GATE Questions

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Let S be the sample space.
Here n(S)= 23 = 8
Let E be the event of getting atmost two heads. Then,
n(E) = {(H,T,T), (T,H,T), (T,T,H), (H,H,T), (T,H,H), (H,T,H)}
Required probability = n(E)/n(S) = 6/8 = 3/4.

For 1 hour, 20 minutes is slower, then for
06 miuntes - 2 minutes is slower
30 minutes - 10 minutes
Actual time | false time
12 12
01 PM 12:40 PM (20 minutes slower)
02 PM 01:20 PM
03 PM 02:00 PM

So, when actual time is 3pm, the false time is 2 pm.
So, it loses 60 minutes when it shows 2 pm.

Here pairs interchanged are

2, 4 

3, 8

5, 6

Unchanged are 0, 1, 7, 9

For this we have to find the LCM of 24, 36 and 30

LCM of 24, 36 and 30 = 360 sec

360/60 min = 6 minutes.

Given a secret is told to 3 persons in 3 minutes.
And if the process continues with each person saying 3 other persons,
In 30 minutes => the rocess for 10 times because each person time is 3 minutes.
Required number of persons = 3 + 32 + 33 + .... + 39 + 310

Now it forms a geometric progression,

Sum to n terms is S = arn - 1r - 1

Here a = 3, r = 3

 
=> 59048 x 3 /2

= 88572.

Given A,B,C can complete a work in 15,20 and 30 respectively.

The total work is given by the LCM of 15, 20, 30 i.e, 60.

A's 1 day work = 60/15 = 4 units

B's 1 day work = 60/20 = 3 units

C's 1 day work = 60/30 = 2 units

(A + B + C) worked for 2 days = (4 + 3 + 2) 2 = 18 units

 Let B + C worked for x days = (3 + 2) x = 5x units

C worked for 2 days = 2 x 2 = 4 units

Then, 18 + 5x + 4 = 60

22 + 5x = 60

5x = 38

x = 7.6

Therefore, total number of days taken to complete the work = 2 + 7.6 + 2 = 11.6 = 11 3/5 days.

Here in 2nd column if you add the individual digits

 we get  3 + 7 + 0 =10 , 2 + 2 + 4 = 8 , 7 + 3 + 0 = 10

7   10   3  --> 7+3 =10

6   8     2  --> 6+2 =8

x   10   1  --> x+1 =10

Here we can observe that by adding 1st and 3rd column elements we get 2nd column elements

 --> x = 9

Currently, the Melbourne Cricket Ground is the world's largest cricket stadium in the world with a total capacity of 100,024. The boundary line of this ground is 85–92 meters from the middle of the pitch which is the highest of all the Cricket grounds around the world. While Kolkata's Eden Gardens is reportedly No. 2 with a capacity of 66,000. 

The Sardar Patel Gujarat Stadium, also known as Motera Stadium getting built in Ahmedabad will accommodate 1.1 lakh cricketing fans inside the stadium overtaking current record-holder Melbourne Cricket Ground .