CBSE Class 10 Previous Year Questions
Board: CBSE Class 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
14 chapters covering Real Numbers, Polynomials, Quadratic Equations, Arithmetic Progressions, Trigonometry, Circles, Constructions, Statistics, Probability, and more.
Real Numbers
Q1. Prove that √3 is irrational. [2023 – 3 marks]
Solution: Assume √3 = p/q (reduced). Then 3q² = p². So p=3k → 3q²=9k² → q²=3k². Contradiction as p,q coprime. Hence √3 is irrational.
Q2. Find HCF and LCM of 12, 15, 21 using prime factorization. [2022 – 2 marks]
Solution: 12=2²×3, 15=3×5, 21=3×7. HCF=3. LCM=2²×3×5×7=420.
Q3. Find the largest number dividing 245 and 1029 leaving remainder 5 in each case. [2021 – 3 marks]
Solution: Required number = HCF(245-5, 1029-5) = HCF(240, 1024) = 16.
Q4. Show that any positive odd integer is of the form 6q+1, 6q+3, or 6q+5. [2019 – 3 marks]
Solution: Let a be any odd integer, b=6. By Euclid, a=6q+r, 0≤r<6. r=0,2,4 give even a; r=1,3,5 give odd a. So odd a = 6q+1, 6q+3, or 6q+5.
Q5. Find LCM of 96 and 404 by prime factorization and verify HCF. [2020 – 3 marks]
Solution: 96=2⁵×3, 404=2²×101. LCM=2⁵×3×101=9696. HCF=2²=4. LCM×HCF=9696×4=96×404. Verified.
Q6. Prove that 5-√3 is irrational given √3 is irrational. [2023 – 3 marks]
Solution: Assume 5-√3 = p/q rational. Then √3 = 5-p/q = (5q-p)/q rational. Contradiction since √3 is irrational. Hence 5-√3 is irrational.
Q7. Find HCF of 867 and 255 using Euclid lemma. [2020 – 2 marks]
Solution: 867=255×3+102, 255=102×2+51, 102=51×2+0. HCF=51.
Polynomials
Q1. Find zeros of 2x²-7x+3 and verify relationship. [2023 – 3 marks]
Solution: 2x²-7x+3=(2x-1)(x-3). Zeros: 1/2, 3. Sum=7/2=-(-7)/2. Product=3/2=3/2. Verified.
Q2. Find quadratic polynomial with sum and product of zeros 1/4 and -1. [2022 – 2 marks]
Solution: x²-(sum)x+product = x²-x/4-1 = 4x²-x-4=0.
Q3. If α,β are zeros of x²-5x+6, find α+β and αβ. [2020 – 2 marks]
Solution: α+β = -(-5)/1 = 5. αβ = 6/1 = 6.
Q4. Find all zeros of x³-3x²-2x+6 if two zeros are ±√2. [2019 – 3 marks]
Solution: (x-√2)(x+√2)=x²-2 divides polynomial. (x³-3x²-2x+6)÷(x²-2)=x-3. Third zero=3.
Q5. Find a quadratic polynomial where zeros are 2 and -3. [2021 – 2 marks]
Solution: Sum = 2+(-3) = -1, Product = 2×(-3) = -6. Polynomial: x²+x-6.
Quadratic Equations
Q1. Find roots of 2x²+x-6=0. [2023 – 2 marks]
Solution: 2x²+x-6=0 → 2x²+4x-3x-6=0 → 2x(x+2)-3(x+2)=0 → (2x-3)(x+2)=0. x=3/2 or x=-2.
Q2. Sum of two numbers is 15 and sum of squares is 113. Find numbers. [2022 – 3 marks]
Solution: x+y=15, x²+y²=113. x²+(15-x)²=113 → 2x²-30x+112=0 → x=7,8. Numbers: 7 and 8.
Q3. Find discriminant of 2x²-4x+3=0 and nature of roots. [2020 – 2 marks]
Solution: D=(-4)²-4(2)(3)=16-24=-8<0. Roots are not real (imaginary).
Q4. Find k for which x²+5kx+16=0 has equal roots. [2021 – 3 marks]
Solution: D=0 → (5k)²-4(1)(16)=0 → 25k²=64 → k=±8/5.
Q5. A train travels 360 km at uniform speed. If speed is 5 km/h more, it takes 1 hour less. Find speed. [2019 – 3 marks]
Solution: Let speed=x km/h. 360/x – 360/(x+5)=1 → 360(x+5-x)=x(x+5) → x²+5x-1800=0 → x=40 km/h.
Arithmetic Progressions
Q1. Find sum of first 20 terms of AP: 2,7,12,… [2023 – 2 marks]
Solution: a=2, d=5. S₂₀=20/2[4+19(5)]=10(99)=990.
Q2. How many terms of AP 3,5,7,… give sum 120? [2022 – 3 marks]
Solution: S=n/2[6+(n-1)2]=n(2n+4)/2=n(n+2)=120. n²+2n-120=0 → n=10.
Q3. Find nth term of AP: 5,8,11,14,… [2020 – 2 marks]
Solution: a=5, d=3. an=5+(n-1)3=3n+2.
Q4. Which term of AP 21,18,15,… is -81? [2021 – 2 marks]
Solution: a=21, d=-3. an=21+(n-1)(-3)=-81 → 21-3n+3=-81 → -3n=-105 → n=35.
Q5. Find sum of all two-digit numbers divisible by 3. [2019 – 3 marks]
Solution: Numbers: 12,15,…,99. n=(99-12)/3+1=30. S=30/2[12+99]=15×111=1665.
Compiled by Monomath.com | Ajay Yadav (Math King) | 15+ Years Teaching Experience