GATE Questions

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Given in the question that, there are 7 boys and 6 girls. 

Team members = 5

Now, required number of ways in which a team of 5 having atleast 3 girls in the team = 

$$\begin{gathered} 6C3 x 7C2 + 6C4 x 7C1 + 6C5 \\ = 6x5x43x2x1 x 7x62x1 + 6x5x4x34x3x2x1 x 7 + 6x5x4x3x25x4x3x2x1 \\ = 420 + 105 + 6 \\ = 531. \end{gathered}$$

a. P's investment = (80000 x 6 + 60000 x 6) = 840000 for 1 month.

b & c. Q's investment = 80% of Rs. 60000 for 8 months.

= Rs.(48000 x 8) for 1 month = 384000 for 1 month

P : Q = 840000 : 384000 = 35 : 16.

But, the total profit is not given, so data is inadequate.

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.

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).

Covalent type of bonding joins The two hydrogen atoms are joned by Covalent type of bonding.

In this type of bonding, electrons are shared between the atoms in order to fill there valence shells. Thus sharing of electrons take place in between the hydrogen atoms.

*  The Gulf of Mexico, bordered by the United States, Mexico, and the island nation of Cuba, is the worlds largest gulf.

*  It has a coastline of about 5,000 kilometers (3,100 miles).

*  The Gulf of Mexico is connected to the Atlantic Ocean by the Straits of Florida, between Cuba and the U.S. state of Florida.

*  It is largely surrounded by the North American continent.

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