GATE Questions

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Let 'd' be the distance and 's' be the speed and 't' be the time
d=sxt
45 mins = 3/4 hr and 48 mins = 4/5 hr
As distance is same in both cases;
s(3/4) = (s-5)(4/5)
3s/4 = (4s-20)/5
15s = 16s-80
s = 80 km.
=> d = 80 x 3/4 = 60 kms.

The Ezra Cup is a popular polo tournament conducted annually in India. The Calcutta Polo Club runs this oldest and first ever Polo Trophy. The first Ezra Cup was held in 1880. After a period of inactivity, it has now been revived by Mr. Keshav Bangur, Calcutta Polo Club's president.

We know that perimeter of rectangle = 2(l+b) = 2(8+7)= 30cm
Given perimeter of square is twice the perimeter of rectangle = 2(30) = 60cm
Therefore, side of the square is = 1/4 x 60 = 15cm
Circumference of the required semicircle = πr + 2r = 227× 152 + 2×152 = 23.57 + 15 = 38.57cm.

Given equation is  

  192.5 ×19p = 197   

Here it is in the form of am × an = am+n  

 Here m = 2.5 , n = p, m+n = 7

 => 2.5 + p = 7 

 => p = 7 - 2.5

 => p = 4.5

Speed in downstream = 96/8 = 12 kmph

Speed of current = 4 km/hr

Speed of the boatman in still water = 12 – 4 = 8 kmph

Speed in upstream = 8 – 4 = 4 kmph

Time taken to cover 8 km upstream = 8/4 = 2 hours.

P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize) 

 = 1-16C1× 14C1×12C1×10C116C4=1539

The given puzzle follows a pattern that,

Number - <last digit> <sum of all digits>.

111 - 13

112 - 24

113 - 35

So 

117 - 79

1.12.91 is the first Sunday of December 91.
So, 3.12.91 is the first Tuesday of the month.
Clearly, 10.12.91, 17.12.91, 24.12.91 and 31.12.91 are also Tuesdays.
So, 24.12.91 is the fourth Tuesday.