A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.

If R gets Rs. 1000 more than S, what is the share of Q (in Rs.) ?

A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.

Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and SP = 3 cm. What is the shortest distance between PQ and SR (in cm) ?

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.

What is the maximum number of squares without a "hole in the interior" that can be formed within the 4 $$\times$$ 4 grid using the unit squares as building blocks?

An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard. If the security guard does not move around the posted location and has a 360$$^\circ$$ view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R, and S, where the security guard can be posted to watch over the entire inner space of the gallery.