GATE Questions

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Given total number of cows = k
Now, 1st son share = k/2
2nd son share = k/4
3rd son share = k/5
4th son share = 9

(k) + (k/4) + (k/5) + 9 = k
=> k - (19k/20) = 9
=> (20k-19k)/20 = 9
=> k = 180.

Days remaining 124 – 64 = 60 days

Remaining work = 1 - 2/3 = 1/3

Let men required men for working remaining days be 'm'

So men required = (120 x 64)/2 = (m x 60)/1 => m = 64

Men discharge = 120 – 64 = 56 men.

2nd Jan 1901 means
(1900 years and 2 day)
Now, 1600 years have 0 odd day
300 years have 1 odd day
2 days has 2 odd day
Total no. of odd days = 0 + 1 + 2 = 3 days
Hence, the day on 2nd Jan 1901 was Wednesday.

Here If you notice the difference, There is no question mark (?) at the end of the puzzle.

In that case, "What" is the name of the 5th child.

In the given number puzzle,

Sum of Row 1 = 14

Sum of Row 2 = 23

Sum of Row 3 = 13 + ?

Sum of Column 1 = 16 

Sum of Column 2 = 23 

Sum of Column 3 = 11 + ?

Diagonal 1 sum = 17

Diagonal 2 sum = 14 + ?

From the above analysis,

Sum of Row 2 = Sum of Column 2 = 23

Sum of Row 1 = Sum of Column 3 = 14 = 11 + ?    .............(1)

Sum of Row 3 = Sum of Column 1 = 16 = 13 + ?    .............(2)

Diagonal 1 sum = Diagonal 2 sum = 17 = 14 + ?    .............(3)

Hence,

From (1), (2) & (3)

? = 3

A conjugate acid, is a species formed by the reception of a proton (H+) by a base—in other words, it is a base with a hydrogen ion added to it.

On the other hand, a conjugate base is what is left over after an acid has donated a proton during a chemical reaction. Hence, a conjugate base is a species formed by the removal of a proton from an acid.

Because some acids are capable of releasing multiple protons, the conjugate base of an acid may itself be acidic.

Represented as the following chemical reaction:

Acid + Base ⇌ Conjugate Base + Conjugate Acid

The water molecule is the conjugate acid of the hydroxide ion after the latter received the hydrogen proton donated by ammonium. On the other hand, ammonia is the conjugate base for the acid ammonium after ammonium has donated a hydrogen ion towards the production of the water molecule. We can also refer to OH- as a conjugate base of H2O, since the water molecule donates a proton towards the production of NH+4 in the reverse reaction, which is the predominating process in nature due to the strength of the base NH3 over the hydroxide ion.

Once it is decided to place funds in the hands of the committee of local representatives, it is necessary to decide guidelines and norms for the functioning of the committee. Hence I follows. II is not related to the statement.