GATE Questions

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= 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.

% Profit with respect to A = 40 + 50 + (40 x 50)/100 = 90 + 20 = 110 %.

In the given puzzle, the logic behind is

9 = 72 => 9 x 8 = 72

8 = 56 => 8 x 7 = 56

7 = 42 => 7 x 6 = 42

6 = 30 => 6 x 5 = 30

5 = 20 => 5 x 4 = 20

Similarly,

4 = 12 => 4 x 3 = 12

3 = 6 => 3 x 2 = 6

Imension of the duster is assumed as 5x5x7 cm3

Volume of the duster below the water layer
= volume of water increased
= πxrxrxh = 3.14×52×2.14 ≈ 168 cm3

Total volume of the duster = 5×5×7 = 175 cm3

Percentage of the duster part below the layer = 168×100/175 = 96%

Percentage of the duster part above the layer = 4%

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

It is Tomorrow. It always be tomorrow which represents coming but never arrives.

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.

Number of pages typed by Adam in 1 hour = 36/6 = 6
Number of pages typed by Smith in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (6 + 8) = 14
Time taken by both to type 110 pages = (120 * 1/14) = 847 = 8 hrs 34 min.