SSC CPO 5th Oct 2023 Shift 1

A cylinder has some water in it at a height of 16 cm. If a sphere of radius 9 cm is put into it, then find the rise in the height of the water if the radius of the cylinder is 12 cm.

A can do $$\frac{1}{5}$$ of a piece of work in 20 days, B can do 30% of the same work in 36
days, while C can do 80% of the same work in 160 days. Band C together started and worked for x days. After x days B left the work, and A joined C and both completed the remaining work in (x - 41) days. If the ratio between the work done by (B + C) together to the work done by (A + C) together is 19 : 6, then what fraction of the same work can be completed by C alone in 2x days?

If the radius of two circles be 6 cm and 9 cm and the length of the transverse common tangent be 20 cm, then find the distance between the two centres.

Nikunj goes 4 kilometres against the current of a stream in 1 hour, and 2 kilometres along the current in 15 minutes. How long will it take him to go 7 kilometres in stationary water?

At 7: 30 P.M. the owner of a Cycle noticed that a thief is taking away his cycle from his home and is cycling in a particular direction at an estimated speed of 10 km per hour. He informed the police about the theft and the policeman started from the same point, half an hour later than the time of the theft but with a speed of 12 km per hour. At what time will Policeman catch the thief?

The pie chart below shows the spendings of a state on various sports during a particular year:

image

If the total amount spent on sports during the year was ₹5,00,000 then how much (in₹) was spent on cricket and
hockey together?

In a $$\triangle ABC$$, the bisectors of angle ABC and angle ACB intersect each other at point O. If the angle BOC is $$125^{\circ}$$, then the angle BAC is equal to:

Two trains Mumbai Rajdhani and Kissan Express of lengths 850 m and 700 m are 1050 m apart, and are running on parallel tracks towards each other. Mumbai Rajdhani is running at 62 km/h and Kissan Express is running at 55 km/h. In how much time (in sec) will the trains cross each other?

If $$\sin \beta =\frac{1}{3}, (\sec \beta - \tan \beta)^{2}$$ is equal to:

A right square pyramid having lateral surface area is 624 $$cm^{2}$$ . If the length of the diagonal of the square is $$24\sqrt{2}$$, then the volume of the pyramid is: