200 questions asked across 4 exam years, newest first
Two athletes are participating in a race on a circular track of 220 m. Ravi runs at the speed of 22 m/s, while Kapil runs at the speed of 11 m/s. They start from the same point, at the same time, and in the same direction. After how many seconds will they meet for the first time?
Answer: B
From a point A, which is at a distance of 17 cm from the centre C of a circle with radius 8 cm, the pair of tangents AB and AD to the circle are drawn. The area of the quadrilateral ABCD is _____ cm².
Answer: C
A thief takes off on his bike at a certain speed, after seeing a police car at a distance of 250 m. The police car starts chasing the thief and catches him. If the thief runs 1.5 km before being caught and the speed of the police car is 70 km/h, then what is the speed of thief's bike (in km/h)?
Answer: D
In a circular race of 1600 m in length, Bhaskar and Vinay start with speeds of 27 km/h and 45 km/h starting at the same time from the same point. When will they meet for the first time on the track when running in the opposite directions and the same direction, respectively?
Answer: B
Suppose P starts walking at a speed of 8 km/h. After 8 hours B started travelling on a bicycle at a speed of 24 km/h. The distance from the starting B can catch A is:
Answer: B
A policeman noticed a thief at some distance. The policeman started running to catch the thief and the thief also started running at the same time. The speed of both policeman and the thief was 12 km per hour and 10 km per hour, respectively. It took 30 minutes for the policeman to catch the thief. Find the initial distance (in metres) between them.
Answer: A
The radius of a circle is 12.5 cm and the length of one its chords is 11 cm. What is the distance of the chord from the centre? (correct to one decimal place)
Answer: C
A thief is spotted by a policeman from a distance of 100 m. The thief starts running and the policeman chases him. If the speed of thief and policeman are 21 km/h and 23 km/h, respectively, then how far will the thief have to run before he is over taken?
Answer: B
Two goods trains 132 m and 108 m in length are running towards each other on parallel tracks. The first train is running at a speed of 32 km/h and the second at a speed of 40 km/h. How much time will they take to cross each other after meeting?
Answer: A
A policeman is chasing a thief at a speed of 82 km/h. The thief is 1300 m away and is running at a speed of 64 km/h. In how much time will the policeman catch the thief if both are riding on bikes?
Answer: C
A thief is noticed by a policeman from a distance of 92 m. The thief starts running and the policeman chases him. The thief and the policeman run at the speed of 90 km/h and 104.4 km/h, respectively. In how much time will the policeman catch the thief?
Answer: D
If in a circle a chord of length 14 cm is at a distance of 24 cm from its centre, then the length of the radius of the circle is:
Answer: B
A boat covers a distance of 55 km downstream in 5 hours while it takes 11 hours to cover the same distance upstream. What is the speed of the boat?
Answer: A
Two trains of lengths 150 m and 250 m run on parallel lines. When they run in the same direction, they take 20 seconds to cross each other and, when they run in the opposite direction, they take 5 seconds to cross each other. What is the speed of the two trains?
Answer: B
The radius of the circle is 10 cm and the perpendicular distance from the chord to the centre is 6 cm. The length of the chord is:
Answer: C
A thief is spotted by a policeman from a distance of 200 metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief is 9 km/h and that of the policeman 10 km/h, how far will the thief have to run before he is overtaken?
Answer: A
A thief is spotted by a policeman from a distance of 195 metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief is 22 km/h and that of the policeman is 27 km/h, then how far would the thief have run (in m) before he is overtaken?
Answer: A
A motorboat travelling at some speed can cover 24 km upstream and 40 km downstream in 17 hours. At the same speed, it can travel 32 km downstream and 12 km upstream in 10 hours. The speed of the stream is:
Answer: C
A chord of length 32 cm is drawn at a distance of 12 cm from the centre of a circle. Find the radius of the circle.
Answer: D
In a circular race of 4800m, A and B start from the same point and at the same time with speeds of 36 km/h and 54 km/h. When will they meet again for the first time on the track if they are running in the opposite direction?
Answer: C
A man can row a distance of 6 km in 1 hour in still water. He can row the same distance in 45 minutes with the current. Find the total time taken by him to row a distance of 16 km with the current and to return to the starting point.
Answer: D
Akshara and Siddharth travel from point P to Q, a distance of 72 km at a rate of 8 km/h and 10 km/h, respectively. Siddharth reaches Q first and returns immediately and meets Akshara at R. Find the distance from P to R.
Answer: B
AB and CD are two parallel chords drawn in a circle with centre O. The distance between the two chords is 21 cm. If the lengths of AB and CD are 24 cm and 18 cm, respectively, then the radius of the circle is equal to:
Answer: A
A boat can travel 78 km upstream and back in a total of 32 hours. It can travel 15 km upstream and 52 km downstream in a total of 9 hours. How much distance will the boat cover in 12 hours in still water?
Answer: C
P and Q start running in opposite directions on a circular track from the same point. If their speeds are 10 m/s and 8 m/s, respectively, then after what time will they meet if the length of the track is 1620 m?
Answer: D
