The Gateway to Computer Science Excellence
For all GATE CSE Questions
Toggle navigation
Facebook Login
or
Email or Username
Password
Remember
Login
Register

I forgot my password
Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
Prev
Blogs
New Blog
Exams
Recent questions tagged functions
Materials:
Functions
+1
vote
1
answer
1
ISI2014DCG5
Consider the sets defined by the real solutions of the inequalities $A = \{(x,y):x^2+y^4 \leq 1\} \:\:\:\:\:\:\: B=\{(x,y):x^4+y^6 \leq 1\}$ Then $B \subseteq A$ $A \subseteq B$ Each of the sets $A – B, \: B – A$ and $A \cap B$ is nonempty none of the above
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

79
views
isi2014dcg
calculus
functions
sets
+2
votes
1
answer
2
ISI2014DCG6
If $f(x)$ is a real valued function such that $2f(x)+3f(x)=154x$, for every $x \in \mathbb{R}$, then $f(2)$ is $15$ $22$ $11$ $0$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

51
views
isi2014dcg
calculus
functions
+2
votes
3
answers
3
ISI2014DCG7
If $f(x) = \dfrac{\sqrt{3} \sin x}{2+\cos x}$, then the range of $f(x)$ is the interval $[1 , \sqrt{3}{/2}]$ the interval $[\sqrt{3}{/2}, 1]$ the interval $[1, 1]$ none of these
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

39
views
isi2014dcg
calculus
functions
range
+1
vote
0
answers
4
ISI2014DCG21
Suppose that the function $h(x)$ is defined as $h(x)=g(f(x))$ where $g(x)$ is monotone increasing, $f(x)$ is concave, and $g’’(x)$ and $f’’(x)$ exist for all $x$. Then $h(x)$ is always concave always convex not necessarily concave None of these
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

16
views
isi2014dcg
calculus
functions
maximaminima
convexconcave
0
votes
1
answer
5
ISI2014DCG24
Let $f(x) = \dfrac{2x}{x1}, \: x \neq 1$. State which of the following statements is true. For all real $y$, there exists $x$ such that $f(x)=y$ For all real $y \neq 1$, there exists $x$ such that $f(x)=y$ For all real $y \neq 2$, there exists $x$ such that $f(x)=y$ None of the above is true
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

12
views
isi2014dcg
calculus
functions
0
votes
0
answers
6
ISI2014DCG33
Let $f(x)$ be a continuous function from $[0,1]$ to $[0,1]$ satisfying the following properties. $f(0)=0$, $f(1)=1$, and $f(x_1)<f(x_2)$ for $x_1 < x_2$ with $0 < x_1, \: x_2<1$. Then the number of such functions is $0$ $1$ $2$ $\infty$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

16
views
isi2014dcg
calculus
functions
limits
+1
vote
1
answer
7
ISI2014DCG37
Let $f: \bigg( – \dfrac{\pi}{2}, \dfrac{\pi}{2} \bigg) \to \mathbb{R}$ be a continuous function, $f(x) \to +\infty$ as $x \to \dfrac{\pi^}{2}$ and $f(x) \to – \infty$ as $x \to \dfrac{\pi^+}{2}$. Which one of the following functions satisfies the above properties of $f(x)$? $\cos x$ $\tan x$ $\tan^{1} x$ $\sin x$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

15
views
isi2014dcg
calculus
functions
limits
continuity
0
votes
0
answers
8
ISI2014DCG43
Let $f(x) = \begin{cases}\mid \:x \mid +1, & \text{ if } x<0 \\ 0, & \text{ if } x=0 \\ \mid \:x \mid 1, & \text{ if } x>0. \end{cases}$ Then $\underset{x \to a}{\lim} f(x)$ exists if $a=0$ for all $a \in R$ for all $a \neq 0$ only if $a=1$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

