I. 2P,2R,2S,2T,2U

II. P-3,R-3,S-3,T-3,U-3

III. P^{2}, R^{2}, S^{2}, T^{2},
U^{2}

No Explaination.

Factorization of 162 is 2×3×3×3×3 y×162 is a perfect cube y×2×3×3×3×3 Perfect cube For perfect cube 2's & 3's are two more required each.

Out of six people, 3 place definitely occupied by right handed people as atleast 2 women are there so these two will sit adjacently. Now as only one seat is left it will be occupied by a left handed man because on right side of this seat is sitting an right handed man.

Therefore, answer should be 2 women.

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot. If in a flood, the water level rises to 525m. Which of the villages P,Q,R,S,T get submerged?

The given contour is a hill station, the peak point of this hill station is P, it is under a contour of 550. At floods, the water level is 525m. So the village of R, S and T are under a contour of 500. Therefore these villages are submerged.

As there are 4 people A,G,N,S and 4 colours so without any restriction total ways have to be 4×4 = 16 Now, Arun⟶dislikes Red and Shweta⟶dislikes white So 16-2=14 ways