Q1. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
(a) 10 days
(b) 12 days
(c) 15 days
(d) 20 days
Q2. A boy and girl together fill a cistern with water. The boy pours 4 litres of water every 3 minutes and the girl pours 3 litres of water every 4 minutes. How much time will it take to fill 100 litres of water in the cistern?
(a) 36 minutes
(b) 42 minutes
(c) 48 minutes
(d) 44 minutes
Q3. A train 100m long is running at the speed of 30 km/hr. The time (in second) in which it passes a man standing near the railway line is:
Q4. A train crosses a pole in 15 seconds and a platform 100 metres long in 25 seconds. Length of train (in metres) is
Q5. Two trains travel in the same direction at the speed of 56 km/hr and 29 km/hr. respectively. The faster train passes a man in the slower train in 10 seconds. The length of the faster train (in metres) is
Q6. The total surface area of a sphere is 8? square unit. The volume of the sphere is
(a) (8√2/3) π cubic unit
(b) (8/3)? cubic unit
(c) (8√3)? cubic unit
(d) (8√3/5)π cubic unit
Q7. A cylinder has ‘r’ as the radius of the base and ‘h’ as the height. The radius of base of another cylinder, having double the volume but the same height as that of the first cylinder must be equal to
Q8. The ratio of height and the diameter of a right circular cone is 3 : 2 and its volume is 1078 cc, then (taking ? = 22/7) its height is:
(a) 7 cm
(b) 14 cm
(c) 21 cm
(d) 28 cm
Q9. If S1 and S2 be the surface areas of a sphere and the curved surface area of the circumscribed cylinder respectively, then S1 is equal to
(a) (3/4) S2
(b) (1/2) S2
(c) (2/3) S2
Q10. A metallic hemisphere is melted and recast in the shape of cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then:
(a) H = 2R
(b) H = (2/3) R
(c) H = √3R
(d) B = 3R
Sol. Speed = 30 km/hr = 30 × (5/18) m/sec.
= (25/3) m/sec
So, time = D/S=100/(25/3) = 12 sec.
Sol. We can inferred that train crosses only platform not its length in 25 – 15 = 10 second
⇒ Speed of the train = (100 metres)/(10 sec) = 10 m/s
∵ Train crosses the pole in 15 seconds and we know when train crosses a pole/tree/man this case it covers the equal distance of its length.
Length of train = 15 × 10
= 150 metres.
Sol. When a faster train crosses the man who sits in the other train, on that time faster train covers the distance equal to its length but the relative speed (opposite/same direction) is considered in respect of man.
Relative speed of the trains = (56 – 29) km/h = 27 km/h
Length of faster train = Distance covered by faster train in 10 second with Relative speed of 27 km/h
= 27 km/h × 10 sec.
= 27 × (5/18) × 10 m.
= 75 metres
Sol. Let the radius of base of second cylinder = R
⇒2(πr^2 h)=πR^2 h
Sol. Let height and diameter be 3x and 2x
⇒1/3 πx^2 × 3x=1078
⇒ x = 7
⇒ height = 7 × 3 = 21 cm
Sol. Height of cylinder = Diameter of sphere
⇒S1/S2 =(4πr^2)/(2πr×h)=(4r^2)/(4r^2 )=1/1
Sol. When we change shape of a solid figure, volume remains constant,
∴ Volume of Hemisphere = Volume of cone
2/3 πR^3 = (1/3) πR^2 h
∴ 2R = h