Functions

Question 1
Suppose that f: \mathbb{R} \rightarrow \mathbb{R} is a continuous function on the interval [-3,3] and a differentiable function in the interval (-3,3) such that for every x in the interval, f'(x) \leq 2. If f(-3) =7, then f(3) is at most __________
A
19
B
32
C
11
D
54
GATE CSE 2021 SET-2   Discrete Mathematics
Question 2
Consider the following sets, where n\geq 2:

S1: Set of all nxn matrices with entries from the set \{a, b, c\}
S2: Set of all functions from the set\{0,1,2,...,n^2-1\} to the set \{0, 1, 2 \}

Which of the following choice(s) is/are correct?
[MSQ]
A
There does not exist a bijection from S1 to S2
B
There exists a surjection from S1 to S2
C
There exists a bijection from S1 to S2
D
There does not exist an injection from S1 to S2
GATE CSE 2021 SET-2   Discrete Mathematics
Question 3
If the ordinary generating function of a sequence \{a_{n}\}_{n=0}^{\infty} \; is \; \frac{1+z}{(1-z)^{3}} then a_{3}-a_{0} is equal to ______.
A
16
B
17
C
15
D
14
GATE CSE 2017 SET-2   Discrete Mathematics
Question 4
If g(x)=1-x and h(x)=\frac{x}{x-1}, then \frac{g(h(x))}{h(g(x))} is:
A
\frac{h(x)}{g(x)}
B
\frac{-1}{x}
C
\frac{g(x)}{h(x)}
D
\frac{x}{(1-x)^{2}}
GATE CSE 2015 SET-1   Discrete Mathematics
Question 5
Let A be a finite set having x elements and let B be a finite set having y elements. What is the number of distinct functions mapping B into A.
A
x^{y}
B
2^{(x+y)}
C
y^{x}
D
y ! /(y-x) !
ISRO CSE 2014   Discrete Mathematics
Question 6
Consider the set of all functions f:{0,1,...,2014}\rightarrow{0,1...,2014} such that f(f(i))=i, for 0\leqi\leq2014 . Consider the following statements.
P. For each such function it must be the case that for every i, f(i) = i,
Q. For each such function it must be the case that for some i,f(i) = i,
R. Each such function must be onto.
Which one of the following is CORRECT?
A
P, Q and R are true
B
Only Q and R are true
C
Only P and Q are true
D
Only R is true
GATE CSE 2014 SET-3   Discrete Mathematics
Question 7
Let S denote the set of all functions f:{\{0,1\}}^{4} \rightarrow \{0,1\}. Denote by N the number of functions from S to the set {0,1}. The value of log_{2} log_{2}N is______.
A
4
B
8
C
16
D
32
GATE CSE 2014 SET-1   Discrete Mathematics
Question 8
How many onto (or surjective) functions are there from an n-element ( n \geq 2 ) set to a 2-element set?
A
2^{n}
B
2^{n}-1
C
2^{n}-2
D
2(2^{n}-2)
GATE CSE 2012   Discrete Mathematics
Question 9
Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a \in A. Which of the following statements is always true for all such functions f and g?
A
g is onto \implies h is onto
B
h is onto \implies f is onto
C
h is onto \implies g is onto
D
h is onto \implies f and g are onto
GATE IT 2005   Discrete Mathematics
Question 10
Let f: B \rightarrow C and g: A \rightarrow B be two functions and let h = f\cdotg. Given that h is an onto function which one of the following is TRUE?
A
f and g should both be onto functions
B
f should be onto but g need to be onto
C
g should be onto but f need not be onto
D
both f and g need to be onto
GATE CSE 2005   Discrete Mathematics
There are 10 questions to complete.

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