The area of the shaded region in cm² is

• $\left(\mathrm{\pi } - \sqrt{2}\right)$

• ($\mathrm{\pi }$ - 2)

• $\left(\frac{\mathrm{\pi }}{4} - \frac{\sqrt{2}}{2}\right)$

• $\left(\mathrm{\pi } + 2\right)$

The angles of a right-angled triangle shaped garden are in the arithmetic progression and the smallest side is 10.00 m. The total length of the fencing of the garden in m is:

• 60.00

• 47.32

• 12.68

• 22.68

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

Two moles each of O₂ and H₂ are in two separate containers. The two are made to react in a third container to form water vapor until. H₂ is exhausted. When the temperature of the mixture in the third container was restored to 150°C, its pressure became 1 atmosphere. The volume of the third container must be

• V₀

• $\frac{5{\mathrm{V}}_0}{4}$

• $\frac{3{\mathrm{V}}_0}{2}$     

• 2V₀

Helium and argon gases in two separate containers are at the same temperature and so have different root-mean-square (r.m.s) velocities. The two are mixed in a third container keeping the same temperature. The r.m.s velocity of the helium atoms in the mixture is

• More than what it was before mixing

• Less than what it was before mixing

• Equal to what it was before mixing          

• Equal to that of argon atoms in the mixture.

The mineral tale is used in the manufacture of soap because it

a. Gives bulk to the product

b. Kills bacteria

c. Gives fragrance

d. Is soft and does not scratch the skin

Which of the above statements is/ are correct?

• d

• a and c

• a and b

• a and d

100 gm of an inorganic compound X.5H₂O containing a volatile impurity was kept in an oven at 150°C for 60 minutes. The weight of the residue after heating is 8 gm. The percentage of impurity in X was

• 10

• 8

• 20

• 80

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