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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

Sharpen your problem-solving skills with 10 handpicked previous years’ IIT JEE Mathematics questions. Designed to mirror the real exam experience, this quiz will test your grasp on essential concepts across algebra, calculus, coordinate geometry, and more.✅ Attempt all questions✅ Each correct answer earns 4 marks✅ Review your answers with detailed explanations after submission Best of luck! 🧠✍️ IIT JEE Maths Practice Paper – Part 10 (Previous Years’ Questions) If \( \int (3x^2 + 4x + 2) dx \), the result is: a) x³ + 2x² + 2x + C b) x³ + 2x² + x + C c) x³ + 2x² + 4x + C d) x³ + x² + x + C The limit \( \lim_{x \to 0} \frac{\sin 3x}{x} \) equals: a) 1 b) 3 c) 0 d) ∞ If A = {1,2,3}, number of subsets of A is: a) 3 b) 8 c) 6 d) 4 The derivative of \( e^{2x} \) is: a) 2e^x b) e^{2x} c) 2e^{2x} d) e^x The value of \( \cos 60^\circ \) is: a) 0 b) 1 c) 1/2 d) √3/2 If \( x = 2 \) is a solution of \( x^2 – kx + 4 = 0 \), then k is: a) 6 b) 4 c) 3 d) 2 The general solution of \( \frac{dy}{dx} = y \) is: a) y = x b) y = e^x c) y = Ce^x d) y = Cx The number of permutations of the word “MATH” is: a) 24 b) 12 c) 16 d) 4 The distance between (1,2) and (4,6) is: a) 5 b) 4 c) √13 d) √25 If \( \tan \theta = 1 \), then \( \theta \) is: a) 30° b) 90° c) 45° d) 60° Submit

🧮 Part 9 – IIT JEE Maths Practice Paper (PYQs)Sharpen your problem-solving skills with this fresh set of 10 handpicked previous years’ IIT JEE Mathematics questions. Each question has detailed explanations to help you understand the concept behind the correct answer. Ideal for self-assessment and revision. All the best! IIT JEE Maths Practice – Part 9 Test your understanding with 10 previous years’ questions from Vector Algebra, Calculus, and Coordinate Geometry. The angle between vectors a = i + 2j and b = 2i + 4j is: 0° 30° 45° 60° The derivative of sin⁻¹(x) is: 1/√(1−x²) x/√(1−x²) −1/√(1−x²) √(1−x²) Area of triangle with vertices (0,0), (1,0), (0,1) is: 1 0.5 2 1.5 If A is a 3×3 matrix and |A| = 5, then |2A| is: 40 80 160 8 The slope of the line perpendicular to y = 3x + 7 is: −1/3 3 −3 1/3 The value of lim(x→0) (sin x)/x is: 0 1 ∞ Does not exist A function is even if: f(x) = −f(x) f(x) = f(−x) f(−x) = −f(x) f(x) = 0 The integral of 1/x dx is: x ln|x| + C 1/x² e^x The point (2,3) lies on which quadrant? I II III IV Distance between points (0,0) and (3,4): 5 7 4 3 Submit Answers

Prepared by Nigam Sir, Practice 10 fresh IIT JEE Maths questions based on previous year papers. This set covers key concepts from algebra, trigonometry, calculus, and matrices. ✅ Instant feedback with explanations🧪 4 marks per correct answer📘 No login or backend needed Attempt the quiz below and check how many you get right! IIT JEE Maths Practice Paper – Previous Years’ Questions (Part 8) 1. If x + y = 10 and x – y = 4, what is the value of x? 3 5 7 8 2. The value of sin(30°) is: √3/2 1/2 1 0 3. What is the value of the determinant |1 2; 3 4|? 2 10 –2 –10 4. Which of the following is a solution to x² – 4 = 0? x = 2 only x = –2 only x = ±2 x = 0 5. The value of log₁₀(1) is: 1 0 undefined 10 6. If A = πr² and r = 3, then A = 6π 9π 12π π/3 7. Which of the following functions is even? f(x) = x³ f(x) = sin(x) f(x) = cos(x) f(x) = tan(x) 8. What is the slope of y = 3x + 2? 3 2 1 –3 9. d/dx (x³) = ? x² 2x 3x² 3x 10. If A = {1, 2}, B = {3, 4}, number of elements in A × B is: 2 3 4 6 Submit

Revise important JEE Maths concepts with this set of 10 MCQs from previous year papers. Covers algebra, calculus, matrices, trigonometry, and more. ✅ Instant evaluation with score and explanations📘 4 marks per correct answer⚙️ No login or backend required Perfect for quick practice and concept reinforcement! IIT JEE Maths Practice Paper – Previous Years’ Questions (Part 7) 1. The sum of the roots of the equation 2x² – 3x + 5 = 0 is: –5/2 –3/2 3/2 5/2 2. The domain of the function f(x) = √(x – 2) is: x > 2 x ≥ 2 x < 2 All real x 3. What is the value of tan(45°)? 0 1 √3 Undefined 4. If A = [1 2; 3 4], then trace of A is: 4 5 6 7 5. The number of ways to arrange the letters of the word “MATH” is: 12 16 24 32 6. If log₁₀(100) = x, then x = 1 0 2 10 7. Derivative of sin²(x) is: 2sin(x) 2sin(x)cos(x) cos²(x) 2cos(x) 8. The angle between two perpendicular lines is: 0° 45° 60° 90° 9. Area of a triangle with base = 6 and height = 4 is: 12 24 18 10 10. ∫ cos(x) dx = sin(x) + C –sin(x) + C cos(x) + C tan(x) + C Submit