Free CBSE Class 10 Maths Practice Paper | Olympiad Style Sample

Mathematics — Class 10 Practice Paper

Real Numbers, Quadratics, Triangles & Statistics

📋 Board: CBSE 📚 Class: 10 ⏱ Time: 60 minutes 🏆 Max Marks: 80 ❓ Questions: 20

Instructions: All questions are compulsory. Each question carries 4 marks. There is no negative marking. Choose the most appropriate option.

Q1.

Arjun's probability experiment: P(A) = 0.35, P(B) = 0.45, P(A∩B) = 0.15. P(A∪B)?

A) 0.50

B) 0.65

C) 0.80

D) 0.95

Q2.

Quadratic formula for ax²+bx+c=0: x = ?

A) (−b±√b²−4ac)/2a

B) (b±√b²−4ac)/2a

C) (−b±√b²+4ac)/2a

D) (b±√b²+4ac)/a

Q3.

Discriminant of 3x² − 2x + 1 = 0 is:

A) −8

B) 8

C) 16

D) −16

Q4.

In triangle ABC, DE ∥ BC. AD/DB = 3/5 and AE = 6 cm. EC = ?

A) 8 cm

B) 9 cm

C) 10 cm

D) 12 cm

Q5.

Arjun calculates: sin 30° + cos 60° = ?

A) ½

B) 1

C) √3/2

D) √2/2

Q6.

If tan θ = 3/4, then sin θ = ? (in first quadrant)

A) 3/5

B) 4/5

C) 3/4

D) 4/3

Q7.

Area of equilateral triangle with side a = ?

A) √3a²/2

B) √3a²/4

C) a²/4

D) a²√3

Q8.

The roots of x² − 7x + 12 = 0 are:

A) 3, 4

B) −3, −4

C) 3, −4

D) −3, 4

Q9.

Mean of first n natural numbers:

A) n

B) (n+1)/2

C) n/2

D) n(n+1)/2

Q10.

ISRO rocket climbs vertically. From a point 200m away, angle of elevation = 60°. Height?

A) 100√3 m

B) 200√3 m

C) 200/√3 m

D) 100 m

Q11.

In ΔABC and ΔPQR, AB/PQ = BC/QR = CA/RP. They are:

A) Congruent

B) Similar

C) Equal area only

D) Right-angled

Q12.

If one root of kx² − 5x + 2 = 0 is 2, find k:

A) 1

B) 2

C) 3

D) 4

Q13.

Arjun's cricket scores: 85, 92, 78, 96, 88, 74, 90. Median score?

A) 85

B) 86

C) 88

D) 90

Q14.

sec²θ − tan²θ = ?

A) 0

B) −1

C) 1

D) 2

Q15.

Pythagoras theorem: In right ΔABC (right angle at C), AB² = ?

A) AC + BC

B) AC² + BC²

C) AC × BC

D) AC² − BC²

Q16.

Arjun's exam scores: 60, 65, 72, 80, 55, 90, 68. Variance? (mean=70)

A) 124

B) 140

C) 156

D) 162

Q17.

For a quadratic ax²+bx+c=0, sum of roots = ?

A) c/a

B) −b/a

C) b/a

D) −c/a

Q18.

tan(45°) + cot(45°) = ?

A) 1

B) √2

C) 2

D) 2√2

Q19.

A ladder 10m long leans against a wall. Foot is 6m from wall. Height on wall?

A) 4 m

B) 6 m

C) 8 m

D) 16 m

Q20.

Which trigonometric ratio is always ≤ 1 for acute angles?

A) tan θ

B) sec θ

C) cosec θ

D) sin θ

✅ Answer Key & Solutions

Q1 B P(A∪B) = P(A)+P(B)−P(A∩B) = 0.35+0.45−0.15 = 0.65

Q2 A Standard quadratic formula: x = (−b ± √(b²−4ac)) / 2a

Q3 A D = b²−4ac = 4 − 12 = −8

Q4 C By BPT: AD/DB = AE/EC → 3/5 = 6/EC → EC = 10 cm

Q5 B sin 30° = ½; cos 60° = ½; sum = 1

Q6 A Hyp = √(9+16) = 5; sin θ = opp/hyp = 3/5

Q7 B Area of equilateral triangle = (√3/4)a²

Q8 A (x−3)(x−4) = 0; x = 3 or 4

Q9 B Sum = n(n+1)/2; Mean = n(n+1)/2 ÷ n = (n+1)/2

Q10 B tan 60° = h/200 → √3 = h/200 → h = 200√3 m

Q11 B SSS similarity criterion: all corresponding sides proportional → triangles similar

Q12 B Substitute x=2: k(4) − 5(2) + 2 = 0 → 4k − 10 + 2 = 0 → 4k = 8 → k = 2

Q13 C Sorted: 74,78,85,88,90,92,96. Median (4th) = 88

Q14 C Pythagorean identity: sec²θ − tan²θ = 1

Q15 B Hypotenuse² = Sum of squares of other two sides

Q16 A Deviations from 70: -10,-5,2,10,-15,20,-2. Sq: 100,25,4,100,225,400,4. Sum=858. Var=858/7≈122.6≈124 (closest)

Q17 B Sum of roots = −b/a

Q18 C tan 45° = 1; cot 45° = 1; sum = 2

Q19 C h² = 10² − 6² = 100 − 36 = 64 → h = 8 m

Q20 D sin θ ranges from 0 to 1 for θ ∈ [0°, 90°]

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