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CAT 2004 | Question: 62
Answer the questions on the basis of the information given below: $f_{1}(x) = \left\{\begin{matrix} x & 0 \leq x \leq 1 \\ 1 & x \geq 1 \\ 0 & \text{otherwise} \end{matrix}\right.$ $f_{2}(x) = f_{1}(-x) \;\; \text{for all} \; x $ ... $f_2(-x) = f_4(x) \: \text{for all }\;x$ $f_1(x) + f_3(x) = 0 \: \text{for all }\;x$

Lakshman Patel RJIT asked in Quantitative Aptitude Mar 30

by Lakshman Patel RJIT

12.0k points

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1 vote

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2

CAT 2021 Set-3 | Quantitative Aptitude | Question: 12
If $f(x) = x^{2} – 7x$ and $g(x) = x + 3,$ then the minimum value of $f(g(x)) – 3x$ is $ -16$ $ -15$ $ -20$ $ -12$

soujanyareddy13 asked in Quantitative Aptitude Jan 20

by soujanyareddy13

2.7k points

99 views

1 vote

1 answer

3

CAT 2021 Set-2 | Quantitative Aptitude | Question: 15
For all real values of $x,$ the range of the function $f(x) = \dfrac{x^{2} + 2x + 4}{2x^{2} + 4x + 9}$ is $ \left(\frac{3}{7}, \frac{1}{2} \right)$ $ \left[\frac{3}{7}, \frac{1}{2} \right)$ $ \left[\frac{3}{7}, \frac{8}{9} \right)$ $ \left[\frac{4}{9}, \frac{8}{9} \right]$

soujanyareddy13 asked in Quantitative Aptitude Jan 20

by soujanyareddy13

2.7k points

97 views

1 vote

1 answer

4

CAT 2021 Set-1 | Quantitative Aptitude | Question: 8
$f(x) = \dfrac{x^{2} + 2x – 15}{x^{2} – 7x – 18}$ is negative if and only if $ – 2 < x < 3 \; \text{or} \; x > 9 $ $ x < – 5 \; \text{or} \; 3 < x < 9 $ $ – 5 < x < – 2 \; \text{or} \; 3 < x < 9 $ $ x < – 5 \; \text{or} \; – 2 < x < 3 $

soujanyareddy13 asked in Quantitative Aptitude Jan 19

by soujanyareddy13

2.7k points

101 views

1 vote

1 answer

5

CAT 2020 Set-3 | Question: 58
If $ f(x+y) = f(x) f(y) $ and $ f(5) = 4,$ then $ f(10) – f(-10) $ is equal to $0$ $15.9375$ $3$ $14.0625$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

by soujanyareddy13

2.7k points

169 views

2 votes

1 answer

6

CAT 2020 Set-2 | Question: 72
Let $f(x) = x^{2} + ax + b $ and $g(x) = f(x+1) – f(x-1).$ If $ f(x) \geq 0 $ for all real $x,$ and $ g(20) = 72,$ then the smallest possible value of $b$ is $1$ $16$ $0$ $4$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

by soujanyareddy13

2.7k points

122 views

1 vote

1 answer

7

CAT 2020 Set-1 | Question: 68
If $f\left ( 5+x \right )= f\left ( 5-x \right )$ for every real $x,$ and $f\left ( x \right )=0$ has four distinct real roots, then the sum of these roots is $0$ $40$ $10$ $20$

soujanyareddy13 asked in Quantitative Aptitude Sep 16, 2021

by soujanyareddy13

2.7k points

150 views

1 vote

1 answer

8

CAT 2019 Set-2 | Question: 95
Let $f$ be a function such that $f (mn) = f (m) f (n)$ for every positive integers $m$ and $n$. If $f (1), f (2)$ and $f (3)$ are positive integers, $f (1) < f (2),$ and $f (24) = 54$, then $f (18)$ equals _______

go_editor asked in Quantitative Aptitude Mar 20, 2020

13.4k points

237 views

2 votes

1 answer

9

CAT 2018 Set-1 | Question: 93
If $f(x+2)=f(x)+f(x+1)$ for all positive integers $x$, and $f(11)=91,f(15)=617$, then $f(10)$ equals ________

