GATE Questions

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Let the Original capital amount be Rs. P

Given after 2 years the amount is Rs. 10000

Rate of interest = 30%

According to the question,

$$\begin{gathered} P x 130100 x 130100 = 10000 \\ => P = 1000000169 = 5917 \end{gathered}$$

Therefore, the capital amount P = Rs. 5917

From the assumption and trial and error method,

last three digits sum must leave the same digit as the answer. It is possible only if the answer must be units digit number leaving tens digit as carry.

And the possible 3rd digit is 5. Since 5 + 5 + 5 = 15 

Now, 2nd step is  1 + x + x + x = 5

=> 3x = 4

It is possible with x = 8. 8 + 8 + 8 + 1 = 25 leaving 2 as carry. 

Now, 3rd step is 2 + x + x + x = 5 => x = 1

Hence, the three dgits are 1, 8, 5.

185 + 185 + 185 = 555. 

Total age of players in team = 22 x 11 = 242
When coach is included, total members = 12, Avg age increases by one becomes 23
Total age when coach is included = 23x12 = 276
Age of coach = 276-242 = 34 yrs.

Ankit's daughter's mother---Ankit's wife; Ankit's wife's father---Ankit's father-in-law;
Father-in-law's daughter--- Ankit's sister-in-law. So, Sanvi is sister-in-law of Ankit.

= log tan10+log tan890 + log tan20+ log tan880+⋯⋯+log tan450  

= log [tan10 × tan890] + log [tan20 × tan880 ] +⋯⋯+log1  

∵ tan(90-θ)=cotθ and tan 450=1  

= log 1 + log 1 +.....+log 1 

= 0.

Half of the cloth = 37.5/2
From 1 meter he will make 8 pieces
=> in 37.5/2 ---- ?

37.5/2 x 8

= 150.

In terms of the Earth's atmosphere, they occupy regions called the thermosphere and the exosphere. The layer through which a satellite orbits depends on the satellite's function and the kind of orbit it has.

The thermosphere is a region of very high temperature that extends from the top of the mesosphere at around 85 kilometers (53 miles) up to 640 kilometers (400 miles) above the Earth's surface. It is called the thermosphere because temperatures can reach up to 1,500 degrees Celsius (2,732 degrees Fahrenheit).

However, despite the high temperatures, the pressure is very low, so satellites don't suffer heat damage.

Speed of the train relative to man

= (125/10) m/sec = (25/2) m/sec.

[(25/2) x (18/5)] km/hr = 45 km/hr.

Let the speed of the train be 'x' km/hr.

Then, relative speed = (x - 4) km/hr.

x - 4 = 45 => x = 49 km/hr.