7
views
isi2014dcg
calculus
functions
limits
0
votes
0
answers
9
ISI2014DCG45
Which of the following is true? $\log(1+x) < x \frac{x^2}{2} + \frac{x^3}{3} \text{ for all } x>0$ $\log(1+x) > x \frac{x^2}{2} + \frac{x^3}{3} \text{ for all } x>0$ $\log(1+x) > x \frac{x^2}{2} + \frac{x^3}{3} \text{ for some } x>0$ $\log(1+x) < x \frac{x^2}{2} + \frac{x^3}{3} \text{ for some } x>0$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

15
views
isi2014dcg
calculus
functions
logarithms
0
votes
0
answers
10
ISI2014DCG48
If $x$ is real, the set of real values of $a$ for which the function $y=x^2ax+12a^2$ is always greater than zero is $ \frac{2}{3} < a \leq \frac{2}{3}$ $ \frac{2}{3} \leq a < \frac{2}{3}$ $ \frac{2}{3} < a < \frac{2}{3}$ None of these
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

7
views
isi2014dcg
calculus
functions
quadraticequations
0
votes
1
answer
11
ISI2014DCG49
Let $f(x) = \dfrac{x}{(x1)(2x+3)}$, where $x>1$. Then the $4^{th}$ derivative of $f, \: f^{(4)} (x)$ is equal to $ \frac{24}{5} \bigg[ \frac{1}{(x1)^5}  \frac{48}{(2x+3)^5} \bigg]$ ... $\frac{64}{5} \bigg[ \frac{1}{(x1)^5} + \frac{48}{(2x+3)^5} \bigg]$
asked
Sep 23
in
Others
by
Arjun
Veteran
(
424k
points)

32
views
isi2014dcg
calculus
derivative
functions
+1
vote
2
answers
12
ISI2015MMA16
If two real polynomials $f(x)$ and $g(x)$ of degrees $m\: (\geq 2)$ and $n\: (\geq 1)$ respectively, satisfy $f(x^2+1)=f(x)g(x),$ for every $x \in \mathbb{R}$, then $f$ has exactly one real root $x_0$ such that $f’(x_0) \neq 0$ $f$ has exactly one real root $x_0$ such that $f’(x_0) = 0$ $f$ has $m$ distinct real roots $f$ has no real root
asked
Sep 23
in
Numerical Ability
by
Arjun
Veteran
(
424k
points)

42
views
isi2015mma
numericalability
quadraticequations
functions
nongate
0
votes
0
answers
13
ISI2015MMA23
Let $X$ be a nonempty set and let $\mathcal{P}(X)$ denote the collection of all subsets of $X$. Define $f: X \times \mathcal{P}(X) \to \mathbb{R}$ by $f(x,A)=\begin{cases} 1 & \text{ if } x \in A \\ 0 & \text{ if } x \notin A \end{cases}$ Then $f(x, A \cup B)$ ... $f(x,A)+f(x,B)\:  f(x,A) \cdot f(x,B)$ $f(x,A)\:+ \mid f(x,A)\:  f(x,B) \mid $
asked
Sep 23
in
Set Theory & Algebra
by
Arjun
Veteran
(
424k
points)

5
views
isi2015mma
settheory
functions
nongate
0
votes
0
answers
14
ISI2015MMA30
Suppose that a function $f$ defined on $\mathbb{R} ^2$ satisfies the following conditions: $\begin{array} &f(x+t,y) & = & f(x,y)+ty, \\ f(x,t+y) & = & f(x,y)+ tx \text{ and } \\ f(0,0) & = & K, \text{ a constant.} \end{array}$ Then for all $x,y \in \mathbb{R}, \:f(x,y)$ is equal to $K(x+y)$ $Kxy$ $K+xy$ none of the above
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

6
views
isi2015mma
calculus
functions
nongate
+1
vote
1
answer
15
ISI2015MMA33
If $f(x)$ is a real valued function such that $2f(x)+3f(x)=154x,$ for every $x \in \mathbb{R}$, then $f(2)$ is $15$ $22$ $11$ $0$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

