A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given option for the missing piece when assembled will form a rectangle? The piece can be moved. rotated or flipped to assemble with the above piece.

Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations:

Observation I : S is taller than R.

Observation II : Q is the shortest of all.

Observation III : U is taller than only one student.

IV : T is taller than S but is not the tallest.

The number of students that are taller than R is the same as the number of students shorter than ________.

If P = 3, R = 27, T = 243, then Q + S = ______.

Three of the five students allocated to a hostel put in special requests to the warden. Given the floor plan of the vacant rooms, select the allocation plan that will accommodate all their requests.

Request by X: Due to pollen allergy, I want to avoid a wing next to the garden.

Request by Y: I want to live as far from the washrooms as possible, since I am very sensitive to smell.

Request by Z: I believe in Vaastu and so want to stay in the South-west wing.

The shaded rooms are already occupied. WR is washroom.