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2921
CAT 2012 | Question: 31
The following question has a paragraph from which a sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way. RD Laing developed a broad range of thought on interpersonal psychology. This deals ... not to be referred to by the preferred euphemisms of the drug companies,who prefer to call them side effects .
The following question has a paragraph from which a sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate...
Chandanachandu
332
points
488
views
Chandanachandu
asked
Mar 5, 2020
English Language
cat2012
verbal-ability
passage-reading
+
–
0
votes
0
answers
2922
CAT 2012 | Question: 30
The side of an equilateral triangle is $10$ cm long. By drawing parallels to all its sides, the distance between any two parallel lines being the same. The triangle is divided into smaller equilateral triangle, each of which has sides of length $1$ cm. How many such small triangles are formed? $60$ $90$ $120$ None of these
The side of an equilateral triangle is $10$ cm long. By drawing parallels to all its sides, the distance between any two parallel lines being the same. The triangle is di...
Chandanachandu
332
points
691
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
geometry
+
–
0
votes
0
answers
2923
CAT 2012 | Question: 29
A student is asked to form numbers between $3000$ and $9000$ with digits $2,3,5,7$ and $9$. If no digit is to be repeated, in how many ways can the student do so? $24$ $120$ $60$ $72$
A student is asked to form numbers between $3000$ and $9000$ with digits $2,3,5,7$ and $9$. If no digit is to be repeated, in how many ways can the student do so?$24$$12...
Chandanachandu
332
points
624
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
number-systems
+
–
0
votes
0
answers
2924
CAT 2012 | Question: 28
When asked for his taxi number, the driver replied, “If you divide the number of my taxi by $2,3,4,5,6$ each time you will find a reminder of one. But, if you divide it by $11$, the remainder is zero.You will also not find any other driver with a taxi having a lower number who can say the same”. What is the taxi number? $121$ $1001$ $1881$ $781$
When asked for his taxi number, the driver replied, “If you divide the number of my taxi by $2,3,4,5,6$ each time you will find a reminder of one. But, if you divide it...
Chandanachandu
332
points
1.0k
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
number-systems
+
–
0
votes
0
answers
2925
CAT 2012 | Question: 24
A solid sphere of radius $12$ inches and cast into a right circular cone whose base diameter is $\sqrt{2}$times its slant height. If the radius of the sphere and the cone are the same, how many such cones can be made and how much material is left out? $4$ and $1$ cubic inch $3$ and $12$ cubic inches $4$ and $0$ cubic inch $3$ and $6$ cubic inches
A solid sphere of radius $12$ inches and cast into a right circular cone whose base diameter is $\sqrt{2}$times its slant height. If the radius of the sphere and the cone...
Chandanachandu
332
points
578
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
mensuration
+
–
0
votes
0
answers
2926
CAT 2012 | Question: 23
If $ax^{2}+bx+c= 0$ and $2a,b$ and $2c$ are in arithmetic progression, which of the following are the roots of the equation? $a,c \\$ $-a,-c \\$ $-\dfrac{a}{2},-\dfrac{c}{2} \\$ $-\dfrac{c}{a},-1$
If $ax^{2}+bx+c= 0$ and $2a,b$ and $2c$ are in arithmetic progression, which of the following are the roots of the equation?$a,c \\$$-a,-c \\$$-\dfrac{a}{2},-\dfrac{c}{2}...
Chandanachandu
332
points
476
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
quadratic-equations
+
–
0
votes
0
answers
2927
CAT 2012 | Question: 27
$S$ is a set given by $S=\{1,2,3,\dots,4n\}$, where $n$ is a natural number. $S$ is partitioned into $n$ disjoint subsets $A_{1},A_{2},A_{3}\dots,A_{n}$ each containing four elements. It is given that in everyone of these subsets there is one element, ... equal to $2$ $n\neq2$ but can be equal to $1$ It is possible to satisfy the requirement for $n=1$ as well as for $n=2$
$S$ is a set given by $S=\{1,2,3,\dots,4n\}$, where $n$ is a natural number. $S$ is partitioned into $n$ disjoint subsets $A_{1},A_{2},A_{3}\dots,A_{n}$ each containing f...
