, 1]], then A⁵ equals	Mathematics/Applied Mathematics Algebra of matrices	Hard
32	The value of the determinant of [[2, 3], [1, 4]] is	Mathematics/Applied Mathematics Determinants	Easy
33	If two rows of a square matrix are identical, its determinant is	Mathematics/Applied Mathematics Determinants	Easy
34	A is a 3 × 3 matrix with \|A\| = 4. What is \|2A\|?	Mathematics/Applied Mathematics Determinants	Medium
35	What is the area of the triangle with vertices (1, 0), (6, 0) and (4, 3)?	Mathematics/Applied Mathematics Determinants	Medium
36	In the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 10]], what is the cofactor of the element in row 1, column 2?	Mathematics/Applied Mathematics Determinants	Hard
37	A square matrix A has an inverse if and only if	Mathematics/Applied Mathematics Adjoint and inverse of a matrix	Easy
38	The inverse of [[2, 1], [5, 3]] is	Mathematics/Applied Mathematics Adjoint and inverse of a matrix	Easy
39	If A is a 3 × 3 matrix with \|A\| = 5, then \|adj A\| equals	Mathematics/Applied Mathematics Adjoint and inverse of a matrix	Medium
40	If A and B are invertible matrices of the same order, then (AB)⁻¹ equals	Mathematics/Applied Mathematics Adjoint and inverse of a matrix	Medium
41	A = [[3, 1], [−1, 2]] satisfies A² − 5A + 7I = O. Which expression gives A⁻¹?	Mathematics/Applied Mathematics Adjoint and inverse of a matrix	Hard
42	If \|A\| ≠ 0 for the system AX = B, then the system	Mathematics/Applied Mathematics Solving systems of linear equations	Easy
43	The solution of x + y = 5 and x − y = 1 is	Mathematics/Applied Mathematics Solving systems of linear equations	Easy
44	For AX = B, suppose \|A\| = 0 and (adj A)B ≠ O. Then the system	Mathematics/Applied Mathematics Solving systems of linear equations	Medium
45	For which value of k does the system kx + 2y = 3, 2x + y = 5 have no solution?	Mathematics/Applied Mathematics Solving systems of linear equations	Medium
46	The system x + y + z = 6, y + 3z = 11, x − 2y + z = 0 has the solution	Mathematics/Applied Mathematics Solving systems of linear equations	Hard
47	If f(x) = kx + 1 for x ≤ 2 and f(x) = 3x − 1 for x > 2, for which value of k is f continuous at x = 2?	Mathematics/Applied Mathematics Continuity and differentiability	Easy
48	At x = 0, the function f(x) = \|x\| is	Mathematics/Applied Mathematics Continuity and differentiability	Easy
49	The derivative of sin(x²) with respect to x is	Mathematics/Applied Mathematics Continuity and differentiability	Medium
50	If f(x) = x² for x ≤ 1 and f(x) = ax + b for x > 1 is differentiable at x = 1, then (a, b) equals	Mathematics/Applied Mathematics Continuity and differentiability	Medium