GSEB Std 10 Previous Year Questions
Board: GSEB Std 10 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
Gujarat Board SSC Mathematics chapter-wise PYQs covering Real Numbers, Polynomials, Linear Equations, Quadratic Equations, Arithmetic Progression, Trigonometry, Statistics, Probability, and more.
Real Numbers
Q1. Find HCF of 120 and 150 using prime factors. [2019 – 1 marks]
Solution: 120=2³×3×5, 150=2×3×5². HCF=2×3×5=30.
Q2. Prove √5 is irrational. [2020 – 2 marks]
Solution: Assume √5=p/q reduced. 5q²=p² ⇒ p=5k. 5q²=25k² ⇒ q²=5k². Contradiction.
Q3. Find LCM and HCF of 6,72,120. [2022 – 2 marks]
Solution: 6=2×3, 72=2³×3², 120=2³×3×5. HCF=2×3=6. LCM=2³×3²×5=360.
Q4. Prove 1/√3 is irrational. [2023 – 2 marks]
Solution: Assume 1/√3=p/q. Then √3=q/p rational. Contradiction. Hence irrational.
Polynomials
Q1. Find zeros of x²-3. [2020 – 1 marks]
Solution: x²-3=0 ⇒ x²=3 ⇒ x=±√3.
Q2. Find α+β and αβ for x²-5x+6. [2022 – 1 marks]
Solution: α+β=5, αβ=6.
Q3. Check if 3 is zero of polynomial 2x²-5x-3. [2023 – 2 marks]
Solution: P(3)=2(9)-5(3)-3=18-15-3=0. Yes, 3 is a zero.
Linear Equations in Two Variables
Q1. Solve: x+y=7, x-y=3. [2020 – 1 marks]
Solution: Adding: 2x=10 ⇒ x=5. y=7-5=2.
Q2. Find if lines 2x+3y=7 and 6x+9y=14 are consistent. [2022 – 2 marks]
Solution: a₁/a₂=2/6=1/3, b₁/b₂=3/9=1/3, c₁/c₂=-7/-14=1/2. a₁/a₂=b₁/b₂≠c₁/c₂ ⇒ parallel, inconsistent.
Q3. Solve 2x+3y=11 and x-2y=-12 by elimination. [2023 – 2 marks]
Solution: Multiply eq2 by 2: 2x-4y=-24. Subtract: 7y=35 ⇒ y=5. x=2.
Quadratic Equations
Q1. Find roots of x²-7x+12=0. [2021 – 1 marks]
Solution: x²-7x+12=0 ⇒ (x-3)(x-4)=0 ⇒ x=3,4.
Q2. Find discriminant of 2x²-4x+3=0 and state nature. [2020 – 2 marks]
Solution: D=16-24=-8<0. Roots are not real.
Q3. Speed of boat in still water 18 km/h. Upstream 1 hr more than downstream for 24 km. Find speed of stream. [2023 – 3 marks]
Solution: Let s=speed of stream. 24/(18-s)-24/(18+s)=1. 48s=324-s². s²+48s-324=0. s=6 km/h.
Arithmetic Progression
Q1. Find 10th term of AP: 3,7,11,15,… [2022 – 1 marks]
Solution: a=3, d=4. a₁₀=3+9(4)=39.
Q2. Find sum of first 15 terms of AP 5,9,13,… [2020 – 2 marks]
Solution: a=5, d=4. S₁₅=15/2[10+14(4)]=15/2[66]=495.
Q3. Which term of AP 2,5,8,… is 47? [2023 – 2 marks]
Solution: a=2, d=3. an=2+(n-1)3=47 ⇒ 3n-1=47 ⇒ n=16. 16th term.
Trigonometry
Q1. Find sin²60°+cos²60°. [2021 – 1 marks]
Solution: sin60=√3/2, cos60=1/2. sin²+cos²=3/4+1/4=1.
Q2. Prove (1-sinθ)(1+sinθ)=cos²θ. [2020 – 2 marks]
Solution: (1-sinθ)(1+sinθ)=1-sin²θ=cos²θ.
Q3. If tanA=3/4, find sinA and cosA. [2022 – 2 marks]
Solution: tanA=opp/adj=3/4. hyp=5. sinA=3/5, cosA=4/5.
Statistics
Q1. Find mean of 2,4,6,8,10. [2021 – 1 marks]
Solution: Mean=(2+4+6+8+10)/5=30/5=6.
Q2. Find median of 3,7,2,9,5. [2020 – 2 marks]
Solution: Sorted: 2,3,5,7,9. Median=5.
Q3. Mode of 1,2,2,3,3,3,4,5. [2022 – 1 marks]
Solution: Mode=3 (occurs 3 times).
Compiled by Monomath.com | Ajay Yadav (Math King) | 15+ Years Teaching Experience