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Recent questions tagged functions
Materials:
Functions
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1
ISRO202078
In the following procedure Integer procedure P(X,Y); Integer X,Y; value x; begin K=5; L=8; P=x+y; end $X$ is called by value and $Y$ is called by name. If the procedure were invoked by the following program fragment K=0; L=0; Z=P(K,L); then the value of $Z$ will be set equal to $5$ $8$ $13$ $0$
asked
6 days
ago
in
Programming
by
Satbir
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23.8k
points)

111
views
isro2020
programming
functions
normal
+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, 2019
in
Calculus
by
Arjun
Veteran
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430k
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65
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, 2019
in
Calculus
by
Arjun
Veteran
(
430k
points)

48
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, 2019
in
Calculus
by
Arjun
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430k
points)

25
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, 2019
in
Calculus
by
Arjun
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(
430k
points)

19
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, 2019
in
Calculus
by
Arjun
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(
430k
points)

26
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, 2019
in
Calculus
by
Arjun
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(
430k
points)

27
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, 2019
in
Calculus
by
Arjun
Veteran
(
430k
points)

14
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, 2019
in
Calculus
by
Arjun
Veteran
(
430k
points)

21
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, 2019
in
Calculus
by
Arjun
Veteran
(
430k
points)

12
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, 2019
in
Others
by
Arjun
Veteran
(
430k
points)

40
views
isi2014dcg
calculus
differentiation
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, 2019
in
Numerical Ability
by
Arjun
Veteran
(
430k
points)

54
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, 2019
in
Set Theory & Algebra
by
Arjun
Veteran
(
430k
points)

9
views
isi2015mma
sets
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, 2019
in
Calculus
by
Arjun
Veteran
(
430k
points)

14
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, 2019
in
Calculus
by
Arjun
Veteran
(
430k
points)

16
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, 2019
in
Calculus
by
Arjun
Veteran
(
430k
points)

22
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, 2019
in
Calculus
by
Arjun
Veteran
(
430k
points)

13
views
isi2015mma
calculus
functions
nongate
+1
vote
1
answer
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, 2019
in
Linear Algebra
by
Arjun
Veteran
(
430k
points)

51
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, 2019
in
Others
by
Arjun
Veteran
(
430k
points)

11
views
isi2015mma
functions
nongate
+1
vote
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

27
views
isi2015dcg
functions
+2
votes
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

22
views
isi2015dcg
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

20
views
isi2015dcg
sets
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

31
views
isi2015dcg
functions
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, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

19
views
isi2015dcg
calculus
functions
0
votes
1
answer
25
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

14
views
isi2016dcg
sets
functions
0
votes
1
answer
26
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

15
views
isi2016dcg
sets
functions
0
votes
0
answers
27
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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

10
views
isi2016dcg
sets
functions
0
votes
0
answers
28
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, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

13
views
isi2016dcg
calculus
functions
curves
nongate
+1
vote
1
answer
29
ISI2016DCG50
The domain of the function $\ln(3x^{2}4x+5)$ 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, 2019
in
Set Theory & Algebra
by
gatecse
Boss
(
17.5k
points)

22
views
isi2016dcg
functions
0
votes
0
answers
30
ISI2016DCG58
Let $y=\left \lfloor x \right \rfloor$ where $\left \lfloor x \right \rfloor$ 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, 2019
in
Calculus
by
gatecse
Boss
(
17.5k
points)

11
views
isi2016dcg
calculus
continuity
differentiation
functions
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