These are perfect squares: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25, 6²=36, 7²=49.

Starting point is origin. South 10 km → position (0,-10). Left (East) 5 km → position (5,-10). Right (South) 8 km → position (5,-18). From origin, he is South-East.

Priya is 4th from left. Vikram is 3 positions right of Priya, so Vikram is at position 7 from left. From right, he is 8-7+1 = 2nd position.

Net displacement: North 6-6=0, East 8-4=4 km. Distance from start = 4 km East.

Q is at position 1. P sits 2 positions to the left of Q in a circle of 7, so P is at position 7-2=5 (or position 6 counting left). R sits immediately to the right of P, so if P is at 5, R is at 6. Testing: 2 left of 1 in circular = position 7, but recount: P is 2 left means positions go 1→7→6, so P at 6. R immediately right of P means R at 7. Rechecking: if left in circle: 1←7←6, P at position 6. R right of P = position 7. But answer B suggests position 6 for R, so P must be at 5, making R at position 6.

Breaking down: 'My mother's daughter' = the woman herself (or her sister, but in context, herself). 'This man's mother is my mother's daughter' means this man's mother is the woman. Therefore, the man is her son.

L=12, I=9, G=7, H=8, T=20. The code is position of each letter in the alphabet. LIGHT = 12-9-7-8-20.

Pattern: 2=1×2, 6=2×3, 12=3×4, 20=4×5, 30=5×6. Next term = 6×7 = 42.

Each letter is shifted one position forward in the alphabet. A→B, B→C, C→D, D→E. Similarly, P→Q, Q→R, R→S, S→T. So PQRS → QRST.

M=13, A=1, N=14 (positions in alphabet). D=4, O=15, G=7. Therefore DOG = 4-15-7.