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CAT 2016 | Question: 100
If three positive real numbers $x,y,z$ satisfy $y–x=z–y$ and $xyz = 4$, then what is the minimum possible value of $y$?$2^{(1/3)}$$2^{(2/3)}$$2^{(1/4)}$$2^{(3/4)}$
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CAT 2015 | Question: 92
Let $x<0,\:0<y<1,\:z>1$. Which of the following may be false?$\left (x ^{2} -z^{2}\right )$ has to be positive.$yz$ can be less than one.$xy$ can never be zero.$\left (y ...
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CAT 2019 Set-1 | Question: 83
If $(5.55)^{x}=(0.555)^{y}=1000$, then the value of $\frac{1}{x}-\frac{1}{y}$ is$3$$1$$\frac{1}{3}$$\frac{2}{3}$
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CAT 2011 | Question: 51
Given $\text{a}$ and $\text{b = a-b; a}$ and $\text{b}$ but $\text{c=a+c-b; a}$ or $\text{b=b-a; a}$ but not $\text{b= a+b}$; find $1$ or $(2$ but not $(3$ or $(4$ and $5...
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CAT 2011 | Question: 53
Consider the following operators defined below$x@y$: gives the positive difference of $x$ and $y.$$x\$y$: gives the sum of squares of $x$ and $y.$$x₤y$: gives the positiv...
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CAT 2011 | Question: 52
Consider the following operators defined below$x@y$: gives the positive difference of $x$ and $y.$$x\$y$: gives the sum of squares of $x$ and $y.$$x₤y$: gives the positiv...
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CAT 2012 | Question: 13
If $a= \dfrac{x}{y+z},b= \dfrac{y}{z+y},c= \dfrac{z}{x+y}$, then which of the following statements is/are true?$\dfrac{b+c-1}{yz}+\dfrac{a+c-1}{xz}+\dfrac{a+b-1}{yx}=1 \\...
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CAT 2010 | Question: 1
If $r, s$ and $t$ are consecutive odd integers with $r < s < t$, which of the following must be true?$rs = t$$r + t = 2t – s$$r + s = t – 2$$r + t = 2s$
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CAT 2010 | Question: 8
Consider the following statements:If $a^{x}=b,b^{y}=c,c^{z}=a,$ then $xyz=1$If $p=a^{x},q=a^{y},\left ( p^{y}q^{y} \right )^{z}=a^{2},$ then $xyz=1$If $x^{a}=y^{b}=z^{c}$...
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CAT 2003 | Question: 2-89
If three positive real numbers $x, y, z$ satisfy $y – x = z – y$ and $x y z = 4,$ then what is the minimum possible value of $y?$$2^{\frac{1}{3}}$$2^{\frac{2}{3}}$$2^{\fr...
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CAT 2003 | Question: 2-81
Two binary operations $\oplus$ and $*$ are defined over the set $\{a, e, f, g, h\}$ as per the following tables$\oplus$aefghaaefgheefghaffghaegghaefhhaefg $\ast$aefghaaaa...
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1 answers 1 answer
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CAT 2003 | Question: 2-80
Two binary operations $\oplus$ and $^ \ast $ are defined over the set $\{a, e, f, g, h\}$ as per the following tables$\oplus$aefghaaefgheefghaffghaegghaefhhaefg $\ast$aef...
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CAT 2003 | Question: 2-79
Two binary operations $\oplus$ and $^\ast$ are defined over the set $\{a, e, f, g, h\}$ as per the following tables$\oplus$aefghaaefgheefghaffghaegghaefhhaefg$^\ast$aefgh...
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CAT 2003 | Question: 2-57
Let $x$ and $y$ be positive integers such that $x$ is prime and $y$ is composite. Then,$y – x$ cannot be an even integer$xy$ cannot be an even integer.$\frac{x+y}{x}$ can...
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CAT 2003 | Question: 2-54
If $a, a + 2$ and $a + 4$ are prime numbers, then the number of possible solutions for $a$ is:onetwothreemore than three
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CAT 2003 | Question: 2-53
Let $a, b, c, d$ and $e$ be integers such that $a = 6b = 12c,$ and $2b = 9d = 12e.$ Then which of the following pairs contains a number that is not an integer?$\left[ \fr...
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CAT 2000 | Question: 74
$\text{A, B, C}$ are three numbers. Let $@ \text{(A, B)} =$ average of $\text{A}$ and $\text{B}$, $/ \text{(A, B)} = $ product of $\text{A}$ and $\text{B}$, and $\text{X...
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CAT 2001 | Question: 42
Let $b$ be a positive integer and $a = b^2 – b$. If b $\geq$ 4, then $a^2 – 2a$ is divisible by$15$$20$$24$None of these
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CAT 2001 | Question: 37
Let $x, y$ be two positive numbers such that $x + y =1.$ Then, the minimum value of $\left(x+ \frac{1}{x} \right)^2 + \left(y + \frac{1}{y}\right)^2$ is$12$$20$$12.5$$13....
