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.

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

Time taken to meet the first time = length of track/relative speed

Given the length of the track is 600 m

The relative speed = 25 + 35 = 60 kmph = 60 x 5/18 m

Therefore Time = 60025+35518= 600/60 x (18/5) = 36 sec.

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%

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

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

Pageant is most similar in meaning to Show.

Given 5:6 :: 7:10 :: 6:5

We know that compound ratio is calculated as
a:b :: c:d :: e:f
(axcxe):(bxdxf)

=> (5x7x6):(6x10x5)
=> (210):(300)
= 7:10