Chandanachandu
332
points
411
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
arithmetic-mean
+
–
0
votes
0
answers
2928
CAT 2012 | Question: 26
Letters of the word ATTRACT are written on cards and are kept on a table. Manish is asked to lift three cards at a time, write all possible combinations of the three letters on a piece of paper and then replace the three cards. The exercise ends when all possible ... , which look the same when seen in a mirror. How many words is he left with? $40$ $20$ $30$ None of these
Letters of the word “ATTRACT” are written on cards and are kept on a table. Manish is asked to lift three cards at a time, write all possible combinations of the thre...
Chandanachandu
332
points
1.0k
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
permutation-combination
+
–
1
votes
1
answer
2929
CAT 2012 | Question: 25
If $\log _{x}(a-b)-\log _{x}(a+b)=\log _{x}\left(\dfrac{b}{a}\right)$, find $\dfrac{a^{2}}{b^{2}}+\dfrac{b^{2}}{a^{2}}$. $4$ $2$ $3$ $6$
If $\log _{x}(a-b)-\log _{x}(a+b)=\log _{x}\left(\dfrac{b}{a}\right)$, find $\dfrac{a^{2}}{b^{2}}+\dfrac{b^{2}}{a^{2}}$.$4$$2$$3$$6$
Chandanachandu
332
points
725
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
logarithms
+
–
0
votes
0
answers
2930
CAT 2012 | Question: 22
Find the complete set of values that satisfy the relations $\mid \mid x\mid-3\mid< 2$ and $\mid \mid x\mid-2\mid< 3$. $(-5,5)$ $(-5,-1)\cup(1,5)$ $(1,5)$ $(-1,1)$
Find the complete set of values that satisfy the relations $\mid \mid x\mid-3\mid< 2$ and $\mid \mid x\mid-2\mid< 3$.$(-5,5)$$(-5,-1)\cup(1,5)$$(1,5)$$(-1,1)$
Chandanachandu
332
points
396
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
inequalities
+
–
0
votes
0
answers
2931
CAT 2012 | Question: 21
In the figure given, $\text{OABC}$ is a parallelogram. The area of the parallelogram is $21$ sq units and the point $\text{C}$ lies on the line $x= 3$. Find the coordinates of $\text{B}$. $(3,10)$ $(10,3)$ $(10,10)$ $(8,3)$
In the figure given, $\text{OABC}$ is a parallelogram. The area of the parallelogram is $21$ sq units and the point $\text{C}$ lies on the line $x= 3$. Find the coordinat...
Chandanachandu
332
points
567
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
geometry
cartesian-coordinates
+
–
0
votes
0
answers
2932
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 $\text{C}$ leaves. $\text{A}$ total of $₹18000$ is paid for the work and $\text{B}$ gets $₹6000$ more than $\text{C}$. For how many days did $\text{A}$ work? $2$ $4$ $6$ $8$
$\text{A, B}$ 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...
Chandanachandu
332
points
427
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
work-time
work-cost
+
–
0
votes
0
answers
2933
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 overtakes it after covering $30\%$ of the distance $\text{PQ}$. After that, the cars continue. On ... the time taken by car $\text{B}$ to cover the distance $\text{PQ}$ (in hours). $3$ $4$ $5$ $3\frac{1}{3}$
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...
Chandanachandu
332
points
495
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
speed-distance-time
+
–
0
votes
3
answers
2934
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. On replacing $14\;\text{L}$ of this solution with pure milk the ratio of milk and water changed to $5:3$. What is the volume of the water added? $12\;\text{L}$ $60\;\text{L}$ $32\;\text{L}$ $24\;\text{L}$
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. ...
Chandanachandu
332
points
804
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
alligation-mixture
+
–
0
votes
0
answers
2935
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 the tournament was such that in the preliminary stage each of these teams, would play the other teams ... at the end of the preliminary stage, then atleast how many points did it have? $16$ $17$ $18$ $20$
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...
