GATE Questions

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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

Let the three numbers be x, y, z.

From the gien data,

x = 2y ....(1)

x = z/2 => z = 2(2y) = 4y .....(From 1)  ...........(2)

Given average of three numbers = 56

Then,

$$\begin{gathered} x + y + z3 = 56 \\ 2y + y + 4y3 = 56 (From 1 & 2) \\ 7y = 56 x 3 \\ y = 24 \end{gathered}$$

Now,

x = 2y => x = 2 x 24 = 48

z = 4y = 4 x 24 = 96

Now, the highest number is z = 96 & smallest number is y = 24

Hence, required sum of highest number and smallest number

= z + y

= 96 + 24

= 120.

National Income is the total income value of the goods and services produced by the residents of a country, usually during the period of one year.

National Income is categorized into 6 components. They are :

1. Compensation of Employees (Wages and Benefits)
2. Corporate Profits
3. Rental Income
4. Proprietors Income (Income of unincorporated business)
5. Net Interest

The Largest Component of National Income is Compensation of Employees.

The Largest component of National Income in India is Service Sector.

In purifying drinking water alum is used for coagulation of mud particles.

DPI [Dots Per Inch] is a measurement of output quality of printer resolution. It represents number of ink dots the printer can place in an area of one square inch. The lesser the DPI the less sharper the image and vice versa.

Therefore, a printer that may have 400 DPI, a printer that can print 400 x 400 per square inch or 1,60,000 dots per inch.

When atoms react they do so in order to reach the lowest energy, which is the most stable. The electrons orbitals will overlap in the way that reduces the energy the most. Orbitals of similar energy will produce the greatest stabilisation.The answer you gave isn't the whole story, it depends what species is reacting with what. The effective nuclear charge on the atom will affect the energy of the valance electrons.

Hence, the reactivity of an atom arises from the existence of unpaired electrons in the valence shell.

The order of basicity in ammonia is different in gaseous phases vs. aqueous phases due to hydrogen bonding.

So in gaseous phases it's the well known: 3' > 2' > 1'> NH3. Just so we're on the same page, this is due to the inductive effect of electron donating alkyl groups--they destabilize the lone pair on nitrogen atom, making nitrogen more basic.

But in aqueous phase, the order is slightly different: 2'> 1'> 3' > NH3.