go_editor asked in Quantitative Aptitude Mar 20, 2020

13.4k points

233 views

1 vote

1 answer

10

CAT 2017 Set-2 | Question: 89
Let $f\left ( x \right )=x^{2}$ and $g\left ( x \right )=2^{x}$, for all real $x$. Then the value of $ f \left ( f\left ( g\left ( x \right ) \right )+g\left( f\left ( x \right ) \right ) \right)$ at $x=1$ is $16$ $18$ $36$ $40$

go_editor asked in Quantitative Aptitude Mar 16, 2020

13.4k points

184 views

1 vote

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11

CAT 2017 Set-2 | Question: 98
Let $f\left ( x \right )=2x-5$ and $g\left ( x \right )=7-2x.$ Then $ \mid f\left ( x \right ) + g\left ( x \right ) \mid=\mid f(x) \mid + \mid g\left ( x \right ) \mid$ if and only if $5/2<x<7/2$ $x\leq 5/2$ or $x\geq 7/2$ $x< 5/2$ or $x\geq 7/2$ $5/2\leq x\leq 7/2$

go_editor asked in Quantitative Aptitude Mar 16, 2020

13.4k points

232 views

1 vote

1 answer

12

CAT 2017 Set-2 | Question: 97
If $f\left ( ab \right )=f\left ( a \right )f\left ( b \right )$ for all positive integers $a$ and $b$, then the largest possible value of $f\left (1\right )$ is $1$ $2$ $0$ $3$

go_editor asked in Quantitative Aptitude Mar 16, 2020

13.4k points

163 views

1 vote

1 answer

13

CAT 2017 Set-1 | Question: 99
If $f( x)=\dfrac{5x+2}{ 3x-5}$ and $g( x )=x^{2}-2x-1,$ then the value of $g( f( f( 3 ) ) )$ is $2$ $1/3$ $6$ $2/3$

go_editor asked in Quantitative Aptitude Mar 13, 2020

13.4k points

175 views

1 vote

1 answer

14

CAT 2016 | Question: 73
$A, S, M$ and $D$ are functions of $x$ and $y$, and they are defined as follows. $A(x, y) = x + y$ $M(x, y) = xy$ $S(x,y)= x-y$ $D(x,y)= x/y, y\neq 0$ What is the value of $M(M(A(M(x, y), S(y, x)), x), A(y, x))$ for $x = 2, y = 3$? $60$ $140$ $25$ $70$

go_editor asked in Quantitative Aptitude Mar 11, 2020

13.4k points

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15

CAT 2015 | Question: 81
The set of all positive integers is the union of two disjoint subsets$:\left \{ f\left ( 1 \right ),f\left ( 2 \right ), \dots, f\left ( n \right ), \dots \right \}$ ... $n \geq 1$. What is the value of $g\left ( 1 \right )?$ $0$ $2$ $1$ Cannot be determined

go_editor asked in Quantitative Aptitude Mar 9, 2020

13.4k points

205 views

1 vote

1 answer

16

CAT 2015 | Question: 82
For all non-negative integers $x$ and $y$, $f(x,y)$ is defined as below. $f( 0,y) = y+1$ $f(x+1,0) = f( x, 1)$ $f( x+1, y+1) = f\left( x,f( x+1,y) \right)$ Then what is the value of $f(1,2)$ ________

go_editor asked in Quantitative Aptitude Mar 9, 2020

13.4k points

2.0k views

1 vote

1 answer

17

CAT 2011 | Question: 4
$\begin{array}{}Let\;f_{n+1}(x)&=f_n(x)+1\;\text{if $n$ is a multiple of 3}\\ &=f_n(x)-1\;\text{otherwise.}\end{array}$ If $f_1(1)=0$, then what is $f_{50}(1)$? $-18$ $-16$ $-17$ Cannot be determined

Krithiga2101 asked in Quantitative Aptitude Mar 9, 2020

by Krithiga2101

268 points

305 views

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18

CAT 2011 | Question: 20
Consider the function given by $f(x) =\mid x-1\mid-x$ What is the area of the triangle bounded by the graph of the given function with the coordinate axis given by $x=0\:\text{and}\:y=0$? $2$ $\large\frac{1}{4}$ $\large\frac{1}{2}$ $1$

Krithiga2101 asked in Quantitative Aptitude Mar 9, 2020

by Krithiga2101

268 points

203 views

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19

CAT 2011 | Question: 17
The graphs given alongside represent two functions $f(x)\:\text{and}\:g(x)$ respectively. Which of the following is true? $g(x)=[f(x)]$ $g(x)=f(-x)$ $g(x)=-f(x)$ None of these

Krithiga2101 asked in Quantitative Aptitude Mar 9, 2020

by Krithiga2101

268 points

200 views

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20

CAT 2011 | Question: 21
Consider the function given by $f(x) =\mid x-1\mid-x$ Which of the following is not true about the graph of $f(x)$? A portion of the graph is parallel to the line $y = 25$. A portion of graph is in 2nd quadrant. Some portion of graph lies in 1st quadrant. Some portion of graph lies in 3rd quadrant.

