Answer: Option C

Explanation:

Therefore, it is clear that he is in the North from his house.

Answer: Option D

Explanation:

Required distance = 40 - 20 = 20 km.

Answer: Option C

Explanation:

Required distance = AE
                             = 20 + 15
                             = 35 m towards east.

Answer: Option

Explanation:

Therefore, it is clear that Sundar will face towards North

Answer: Option C

Explanation:

Required distance = AE
                            = 5 + 10 
                            = 15 km

Answer: Option C

Explanation: 6√34 m
PQ = √30² + 18²

Answer: Option B

Explanation: 30 Km

Please refer to explanation image, 
Naresh starts from home at A, moves 20 Km in south upto B. Then he turns right and moves 10 Km upto C, then he turns right and moves 20 Km upto D, then he turns lefts and moves 20 Km upto E.
So from image it is clear that, if he moves straight then he will have to move AD+DE, AD = BC = 10 Km
So, he will have to move 10 + 20 = 30 Km

Answer: Option B

Explanation: 100 metre

Clearly, the child moves from A to B 90 metres eastwards upto B, then turns right and moves 20 metre upto C, then turns right and moves upto 30 metre upto D. Finally he turns right and moves upto 100 metre upto E.
So AB = 90 metre, BF = CD = 30 metre,
So, AF = AB - BF = 60 metre
Also DE = 100 metre, DF = BC = 20 metre
So, EF = DE - DF = 80 metre
as we can see in image that triangle AFE is a right angled triangle and we are having two sides, need to calculate third one, so we can apply Pythagoras theorem here 
egin{aligned}
A = AE = √{AF² + EF²} \
= √{(60)²+(80)²} \
= √{3600+6400} \
= √{10000} = 100
end{aligned}
So from starting point his father was 100 metre away.

Answer: Option B

Explanation:
Please check the movements of Gaurav in the figure.
Now, Gaurav distance from his initial position A to E
AE = (AD+DE) = 40 + 20 = 60 metres.

Answer: Option B

Explanation: 35 metre, East

The movements of Rohit are shown in figure.
Rohit's distance from the starting point A will be
AE = AD+DE = 20 + 15 = 35 metre
And direction with reference to the starting point is east.