Correct Answer: C. 5.5 utils

Explanation

Average utility will be the total utility derived form the consumption of a commodity divided by the number of units consumed. Thus we have;

22

Correct Answer: C. abab

Explanation

(a) P(obtaining a 3 from a die) = \(\frac{1}{6}\)

P(obtaining a tail in 2 coins tossed at once) = \(\frac{1}{2}\).

\(\therefore\) P(obtaining 3 and a tail = \(\frac{1}{6} \times \frac{1}{2} = \frac{1}{12}\)

(b) No of black marbles = n(B) = 7

No of red marbles = n(R) = 3

Total marble = 10

(i) P(red then black) = P(1st red, then black) or P(1st black, then red)

= \(\frac{3}{10} \times \frac{7}{9} + \frac{7}{10} \times \frac{3}{9}\)

= \(\frac{7}{15}\)

(ii) Prob (two blacks) = \(\frac{7}{10} \times \frac{6}{9} = \frac{7}{15}\)

Explanation

(a) Population census is the head count of all nationals of a country at a particular time. It is usually carried out once in every 10 years. It provides information about age, sex, occupation, residence etc.

(bi) Implications of optimum population:Optimum population may be defined as the population which combines with the available resources and the given level of existing technology to secure a maximum return per head. An optimum population is the population that produces full employment and the highest standard of living in a country. Optimum population is a dynamic population that changes with the changing quantity and quality of a country's available resources.

(bii)Implications of over population: Over population is the population that exceeds the available resources of a country. Its implications are:

(i) It will lead to unemployment.

(ii) Over population causes a fall in the standard of living of the people of a country.

(iii) It causes shortage of social amenities like schools, roads, pipe borne water and electricity.

(iv) Overpopulation will reduce output per head.

(v) It leads to congestion in the cities.

(vi) Over population leads to high rate of illiteracy.

(vii) Over population leads to high import bills.

Correct Answer: B. feudalism

Explanation

Feudalism is a system of land ownership and duties

Correct Answer: B. committee stage

Correct Answer: D. \(48\pi cm^{2}s^{-1}\)

Explanation

Surface area of sphere, \( A = 4\pi r^{2}\)

\(\frac{\mathrm d A}{\mathrm d r} = 8\pi r\)

The rate of change of radius with time \(\frac{\mathrm d r}{\mathrm d t} = 3cm s^{-1}\)

\(\frac{\mathrm d A}{\mathrm d t} = (\frac{\mathrm d A}{\mathrm d r})(\frac{\mathrm d r}{\mathrm d t})\)

= \(8\pi \times 2cm \times 3cm s^{-1} = 48\pi cm^{2}s^{-1}\)

Correct Answer: C. 120 N

Correct Answer: A. premature dropping of fruits

Correct Answer: B. intensive agriculature and fertile soils