GATE Practice Question and Answer

Q: 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 1

  • 1
    42.2 mts
    Correct
    Wrong
  • 2
    33.45 mts
    Correct
    Wrong
  • 3
    66.6 mts
    Correct
    Wrong
  • 4
    58.78 mts
    Correct
    Wrong
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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 0

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    copper(II) hydroxide
    Correct
    Wrong
  • 2
    sodium chloride
    Correct
    Wrong
  • 3
    silver nitrate
    Correct
    Wrong
  • 4
    potassium sulfate
    Correct
    Wrong
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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 0

  • 1
    Frogs
    Correct
    Wrong
  • 2
    Crabs
    Correct
    Wrong
  • 3
    Snakes
    Correct
    Wrong
  • 4
    Cockroach
    Correct
    Wrong
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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 0

  • 1
    8 m/h
    Correct
    Wrong
  • 2
    5 m/h
    Correct
    Wrong
  • 3
    7 m/h
    Correct
    Wrong
  • 4
    6 m/h
    Correct
    Wrong
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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 0

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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 0

  • 1
    49.6%
    Correct
    Wrong
  • 2
    50.4%
    Correct
    Wrong
  • 3
    33.67%
    Correct
    Wrong
  • 4
    66.66%
    Correct
    Wrong
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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 0

  • 1
    14
    Correct
    Wrong
  • 2
    16
    Correct
    Wrong
  • 3
    18
    Correct
    Wrong
  • 4
    20
    Correct
    Wrong
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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 0

  • 1
    0.0625
    Correct
    Wrong
  • 2
    0.0210
    Correct
    Wrong
  • 3
    0.03145
    Correct
    Wrong
  • 4
    0.3210
    Correct
    Wrong
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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.

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