IIT JEE Practice Question and Answer
8Q: A jogger running at 9 km/hr along side a railway track is 260 m ahead of the engine of a 140 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger ? 1736 05b5cc6e5e4d2b4197774ed29
5b5cc6e5e4d2b4197774ed29- 125 secfalse
- 240 sectrue
- 338 secfalse
- 432 secfalse
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Answer : 2. "40 sec"
Explanation :
Answer: B) 40 sec Explanation: Speed of train relative to jogger = 45 - 9 = 36 km/hr.= 36 x 5/18 = 10 m/sec. Distance to be covered = 260 + 140 = 400 m. Time taken = 400/10 = 40 sec.
Q: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high ? 1406 05b5cc6e5e4d2b4197774ed1f
5b5cc6e5e4d2b4197774ed1f- 113 mtrue
- 214 mfalse
- 315 mfalse
- 416 mfalse
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Answer : 1. "13 m"
Explanation :
Answer: A) 13 m Explanation: The length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high is => d2 = 122 + 42 + 32 = 13mts.
Q: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case ? 6273 05b5cc6e5e4d2b4197774ed24
5b5cc6e5e4d2b4197774ed24- 1693false
- 2741false
- 3528true
- 4654false
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Answer : 3. "528"
Explanation :
Answer: C) 528 Explanation: Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)= (1200)(30)(3) kg. Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k As the same provisions are available=> (1200)(30)(3) = (1200 + x)(25)(2.5) x = ([(1200)(30)(3)] / (25)(2.5)) - 1200 => x = 528.
Q: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes). 3909 05b5cc6e5e4d2b4197774ed15
5b5cc6e5e4d2b4197774ed15- 118 minfalse
- 230 mintrue
- 327 minfalse
- 432 minfalse
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Answer : 2. "30 min"
Explanation :
Answer: B) 30 min Explanation: Distance travelled by Ramu = 45 x 4 = 180 km Somu travelled the same distance in 6 hours. His speed = 180/6 = 30 km/hr Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr. Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken = 0.5 hours = 30 minutes.
Q: Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes ? 3620 05b5cc6e5e4d2b4197774ed1a
5b5cc6e5e4d2b4197774ed1a- 121 mintrue
- 224 minfalse
- 320 minfalse
- 422 minfalse
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Answer : 1. "21 min"
Explanation :
Answer: A) 21 min Explanation: Let the pipe B be closed after 'K' minutes. 30/16 - K/24 = 1 => K/24 = 30/16 - 1 = 14/16 => K = 14/16 x 24 = 21 min.
Q: The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2. Find their incomes ? 5147 05b5cc6e5e4d2b4197774ed0b
5b5cc6e5e4d2b4197774ed0b- 1200, 400false
- 2100, 300false
- 3100, 200false
- 4150, 200true
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Answer : 4. "150, 200"
Explanation :
Answer: D) 150, 200 Explanation: The incomes of A and B be 3P and 4P. Expenditures = Income - Savings (3P - 100) and (4P - 100) The ratio of their expenditure = 1:2 (3P - 100):(4P - 100) = 1:2 2P = 100 => P = 50 Their incomes = 150, 200
Q: 217 x 217 + 183 x 183 = ? 1521 05b5cc6e5e4d2b4197774ed10
5b5cc6e5e4d2b4197774ed10- 184521false
- 287487false
- 380578true
- 478458false
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Answer : 3. "80578"
Explanation :
Answer: C) 80578 Explanation: 2172+1832 = 200+172+200-172 It is in the form of a+b2+a-b2=2a2+b2 = 2(40000 + 289) = 80578.
Q: How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together ? 2352 05b5cc6e5e4d2b4197774ed01
5b5cc6e5e4d2b4197774ed01- 17false
- 29true
- 311false
- 45false
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Answer : 2. "9"
Explanation :
Answer: B) 9 Explanation: LCM of 2, 3, 7 is 42. => (700 – 300)/42 = 9 22/42 => 9 Numbers.