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

Practice important IIT JEE Trigonometry questions from previous years’ papers with this quiz (Part 12). Each correct answer gives you 4 marks. See your result instantly after submission. Note: These are Easy Questions, Difficulty level will be raised in upcoming videos, please bookmark this website. IIT JEE Maths Practice Paper – Trigonometry (Part 12) 1. The value of sin²θ + cos²θ is: a) 0 b) 1 c) 2 d) None 2. The general solution of sinθ = 0 is: a) nπ b) 2nπ c) nπ/2 d) π/2 + nπ 3. The value of tan 45° is: a) 0 b) 1 c) √3 d) ∞ 4. sin(2A) equals: a) 2sinA b) sinA cosA c) 2sinA cosA d) cos²A – sin²A 5. Which of the following is equal to 1? a) sec²θ – tan²θ b) tan²θ – sec²θ c) secθ – tanθ d) None 6. cos(90° – θ) = a) sinθ b) cosθ c) tanθ d) cotθ 7. The period of sinx is: a) 180° b) π/2 c) 2π d) π 8. Which of the following is undefined? a) tan 0° b) cot 0° c) cos 0° d) sin 90° 9. sin30° + cos60° equals: a) 0 b) 1 c) 2 d) √2 10. Which of these identities is correct? a) sin²θ = 1 + cos²θ b) tanθ = sinθ/cosθ c) sinθ = 1/cosecθ d) All of the above Submit Answers

Topic: Sets, Relations and FunctionsPractice 10 handpicked previous year IIT JEE questions. Test your concepts of domains, ranges, types of relations and functions, and more. Each question carries 4 marks. No negative marking here—just practice and learn! IIT JEE Maths Practice Paper – Part 11: Sets, Relations and Functions 1. Let A = {1, 2, 3}, B = {3, 4, 5}. What is A ∩ B? a) {1, 2} b) {3} c) {1, 2, 3, 4, 5} d) { } 2. If f(x) = x² + 1, then f(2) is: a) 5 b) 3 c) 6 d) 7 3. If A = {x ∈ N : x < 6}, then set A is: a) {0,1,2,3,4,5} b) {1,2,3,4,5} c) {2,4,6} d) Infinite set 4. If f: R → R is defined by f(x) = 2x + 3, then f is: a) One-one b) Onto c) Bijective d) Constant 5. Number of subsets of a set with 3 elements is: a) 6 b) 9 c) 8 d) 4 6. If A = {1, 2}, B = {a, b}, then number of relations from A to B is: a) 2 b) 4 c) 8 d) 16 7. The number of functions from set A (3 elements) to B (2 elements) is: a) 6 b) 8 c) 4 d) 2 8. Which of the following is a function? a) {(1,2), (1,3)} b) {(2,1), (3,1)} c) {(2,3), (3,4)} d) {(1,2), (2,1), (2,3)} 9. Domain of f(x) = √(x-1) is: a) x ≥ 0 b) x ≥ 1 c) x < 1 d) All real x 10. Range of f(x) = x² where x ∈ R is: a) All real numbers b) R+ c) [0, ∞) d) (−∞, ∞) Submit Quiz