GATE Questions

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Second gun shot take 30 sec to reach rahul imples distance between two.

given speed of sound = 330 m/s

Now, distance = 330 m/s x 30 sec 

Hence, speed of the bus = d/t = 330x30/(14x60 + 30) = 330/29 m/s.

Given that,

Members in football team = n(f) = 10

Members in science club = n(s) = 14

Members in both football team and science club = n(f ^ s) = 5

Then, Members in only football team = n(F) = 10 - 5 = 5

Members in only science team = n(S) = 14 - 5 = 9

Hence, members in only football or science team = n(FUS) = n(F) + n(S) - n(f^s) 

= 9 + 5 - 5

= 9.

Hence, many students belong to only science club team or football team = 9.

Let y be the total number of loaves
a be the remaining loaves after 1st thief
b be the remaining loaves after 2nd thief
and c, d..so on after 3 and 4 th
e = 0 be the remaining loaves after 5th thief

a = y - (y/2 + 1/2)
= y/2 - 1/2

b = a - (a/2 + 1/2)
= a/2 - 1/2

c = b - (b/2 + 1/2)
= b/2 - 1/2

d = c - (c/2 + 1/2)
= c/2 - 1/2

e = d - (d/2 + 1/2)
= d/2 - 1/2
we know that, e = 0,
thus by substitution, we get
d = 1
c = 3
b = 7
a = 15
y = 31
Therefore total number of bread loaves in bakery was 31.

If LCM = HCF then, the two numbers are equal.

If a number to be divisile by 88, it should be divisible by both "8" and "11"

Check for '8' :
For a number to be divisible by "8", the last 3-digit should be divisible by "8"
Here 72x23y --> last 3-digit is '23y'
So y=2 [ (i.e) 232 is absolutely divisible by "8"]

Chech for '11' :
For a number to be divisible by "11" , sum of odd digits - sum of even digits should be divisible by "11"
(7 + x + 3) - (2 + 2 + y)
(7 + x + 3) - (2 + 2 + 2)
(10 + x) - 6 should be divisible by "11"
for x = 7
=> 17 - 6 = 11 [ which is absolutely divisible by "11"]

So x = 7 , y= 2.

The poison was in the ice. When the girl drank the iced tea, the ice was still fully frozen. Gradually, as the ice cubes melted the poison was released into the drink.

Hence, the girl who died, drunk the tea after the ice melted. So, she was died. 

Derby Cup is associated with horse racing in United Kingdom.