PGDBA 2019

Instructions

Answer the questions based on the following information.
The following bar diagram represents the number of daily wages (in rupees) of 100 labourers in different wage classes on a construction site. Here the class interval a-b includes all wages (in rupees) greater than or equal to a and less than b except for the interval 360-400, where both the end points are included.

No.of labourers 

                                                   Wages in Rupees

Question 1

The number of labourers receiving at least 320 is:

Question 2

The number of labourers receiving less than Rs.250 is

Question 3

The maximum wage (in Rupees), such that at least 50% of the labourers definitely earn more than that, is

Instructions

Answer the questions based on the following information.
The following table gives month-wise arrivals of foreign tourists in India in the years 2016 & 2017.
Table: Month-wise Arrivals of Foreign Tourists (in Thousands) in India (2016-2017)


Question 4

In which month of 2017 is the percentage increase over the corresponding month of the previous year the minimum?

Question 5

In which month of 2017 is the percentage increase over the previous month the maximum?


Instructions

For the following questions answer them individually

Question 6

If $$ f(x) = \log_{e}({\frac{2 - x}{9 - x^2}})$$, then the domain of the function $$f$$ is

Question 7

If the system of linear equations
$$2x+ y+7z = a$$
$$6x-2y+11z = b$$
$$2x-y+3z = c$$ 
has infinite number of solutions, then $$a, b, c$$ must satisfy

Question 8

If $$\alpha, \beta$$ are the roots of the equation $$x^2 + 3x - 3$$ , then the value of $$(\alpha + 1)^{-1} + (\beta +1)^{-1}$$ is equal to

Question 9

The number of real roots of the equation 

$$(e^x + e^{-x})^3 + 3(e^x + e^{-x})^2 + 3(e^x + e^{-x}) = 7$$

Question 10

Let $$x = -\frac{1}{1!}\cdot\frac{3}{4} + \frac{1}{2!}\cdot(\frac{3}{4})^2 -\frac{1}{3!}\cdot(\frac{3}{4})^3 +$$.... and $$y = x - \frac{x^2}{2} + \frac{x^3}{3} - $$..... then the value of y is

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