  # ISRO Scientist or Engineer Computer Science Dec 2017

Instructions

For the following questions answer them individually

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 Question 2

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

# If x = -1 and x = 2 are extreme points of $$f(x) = \alpha \log \mid x \mid + \beta x^2 + x$$ then 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 Question 6

# The proposition $$(P \Rightarrow Q) \wedge (Q \Rightarrow P)$$ is a 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 sometrigonometric functions are not periodic” can be logically represented as 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 Question 9

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