GATE Questions

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Nutrients that are needed in large amounts are called Macronutrients.

There are three macronutrients required by humans:

1. carbohydrates (sugar),

2. lipids (fats), and

3. proteins.

Each of these macronutrients provides energy in the form of calories.

Some other macronutrients are: nitrogen (N), phosphorus (P), potassium (K), calcium (Ca), sulfur (S), magnesium (Mg), sodium (Na).

Given two lines are parallel

pa+b=2

b=-pa+2..........(1)

3a+b=4

b=-3a+4 ...........(2)

m₁ = -p

m₂= -3

The condition for the two lines to be parallel is m₁=m₂

p = 3

The number of ways in which the letters of the word RAILINGS can be arranged such that R & S always come together is

Count R & S as only 1 space or letter so that RS or SR can be arranged => 7! x 2!

But in the word RAILINGS, I repeated for 2 times => 7! x 2!/2! = 7! ways = 5040 ways.

Scores of individuals :

Dhoni= 80,30,10,10,1
Raina=100,25,3,2,1
Kholi=85,20,15,10,1
Shikhar=90,20,15,3,3

Above combination satisfies all conditions given in the question.

Answer 1) Raina

Answer 2) Kohli and Shikhar

Answer 3) Dhoni

True, Air is a Mixture.

Air is considered as mixture for the following reasons ;

1. Air can be separated into its components like N2, O2 , Argon and CO2 by the process of fractional distillation of liquid air.

2. Air shows the properties of all the gases present in the atmosphere.
For example : Oxygen is good Supporter of combustion. Hence air also is good supporter of combustion.

3. Air does not have a fixed formula.

4. Air has a variable composition because air at different places contains different amount of gases.

5. Heat or Light energy is neither absorbed nor released when air is prepared physical by mixing required amount of gases .

6. Mixture does have fixed boiling Point. It holds good in case of liquid air.

Let the distance he covered each way = d kms

According to the question,

d/45 - d/50 = 1

=> d = 450 kms.

Hence, the total distance he covered in his way = d + d = 2 d = 2 x 450 = 900 kms.

All are blood relation except Daughter-in-law.

Let
x = peacocks
y = deers

2x + 4y = 200
x + y = 72
y = 72 - x
2x + 288 - 4x = 200
x = 44 peacocks
y = 28 deers