GATE Questions

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Metal particles are held together by strong metallic bonds, which is why they have high melting and boiling points. The free electrons in metals can move through the metal, allowing metals to conduct electricity.

Because the electrons in the atom's higher energy levels can separate from the atoms easily, they can be pulled out with very little energy. Because the molecular structure of the metal is such that 'free electrons' are free to move, thus being categorized as electrically conductive.

For example, copper is used for electrical wiring because it is a good conductor of electricity.

Let the rquired number be 'P'

According to the question,

$$\begin{gathered} 100 x P100 = 20 \\ => P = 20 x 100100 = 20 \end{gathered}$$

Hence, 100 percent of the number 20 is 20.

Now, you can also try for

20 percent of what number is 100

$$\begin{gathered} 20 x P100 = 100 \\ => P = 100 x 10020 = 500 \\ => P = 500 \end{gathered}$$

Hence, 20 percent of the number 500 is 100.

Water required = 4000 x 140 = 560000 lit = 560 cu.m (1 cu.m = 1000 lit)

Volume of tank = 18 x 12 x 8 = 1728 cu.m

Water of this tank will suffice for = 1728/560 = 3 days.

Manju borrows Rs. 5000 for 2 years at 4% p.a. simple interest 

She also lends it at 6 1⁄4% p.a for 2 years 

=> Total Gain = 6 1/4% − 4% = 2 1/4%

So her gain in the transaction for 1 year

= The simple interest she gets for Rs.5000 for 1 year at 2 1⁄4% per annum

= PTR100=5000×94×1100 = Rs. 112.5/ year.

Let the amount invested by saketh = RS. p

Now, that of sandeep = 20,000 x 6

saketh = 12 x p

Ratio of their earnings = 120000 : 12p = 6000 : (9000 - 6000)

=> $$\begin{gathered} 12000012p = 60003000 \\ => p= Rs. 5000 \end{gathered}$$

Hence, the amount investe by saketh  = Rs. p  = Rs. 5000.

P1+20100n > 2P 

Now, (6/5 x 6/5 x 6/5 x 6/5) > 2.

So, n = 4 years.

Let the actual distance be t kms

Now, According to the data,

$$\begin{gathered} 5t + 860 = 6t \\ => 560t + 860 = 6t \\ => 60t + 8 = 72t \\ => 8 = 12t \\ => t = 8/12 = 2/3 hrs \end{gathered}$$

Now, the total distance = 6t = 6 x 2/3 = 2 x 2 = 4 kms.

Let the length of the 1st train = L mts

Speed of 1st train = 48 kmph

Now the length of the 2nd train = L/2 mts

Speed of 2nd train = 42 kmph

Let the length of the bridge = D mts

Distance = L + L/2 = 3L/2

Relative speed = 48 + 42 = 90 kmph = 90 x 5/18 = 25 m/s(opposite)

Time = 12 sec

=> 3L/2x25 = 12

=> L = 200 mts

Now it covers the bridge in 45 sec

=> distance = D + 200

Time = 45 sec

Speed = 48 x5/18 = 40/3 m/s

=> D + 200/(40/3) = 45

=> D = 600 - 200 = 400 mts

Hence, the length of the bridge = 400 mts.