Chandanachandu
332
points
525
views
Chandanachandu
asked
Mar 5, 2020
Logical Reasoning
cat2012
logical-reasoning
logic-puzzles
+
–
0
votes
0
answers
2936
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 the tournament was such that in the preliminary stage each of these teams, would play the other ... the preliminary stage, then what is the maximum number of points it could have scored? $12$ $14$ $16$ $20$
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...
Chandanachandu
332
points
340
views
Chandanachandu
asked
Mar 5, 2020
Logical Reasoning
cat2012
logical-reasoning
logic-puzzles
+
–
0
votes
0
answers
2937
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 the tournament was such that in the preliminary stage each of these teams, would play the other ... then what is the minimum number of points it would scored in the preliminary stage? $8$ $10$ $12$ $16$
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...
Chandanachandu
332
points
437
views
Chandanachandu
asked
Mar 5, 2020
Logical Reasoning
cat2012
logical-reasoning
logic-puzzles
+
–
0
votes
0
answers
2938
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? $\dfrac{b+c-1}{yz}+\dfrac{a+c-1}{xz}+\dfrac{a+b-1}{yx}=1 \\$ $\dfrac{x^{2}}{a(1-bc)}= \dfrac{y^{2}}{b(1-ca)}= \dfrac{z^{2}}{c(1-ab)} \\$ $(a+b)c+(b+c)a+(a+c)b= \dfrac{2(x+y+z)(xy+xz+yz)-6xyz}{(x+y)(y+z)(z+x)}$ I and II I and III II and III None of these
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 \\...
Chandanachandu
332
points
415
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
algebra
+
–
0
votes
1
answer
2939
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 $\bigg(\alpha+\dfrac{\alpha }{\beta }\bigg)$ and $\bigg(\beta +\dfrac{\beta}{\alpha}\bigg)$ $15x^{2}+71x+210= 0$ $5x^{2}-22x+56= 0$ $3x^{2}-44x+78= 0$ Cannot be determined
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 }...
Chandanachandu
332
points
611
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
quadratic-equations
+
–
0
votes
0
answers
2940
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? Yes No Will have real roots for $x< 0$ Will have real roots for $x> 0$
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...
Chandanachandu
332
points
416
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
number-systems
+
–
0
votes
0
answers
2941
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 rectangle has its diagonal greater than $‘a\text{’}$ is (in terms of $\%)$ $29.3 \%$ $21.5\%$ $66.66\%$ $33.33\%$
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 ...
Chandanachandu
332
points
424
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
geometry
+
–
3
votes
0
answers
2942
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 by $2$, the number becomes $100$. Only I Only II Neither I nor II Both I and II
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...
Chandanachandu
332
points
1.1k
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
number-systems
+
–
0
votes
0
answers
2943
CAT 2012 | Question: 9
$p$ is a prime and $m$ is a positive integer. How many solutions exist for the equation $p^{6}-p= (m^{2}+m+6)(p-1)$? $0$ $1$ $2$ $\text{Infinite}$
$p$ 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$$\text{Infinite}$
Chandanachandu
332
points
401
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
number-systems
+
–
1
votes
1
answer
2944
CAT 2012 | Question: 8
If $(a^{2}+b^{2}),(b^{2}+c^{2})$ and $(a^{2}+c^{2})$ are in geometric progression, which of the following holds true? $b^{2}-c^{2}= \dfrac{a^{4}-c^{4}}{b^{2}+a^{2}} \\$ $b^{2}-a^{2}= \dfrac{a^{4}-c^{4}}{b^{2}+c^{2}} \\$ $b^{2}-c^{2}= \dfrac{b^{4}-a^{4}}{b^{2}+a^{2}} \\$ $b^{2}-a^{2}= \dfrac{b^{4}-c^{4}}{b^{2}+a^{2}}$
If $(a^{2}+b^{2}),(b^{2}+c^{2})$ and $(a^{2}+c^{2})$ are in geometric progression, which of the following holds true?$b^{2}-c^{2}= \dfrac{a^{4}-c^{4}}{b^{2}+a^{2}} \\$$b^...
Chandanachandu
332
points
619
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
geometric-progression
+
–
0
votes
0
answers
2945
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 $\text{QN} = 10, \text{OR} = 40/7$. Find $\text{OP}$. $4.8$ $4.5$ $4$ $5$
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,...
