Question : Three men step off together from the same spot. Their steps measure 63 cm, 70 cm, and 77 cm, respectively. The minimum distance each should cover so that all can cover the distance in complete steps is:

Option 1: 9630 cm

Option 2: 9360 cm

Option 3: 6930 cm

Option 4: 6950 cm

Question : The circumference of the two circles is 110 cm and 330 cm respectively. What is the difference between their radii?

Option 1: 70 cm

Option 2: 15 cm

Option 3: 46 cm

Option 4: 35 cm

Question : Three circles of radius 6 cm each touch each other externally. Then the distance of the centre of one circle from the line joining the centres of the other two circles is equal to:

Option 1: $6\sqrt{5}\;\mathrm{cm}$

Option 2: $6\sqrt{3}\;\mathrm{cm}$

Option 3: $6\sqrt{2}\;\mathrm{cm}$

Option 4: $6\sqrt{7}\;\mathrm{cm}$

Question : Three cubes of iron whose edges are 6 cm, 8 cm, and 10 cm, respectively, are melted and formed into a single cube. The edge of the cube formed is:

Option 1: 12 cm

Option 2: 14 cm

Option 3: 16 cm

Option 4: 18 cm

Question : A metallic cube has sides of length 12 cm. It is melted and recast into three small cubes. Of these cubes, two have sides measuring 6 cm and 8 cm, respectively. The length of each side of the third cube is:

Option 1: 7 cm

Option 2: 9 cm

Option 3: 10 cm

Option 4: 5 cm

Question : Three solid metallic spheres of radii 1 cm, 6 cm, and 8 cm, respectively, are melted and recast into a single solid sphere. The radius of the new sphere formed is:

Option 1: 9.0 cm

Option 2: 5.9 cm

Option 3: 7.7 cm

Option 4: 8.5 cm