A country has the following types of traffic signals.
$3$ red lights = stop;
$2$ red lights = turn left;
$1$ red light = turn right;
$3$ green lights = go at $100$ kmph speed;
$2$ green lights = go at $40$ kmph speed
$1$ green light = go at $20$ kmph speed.
A motorist starts at a point on a road and follows all traffic signals literally. His car is heading towards the north. He encounters the following signals (the time mentioned in each case below is applicable after crossing the previous signal)
Starting point: $1$ green light;
After half an hour, $1$st signal: $2$ red and $2$ green lights;
After $15$ minutes, $2$nd signal: $1$ red light
After half an hour, $3$rd signal: $1$ red and $3$ green lights;
After $24$ minutes, $4$th signal: $2$ red and $2$ green lights;
After $15$ minutes, $5$th signal: $3$ red lights;

What is the position (radial distance) of the motorist when he reaches the last signal?

A girl was riding a bicycle towards the north. Then she turned left and from left she went ahead $1$ km. Then she found herself at $2$ km, from the starting point. At the beginning towards the north, how much distance she covered:

(A) $\sqrt{3}$ km

(B) $\sqrt{2}$ km.

(C) $\sqrt{1}$ km.

(D) $\sqrt{5}$ km.

A shopper in a mart loads his trolley and walks $30 m$ through an alley which is going South, then he turns to his left and walks $10 m$, then he turns North and walks another $10 m$, then he turns West and walks $45 m$ and then he turns North and walks $20 m$.

Where is he now with reference to his starting position?

Sunil and Manohar are playing carom. If Sunil is facing the North–East direction, then which direction is his opponent Manohar facing?

Direction: Study the following question carefully and choose the correct option given below.
Having heard a sound, a policeman moves $4 \mathrm{km}$ in the south direction from its post towards A. At that point, he hears one more sound and moves $4 \mathrm{km}$ towards his left to reach point B. At B, he discovered that sound was coming from the left of B. He moves $4 \mathrm{km}$ left of B to reach the place sound was coming from. In which direction should he move to reach his post finally:
(A) West
(B) East
(C) North
(D) South

X walks $3$ km to the south then moves right and walks $5$ km. Again he moves right and walks $7$ km. Finally, in which direction X was moving?

(A) North

(B) West

(C) South

(D) East

A man walking towards the north covers distance of $15.6$ km, then moves $7$ km. to left. Again he moves left covering $31$ km, again he moves left and then stops after covering $7$ km. Now, how far is he from his house?

(A) $60.5$ km. 

(B)$46.5$ km.

(C) $8.5$ km.

(D) $15.5$ km.

Shivani started running from her office. She first ran for $16 \mathrm{kms}$ towards the north, then she turned towards the east and ran $\sqrt{68} \mathrm{kms}$ in that direction. How far and in which direction is Shivani from her office?