GSEB Std 12 Previous Year Questions
Board: GSEB Std 12 Previous Year Questions | Chapter-wise Previous Year Questions (2016-2025)
Practice with real exam questions solved by Ajay Yadav (Math King of Katargam). Download the complete PDF or browse questions below.
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Chapter-wise Questions
Gujarat Board HSC Mathematics chapter-wise PYQs covering Relations & Functions, Inverse Trigonometry, Matrices, Determinants, Continuity, Differentiation, Integration, Differential Equations, Vector Algebra, 3D Geometry, Linear Programming, and Probability.
Relations and Functions
Q1. If f(x)=x³, find f^{-1}(8). [2020 – 1 marks]
Solution: f^{-1}(x)=∛x. f^{-1}(8)=2.
Q2. Show f:R→R given by f(x)=2x+3 is invertible. Find f^{-1}. [2019 – 3 marks]
Solution: One-one & onto. y=2x+3 ⇒ x=(y-3)/2. f^{-1}(x)=(x-3)/2.
Q3. Check if R={(1,1),(2,2),(3,3)} is reflexive, symmetric, transitive. [2022 – 1 marks]
Solution: All reflexive pairs present. Symmetric & transitive vacuously. Yes, equivalence relation.
Inverse Trigonometric Functions
Q1. Find principal value of sin^{-1}(1/2). [2020 – 1 marks]
Solution: π/6.
Q2. Find principal value of cos^{-1}(-√3/2). [2018 – 1 marks]
Solution: cos(5π/6)=-√3/2. Principal value=5π/6.
Q3. Prove tan^{-1}(1/2)+tan^{-1}(1/3)=π/4. [2023 – 2 marks]
Solution: tan^{-1}(1/2+1/3)/(1-1/6)=tan^{-1}(1)=π/4.
Matrices
Q1. Find x if [[4,4],[x,1]] is singular. [2018 – 1 marks]
Solution: 4-4x=0 ⇒ x=1.
Q2. If A=[[3,1],[-1,2]], show A²-5A+7I=0. [2020 – 2 marks]
Solution: A²=[[8,5],[-5,3]]. A²-5A+7I=0. Verified.
Q3. If A=[[1,2],[2,1]], find A^{-1}. [2019 – 2 marks]
Solution: |A|=-3. adj A=[[1,-2],[-2,1]]. A^{-1}=[[-1/3,2/3],[2/3,-1/3]].
Determinants
Q1. Evaluate |[[2,3],[4,5]]|. [2019 – 1 marks]
Solution: 10-12=-2.
Q2. If |A|=5, find |adj A| for 3×3. [2018 – 1 marks]
Solution: |adj A|=|A|²=25.
Q3. Solve: x+2y=7, 3x+4y=17 using matrix method. [2017 – 3 marks]
Solution: |A|=-2. x=|[[7,2],[17,4]]|/-2=(28-34)/-2=3. y=|[[1,7],[3,17]]|/-2=(17-21)/-2=2.
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