GATE Questions

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(100-x)%  of 88% of 8400 = 6896

=> 100-x10088100x8400 = 6896

=> x = 6.709%

We can select atleast one item from 6 different items = 26-1  

Similarly we can select atleast one item from other set of 6 different items in 26-1 ways. 

Required number of ways = (26-1)26-1 = 26-12 = 3969

Let the selling price of the rice = Rs.P/kg

Now, according to the question,

1040 - 100p = 30p

=> p = 8/kg

Hence, the selling price of the rice = Rs. 8/kg

Given,

mean of 100 observations is 40

=> Total of 100 observations = 40 x 100 = 4000

84 is misread as 48

=> Difference = 84 - 48 = 36

=> Now, new total of 100 observations = 4000 + 36 = 4036

Correct Mean = 4036/100 = 40.36

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.

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.

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

Because the refractive index of glass is highest, light travels slowly in Glass. 

We know that the speed of light depends on the refraction index. The higher the index of refraction is, the slower the speed of light is.

R.I of air and vacuum = 0 (air is a teeny bit more but can be taken as 0)
R.I of water = 1.33
R.I of glass = 1.4.

Hence, Light travels slowest in Glass.