Chandanachandu
332
points
459
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
geometry
+
–
1
votes
1
answer
2946
CAT 2012 | Question: 6
Find the remainder of $2^{1040}$ divided by $131$. $1$ $3$ $5$ $7$
Find the remainder of $2^{1040}$ divided by $131$.$1$$3$$5$$7$
Chandanachandu
332
points
810
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
number-systems
+
–
1
votes
1
answer
2947
CAT 2012 | Question: 5
If the roots of the equation $(a^{2}+b^{2})x^{2}+2(b^{2}+c^{2})x+(b^{2}+c^{2})= 0$ are real, which of the following must hold true? $c^{2}\geq a^{2}$ $c^{4}\geq a^{2}(b^{2}+c^{2})$ $b^{2}\geq a^{2}$ $a^{4}\leq b^{2}(a^{2}+c^{2})$
If the roots of the equation $(a^{2}+b^{2})x^{2}+2(b^{2}+c^{2})x+(b^{2}+c^{2})= 0$ are real, which of the following must hold true?$c^{2}\geq a^{2}$$c^{4}\geq a^{2}(b^{2}...
Chandanachandu
332
points
518
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
quadratic-equations
+
–
1
votes
1
answer
2948
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? $2^{\frac{1}{3}} \\$ $3^{\frac{1}{4}} \\$ $4^{\frac{1}{6}} \\$ $10^{\frac{1}{12}}$
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...
Chandanachandu
332
points
458
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
number-systems
+
–
1
votes
1
answer
2949
CAT 2012 | Question: 3
What is the sum of all the $2$-digit numbers which leave a remainder of $6$ when divided by $8$? $612$ $594$ $324$ $872$
What is the sum of all the $2$-digit numbers which leave a remainder of $6$ when divided by $8$?$612$$594$$324$$872$
Chandanachandu
332
points
593
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
number-systems
+
–
1
votes
1
answer
2950
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 $\text{P}$ as a factor? $20$ $24$ $23$ $21$
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...
Chandanachandu
332
points
1.2k
views
Chandanachandu
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
number-systems
+
–
0
votes
0
answers
2951
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}$ starting from the $4$th term to the $60$th term. $1980.50$ $1985.55$ $1990.55$ $1975.55$
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...
Lakshman Bhaiya
13.8k
points
386
views
Lakshman Bhaiya
asked
Mar 5, 2020
Quantitative Aptitude
cat2012
quantitative-aptitude
sequences&series
+
–
1
votes
1
answer
2952
CAT 2010 | Question: 3
$\text{P, Q and R}$ are three consecutive odd numbers in ascending order. If the value of three times $\text{P}$ is three less than two times $\text{R}$, find the value of $\text{R}$. $5$ $7$ $9$ $11$
$\text{P, Q and R}$ are three consecutive odd numbers in ascending order. If the value of three times $\text{P}$ is three less than two times $\text{R}$, find the value o...
Arjun
8.6k
points
667
views
Arjun
asked
Mar 1, 2020
Quantitative Aptitude
cat2010
quantitative-aptitude
number-systems
+
–
1
votes
1
answer
2953
CAT 2010 | Question: 4
Consider the following statements : When two straight lines intersect, then : adjacent angles are complementary adjacent angles are supplementary opposite angles are equal opposite angles are supplementary Of these statements: (I) and (III) are correct (II) and (III) are correct (I) and (IV) are correct (II) and (IV) are correct
Consider the following statements :When two straight lines intersect, then :adjacent angles are complementaryadjacent angles are supplementaryopposite angles are equalopp...
Arjun
8.6k
points
880
views
Arjun
asked
Mar 1, 2020
Quantitative Aptitude
cat2010
quantitative-aptitude
geometry
+
–
2
votes
1
answer
2954
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$
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$
Arjun
8.6k
points
1.1k
views
Arjun
asked
Mar 1, 2020
Quantitative Aptitude
cat2010
quantitative-aptitude
algebra
+
–
0
votes
0
answers
2955
CAT 2010 | Question: 2
Let $\text{S}$ be the set of rational numbers with the following properties: $\frac{1}{2}\in \text{S}$ If $x\in \text{S}$ then both $\frac{1}{x+1}\in \text{S}$ and $\frac{x}{x+1}\in \text{S}$ ... all rational numbers in the interval $-1 < x < 0$. $\text{S}$ contains all rational numbers in the interval $1 < x <\infty$.
