JEE Main Previous Year Questions
Board: JEE Main Previous Year Questions | Chapter-wise Previous Year Questions (2016-2025)
Practice with real exam questions solved by Ajay Yadav (Math King). Download the complete PDF or browse questions below.
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Chapter-wise Questions
14 chapters covering Sets & Functions, Complex Numbers, Matrices & Determinants, P&C, Binomial Theorem, Sequences, Limits, Differentiation, Integration, Differential Equations, Coordinate Geometry, Vector & 3D, Trigonometry, and Statistics & Probability.
Sets, Relations & Functions
Q1. If A={1,2,3,4,5}, B={2,4,6,8}, find A-B. [2020 – 1 marks]
Solution: A-B={1,3,5}.
Q2. Check if f:R→R given by f(x)=x² is one-one. [2018 – 1 marks]
Solution: f(-1)=f(1)=1 but -1≠1. Not one-one.
Q3. If n(A)=5, n(B)=4, find n(A×B). [2022 – 1 marks]
Solution: n(A×B)=5×4=20.
Complex Numbers & Quadratic Equations
Q1. Find modulus of (1+i)/(1-i). [2020 – 1 marks]
Solution: |(1+i)/(1-i)|=|1+i|/|1-i|=√2/√2=1.
Q2. Find argument of -1-√3 i. [2019 – 1 marks]
Solution: θ=tan^{-1}(-√3/-1)=π/3 but both negative, so θ=π+π/3=4π/3 or -2π/3.
Q3. Find square root of 7+24i. [2018 – 2 marks]
Solution: √(7+24i)=±(4+3i). Check: (4+3i)²=16+24i-9=7+24i.
Matrices & Determinants
Q1. If A=[[1,2],[3,4]], find A^{-1}. [2018 – 1 marks]
Solution: |A|=-2. adj A=[[4,-2],[-3,1]]. A^{-1}=[[-2,1],[3/2,-1/2]].
Q2. Find x if |[[x,2],[3,4]]|=2. [2019 – 1 marks]
Solution: 4x-6=2 ⇒ x=2.
Q3. If A=[[3,1],[-1,2]], show A²-5A+7I=0. [2020 – 2 marks]
Solution: A²=[[8,5],[-5,3]]. A²-5A+7I=[[0,0],[0,0]].
Permutations & Combinations
Q1. How many 3-digit numbers from 1,2,3,4,5 without repetition? [2020 – 1 marks]
Solution: 5×4×3=60.
Q2. Find n if nC5=nC3. [2022 – 1 marks]
Solution: nC5=nC3 ⇒ n=8.
Q3. How many ways to arrange letters of MATHEMATICS? [2019 – 2 marks]
Solution: 11 letters: M(2),A(2),T(2),H,E,I,C,S. Ways=11!/(2!2!2!).
Limits & Continuity
Q1. Evaluate lim x→0 sin x/x. [2020 – 1 marks]
Solution: 1.
Q2. Check continuity of f(x)=|x| at x=0. [2019 – 1 marks]
Solution: LHL=RHL=f(0)=0. Continuous.
Q3. Find k: f(x)={kx²,x≤1; 2x+1,x>1} continuous at x=1. [2022 – 2 marks]
Solution: k(1)=2(1)+1 ⇒ k=3.
Compiled by Monomath.com | Ajay Yadav (Math King) | 15+ Years Teaching Experience