GATE Questions

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Diamond is the hardest substance available on Earth.

Diamond is the hardest substance available on Earth due to the giant molecular structure of diamond in which each carbon atom is covalently bonded to four other carbon atoms. A covalent bond is very strong and requires a large amount of energy to break itself, and diamond has many covalent bonds.

Time from 12 p.m. on Tuesday to 2 p.m. on the following Tuesday = 7 days 2 hours.
= 170 hours.
The watch gains = (2 + 4 x 4/5) min
= 34/5 min. in 170 hrs.
Now, 34/5 min are gained in 170 hrs.
Then, 2 min are gained in (170 x 5/34 x 2) hrs.
Watch is correct after 2 days 2 hrs after 12 p.m. on Tuesday, i.e., it will be correct at 2 p.m. on Thursday.

Given that, a woman has seven children. Half of them are boys. 

Half of 7 is 3.5 which is not possible. And it is possible in only one way that all the children must be boys. Then half of them are boys.

Mahadev Govind Ranade is known as the father of Indian Economics. M G Ranade advocated social reforms such as widow re-marriage, liberation of women & emancipation of the oppressed classes.

He was Known to be the mentor & political guru of Gopal Krishna Gokhale & Bal Gangadhar Tilak.

We know that,

Total number of balls n(S) = 26

Number of vowels n(E) = 5

Hence, required probability = n(E)/n(S) = 5/26.

3/15 + 4/16 + x/24 = 1

⇒x=1315

Profit would be maximum if watches are brought for Rs. 200 and sold for Rs. 425
Profit = Rs. (425 - 200) = Rs. 225
Profit of 9 watches = Rs. 225 x 9 = Rs.2,025.

Let Rs. K invested in each scheme

Two years C.I on 20% = 20 + 20 + 20x20/100 = 44%

Two years C.I on 15% = 15 + 15 + 15x15/100 = 32.25%

Now,

(P x 44/100) - (P x 32.25/100) = 528.75

=> 11.75 P = 52875

=> P = Rs. 4500

Hence, total invested money = P + P = 4500 + 4500 = Rs. 9000.