PGDBA 2018 Question Paper

Instructions

For the following questions answer them individually

PGDBA 2018 - Question 31


How many distinct 5 x 5 matrices are there such that each entry is either 0 or 1 and each row sum and each column sum is 4?

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PGDBA 2018 - Question 32


The sum of an infinite geometric series of real numbers is 14, and the sum of the cubes of the terms of this series is 392. The first term of the series is

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PGDBA 2018 - Question 33


The radius of the incircle of the triangle formed by the x-axisand the lines 3x + 4y - 24 = 0, 3x - 4y + 24 = 0 is

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PGDBA 2018 - Question 34


The expression $$\tan^{-1}\left(\frac{1}{1 + 1.2}\right) + \tan^{-1}\left(\frac{1}{1 + 2.3}\right) + \tan^{-1}\left(\frac{1}{1 + 3.4}\right) + ........ + \tan^{-1}\left(\frac{1}{1 + n(n + 1)}\right)$$ simplifies to

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PGDBA 2018 - Question 35


Let $$g(x) = f(x) + f(2 + x)$$, where $$f(x) = \begin{cases}1 - \mid x \mid, & \mid x \mid \leq 1\\0, & \mid x \mid > 1\end{cases}$$ The number of points where the function g is not differentiable is

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PGDBA 2018 - Question 36


If $$A = \left(\begin{array}{c}1 & 0\\ -1 & 1\end{array}\right)$$, then $$A^{50}$$ is

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PGDBA 2018 - Question 37


A curve is drawn such that the slope at any point P = (x,y) is equal to x. The curve represents a family of

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PGDBA 2018 - Question 38


Let f be a differentiable function on [-2, 2] such that f(-2) = 1, f(2) = 5 and $$\mid \frac{df(x)}{dx}\mid \leq 1$$ for all $$x \epsilon [-2, 2]$$. The value of f(0) is

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PGDBA 2018 - Question 39


For a set S, we denote by S', the complement of the set S. Let X, Y, Z be Sets such that $$Y \subseteq X$$. Which of the following is always true?

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PGDBA 2018 - Question 40


A sequence $$\left\{x_n \right\}$$ of real numbers is defined as follows:

$$x_0 = 1, x_1 = 2,$$ and $$x_n = \frac{1 + x_{n - 1}}{x_{n - 2}}$$ for n = 2, 3, 4 ...
It follows that $$x_{2018}$$ is

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