8
views
isi2015mma
calculus
functions
nongate
0
votes
1
answer
16
ISI2015MMA34
If $f(x) = \dfrac{\sqrt{3}\sin x}{2+\cos x}$, then the range of $f(x)$ is the interval $[1, \sqrt{3}/2]$ the interval $[ \sqrt{3}/2, 1]$ the interval $[1, 1]$ none of the above
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

15
views
isi2015mma
calculus
functions
range
trigonometry
nongate
+1
vote
1
answer
17
ISI2015MMA36
For nonnegative integers $m$, $n$ define a function as follows $f(m,n) = \begin{cases} n+1 & \text{ if } m=0 \\ f(m1, 1) & \text{ if } m \neq 0, n=0 \\ f(m1, f(m,n1)) & \text{ if } m \neq 0, n \neq 0 \end{cases}$ Then the value of $f(1,1)$ is $4$ $3$ $2$ $1$
asked
Sep 23
in
Calculus
by
Arjun
Veteran
(
424k
points)

8
views
isi2015mma
calculus
functions
nongate
0
votes
0
answers
18
ISI2015MMA37
Let $a$ be a nonzero real number. Define $f(x) = \begin{vmatrix} x & a & a & a \\ a & x & a & a \\ a & a & x & a \\ a & a & a & x \end{vmatrix}$ for $x \in \mathbb{R}$. Then, the number of distinct real roots of $f(x) =0$ is $1$ $2$ $3$ $4$
asked
Sep 23
in
Linear Algebra
by
Arjun
Veteran
(
424k
points)

21
views
isi2015mma
linearalgebra
determinant
functions
0
votes
0
answers
19
ISI2015MMA67
Given two real numbers $a<b$, let $d(x,[a,b]) = \text{min} \{ \mid xy \mid : a \leq y \leq b \} \text{ for }  \infty < x < \infty$. Then the function $f(x) = \frac{d(x,[0,1])}{d(x,[0,1]) + d(x,[2,3])}$ satisfies $0 \leq f(x) < \frac{1}{2}$ for every $x$ ... $f(x)=1$ if $ 0 \leq x \leq 1$ $f(x)=0$ if $0 \leq x \leq 1$ and $f(x)=1$ if $ 2 \leq x \leq 3$
asked
Sep 23
in
Others
by
Arjun
Veteran
(
424k
points)

7
views
isi2015mma
functions
nongate
0
votes
1
answer
20
ISI2015DCG27
If $A$ be the set of triangles in a plane and $R^{+}$ be the set of all positive real numbers, then the function $f\::\:A\rightarrow R^{+},$ defined by $f(x)=$ area of triangle $x,$ is oneone and into oneone and onto manyone and onto manyone and into
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

20
views
isi2015dcg
functions
triangles
+1
vote
1
answer
21
ISI2015DCG36
Suppose $X$ and $Y$ are finite sets, each with cardinality $n$. The number of bijective functions from $X$ to $Y$ is $n^n$ $n \log_2 n$ $n^2$ $n!$
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

15
views
isi2015dcg
settheory
functions
0
votes
0
answers
22
ISI2015DCG37
Suppose $f_{\alpha} : [0,1] \to [0,1],\:\: 1 < \alpha < \infty$ is given by $f_{\alpha} (x) = \frac{(\alpha +1)x}{\alpha x+1}$ Then $f_{\alpha}$ is A bijective (oneone and onto) function A surjective (onto ) function An injective (oneone) function We cannot conclude about the type
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

14
views
isi2015dcg
settheory
functions
+1
vote
1
answer
23
ISI2015DCG49
The domain of the function $\text{ln}(3x^24x+5)$ is set of positive real numbers set of real numbers set of negative real numbers set of real numbers larger than $5$
asked
Sep 18
in
Calculus
by
gatecse
Boss
(
16.8k
points)

