GATE Questions

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In the given series, each letter moves seven letters forward to obtain the next.
So, XZV replaces ? in the series.

Number of runs scored more to increse the ratio by 1 is 26 - 14 = 12
To raise the average by one (from 14 to 15), he scored 12 more than the existing average.
Therefore, to raise the average by five (from 14 to 19), he should score 12 x 5 = 60 more than the existing average. Thus he should score 14 + 60 = 74.

CP of 1000gm = Rs. 10
SP of 800gm = Rs. 12
SP of 1000gm =12x1000/800 = Rs. 15

Now take 1000gm as reference to calculate profit.
Profit=SP-CP=15-10=Rs. 5
Profit % = 5x100/10 = 50%

Sony and her brother's age sum is 31
Let Sony's mother's age be 'x'.
Now the conditions given for both of their ages related to their mom is
1/5(x-15) + 3/5(x-10) = 31
x-15 + 3x-30 = 155
4x-45 = 155
4x = 200
x = 50
So, Mother's age = 50.

Cross verification : 15 years ago age = 35 => Sony age = 7
10 years ago age = 40 => bro age = 24

Sum = 24 + 7 = 31.

The interval between object pass the same point is 4 sec.

That means in 2 sec, object reaches the top and in next 2 sec, it again reaches the same point.

By the info given, we can find the velocity of that point by using : v=u+(-gt)

0= u - 10×2

u = 20

Then the velocity at 25m is 20m/sec.

so the initial velocity is

$$\begin{gathered} -v2 = u2 + (-2gh) \\ 400 = u2 - 2x 10 x 25 \\ u2 = 900 \\ => u = 30 m/s \end{gathered}$$

Let the original speed and time is S and T
then distance = S x T
Now the speed changes to 2/3S and T is T+20
As the distance is same
S x T = 2/3Sx(T+20)
solving this we get t = 40 minutes
=40/60 = 2/3 hour

The 8 letters can be written in 8! ways.
n(S) = 8!
Let E be the event that the letters b,c,d,e always come together when the first 8 alphabets are written down.
Now the letters a, (bcde), f, g and h can be arranged in 5! ways.
The letters b,c,d and e can be arranged themselves in 4! ways.
n(E) = 5! x 4!
Now, the required P(E) = n(E)/n(S) = 5! x 4!/8! = 1/14
Hence the answer is 1/14. 

The twentieth element in the above arrangement is 'E'.
Then, the sixth element to the left of 'E' is 'L'.