Matrices and Determinants are essential topics in JEE Mathematics that test conceptual understanding and application in solving systems of equations, transformations, and inverse operations. This practice set is designed to reinforce these foundational concepts. Topic: Matrices and Determinants 1. If A = [[2, 3], [4, 5]], then |A| is: a) 2 b) -2 c) -1 d) 10 2. If A is a 2×2 matrix such that A² = I, then A is: a) Invertible b) Non-invertible c) Null matrix d) Diagonal 3. For a 3×3 matrix A, the value of |kA| is: a) k³|A| b) k²|A| c) k|A| d) |A| 4. If A is a singular matrix, then |A| is: a) 1 b) -1 c) 0 d) Infinite 5. If A and B are square matrices of the same order and AB = BA, then: a) A and B are equal b) A is symmetric c) A and B commute d) B is a zero matrix 6. If A is an orthogonal matrix, then A⁻¹ is: a) A b) Aᵀ c) -A d) None of these 7. The adjoint of a diagonal matrix is: a) Same diagonal matrix b) Zero matrix c) Inverse matrix d) Transpose 8. The determinant of a skew-symmetric matrix of odd order is: a) 0 b) 1 c) -1 d) Not defined 9. Which matrix has no inverse? a) Identity matrix b) Orthogonal matrix c) Singular matrix d) Diagonal matrix 10. Which of the following is true for all invertible matrices A and B? a) (AB)⁻¹ = A⁻¹B⁻¹ b) (AB)⁻¹ = B⁻¹A⁻¹ c) (A + B)⁻¹ = A⁻¹ + B⁻¹ d) A⁻¹ + B⁻¹ = (AB)⁻¹ Submit Answers

Part 19 – ProbabilityThis section contains 10 multiple-choice questions from previous IIT JEE exams focused on Probability. These questions are designed to test your understanding of fundamental probability concepts including independent and dependent events, Bayes’ theorem, and conditional probability. Part 19 – IIT JEE Maths Practice Paper: Probability Instructions: Each correct answer gives 4 marks. No negative marking. Choose the best answer for each question and click “Submit” to view your score and explanations. Two dice are thrown simultaneously. What is the probability that the sum is divisible by 4? a) 1/4 b) 1/3 c) 5/18 d) 1/2 A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is either a red card or a king? a) 7/13 b) 4/13 c) 15/26 d) 8/13 An unbiased coin is tossed 5 times. What is the probability of getting at least 3 heads? a) 1/2 b) 26/32 c) 5/16 d) 11/32 A bag contains 3 red and 5 black balls. Two balls are drawn without replacement. What is the probability both are black? a) 5/14 b) 5/7 c) 5/8 d) 10/21 If A and B are two independent events such that P(A) = 1/3 and P(B) = 1/4, then P(A ∪ B) is: a) 1/2 b) 7/12 c) 1/3 d) 3/4 What is the probability of getting a sum of 7 or 11 when two dice are rolled? a) 2/9 b) 1/6 c) 1/4 d) 5/36 A and B throw a die alternatively. The one who gets a 6 first wins. If A starts, then what is the probability that A wins? a) 5/11 b) 6/11 c) 1/2 d) 7/13 If P(E) = 0.3 and P(F) = 0.4 and E and F are mutually exclusive, find P(E ∪ F). a) 0.12 b) 0.7 c) 1 d) 0.1 If two events A and B are such that P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.3, then P(A|B) is: a) 0.3 b) 0.6 c) 0.9 d) 0.5 In how many ways can 3 boys and 2 girls be selected from 5 boys and 4 girls? a) 40 b) 60 c) 100 d) 10 Submit

