Sample Class 10 / JEE foundation questions — pre-loaded

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1. Find the roots of the quadratic equation: x² - 5x + 6 = 0
2. A cylinder has a radius of 7 cm and height of 10 cm. Find its volume. (Use π = 22/7)
3. If sin θ = 3/5, find cos θ and tan θ.
4. Two trains start from stations A and B simultaneously. Train A travels at 60 km/h and Train B at 80 km/h. If the distance between A and B is 280 km, in how many hours will they meet?
5. Find the value of: log₂(64)
6. Find the HCF and LCM of 24 and 36.
7. A fair die is rolled once. What is the probability of getting an even number?
8. Find the distance between the points A(2, 3) and B(5, 7).
9. Find the compound interest on ₹10,000 at 10% per annum for 2 years (compounded annually).
10. Solve the simultaneous equations: 2x + 3y = 12 and x − y = 1.
11. Find the sum of the first 20 natural numbers.
12. Find the surface area of a sphere of radius 7 cm. (Use π = 22/7)
13. Solve: |x − 3| = 5
14. Find the mean of the data: 5, 8, 12, 15, 20.
15. Differentiate y = x³ + 2x² − 5x + 7 with respect to x.

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Answer key & worked solutions

Step-by-step solutions for the sample questions above. Use them to self-check before generating a fresh AI maths mock test.

1. Q1: Factorise: x² − 5x + 6 = (x − 2)(x − 3) = 0. Roots are x = 2 and x = 3.
2. Q2: Volume of a cylinder V = πr²h = (22/7) × 7² × 10 = (22/7) × 49 × 10 = 1540 cm³.
3. Q3: For a 3-4-5 right triangle, if sin θ = 3/5 then cos θ = 4/5 and tan θ = sin θ / cos θ = 3/4.
4. Q4: They move toward each other, so relative speed = 60 + 80 = 140 km/h. Time to meet = 280 / 140 = 2 hours.
5. Q5: 64 = 2⁶, therefore log₂(64) = 6.
6. Q6: 24 = 2³ × 3 and 36 = 2² × 3². HCF = 2² × 3 = 12. LCM = 2³ × 3² = 72.
7. Q7: Even outcomes: {2, 4, 6} = 3 favourable. Total outcomes = 6. Probability = 3/6 = 1/2.
8. Q8: Distance = √[(5 − 2)² + (7 − 3)²] = √(9 + 16) = √25 = 5 units.
9. Q9: Amount A = P(1 + R/100)ⁿ = 10000 × (1.1)² = 10000 × 1.21 = ₹12,100. Compound interest = 12100 − 10000 = ₹2,100.
10. Q10: From x − y = 1 ⇒ x = y + 1. Substitute: 2(y + 1) + 3y = 12 ⇒ 5y = 10 ⇒ y = 2, x = 3.
11. Q11: Sum = n(n + 1)/2 = 20 × 21 / 2 = 210.
12. Q12: Surface area = 4πr² = 4 × (22/7) × 49 = 616 cm².
13. Q13: |x − 3| = 5 ⇒ x − 3 = 5 or x − 3 = −5 ⇒ x = 8 or x = −2.
14. Q14: Mean = (5 + 8 + 12 + 15 + 20) / 5 = 60 / 5 = 12.
15. Q15: dy/dx = 3x² + 4x − 5.

Tips for Maths Practice

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