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**Class 10 - Maths - 1 Mark Questions Asked in Previous Years Examinations**

**Q1: If secθ.sinθ = 0, find tan θ.**

Answer:

secθ.sinθ = tan θ = 0

⇛ tan θ = tan 0°

∴ θ = 0°

**Q2: If tan(3x + 30°) = 1, find the value of x**

Answer:

tan(3x + 30°) = 1 = tan 45°

3x + 30° = 45°

3x = 45 - 30 = 15

x = 5°

**Q3: When are two triangles said to be similar?**

Answer: Two triangles are said to be similar when corresponding sides are proportional and angles are equal.

**Q4: To divide the line segment AB in the ratio 2:3, a ray AX is drawn such that ∠BAX is acute, AX is marked at equal intervals. Find the minimum number of such marks.**

Answer: Minimum no. of marks = 2 + 3 = 5.

**Q5: What is the maximum number of parallel tangents a circle can have on a diameter?**

Answer: Two tangents.

**Q6: Are two triangles with equal corresponding sides always similar?**

Answer: No, included angles must also be equal.

**Q7: Find the distance of the point (-4, -7) from y-axis?**

Answer: 4 units (The x-coordinate of point is -4)

Using distance formula,

___________________ ___________ Distance = √(0 + 4)² + (7 - 7)² = √(4)² + (0)²

= √16 = 4 units

**Q8: Find the sum of first five multiples of 2.**

Answer: Here a = 2, d = 2, n = 5

S = n[2a + (n-1)d]/2

= 5[2(2) + (5-1)2]/2 = 5 × 6

= 30

**Q9: In the AP series three numbers are 2, x, 26, find the value of x.**

Answer: Common difference will be equal.

x - 2 = 26 - x

⇛ x + x = 26 + 2

⇛ 2x = 28

⇛ x = 14

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Q10: Find the positive root of √3x² + 6 = 9 _______ Answer: √3x² + 6 = 9 (3x² + 6) = 9² ⇛ 3x² = 81 - 6 = 75 ⇛ x² = 25 ⇛ x = 5

**Q11: If α and β are the roots of ax² -bx + c = 0 (a ≠ 0). Find α + β.**

Answer: Sum of roots = α + β = -b/a = -(-b/a) = b/a

**Q12: Explain why 13233354363715 is a composite number?**

Answer: Since the given number ends with digit 5, it is a multiple of 5. ∴ it is a composite number.

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