ISRO Scientist or Engineer Computer Science Dec 2017

Instructions

For the following questions answer them individually

ISRO Scientist or Engineer Computer Science Dec 2017 - Question 1


Suppose A is a finite set with n elements. The number of elements and the rank of the largest equivalence relation on A are

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ISRO Scientist or Engineer Computer Science Dec 2017 - Question 2


Consider the set of integers I. Let D denote “divides with an integer quotient” (e.g. 4D8 but 4D7). Then D is

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ISRO Scientist or Engineer Computer Science Dec 2017 - Question 3


A bag contains 19 red balls and 19 black balls. Two balls are removed at a time repeatedly and discarded if they are of the same colour, but if they are different, black ball is discarded and red ball is returned to the bag. The probability that this process will terminate with one red ball is

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ISRO Scientist or Engineer Computer Science Dec 2017 - Question 4


If x = -1 and x = 2 are extreme points of $$f(x) = \alpha \log \mid x \mid + \beta x^2 + x$$ then

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ISRO Scientist or Engineer Computer Science Dec 2017 - Question 5


Let $$f(x) = \log \mid x \mid$$ and $$g(x) = \sin x$$. If A is the range of $$f(g(x))$$ and B is the range of $$g(f(x))$$ then $$A \cap B$$ is

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ISRO Scientist or Engineer Computer Science Dec 2017 - Question 6


The proposition $$(P \Rightarrow Q) \wedge (Q \Rightarrow P)$$ is a

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ISRO Scientist or Engineer Computer Science Dec 2017 - Question 7


If T (x) denotes x is a trigonometric function, P(x) denotes x is a periodic function and C(x) denotes x is a continuous function then the statement “It is not the case that some
trigonometric functions are not periodic” can be logically represented as

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ISRO Scientist or Engineer Computer Science Dec 2017 - Question 8


The number of elements in the power set of $$\left\{\left\{1, 2 \right\}, \left\{2, 1, 1 \right\}, \left\{2, 1, 1, 2 \right\}\right\}$$ is

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ISRO Scientist or Engineer Computer Science Dec 2017 - Question 9


The function $$f : [0, 3] \rightarrow [1, 29]$$ defined by $$f(x) = 2x^3 - 15x^2 + 36x + 1$$ is

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ISRO Scientist or Engineer Computer Science Dec 2017 - Question 10


If vectors $$\overrightarrow{a} = 2\hat{i} + \lambda \hat{j} + \hat{k}$$ and $$\overrightarrow{b} = \hat{i} + 2 \hat{j} + 3 \hat{k}$$ are perpendicular to each other, then value of $$\lambda$$ is

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