Boost your IIT JEE preparation with Part 18 of our Maths Practice Paper series. This set includes carefully selected Binomial Theorem questions based on previous years’ IIT JEE papers. Practice and test your understanding with instant evaluation — answers, score, and explanations included. IIT JEE Maths Practice Paper – Part 18: Binomial Theorem 1. The middle term in the expansion of (1 + x)18 is: 9th term 10th term 8th term 11th term 2. The coefficient of x3 in the expansion of (2 + x)5 is: 40 80 20 60 3. In the expansion of (1 – 3x)4, the term independent of x is: 81 -81 1 -1 4. The general term in the expansion of (a + b)n is: nCr an-r br nCr ar bn-r nCr an br None of the above 5. In the expansion of (1 + x)10, the sum of coefficients is: 10 0 1024 512 Submit

Boost your problem-solving skills in Permutations and Combinations with 10 carefully selected multiple-choice questions from previous IIT JEE exams. This set helps you master arrangements, selections, and advanced counting principles essential for scoring well in combinatorics. IIT JEE Maths Practice Paper – Part 17: Permutations and Combinations In how many ways can the letters of the word “APPLE” be arranged? a) 120 b) 60 c) 240 d) 100 How many 4-digit numbers can be formed using digits 1, 2, 3, 4, 5 without repetition? a) 120 b) 625 c) 360 d) 256 Number of ways to choose 3 balls from 5 red and 4 green balls: a) 56 b) 84 c) 126 d) 36 How many ways can 3 boys and 2 girls be seated in a row such that the girls do not sit together? a) 72 b) 36 c) 144 d) 60 Number of circular permutations of 6 distinct objects: a) 720 b) 120 c) 60 d) 5040 A committee of 3 is to be formed from 4 men and 3 women. Number of ways it can be done: a) 35 b) 20 c) 30 d) 25 From the word “BANANA”, how many unique permutations can be formed? a) 60 b) 120 c) 360 d) 720 The number of permutations of 5 different books taken 3 at a time: a) 10 b) 60 c) 20 d) 15 If 5 people sit around a round table, how many seating arrangements are possible? a) 120 b) 24 c) 60 d) 30 The number of ways to divide 10 students into 2 groups of 5 each: a) 126 b) 252 c) 462 d) 180 Submit

Strengthen your understanding of complex numbers with this set of 10 previous years’ MCQs from the IIT JEE exam. This practice set tests your grasp on concepts like modulus, argument, conjugates, equations, and geometric representation. Ideal for quick revision and self-evaluation. IIT JEE Maths Practice Paper – Part 16: Complex Numbers 1. If \( z = 1 + i \), then \( |z|^2 \) equals: a) 1 b) 2 c) √2 d) 0 2. The principal argument of \( -1 – i \) is: a) π/2 b) -π/4 c) -3π/4 d) 3π/4 3. The complex number whose modulus is 1 and argument is π/3 is: a) cos(π/3) + i sin(π/3) b) cos(π/3) – i sin(π/3) c) -cos(π/3) + i sin(π/3) d) -cos(π/3) – i sin(π/3) 4. If \( z = x + iy \) and \( |z| = 5 \), which of the following is true? a) x² – y² = 25 b) x² + y² = 25 c) x + y = 25 d) x – y = 25 5. The value of \( i^{2023} \) is: a) 1 b) -1 c) i d) -i Submit

Practice Paper Part 15 – Integration (IIT JEE Maths – Previous Years’ Questions) Sharpen your problem-solving skills with this set of handpicked IIT JEE previous years’ questions from the Integration chapter. These questions are designed to strengthen your conceptual understanding and boost your exam confidence. Each question has detailed explanations to help you learn from mistakes and revise key concepts effectively. IIT JEE Maths Practice Paper – Part 15: Integration 1. ∫ x·ex dx equals: a) x·ex b) ex + C c) (x − 1)·ex + C d) (x + 1)·ex + C 2. ∫ dx / (1 + x2) equals: a) ln|1 + x2| + C b) tan−1(x) + C c) sec−1(x) + C d) x / (1 + x2) + C 3. ∫ sin2(x) dx is: a) x − sin(x)cos(x) + C b) (x/2) − (sin(2x)/4) + C c) −cos2(x) + C d) tan(x) + C 4. ∫ x / √(1 − x2) dx equals: a) −√(1 − x2) + C b) √(1 − x2) + C c) −x√(1 − x2) + C d) −(1 − x2)3/2/3 + C 5. ∫ ex(1 + x) dx equals: a) ex(x − 1) + C b) x·ex + C c) (x + 1)ex + C d) xex − ex + C Submit

