GATE Practice Question and Answer
8Q: The top and bottom of a tower were seen to be at angles of depression 30° and 60° from the top of a hill of height 100 m. Find the height of the tower ? 2679 15b5cc72ce4d2b4197774f79c
5b5cc72ce4d2b4197774f79c- 142.2 mtsfalse
- 233.45 mtsfalse
- 366.6 mtstrue
- 458.78 mtsfalse
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Answer : 3. "66.6 mts"
Explanation :
Answer: C) 66.6 mts Explanation: From above diagramAC represents the hill and DE represents the tower Given that AC = 100 m angleXAD = angleADB = 30° (∵ AX || BD ) angleXAE = angleAEC = 60° (∵ AX || CE) Let DE = h Then, BC = DE = h, AB = (100-h) (∵ AC=100 and BC = h), BD = CE tan 60°=AC/CE => √3 = 100/CE =>CE = 100/√3 ----- (1) tan 30° = AB/BD => 1/√3 = 100−h/BD => BD = 100−h(√3)∵ BD = CE and Substitute the value of CE from equation 1 100/√3 = 100−h(√3) => h = 66.66 mts The height of the tower = 66.66 mts.
Q: Which of the following is not soluble in water? 2679 05b5cc690e4d2b4197774c422
5b5cc690e4d2b4197774c422- 1copper(II) hydroxidetrue
- 2sodium chloridefalse
- 3silver nitratefalse
- 4potassium sulfatefalse
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Answer : 1. "copper(II) hydroxide"
Explanation :
Answer: A) copper(II) hydroxide Explanation: Sodium chloride: The solubility rules tell you that all halides are soluble with the exception of those formed with siver, mercury, and lead ions. Since this is not the case here, sodium chloride will be soluble. Silver nitrate: It is soluble because all nitrates are soluble, without exception. Potassium sulfate: It is soluble because all sulfates are soluble with the exception of those formed with silver, calcium, barium, mercury, lead, and strontium ions. Copper (II) hydroxyde: It is insoluble because all hydroxides are insoluble with the exception of those formed with alkali metal ions and barium.
Q: Which of the following animals have teeth in their stomach? 2678 05b5cc6bde4d2b4197774d8f7
5b5cc6bde4d2b4197774d8f7- 1Frogsfalse
- 2Crabstrue
- 3Snakesfalse
- 4Cockroachfalse
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Answer : 2. "Crabs"
Explanation :
Answer: B) Crabs Explanation:
Q: A motorboat can go 10 miles downstream on a river in 20 min. It takes 30 min for this boat to go back at the same 10 miles. Find the speed of the current ? 2676 05b5cc6bfe4d2b4197774da29
5b5cc6bfe4d2b4197774da29- 18 m/hfalse
- 25 m/htrue
- 37 m/hfalse
- 46 m/hfalse
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Answer : 2. "5 m/h"
Explanation :
Answer: B) 5 m/h Explanation: As the distance travelled is constant, the time taken is inversely proportional to speed. Let 'u' be the speed of the current and 'v' be the speed of the boat. Speed of the boat downstream = v + u & upstream = v - u => v+u/v-u = 30/20 => v/u = 5 => v = 5u => v + u = 6u = 10/20/60 miles/hr => 6u = 30 m/h => u = 5 m/h
Q: What can you catch but not throw? 2675 05b5cc6a3e4d2b4197774cc04
5b5cc6a3e4d2b4197774cc04- Show AnswerHide Answer
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Answer :
Explanation :
A cold or flu illness.
Q: Three strategies P, Q and R have been initiated for cost cutting in a company producing respectively 20%, 30% and 10% savings. Assuming that they operate independently, what is the net saving achieved ? 2673 05b5cc73ae4d2b4197774f8dd
5b5cc73ae4d2b4197774f8dd- 149.6%true
- 250.4%false
- 333.67%false
- 466.66%false
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Answer : 1. "49.6%"
Explanation :
Answer: A) 49.6% Explanation: As these three strategies P, Q and R are independent so these will cut cost one after the other.If initial cost is Rs 100, then20% cost is cut after initializing strategy P, then cost will remain 80% = 80further 30% cost is cut after strategy Q, then cost will remain 70% of 80 = 56further 10% cost is cut after strategy R, then cost will remain 90% of 56 = 50.4 Thus final cost remains 50.4 % of the original cost. Hence net saving is 100 - 50.4 = 49.6 %.
Q: The third proportional to 9 and 12 is ? 2670 05b5cc6e9e4d2b4197774ede8
5b5cc6e9e4d2b4197774ede8- 114false
- 216true
- 318false
- 420false
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Answer : 2. "16"
Explanation :
Answer: B) 16 Explanation: Let the third proportion to 9 & 12 be 'x'. => 9:12 = 12 :p => p = 12x12/9 = 16.
Q: 25% of 25% Is Equal To 2668 05b5cc6bae4d2b4197774d78a
5b5cc6bae4d2b4197774d78a- 10.0625true
- 20.0210false
- 30.03145false
- 40.3210false
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Answer : 1. "0.0625"
Explanation :
Answer: A) 0.0625 Explanation: 25% of 25% means 25/100 of 25/100 i.e, 1/4 of 1/4 or in other words 1/4 x 1/4=1/16 Hence, the answer is 1/16 = 0.0625.

