A ladder of length 13 m leans against a wall. If the foot of the ladder is 5 m away from the wall, find the height reached by the ladder on the wall.
A
10 m
B
11 m
C
12 m
D
13 m
Using Pythagorean theorem: h² + 5² = 13². So h² = 169 - 25 = 144. Therefore h = 12 m.
In a right-angled triangle, if one acute angle is 35°, find the other acute angle.
In a right-angled triangle, the sum of acute angles is 90°. Therefore, other angle = 90° - 35° = 55°.
A sphere has surface area 616 cm². Find its radius (use π = 22/7).
A
7 cm
B
8 cm
C
9 cm
D
10 cm
Surface area of sphere = 4πr² = 616. So 4 × (22/7) × r² = 616. Thus r² = 49, r = 7 cm.
A man invests ₹10,000 at 10% compound interest per annum for 2 years. Find the compound interest.
A
₹2,000
B
₹2,100
C
₹1,100
D
₹1,200
Correct Answer:
B. ₹2,100
Amount = P(1 + r/100)ⁿ = 10000(1.1)² = 10000 × 1.21 = 12100. Compound interest = 12100 - 10000 = ₹2,100.
Two numbers are in the ratio 3:4. If their LCM is 180, find the greater number.
Let numbers be 3k and 4k. LCM(3k, 4k) = 12k = 180. So k = 15. Numbers are 45 and 60. Greater number is 60.
A boat travels downstream for 30 km in 2 hours and upstream for 30 km in 3 hours. Find the speed of the boat in still water.
A
11.5 km/h
B
12.5 km/h
C
13.5 km/h
D
14.5 km/h
Correct Answer:
B. 12.5 km/h
Downstream speed = 30/2 = 15 km/h. Upstream speed = 30/3 = 10 km/h. Speed of boat in still water = (downstream + upstream)/2 = (15 + 10)/2 = 12.5 km/h.
The sum of first n natural numbers is 300. Find n.
Sum of first n natural numbers = n(n+1)/2 = 300. So n(n+1) = 600. Solving: n² + n - 600 = 0. Using quadratic formula: n = 24 (taking positive value).
In triangle ABC, if ∠A = 60°, ∠B = 80°, find ∠C.
Sum of angles in a triangle = 180°. So ∠C = 180° - 60° - 80° = 40°
Find the median of {3, 7, 2, 9, 5, 1, 8}.
Arranging in order: {1,2,3,5,7,8,9}. Median is the middle value = 5
Find the area of a parallelogram with base 15 cm and height 8 cm.
A
60 cm²
B
90 cm²
C
120 cm²
D
180 cm²
Correct Answer:
C. 120 cm²
Area of parallelogram = base × height = 15 × 8 = 120 cm²