Krithiga2101 asked in Quantitative Aptitude Mar 9, 2020

by Krithiga2101

268 points

187 views

1 vote

1 answer

21

CAT 2019 Set-1 | Question: 87
For any positive integer $n$, let $f(n)=n(n+1)$ if n is even, and $f(n)=n+3$ if n is odd. if $m$ is a positive integer such that $8f(m+1)-f(m)=2$, then $m$ equals _______

go_editor asked in Quantitative Aptitude Mar 8, 2020

13.4k points

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22

CAT 2019 Set-1 | Question: 90
Consider a function $f$ satisfying $f(x+y)=f(x)f(y)$ where $x,y$ are positive integers, and $f(1)=2$. If $f(a+1)+f(a+2)+\ldots +f(a+n)=16(2^{n}-1)$ then $a$ is equal to ______

go_editor asked in Quantitative Aptitude Mar 8, 2020

13.4k points

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23

CAT 2013 | Question: 23
If $g(x)=p\mid x \mid-qx^2$, where $p$ and $q$ are constants, then at $x=0, g(x)$ will be maximum when $p>0,q>0$ minimum when $p<0,q<0$ minimum when $p>0,q<0$ maximum when $p>0,q<0$

admin asked in Quantitative Aptitude Mar 6, 2020

by admin

2.4k points

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24

CAT 2013 | Question: 29
Let $f(x)= \dfrac{1}{1+x^2}$ and $g(x)=\dfrac{e^{−x}}{1+[x]}$, where $[x]$ is the greatest integer less than or equal to $x$. Then which of the following domain is true? domain of $(f+g)=R-(-2,-1]$ domain of $(f+g)=R-[-1,0)$ ... Both II and IV Both I and III Both I and IV Both II and III

admin asked in Quantitative Aptitude Mar 6, 2020

by admin

2.4k points

180 views

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25

CAT 2010 | Question: 16
Let $f$ be an injective map with domain $\left \{ x, y, z \right \}$ and the range $\left \{ 1, 2, 3 \right \}$ such that exactly one of the following statements is correct and the remaining are false. $f\left \{x \right \}=1,f\left ( y \right )\neq 1,f\left ( z \right )\neq 2.$ The value of $f^{-1}\left ( 1 \right )$ is $x$ $y$ $z$ None of the above

Arjun asked in Quantitative Aptitude Mar 1, 2020

by Arjun

8.3k points

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1 answer

26

CAT 1999 | Question: 100
Answer the question based on the information given below: Let x and y be real numbers and let $f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$ Which of the following expressions yields $x^2$ as a result? $F(f(x, -x)).G(f(x, -x))$ $F(f(x, x)).G(f(x, x)).4$ $-F(f(x, x)).G(f(x, -x)) \: \log_2 16$ $f(x,x).f(x,x)$

go_editor asked in Logical Reasoning May 14, 2016

13.4k points

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27

CAT 1999 | Question: 98
Answer the question based on the information given below: Let x and y be real numbers and let $f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$ Which of the following statements is true? $F(f(x,y)) .G(f(x,y)) = -F(f(x,y)).G(f(x,y))$ ... $F(f(x,y)) .G(f(x,y)) \neq G(f(x,y)).F(f(x,y))$ $F(f(x,y)) +G(f(x,y)) + f(x,y)= f(-x,-y)$

go_editor asked in Logical Reasoning May 14, 2016

13.4k points

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28

CAT 2000 | Question: 76
Answer the following question based on the information given below. For real numbers $x, y,$ ... $x$ and $y$ are less than $-1$ Both $x$ and $y$ are positive Both $x$ and $y$ are negative $y > x$

