AB is the diameter of the semicircle as shown in the diagram. If AQ – 2AP then which of the following is correct?

• Angle APB = $\frac{1}{2}$ angle AQB

• Angle APB = 2 angle AQB

• Angle APB = angle AQB

• Angle APB = $\frac{1}{4}$ angle AQB

The rabbit population in community A increases at 25% per year while that in  B increases at 50% per year. If the present populations of A and B are equal, the ratio of the number of the rabbits in B to that in A after 2 years will be

• 1.44

• 1.72

• 1.90

• 1.25

On a certain night the moon in its waning phase was a half-moon. AT midnight the moon will be

• On the eastern horizon     

• At 45° angular height above the eastern horizon.

• At the zenith

• On the western horizon

A gemstone is irradiated in a nuclear reactor for 5 days. Ten days after irradiation, the activity of the chromium radioisotope in the gemstone is 600 disintegrations per hour. What is the activity of chromium radioisotope 5 days after irradiation of its half-life is 5 days?

• 300

• 150

• 400

• 1200

Displacement versus time curve for a body is shown in the figure. Select the graph that correctly shows the variation of the velocity with time.

The ends of a rope are fixed to two pegs, such that the rope remains slack. A pencil is placed against the rope and moved, such that the rope always remains taut. The shape of the curve traced by the pencil would be a part of

• A circle

• An ellipse  

• A square

• A triangle

During ice skating, the blades of the ice skater’s shoes exert pressure on the ice. Ice skater can efficiently skate because

• Ice gets converted to water as the pressure exerted on it increases.   

• Ice gets converted to water as the pressure exerted on its decreases.

• The density of ice in contact with the blades decreases.

• Blades do not penetrate into ice.

Four sedimentary rocks A, B, C, and D are intruded by an igneous rock R as shown in the cross-section diagram. Which of the following is correct about their ages?

• A is the youngest followed by B, C, D, and R.

• R is the youngest followed by A, B, C, and D.   

• D is the youngest followed by C, B, A, and R.

• A is the youngest followed by R, B, C, and D.

   

The strain in a solid subjected to continuous stress is plotted.

Which of the following statements is true?

• The solid deforms elastically till the point of failure.

• The solid deforms plastically till the point of failure.

• The solid comes back to original shape and size on failure.

• The solid is permanently deformed on failure.   

Which of the following is indicated by the accompanying diagram?

• a + ab + ab² + …. = a/ (1 – b) for |b| < 1

• a > b implies a³ > b³

• (a + b)² = a² + 2ab + b² 

• a > b implies –a < -b