Showing 21–30 of 44 questions
A man walks 30 km north, then 40 km east. Find his displacement from starting point.
A
50 km
B
70 km
C
60 km
D
√2500 km
EXPLANATION
Displacement = √(30² + 40²) = √(900 + 1600) = √2500 = 50 km
Find the sum of the series 2 + 4 + 8 + 16 + ... up to 10 terms.
A
2046
B
1024
C
2048
D
4094
EXPLANATION
This is a geometric series with a = 2, r = 2, n = 10. Sum = a(r^n - 1)/(r-1) = 2(2¹⁰ - 1)/(2-1) = 2(1024 - 1) = 2046
If cos θ = 3/5 and θ is in the first quadrant, find sin θ.
EXPLANATION
Using sin²θ + cos²θ = 1: sin²θ = 1 - 9/25 = 16/25, so sin θ = 4/5 (positive in first quadrant)
A circle has radius 7 cm. Find the area of the sector with central angle 60°.
A
25.67 cm²
B
51.33 cm²
C
102.67 cm²
D
154 cm²
Correct Answer:
A. 25.67 cm²
EXPLANATION
Area of sector = (θ/360°) × πr² = (60/360) × π × 49 = (1/6) × 22/7 × 49 = 25.67 cm²
In how many ways can 5 people be arranged in a line?
EXPLANATION
Number of arrangements of 5 people = 5! = 5 × 4 × 3 × 2 × 1 = 120.
The distance between points (1, 2) and (4, 6) is:
EXPLANATION
Distance = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.
A person invests Rs. 5000 at 8% per annum simple interest for 3 years. The interest earned is:
A
Rs. 1200
B
Rs. 1000
C
Rs. 1500
D
Rs. 800
Correct Answer:
A. Rs. 1200
EXPLANATION
Simple Interest = (P × R × T)/100 = (5000 × 8 × 3)/100 = 1200.
If x² - 5x + 6 = 0, find the sum of the roots.
EXPLANATION
For ax² + bx + c = 0, sum of roots = -b/a = -(-5)/1 = 5.
What is the probability of getting a prime number when a die is rolled?
EXPLANATION
Prime numbers on a die: 2, 3, 5 (total 3). Total outcomes = 6. Probability = 3/6 = 1/2.
A number when divided by 7 gives quotient 12 and remainder 3. The number is:
EXPLANATION
Using dividend = divisor × quotient + remainder: Number = 7 × 12 + 3 = 84 + 3 = 87.
