751. A can complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr. Find the total journey in km.
A. 220 km
B. 224 km
C. 230 km
D. 234 km
752. A car is running at a speed of 108 kmph. What distance will it cover in 15 seconds ?
A. 45 metres
B. 55 metres
C. 450 metres
D. Cannot be determined
753. A train covers a distance of 10 km in 12 minutes. If its speed is decreased by 5 km /hr, the time taken by it to cover the same distance will be :__________?
A. 10 min
B. 11 min 20 sec
C. 13 min
D. 13 min 20 sec
Speed = (10 X 60/12 ) km/hr = 50 km/hr. New speed = (50 – 5) km / hr = 45 km /hr. So Time taken = ( 10/45 ) hr = ( 2/9X 60 )min 131/3 min = 13 min 20 sec.
Volume of water displaced = (3 X 2 X 0.01) m3 = 0.06 m3.
Mass of man = Volume of water displaced X Density of water
= (0.06 X 1000) kg = 60 kg.
754. The radius of the cylinder is half its height and area of the inner part is 616 sq. cms. Approximately how many litres of milk can it contain ?
755. The capacity of a cylindrical tank is 246.4 litres. If the height is 4 metres, what is the diameter of the base ?
A. 1.4 m
B. 2.8 m
C. 14 m
D. None of these
756. A boat having a length 3 m and breadth 2 m is floating on a lake The boat sinks by 1 cm when a man gets on it. The mass of man is :__________?
A. 12 kg
B. 60 kg
C. 72 kg
D. 96 kg
757. The areas of the three adjacent faces of a rectangular box which meet in a point are known. The product of these areas is equal to :___________?
A. the volume of the box
B. twice the volume of the box
C. the square of the volume of the box
D. the cube root of the volume of the box
Let length = 1, breadth = b and height = h. Then,
Product of areas of 3 adjacent faces = (lb x bh x 1h) = (lbh)2 = (Volume)2.
758. The edges of a cuboid are in the ratio 1 : 2 : 3 and its sun face area is 88 cm2. The volume of the cuboid is :_________?
A. 24 cm3
B. 48 cm3
C. 64 cm3
D. 120 cm3
Let the dimensions of the cuboid be x, 2x and 3x.
Then, 2 (x X 2x + 2x X 3x + x X 3x) = 88
⇔ 2X2 6X2 + 3X2 = 44 ⇔ 11X2 = 44 ⇔ X2 = 4 ⇔ x = 2.
Volume of the Cuboid = (2 X 4 X 6) cm3 = 48 cm3.
759. What is the volume of a cube (in cubic cm) whose diagonal measures 4√3 cm ?
760. A cuboidal, block of 6 cm X 9 cm X 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be_________?
Volume of block = (6 X 9 X 12) cm3 = 648 cm3.
Side of largest cube = H.C.F. of 6 cm, 9 cm, 12 cm = 3 cm.
Volume of this cube = (3 X 3 X 3) = 27 cm3.
Number of cubes = 648/27 = 24.
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