200 questions asked across 4 exam years, newest first
The radius of the circle is 8 cm. The distance of a point lying outside the circle from the centre is 17 cm. The length of the tangent drawn from the outside point to the circle is:
Answer: D
A boatman rows to a place 30 km distant and back in 14 hours. He finds that he can row 10 km with the stream at the same time as 4 km against the stream. Find the speed (in km/h) of the stream.
Answer: D
M and N walk along a circular track. They start at 5:00 a.m. from the same point in the opposite directions. M and N walk at a speed of 5 rounds per hour and 2 rounds per hour, respectively. How many times will they cross each other before 6.30 a.m. on the same day?
Answer: C
From a point T, the length of the tangent to a circle is 32 cm and the distance of T from the center is 40 cm. The diameter (in cm) of the circle is:
Answer: A
A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along with the current in 10 minutes. How long will it take to go 6 km in stationary water?
Answer: A
A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km/h and 11 km/h, respectively.. What is the distance (in metres) between them after 9 minutes?
Answer: A
A boat can go 54 km upstream in 6 hours. If the speed of the stream is 4.8 km/h, then how much time (in hours) will the boat take to cover a distance of 279 km downstream?
Answer: B
In a circular race of 750 m, X and Y start from the same point and at the same time with speeds of 9 km/h and 13.5 km/h, respectively. If they are running in the same direction then, when will they meet again for the first time on the track?
Answer: B
A policeman noticed a thief at a distance of 500 metres. The policeman started running and the thief also started running at the same time. The thief is running at a speed of 15 km/h. It took 15 minutes for the policeman to catch the thief. Find the speed of the policeman (in km/h).
Answer: B
In a circle of radius 5√13 cm, a chord is at a distance of 10 cm from the centre of the circle. Find the length (in cm) of the chord.
Answer: D
Places A and B are 20 km apart on the highway. A car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in one hour. If they travelled towards each other, they met in 12 minutes. What are the speeds (in km/h) of two cars?
Answer: B
The speed of a boat in still water is 18 km/h and the speed of the stream is 3 km/h. How much time (in hours) will it take to cover a distance of 105 km in downstream and in coming back?
Answer: A
The radii of two circle are 5 cm and 10 cm and the distance between their centres is 17 cm. Find the length of the transverse common tangent.
Answer: D
A thief noticed a policeman at a distance of 600 metres. The thief started running and the policeman chased him. The thief and policeman are running at speeds of 12 km/h and 15 km/h, respectively. Find the time (in minutes) required for the policeman to catch the thief.
Answer: C
