GATE Practice Question and Answer

Q: If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x+y is equal to  ? 1695 0

  • 1
    5
    Correct
    Wrong
  • 2
    4
    Correct
    Wrong
  • 3
    3
    Correct
    Wrong
  • 4
    2
    Correct
    Wrong
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Answer : 4. "2"
Explanation :

Answer: D) 2 Explanation: Since 653xy is divisible by 5 as well as 2, so y = 0.Now, 653x0 must be divisible by 8.So, 3x0 must be divisible by 8. This happens when x = 2x + y = (2 + 0) = 2.

Q: If log72 = m, then log4928 is equal to ? 2826 0

  • 1
    1/(1+2m)
    Correct
    Wrong
  • 2
    (1+2m)/2
    Correct
    Wrong
  • 3
    2m/(2m+1)
    Correct
    Wrong
  • 4
    (2m+1)/2m
    Correct
    Wrong
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Answer : 2. "(1+2m)/2"
Explanation :

Answer: B) (1+2m)/2 Explanation: log4928 = 12log77×4   = 12+122log72= 12+log72= 12 + m= 1+2m2.

Q: If x is a whole number, then x²(x² - 1) is always divisible by ? 2579 0

  • 1
    4
    Correct
    Wrong
  • 2
    8
    Correct
    Wrong
  • 3
    12
    Correct
    Wrong
  • 4
    None
    Correct
    Wrong
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Answer : 3. "12"
Explanation :

Answer: C) 12 Explanation: we can do this by trial and error method. Putting x = 2,we get 2²(2² - 1) = 12.checking with other integers, the above equation always gives a value which is a multiple of 12,So, x²(x² - 1) is always divisible by 12.

Q: Which one of the following foreign agencies will assist the municipal agencies to improve quality of municipal schools through its School Excellence Programmes(SEP) ? 1765 0

  • 1
    IMF
    Correct
    Wrong
  • 2
    UNDP
    Correct
    Wrong
  • 3
    ADB
    Correct
    Wrong
  • 4
    UNICEF
    Correct
    Wrong
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Answer : 3. "ADB"
Explanation :

Answer: C) ADB Explanation: Asian Development Bank (ADB) announced that it will assist the municipal agencies to improve quality of municipal schools through its School Excellence Programme (SEP).

Q: If y/(x - z) = (y + x)/z = x/y then find z : y : x ? 2196 0

  • 1
    1:2:3
    Correct
    Wrong
  • 2
    3:2:4
    Correct
    Wrong
  • 3
    4:3:2
    Correct
    Wrong
  • 4
    2:3:4
    Correct
    Wrong
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Answer : 2. "3:2:4"
Explanation :

Answer: B) 3:2:4 Explanation: Given, y/(x - z) = (y + x)/z = x/yyz = xy + x2 - yz - xz ....(1)Also xy = yx-z ⇒x2 -xz = y2 ....(2)Using (1) and (2), we get yz = xy - yz + y22yz = xy + y22z = x + y Only option (B) satisfies the equation.

Q: Who among the following took over as the 25th Director General of the Border Roads(DGBR) ? 1708 0

  • 1
    Lt. Gen. Suresh Sharma
    Correct
    Wrong
  • 2
    Lt. Gen. David R. Syiemlieh
    Correct
    Wrong
  • 3
    Lt. Gen. Srikanth Mishra
    Correct
    Wrong
  • 4
    Lt. Gen. Sanjeev Kumar Shrivastava
    Correct
    Wrong
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Answer : 4. "Lt. Gen. Sanjeev Kumar Shrivastava"
Explanation :

Answer: D) Lt. Gen. Sanjeev Kumar Shrivastava Explanation: Lt. Gen. Sanjeev Kumar Shrivastava took over as the 25th Director General of the Border Roads (DGBR). He has replaced Lt. Gen. Suresh Sharma. Prior to it, he was holding the appointment of Director General Combat Engineers at Integrated Headquarters of Ministry of Defence(Army).

Q: There are 209 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 11 : 8, then how many nurses are there in the hospital? 2452 0

  • 1
    88
    Correct
    Wrong
  • 2
    96
    Correct
    Wrong
  • 3
    108
    Correct
    Wrong
  • 4
    121
    Correct
    Wrong
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Answer : 1. "88"
Explanation :

Answer: A) 88 Explanation: Given,The ratio of the doctors to the nurses is 11 : 8Number of nurses = 8/19 x 209 = 88.

Q: On her deathbed, a grand mother called upon his three grand sons and told them to distribute all her assets worth Rs. 52,500 in the ratio of 1/35 : 1/21 : 1/15 amongst themselves. Find the smallest share amongst the three portions ? 2176 0

  • 1
    Rs. 5422
    Correct
    Wrong
  • 2
    Rs. 10,500
    Correct
    Wrong
  • 3
    Rs. 12,800
    Correct
    Wrong
  • 4
    Rs. 15,000
    Correct
    Wrong
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Answer : 2. "Rs. 10,500"
Explanation :

Answer: B) Rs. 10,500 Explanation: The ratio of distribution should be: 21 x 15 : 15 x 35 : 35 x 21= 315 : 525 : 735 = 3 : 5 : 7The smallest share will be of worth: 3/15 x 52,500 = Rs. 10,500

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