PGDBA 2019


For the following questions answer them individually

Question 21

Let the function $$f$$ be defined on the set of real numbers by 

$$ f(x) = \begin{cases}x^2 - x, & if x < 1\\\frac{x^2 - 1}{3}, &if x \geq 1\end{cases}$$ then which of the following statement is TRUE ?

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Question 22

If $$f'(x)$$ and $$g'(x)$$ exist for all $$x \in R$$, and if $$f'(x)>g'(x)$$ for all $$x \in R$$, then the curve $$y = f(x)$$ and $$y = g(x)$$ in the $$xy$$-plane

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Question 23

The value of the integral $$\int_{-\frac{1}{\sqrt{3}}}^{\frac{1}{\sqrt{3}}} (\frac{x^2 - \tan x}{1 + x^2})dx$$ is equal to

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Question 24

The area enclosed between the parabolas $$y^2 = 16(1 + x )$$ and $$y^2 = 16(1 - x)$$ is

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Question 25

Let $$[x]$$ denote the greatest integer less than or equal to $$x$$. The value of the integral $$\int_{0}^{\sqrt{2}} [x^2]e^x dx$$ is equal to

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Question 26

A function $$f(x) = ax^2 + bx + c$$, where $$a, b, c \in R$$, satisfies the property $$f(x) < x$$ for all $$x \in R$$. Then which of the following statements must always be TRUE ?

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Question 27

The foot of the ladder RS in the following figure is slipping away from the wall RO.

Then the point P(a fixed point on the ladder) lies on

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Question 28

Given that

$$\lim_{x\rightarrow0}\frac{ae^x - be^{-x}}{x + \sin x} = 1$$

Then the value of ab is

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Question 29

If $$\mid \frac{x + 1}{x - 1} \mid > \frac{x + 1}{x - 1}$$, then

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Question 30

How many $$6 \times 7$$ matrices are there with entries in {0,1} such that all the row totals and column totals are odd numbers?

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