Statement A. The following statement is true.

Statement B. The preceding statement is false.

Choose the correct inference from the following:

• Statements A and B are always true.

• Statements A and B can be true if there is at least one statement between A and B.

• Statements A and B can be true if there are at least two statements between A and B

• Statements A and B can never be true, independently

There are two buckets A and B. Initially A has 2 litres of water and B is empty. At every hour 1 litre of water is transferred from A to B followed by returning half litre back to A from B half an hour later. The earliest A will get empty is in:

• 5 h

• 4 h

• 3 H

• 2 h

The triangle formed by the lines y = x, y = 1 - x, and x = 0 in a two-dimensional plane is (x and y axes have the same scale)

• isosceles and right-angled

• isosceles but not right-angled

• right-angles but not isosceles

• neither isosceles nor right-angled

Secondary colours are made by a mixture of three primary colors, red, green, and blue in different proportions; each of the primary colors comes in 8 possible levels. Grey corresponds to equal proportions of Red, green, and blue. How many shades of grey exist in this scheme?

• 8³

• 8

• 3⁸

• 8 × 3

A cubical cardboard made of 1 cm thick cardboard has an outer side of 29 cm. A tight-fitting cubical box of the same thickness is placed inside it, then another one inside it and so on. How many cubical boxes will be there in the entire set?

• 29

• 28

• 15

• 14

A bird leaves its nest and flies away. Its distance x from the nest is plotted as a function of time t. Which of the following plots cannot be right?

327.

At one instant, the hour hand and the minute hand of a clock are one over the other in between the markings for 5 and 6 on the dial. At this instant, the tip of the minute hand

• is closer to the marking for 6

•  is equidistant  from the markings for 5 and 6

• is closer to marking for 5

• is equidistant from the markings for 11 and 12.

A vessel is partially filled with water. More water is added to it at a rate directly proportional to time [.e $\frac{\mathrm{dV}}{\mathrm{dt}} \propto \mathrm{t}$ ]. Which of the following graphs depicts correctly the variation of total volume V of water with time t.

A person walks downhill at 10 km/h, uphill at 6 km/h and on the plane at 7.5 km/h. If the person takes 3 hours to go from a place A to another place b, and 1 hour on the way back, the distance between A and B is

• 15 km

• 23.5 km

• 16 km

• Given data is insufficient to calculate the distance

Five congruent rectangles are drawn inside a big rectangle of perimeter 165 as shown. What is the perimeter of one of the five rectangles?

• 37

• 75

• 15

• 165