PGDBA 2016


For the following questions answer them individually

Question 41

If [a] denotes the greatest integer less than or equal to a for $$a \in R$$, then the value of the integral

$$\int_{0}^{1.7} [x^2] dx$$ is equal to

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Question 42

Which of the following functions is differentiable at x = 0 ?

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Question 43

Let the function f be  given by  $$f(x) = \begin{cases}x + x^2 \sin(\frac{\pi}{x}); & x  \neq 0 \\0; & x = 0\end{cases}$$ 

then $$\left( f'(1) - f'(0) \right)$$ is 

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Question 44

Let the function $$f$$ be given by

$$f(x) = \begin{cases}-(x -1)^4; & x \leq 2\\(x - 3)^3; & x > 2\end{cases}$$

Then local extrema of $$f$$ exist at

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Question 45

The points in the xy-plane, which satisfy the equation
$$\sqrt{(x - 1)^2 + (y + 2)^2} = \sqrt{(x + 3)^2 + (y - 2)^2}$$

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Question 46

Two pairs of straight lines $$x^2 — 7x + 6 = 0$$ and $$y^2 — 14y + 40 = 0$$ intersect to form a rectangle. Let the diagonals of the rectangle intersect at the point W. A circle with center W and with tangents as lines $$y^2 — 14y + 40 = 0$$ intersects lines $$x^2 — 7x + 6 = 0$$ at points P, Q, R, S. The area of the rectangle PQRS is

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Question 47

Normals to the parabola $$y^2 = 4x$$ are drawn at two points P and Q on it. These normals intersect the parabola at the point R (9, -6). Then PQ equals

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Question 48

If $$f : R \rightarrow R$$ be a continuous function satisfying  $$f(x) + f(3 - x) = 4$$, then $$\int_{0}^{3} f(x) dx$$ is equal to 

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Question 49

Let PQRS be a cycle quadrilateral. Let O be the centre of the circumcircle of the quadrilateral. Then which of the following statements is NOT true?

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Question 50

Let $$P$$ and $$Q$$ be two distinct nonempty sets. Then $$(P \cup Q)^c \cup (P^c \cap Q)$$ equals

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