PGDBA 2017

Instructions

Answer the questions based on the following information.
The following table gives the urban population of a country and the percentages of total population in rural and urban areas as recorded in the 10-years censuses during 1901-81.
Table 1. Urban and rural population 1901-1981


Question 21

The percentage increase in total population of the country between 1901 and 1981 is

Question 22

The percentage increase in density of population in the urban areas between 1951 and 1981 is

Question 23

The largest rate of increase in urban population in a decade during 1901-1981 occurred in


Question 24

The rate of urban population growth per year over the period 1901-81 is about

Question 25

The smallest rate of increase in urban population in a decade during 1921-1961 occurred in

Instructions

For the following questions answer them individually

Question 26

If $$a \in R$$, then the equation $$x^2 + x + a = 0$$ and $$x^2 + ax + 1 = 0$$ have a common real root for


Question 27

A man standing x metres north of A tower finds the angle of elevation of as top to be 30° .He then starts walking towards the tower. After walking a distance of x/2 metres, he turns east and walks another x/2 metres. Then he turns south and walks another x/2 metres. The angle of elevation of the top of the tower from his new position is

Question 28

Let the equations of two circles $$C_1$$ and $$C_2$$ be given by $$x^2 + y^2 - 4x - 4y + 6 = 0$$ and $$x^2 + y^2 - 10x - 10y + k = 0$$ respectively, where $$k$$ is a constant. Suppose that $$C_1$$ and $$C_2$$ have exactly two common tangents. Then possible values of $$k$$ are

Question 29

Consider the function

$$f(x) = \begin{cases}2x -1 & if & x < -1\\x^2 + 1 & if & -1\leq x \leq 1\\x + 1 & if & x > 1.\end{cases}$$

Then


Question 30

The sum of the first $$50$$ terms of the series: $$3 + 7 + 13 + 21 + 31 + 43 +...$$ is

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