GATE Questions

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Two men, three women and one child can be selected in ⁴C₂ x ⁶C₃ x ⁵C₁ ways = 600 ways.

Speed of the boat downstream  s=a/t= 60/3 = 20 kmph

Speed of the boat upstream s= d/t = 30/3= 10 kmph

Therefore,  The speed of the stream = speed of downstream - speed of upstream2=5 kmph

According to the question, after the position of the first and third digit interchanged new numbers are
789, 415, 856, 784, 404, 962

962, 856, 789, 784, 404, 415
Here the second lowest number is 404 and the last digit of it is '4'.

Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ x ⁶C₁)

As remaining person can be any one among three couples left.

Required probability = (⁵C₂ x ⁶C₁)/¹⁰C₅
= (10 x 6)/252 = 5/21

Only H and Br form Polar Covalent Bond.

Covalent bonding:

Covalent bonding occurs when pairs of electrons are shared by atoms. Atoms will covalently bond with other atoms in order to gain more stability, which is gained by forming a full electron shell. By sharing their outer most (valence) electrons, atoms can fill up their outer electron shell and gain stability.

1. Polar Covalent Bond

2. Nonpolar Covalent Bond

1. Polar Covalent Bond:

A Polar Covalent Bond is created when the shared electrons between atoms are not equally shared. This occurs when one atom has a higher electronegativity than the atom it is sharing with. The atom with the higher electronegativity will have a stronger pull for electrons (Similiar to a Tug-O-War game, whoever is stronger usually wins). As a result, the shared electrons will be closer to the atom with the higher electronegativity, making it unequally shared.

2. Nonpolar Covalent Bond:

A Nonpolar Covalent Bond is created when atoms share their electrons equally. This usually occurs when two atoms have similar or the same electron affinity. The closer the values of their electron affinity, the stronger the attraction. This occurs in gas molecules; also known as diatomic elements. Nonpolar covalent bonds have a similar concept as polar covalent bonds; the atom with the higher electronegativity will draw away the electron from the weaker one.

Here H and H and N and N form Non-polar covalent bonds. Na and Br form the ionic bond.

|-----------20--------------------|
50                           40

Difference = 20kms

Relative Speed = 50 – 40 = 10 kmph

Time = 20/10 = 2 hours.

Deepa invested Rs.50,000 for 12 months, Rs.(50000 + 20000) for 12 months and Rs.(50000 + 20000 + 20000) for 12 months.
i.e, she invested Rs.50,000 for 12 months, Rs.70000 for 12 months and Rs.90000 for 12 months.
Sushma invested Rs. 70000 for 2 years; i.e, Rs.70000 for 24 months
And, Avanthi invested Rs.70000 for 1 year; i.e, Rs. 70000 for 12 months.

Their investing ratio:
Deepa : Sushma : Avanthi = (50,000 x 12 + 70000 x 12 + 90000 x 12):(70000 x 24):(70000 x 12)
= (25,20,000):(16,80,000):(8,40,000) = 252:168:84 = 3:2:1

Total profit for 3 years = Rs.3,00,000
Therefore, Sushma's share = Rs.(3,00,000 x 2 /(3+2+1)) = Rs.(3,00,000 x 2/6) = Rs.1,00,000.