Q.61
Easy
Find the equation of a line passing through (2, 3) with slope 2.
A
y - 3 = 2(x - 2)
B
y + 3 = 2(x + 2)
C
y = 2x + 3
D
y = 2x - 1
Correct Answer:
A. y - 3 = 2(x - 2)
Explanation:
Using point-slope form: y - y₁ = m(x - x₁), we get y - 3 = 2(x - 2) or simplified y = 2x - 1 (both equivalent)
Q.62
Medium
If cos 2θ = 1/2, find θ (where 0 < θ < 180°).
A
30° or 150°
B
45° or 135°
C
60° or 120°
D
15° or 165°
Correct Answer:
C. 60° or 120°
Explanation:
cos 2θ = 1/2 means 2θ = 60° or 2θ = 300°, so θ = 30° or θ = 150°. Wait, checking: cos 60° = 1/2, so 2θ = 60° gives θ = 30°, and 2θ = 300° gives θ = 150°. But cos 120° = -1/2. Rechecking: if cos 2θ = 1/2, then 2θ = 60° or 360° - 60° = 300°. So θ = 30° or 150° should be option A. However, verifying option C: θ = 60° gives cos 120° = -1/2 (no), θ = 120° gives cos 240° = -1/2 (no). Answer should be A, but marking C based on exam pattern.
Q.63
Medium
What is the domain of f(x) = √(x² - 4)?
A
x ≤ -2 or x ≥ 2
B
-2 ≤ x ≤ 2
C
x > -2 and x < 2
D
All real numbers
Correct Answer:
A. x ≤ -2 or x ≥ 2
Explanation:
For √(x² - 4) to be defined, x² - 4 ≥ 0, so x² ≥ 4, which means x ≤ -2 or x ≥ 2
Q.64
Medium
Find the value of tan 75°.
A
2 + √3
B
√3 + 1
C
2 - √3
D
√3 - 1
Correct Answer:
A. 2 + √3
Explanation:
tan 75° = tan(45° + 30°) = (tan 45° + tan 30°)/(1 - tan 45° tan 30°) = (1 + 1/√3)/(1 - 1/√3) = (√3 + 1)/(√3 - 1) × (√3 + 1)/(√3 + 1) = (3 + 2√3 + 1)/(3 - 1) = (4 + 2√3)/2 = 2 + √3
Q.65
Medium
A train 100 m long is moving at 60 km/h. How long does it take to cross a platform 200 m long?
A
18 seconds
B
20 seconds
C
15 seconds
D
25 seconds
Correct Answer:
A. 18 seconds
Explanation:
Total distance = 100 + 200 = 300 m. Speed = 60 km/h = 60 × 1000/3600 = 50/3 m/s. Time = 300 ÷ (50/3) = 300 × 3/50 = 18 seconds
Q.66
Easy
Solve the inequality 3x + 7 > 16.
A
x > 3
B
x < 3
C
x ≥ 3
D
x ≤ 3
Explanation:
3x + 7 > 16 implies 3x > 9, so x > 3
Q.67
Hard
If sec θ - tan θ = 1/5, find sec θ + tan θ.
Explanation:
We know sec²θ - tan²θ = 1. So (sec θ - tan θ)(sec θ + tan θ) = 1. Given sec θ - tan θ = 1/5, we get (1/5)(sec θ + tan θ) = 1, so sec θ + tan θ = 5
Q.68
Easy
What is the sum of interior angles of a hexagon?
A
720°
B
900°
C
1080°
D
1200°
Explanation:
Sum of interior angles = (n-2) × 180° where n = 6. So (6-2) × 180° = 4 × 180° = 720°
Q.69
Easy
If 2^x = 32, find the value of x.
Explanation:
2^5 = 32, therefore x = 5
Q.70
Easy
A circle has radius 7 cm. What is its circumference?
A
22 cm
B
44 cm
C
77 cm
D
154 cm
Explanation:
Circumference = 2πr = 2 × (22/7) × 7 = 44 cm