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CAT 2001 | Question: 27
If $a, b, c$ and $d$ are four positive real numbers such that $abcd = 1,$ what is the minimum value of $(1 + a)(1 + b)(1 + c)(1 + d)?$$4$$1$$16$$18$
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CAT 2001 | Question: 15
$m$ is the smallest positive integer such that for any integer $n m,$ the quantity $n^3 – 7n^2 + 11n – 5$ is positive. What is the value of $m?$$4$$5$$8$None of these
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CAT 2001 | Question: 3
Let $x, y$ and $z$ be distinct integers, $x$ and $y$ are odd and positive, and $z$ is even and positive. Which one of the following statements cannot be true?$(x − z)^2y$...
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CAT 2000 | Question: 73
$\text{A, B, C}$ are three numbers. Let $@ \text{(A, B)} =$ average of $\text{A}$ and $\text{B}$, $/ \text{(A, B)} = $ product of $\text{A}$ and $\text{B}$, and $\text{X...
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CAT 2000 | Question: 70
Each of the numbers $x_1, x_2,\dots, x_n, n 4,$ is equal to $1$ or $–1.$ Suppose, $x_1x_2x_3x_4 + x_2x_3x_4x_5 + x_3x_4x_5x_6 + \dots + x_{n–3}x_{n–2}x_{n–1}x_n + x_{n–2...
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1 answers 1 answer
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CAT 2000 | Question: 65
Let $x, y$ and $z$ be distinct integers, that are odd and positive. Which one of the following statements cannot be true?$xyz^2$ is odd.$(x − y)^2 z$ is even.$(x + y − z)...
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CAT 2000 | Question: 57
$\begin{array}{|c|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 \\\hline y & 4 & 8 & 14 & 22 & 32 & 44 \\\hline \end{array}$In the above table, for suitably chosen con...
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CAT 2002 | Question: 96
If $pqr=1$ then $\frac{1}{1+p+r^{-1}} + \frac{1}{1+q+r^{-1}} + \frac{1}{1+r+p^{-1}} $ is equivalent to$p+q+r$$\frac{1}{p+q+r}$$1$$p^{-1}+q^{-1}+r^{-1}$
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CAT 2002 | Question: 57
If $x^2 + 5y^2 + z^2 = 2y(2x+z)$, then which of the following statements are necessarily true?$x=2y$$x=2z$$2x=z$Only IOnly IIOnly IIIOnly I and II
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CAT 2002 | Question: 53
For three integers $x, y$ and $z, x+y+z=15,$ and $xy+yz+xz=3.$ What is the largest value which $x$ can take?$3 \sqrt{13}$$\sqrt{19}$$13 /3$$\sqrt{15}$
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CAT 2003 | Question: 1-147
if $x,y,z$ are distinct positive real numbers then $\frac{x^2(y+z) + y^2(x+z) + z^2(x+y)}{xyz}$ would begreater than $4$greater than $5$greater than $6$None of these
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CAT 2003 | Question: 1-131
Let $a, b, c, d$ be the four integers such that $a +b+c+d =4m+1$ where m is a positive integer. Given $m,$ which one of the following is necessarily true?The minimum poss...
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CAT 2003 | Question: 1-121
Choose $1$ if the question can be answered by one of the statements alone but not by the other.Choose $2$ if the question can be answered by using either statement alone....
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CAT 2003 | Question: 1-105
The number of non-negative real roots of $2^x - x - 1 =0$ equals _______$0$$1$$2$$3$
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CAT 2004 | Question: 50
Let $y=\dfrac{1}{2+ \dfrac{1}{3+ \dfrac{1}{2+ \dfrac{1}{3+ \dots } } } }$ what is the value of $y?$$\frac{\sqrt{13} +3} {2}$$\frac{\sqrt{13} -3} {2}$$\frac{\sqrt{15} +3} ...
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CAT 2004 | Question: 49
If $\frac{a}{a+b} = \frac{b}{c+a} = \frac{c}{a+b} = r$, then $r$ cannot take any value except$1/2$$-1$$1/2$ or $-1$-$1/2$ or $-1$
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CAT 2004 | Question: 46
The total number of integer pairs $(x,y)$ satisfying the equation $x+y=xy$ is$0$$1$$2$None of these
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CAT 2009 | Question: 16
If $x=1+2a+3a^{2}+4a^{2}+\dots(-1 < a < 1)$ and$y=1+3b+6b^{2}+10b^{3}+\dots(-1 < b < 1),$then find $1+ab+(ab)^{2}+(ab)^{3}+\dots$ in terms of $x$ and $y$.$\frac{x^{1/2} y...
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CAT 2005 | Question: 26
Let $x=\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-}}}} \dots$ to infinity. Then $x$ equals$3$$\frac{\sqrt{13} -1}{2}$$\frac{\sqrt{13} +1}{2}$$\sqrt{13}$
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CAT 2005 | Question: 08
If $\text{R} = \dfrac{30^{65} – 29^{65}}{30^{64} + 29^{64}}$ then$0 < \text{R} \leq 0.1$$0.1 < \text{R} \leq 0.5$$0.5 < \text{R} \leq 1.0$$\text{R} 1.0$
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CAT 2006 | Question: 58
The number of solutions of the equation $2x+y=40$ where both $x$ and $y$ are positive integers and $x \leq y$ is:$7$$13$$14$$18$$20$
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