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Recent questions tagged cat2012

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CAT 2012 | Question: 20
$\text{A, B}$ and $\text{C}$ can independently do a work in $15$ days, $20$ days and $30$ days, respectively. They work together for some time after which $\text{C}$ leav...
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CAT 2012 | Question: 19
A car $\text{A}$ starts from a point $\text{P}$ towards another point $\text{Q}$. Another car $\text{B}$ starts (also from $\text{P})\; 1$ hour after the first car and ov...
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CAT 2012 | Question: 18
A vessel has a milk solution in which milk and water are in the ratio $4:1$. By addition of water to it, milk solution with milk and water in the ratio $4:3$ was formed. ...
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CAT 2012 | Question: 17
Read the information carefully and answer the questions follow that.A cricket tournament had three teams India, Australia and Sri Lanka taking part in it. The format of t...
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CAT 2012 | Question: 16
Read the information carefully and answer the questions follow that.A cricket tournament had three teams India, Australia and Sri Lanka taking part in it. The format of t...
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CAT 2012 | Question: 15
Read the information carefully and answer the questions follow that.A cricket tournament had three teams India, Australia and Sri Lanka taking part in it. The format of t...
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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 2012 | Question: 14
If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^{2}-10x+15= 0$, then find the quadratic equation whose roots are $\bigg(\alpha+\dfrac{\alpha }{\beta }...
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CAT 2012 | Question: 12
If $x$ is a real number, $[x]$ is greatest integer less than or equal to $x$, then $3[x]+2-[x]= 0$. Will the above equation have any real root?YesNoWill have real roots f...
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CAT 2012 | Question: 11
A rectangle is drawn such that none of its sides has length greater than $‘a\text{’}$. All lengths less than $‘a\text{’}$ are equally likely. The chance that the rectangl...
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CAT 2012 | Question: 10
A certain number written in a certain base is $144$. Which of the following is always true?Square root of the number written in the same base is $12$.If base is increased...
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CAT 2012 | Question: 9
$p$ is a prime and $m$ is a positive integer. How many solutions exist for the equation $p^{6}-p= (m^{2}+m+6)(p-1)$?$0$$1$$2$$\text{Infinite}$
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CAT 2012 | Question: 8
If $(a^{2}+b^{2}),(b^{2}+c^{2})$ and $(a^{2}+c^{2})$ are in geometric progression, which of the following holds true?$b^{2}-c^{2}= \dfrac{a^{4}-c^{4}}{b^{2}+a^{2}} \\$$b^...
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CAT 2012 | Question: 7
In the figure below, $\angle \text{MON} = \angle \text{MPO} = \angle \text{NQO} = 90^{\circ}$ and $\text{OQ}$ is the bisector of $\angle \text{MON}$ and $\text{QN} = 10,...
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CAT 2012 | Question: 6
Find the remainder of $2^{1040}$ divided by $131$.$1$$3$$5$$7$
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CAT 2012 | Question: 5
If the roots of the equation $(a^{2}+b^{2})x^{2}+2(b^{2}+c^{2})x+(b^{2}+c^{2})= 0$ are real, which of the following must hold true?$c^{2}\geq a^{2}$$c^{4}\geq a^{2}(b^{2}...
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CAT 2012 | Question: 4
Which of the terms $2^{\frac{1}{3}},3^{\frac{1}{4}},4^{\frac{1}{6}},6^{\frac{1}{8}}$ and $10^{\frac{1}{12}}$ is the largest?$2^{\frac{1}{3}} \\$$3^{\frac{1}{4}} \\$$4^{\f...
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CAT 2012 | Question: 3
What is the sum of all the $2$-digit numbers which leave a remainder of $6$ when divided by $8$?$612$$594$$324$$872$
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CAT 2012 | Question: 2
Let $\text{P} = \{2,3,4,\ldots 100\}$ and $\text{Q}= \{101,102,103,\ldots 200\}.$ How many elements of $\text{Q}$ are there such that they do not have any element of $\te...
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CAT 2012 | Question: 1
Consider a sequence $\text{S}$ whose $n$th term $T_{n}$ is defined as $1+\frac{3}{n}$, where $n=1,2, \dots$. Find the product of all the consecutive terms of $\text{S}$ s...
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