12
views
isi2015dcg
calculus
functions
domain
0
votes
0
answers
24
ISI2015DCG50
The piecewise linear function for the following graph is $f(x) = \begin{cases} = x, \: x \leq 2 \\ =4, \: 2<x<3 \\ =x+1, \: x \geq 3 \end{cases}$ $f(x) = \begin{cases} = x2, \: x \leq 2 \\ =4, \: 2<x<3 \\ =x1, \: x \geq 3 \end{cases}$ ... $f(x) = \begin{cases} = 2x, \: x \leq 2 \\ =4, \: 2<x<3 \\ =x+1, \: x \geq 3 \end{cases}$
asked
Sep 18
in
Calculus
by
gatecse
Boss
(
16.8k
points)

14
views
isi2015dcg
calculus
functions
0
votes
0
answers
25
ISI2015DCG57
Let $y=\lfloor x \rfloor$, where $\lfloor x \rfloor$ is greatest integer less than or equal to $x$. Then $y$ is continuous and manyone $y$ is not differentiable and manyone $y$ is not differentiable $y$ is differentiable and manyone
asked
Sep 18
in
Calculus
by
gatecse
Boss
(
16.8k
points)

7
views
isi2015dcg
calculus
functions
floor
continuitydifferentiability
0
votes
1
answer
26
ISI2016DCG4
If $f(x)=\begin{bmatrix}\cos\:x & \sin\:x & 0 \\ \sin\:x & \cos\:x & 0 \\ 0 & 0 & 1 \end{bmatrix}$ then the value of $\big(f(x)\big)^2$ is $f(x)$ $f(2x)$ $2f(x)$ None of these
asked
Sep 18
in
Linear Algebra
by
gatecse
Boss
(
16.8k
points)

10
views
isi2016dcg
linearalgebra
matrices
trigonometry
functions
0
votes
1
answer
27
ISI2016DCG27
If $A$ be the set of triangles in a plane and $R^{+}$ be the set of all positive real numbers, then the function $f\::\:A\rightarrow R^{+},$ defined by $f(x)=$ area of triangle $x,$ is oneone and into oneone and onto manyone and onto manyone and into
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

7
views
isi2016dcg
settheory
functions
0
votes
1
answer
28
ISI2016DCG36
Suppose $X$ and $Y$ are finite sets, each with cardinality $n$.. The number of bijective functions from $X$ to $Y$ is $n^{n}$ $n\log_{2}n$ $n^{2}$ $n!$
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

8
views
isi2016dcg
settheory
functions
0
votes
0
answers
29
ISI2016DCG37
Suppose $f_{\alpha}\::\:[0,1]\rightarrow[0,1],\:1<\alpha<\infty$ is given by $f_{\alpha}(x)=\dfrac{(\alpha+1)x}{\alpha x+1}.$ Then $f_{\alpha}$ is A bijective (oneone and onto) function. A surjective (onto) function. An injective (oneone) function. We can not conclude about the type.
asked
Sep 18
in
Set Theory & Algebra
by
gatecse
Boss
(
16.8k
points)

3
views
isi2016dcg
settheory
functions
0
votes
0
answers
30
ISI2016DCG48
The piecewise linear function for the following graph is $f(x)=\begin{cases} = x,x\leq2 \\ =4,2<x<3 \\ = x+1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = x2,x\leq2 \\ =4,2<x<3 \\ = x1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = 2x,x\leq2 \\ =x,2<x<3 \\ = x+1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = 2x,x\leq2 \\ =4,2<x<3 \\ = x+1,x\geq 3\end{cases}$
asked
Sep 18
in
Calculus
by
gatecse
Boss
(
16.8k
points)

7
views
isi2016dcg
calculus
functions
curves
nongate
Page:
1
2
3
4
5
6
...
8
next »
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
Linear Algebra Important Points
GATE 2020
OFFICIAL GATE MOCK TEST RELEASED
IIITH: Winter Research Admissions 2019 (For Spring 2020)
TIFR and JEST exam
Follow @csegate
Recent questions tagged functions
Recent Blog Comments
i also don't have any pdf, actually, I added the...
i don't have , if you have upload it
@mohan123 Do you have all standard book...
bro can be upload all standard book questions in...
it'll take 34 days but for most purpose you can...
50,648
questions
56,455
answers
195,309
comments
100,135
users