IIT JEE Maths Practice Paper – Part 14: Vectors Practice 10 multiple-choice questions from past JEE papers based on the topic of Vectors. Click submit to view your result, score, and explanations. If vector a = 2i + 3j and vector b = i − j, then a · b is: 1 -1 3 5 If vectors a and b are such that |a| = 3, |b| = 4 and a · b = 6, then the angle between them is: 30° 45° 60° 90° Two vectors are perpendicular if: Their magnitudes are equal Their dot product is zero Their cross product is zero They have opposite directions The magnitude of the cross product of vectors a and b is equal to: ab cos θ ab ab sin θ a + b The vector i + j is rotated 90° counterclockwise in the plane. Its new direction is: -j + i -i – j -i + j -j – i If a vector has magnitude 5 and makes an angle of 60° with the x-axis, then its x-component is: 5 5√3 5 cos 60° 5 sin 60° If a · b = 0 and a × b ≠ 0, then: Vectors are parallel Vectors are equal Vectors are perpendicular Vectors are same direction Unit vector along vector 3i + 4j is: 3i + 4j (3/5)i + (4/5)j (4/5)i + (3/5)j (5/3)i + (5/4)j The projection of vector a on b is given by: |a||b| sin θ a · b / |b| a × b ab cos θ If a = i + j and b = i − j, then a × b is: 2k -2k 0 i + k Submit

Test your preparation for IIT JEE Mathematics with these previous years’ Calculus questions. Includes differentiation, integration, limits, continuity, and application-based problems. Ideal for last-minute practice and concept revision. IIT JEE Maths Practice – Calculus 1. The derivative of \( e^{\tan x} \) is: \( \sec^2 x \cdot e^{\tan x} \) \( \tan x \cdot e^{\tan x} \) \( \sec x \cdot e^x \) \( \sec x \cdot \tan x \) 2. If \( f(x) = \ln(\sin x) \), then \( f'(x) \) equals: \( \cot x \) \( \frac{1}{\sin x} \) \( \frac{\cos x}{\sin x} \) \( \cos x \cdot \ln x \) 3. \( \int_0^1 x e^x \, dx \) is: \( e – 2 \) \( 1 \) \( 2e \) \( e – 1 \) 4. Limit \( \lim_{x \to 0} \frac{\sin x}{x} \) equals: 1 0 ∞ Does not exist 5. If \( f(x) = x^2 \), then \( \int f'(x) dx \) is: \( x^2 + C \) \( 2x + C \) \( 2x^2 + C \) \( x^3 + C \) 6. If \( \int_1^2 f(x)dx = 3 \), what is \( \int_1^2 5f(x)dx \)? 15 5 8 1.5 7. If \( y = x^x \), then \( \frac{dy}{dx} \) equals: \( x^x(1 + \ln x) \) \( x^x \ln x \) \( x \ln x \) \( \ln x + 1 \) 8. \( \int \frac{1}{x^2 + 1} dx \) is: \( \tan^{-1}(x) + C \) \( \ln(x^2 + 1) + C \) \( \frac{1}{x^2 + 1} + C \) \( \tan(x) + C \) 9. If a function is differentiable, it is always: Continuous Discontinuous Constant None 10. The area under the curve \( y = x^2 \) from 0 to 2 is: \( \frac{8}{3} \) \( 4 \) \( 2 \) \( \frac{4}{3} \) Submit