GATE Questions

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We know that 1 yard = 3 feet. 

A yardstick which is used for measurement has 3 feet long but it cannot walk.

SP of first article = 1000

Profit = 20%

CP = 100100+P×SP= 5000/6 = 2500/3

SP of second article = 1000

Loss = 20%

CP = 100100-L×SP= 5000/4 = 1250

Total SP = 2000

Total CP = 25003+ 1250 = 6250/3

CP is more than SP, he makes a loss.

Loss = CP-SP = (6250/3)- 2000 = 250/3

Loss Percent =250362503×100= 4%

From above diagram
AC 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.

1/K + 1/L + 1/M = 1/8 (Given)
Also given that K = 2L and L = 2M
=> 1/2L + 1/L + 2/L = 1/8
=> (1 + 2 + 4)/2L = 1/8
=> 2L/7 = 8
=> L = 28 hours.

Donkeys and horses can be breed to make mules and hinnys.

A hinny is a domestic equine hybrid that is the offspring of a male horse, a stallion, and a female donkey, a jenny. It is the reciprocal cross to the more common mule, which is the product of a male donkey, a jack, and a female horse, a mare.

The first person shakes hands with 22 different people, the second person also shakes hands with 22 different people, but one of those handshakes was counted in the 22 for the first person, so the second person actually shakes hands with 21 new people. The third person, 20 people, and so on...
So,
22 + 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
= n(n+1)/2 = 22 x 23 /2 = 11 x 23 = 253.

The simple machine Axe is made up of both the lever arm and a wedge.

Envelope is a letter holder for one letter and in the question it mean that it holds one letter. Eye is also a word which starts and end with E but has one letter in the middle.