go_editor asked in Quantitative Aptitude May 1, 2016

13.4k points

466 views

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29

CAT 2000 | Question: 79
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ ... $(h(x, y, z) - f(x, y, z))/(n(x, y, z) - g(x, y, z))$

go_editor asked in Quantitative Aptitude May 1, 2016

13.4k points

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30

CAT 2000 | Question: 78
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ ... $(j(x, y, z) - g(x, y, z))/h(x, y, z)$ $(f(x, y, z) - h(x, y, z))/f(x, y, z)$

go_editor asked in Quantitative Aptitude May 1, 2016

13.4k points

768 views

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1 answer

31

CAT 2014 | Question: 33
Use the following information for next two questions: A function $f(x)$ is said to be even if $f(-x) = f(x)$, and odd if $f(-x) = -f(x)$. Thus, for example, the function given by $f(x)=x^{2}$ is even, while the ... questions. The sum of two odd functions is always an even function is always an odd function is sometimes odd and sometimes even may be neither odd nor even

go_editor asked in Quantitative Aptitude Apr 27, 2016

13.4k points

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32

CAT 2000 | Question: 88
Answer the following question based on the information given below. For a real number $x,$ let f(x) = 1/(1 + x), if x is non-negative = 1+ x, if x is negative f$^n$(x) = f(f$^{n – 1}$(x)), n = 2, 3, .... $r$ is an integer $\geq 2.$ Then what is the value of $f^{r-1}(-r) + f^r(-r)+f^{r+1}(-r)$? $-1$ $0$ $1$ None of these

go_editor asked in Quantitative Aptitude Apr 25, 2016

13.4k points

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33

CAT 2000 | Question: 84
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$

go_editor asked in Quantitative Aptitude Apr 25, 2016

13.4k points

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34

CAT 2000 | Question: 83
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$

go_editor asked in Quantitative Aptitude Apr 25, 2016

13.4k points

256 views

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35

CAT 2000 | Question: 107
For all non-negative integers $x$ and $y, f(x, y)$ is defined as below $f(0, y) = y + 1$ $f(x + 1, 0) = f(x, 1)$ $f(x + 1,y + 1) = f(x, f(x + 1, y))$ Then, what is the value of $f(1, 2)?$ Two Four Three Cannot be determined

go_editor asked in Quantitative Aptitude Mar 30, 2016

13.4k points

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36

CAT 2000 | Question: 105
The set of all positive integers is the union of two disjoint subsets $\{f(1), f(2),\dots ,f(n),\dots\}$ and $\{g(1), g(2),\dots,g(n),\dots\},$ where $f(1) < f(2) <\dots < f(n) < \dots,$ and $g(1) < g(2) <\dots< g(n) < \dots,$ and $g(n) = f(f(n)) + 1$ for all $n \geq 1.$ What is the value of $g(1)?$ Zero Two One Cannot be determined

go_editor asked in Quantitative Aptitude Mar 30, 2016

13.4k points

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37

CAT 2000 | Question: 87
Answer the following question based on the information given below. For a real number $x$, let f(x) = 1/(1 + x), if x is non-negative = 1+ x, if x is negative f$^n$(x) = f(f$^{n – 1}$(x)), n = 2, 3, .... What is the value of the product, $f(2)f^2(2)f^3(2)f^4(2)f^5(2)$? $\frac{1}{3}$ $3$ $\frac{1}{18}$ None of these

go_editor asked in Quantitative Aptitude Mar 29, 2016

13.4k points

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38

CAT 2000 | Question: 82
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$

go_editor asked in Quantitative Aptitude Mar 29, 2016

13.4k points

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39

CAT 2000 | Question: 77
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ ... $f(x, y, z)/g(x, y, z)$ $(f(x, y, z) + h(x, y, z) - g(x, y, z))/j(x, y, z)$

go_editor asked in Quantitative Aptitude Mar 29, 2016

13.4k points

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40

CAT 2000 | Question: 75
Answer the following question based on the information given below. For real numbers $x, y,$ let $f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\;\text{if}\; (x + y)^{0.5}\;\text{is real} \\ (x + y)^2,\;\text{otherwise} \end{matrix}\right.$ ... $f(x, y) - (g(x, y))^2$ $g(x, y) - (f(x, y))^2$ $f(x, y) + g(x, y)$

go_editor asked in Quantitative Aptitude Mar 29, 2016

13.4k points

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Recent questions tagged functions