Let $\text{S}$ be the set of rational numbers with the following properties:$\frac{1}{2}\in \text{S}$If $x\in \text{S}$ then both $\frac{1}{x+1}\in \text{S}$ and $\frac{x...
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Quantitative Aptitude
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quantitative-aptitude
number-systems
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2956
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 $x^{a}=y^{b}=z^{c}$ and $ab+bc+ca=0$ then $xyz=1$ Of these statements: I and II are correct II and III are correct Only I is correct All I, II and III are correct
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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Quantitative Aptitude
cat2010
quantitative-aptitude
algebra
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2957
CAT 2010 | Question: 6
From a square piece of card-board measuring $2a$ on each side of a box with no top is to be formed by cutting out from each corner a square with sides $b$ and bending up the flaps. The value of $b$ for which the box has the greatest volume is $b= \frac{a}{5}$ $b= \frac{a}{4}$ $b= \frac{2a}{3}$ $b= \frac{a}{2}$
From a square piece of card-board measuring $2a$ on each side of a box with no top is to be formed by cutting out from each corner a square with sides $b$ and bending up ...
Arjun
8.6k
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532
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Arjun
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Mar 1, 2020
Quantitative Aptitude
cat2010
quantitative-aptitude
geometry
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0
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0
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2958
CAT 2010 | Question: 5
A pole has to be erected on the boundary of a circular park of diameter $13$ meters in such a way that the difference of its distances from two diametrically opposite fixed gates $\text{A}$ and $\text{B}$ on the boundary is $7$ meters. The distance of the pole from one of the gates is: $8$ metres $8.25$ metres $5$ metres None these
A pole has to be erected on the boundary of a circular park of diameter $13$ meters in such a way that the difference of its distances from two diametrically opposite fix...
Arjun
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609
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Arjun
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Mar 1, 2020
Quantitative Aptitude
cat2010
quantitative-aptitude
geometry
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1
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1
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2959
CAT 2010 | Question: 10
Let $\text{S}$ denote the infinite sum $2+5x+9x^{2}+14x^{3}+20x^{4}+\ldots$ where $\mid x \mid < 1$ and the coefficient of $x^{n-1}$ is $\dfrac{1}{2}n\left ( n+3 \right ), \left ( n=1,2,\ldots \right ).$ Then $\text{S}$ equals $\frac{2-x}{(1-x)^{3}}$ $\frac{2-x}{(1+x)^{3}}$ $\frac{2+x}{(1-x)^{3}}$ $\frac{2+x}{(1+x)^{3}}$
Let $\text{S}$ denote the infinite sum $2+5x+9x^{2}+14x^{3}+20x^{4}+\ldots$where $\mid x \mid < 1$ and the coefficient of $x^{n-1}$ is $\dfrac{1}{2}n\left ( n+3 \right )...
Arjun
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655
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Arjun
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Mar 1, 2020
Quantitative Aptitude
cat2010
quantitative-aptitude
infinite-geometric-progression
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2
votes
1
answer
2960
CAT 2010 | Question: 9
If $a, b$ and $c$ are three real numbers, then which of the following is not true? $\mid a+b \mid\leq \mid a \mid+\mid b \mid$ $\mid a – b \mid \leq \mid a \mid + \mid b\mid$ $\mid a-b \mid \leq \mid a \mid -\mid b \mid$ $\mid a-c \mid \leq \mid a-b \mid+\mid b-c \mid$
If $a, b$ and $c$ are three real numbers, then which of the following is not true?$\mid a+b \mid\leq \mid a \mid+\mid b \mid$$\mid a – b \mid \leq \mid a \mid + \mid b...
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Quantitative Aptitude
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quantitative-aptitude
absolute-value
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