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Recent questions tagged algebra
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CAT 2022 Set-3 | Quantitative Aptitude | Question: 2
If $c=\dfrac{16 x}{y}+\dfrac{49 y}{x}$ for some non-zero real numbers $x$ and $y,$ then $c$ cannot take the value $-60$ $-50$ $60$ $-70$
admin
asked
in
Quantitative Aptitude
Mar 3, 2023
by
admin
3.7k
points
1.4k
views
cat2022-set3
quantitative-aptitude
algebra
1
vote
1
answer
2
CAT 2020 Set-3 | Question: 55
If $x_{1} = \;– 1$ and $x_{m} = x_{m+1} + (m + 1)$ for every positive integer $m, $ then $x_{100}$ equals $ – 5151 $ $ – 5150 $ $ – 5051 $ $ – 5050 $
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 17, 2021
by
soujanyareddy13
2.7k
points
496
views
cat2020-set3
quantitative-aptitude
algebra
1
vote
1
answer
3
CAT 2020 Set-3 | Question: 59
If $\text{a,b,c}$ are non-zero and $14^{a} = 36^{b} = 84^{c},$ then $6b \left( \frac{1}{c} \;– \frac{1}{a} \right)$ is equal to
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 17, 2021
by
soujanyareddy13
2.7k
points
609
views
cat2020-set3
quantitative-aptitude
algebra
numerical-answer
0
votes
0
answers
4
CAT 2020 Set-3 | Question: 69
How many pairs $(a,b)$ of positive integers are there such that $a \leq b$ and $ab = 4^{2017} \; ?$ $2017$ $2019$ $2020$ $2018$
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 17, 2021
by
soujanyareddy13
2.7k
points
236
views
cat2020-set3
quantitative-aptitude
algebra
2
votes
1
answer
5
CAT 2020 Set-2 | Question: 56
If $\textsf{x}$ and $\textsf{y}$ are positive real numbers satisfying $\textsf{x+y = 102},$ then the minimum possible value of $\textsf{2601} \left( 1 + \frac{1}{\textsf{x}} \right) \left( 1 + \frac{1}{\textsf{y}} \right)$ is
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 17, 2021
by
soujanyareddy13
2.7k
points
481
views
cat2020-set2
quantitative-aptitude
algebra
numerical-answer
2
votes
1
answer
6
CAT 2020 Set-2 | Question: 60
For real $\textsf{x}$ , the maximum possible value of $ \frac{x}{\sqrt{1+x^{4}}}$ is $ \frac{1}{\sqrt{3}}$ $1$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 17, 2021
by
soujanyareddy13
2.7k
points
557
views
cat2020-set2
quantitative-aptitude
algebra
3
votes
1
answer
7
CAT 2020 Set-2 | Question: 71
The number of integers that satisfy the equality $\left( x^{2} – 5x + 7 \right)^{x+1} = 1$ is $2$ $3$ $5$ $4$
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 17, 2021
by
soujanyareddy13
2.7k
points
534
views
cat2020-set2
quantitative-aptitude
algebra
1
vote
1
answer
8
CAT 2020 Set-1 | Question: 57
The number of real$-$valued of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is infinite $1$ $0$ $2$
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 16, 2021
by
soujanyareddy13
2.7k
points
499
views
cat2020-set1
quantitative-aptitude
algebra
1
vote
1
answer
9
CAT 2020 Set-1 | Question: 59
How many distinct positive integer-valued solutions exist to the equation $\left ( x^{2}-7x+11 \right )^{(x^{2}-13x+42)} =1$? $6$ $8$ $2$ $4$
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 16, 2021
by
soujanyareddy13
2.7k
points
493
views
cat2020-set1
quantitative-aptitude
algebra
2
votes
1
answer
10
CAT 2020 Set-1 | Question: 67
If $x=\left ( 4096 \right )^{7+4\sqrt{3}}$, then which of the following equals $64$? $\frac{x^{7}}{x^{2\sqrt{3}}}$ $\frac{x^{7}}{x^{4\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x\frac{4}{\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x^{2\sqrt{3}}}$
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 16, 2021
by
soujanyareddy13
2.7k
points
442
views
cat2020-set1
quantitative-aptitude
algebra
1
vote
1
answer
11
CAT 2020 Set-1 | Question: 69
If $a, b$ and $c$ are positive integers such that $ab=432, bc=96$ and $c<9,$ then the smallest possible value of $a+b+c$ is $56$ $59$ $49$ $46$
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 16, 2021
by
soujanyareddy13
2.7k
points
499
views
cat2020-set1
quantitative-aptitude
algebra
1
vote
1
answer
12
CAT 2020 Set-1 | Question: 72
A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving ... fashion. His total stock exhausts after he takes care of $5$ children. How many toffees were there in his stock initially?
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 16, 2021
by
soujanyareddy13
2.7k
points
698
views
cat2020-set1
quantitative-aptitude
algebra
numerical-answer
1
vote
1
answer
13
CAT 2020 Set-1 | Question: 75
The number of distinct real roots of the equation $\left ( x+\frac{1}{x}\right )^{2}-3\left ( x+\frac{1}{x} \right )+2= 0$ equals
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 16, 2021
by
soujanyareddy13
2.7k
points
615
views
cat2020-set1
quantitative-aptitude
algebra
numerical-answer
1
vote
1
answer
14
NIELIT 2016 MAR Scientist D: 71
A certain number when added to $50\%$ of itself is $27$. What is the number? $7$ $9$ $11$ $18$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 3, 2020
by
Lakshman Bhaiya
13.7k
points
554
views
nielit2016mar-scientistd
quantitative-aptitude
algebra
0
votes
1
answer
15
NIELIT 2016 MAR Scientist D: 70
Twelve less than $4$ times a number is $20$. What is the number? $2$ $4$ $6$ $8$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 3, 2020
by
Lakshman Bhaiya
13.7k
points
616
views
nielit2016mar-scientistd
quantitative-aptitude
algebra
1
vote
1
answer
16
NIELIT 2016 MAR Scientist D: 69
The sum of a number and its double is $69$. What is the number? $46.6$ $34.5$ $23$ $20$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 3, 2020
by
Lakshman Bhaiya
13.7k
points
688
views
nielit2016mar-scientistd
quantitative-aptitude
algebra
0
votes
1
answer
17
NIELIT 2019 Feb Scientist D - Section D: 3
A school has $378$ girls and $675$ boys. All the students divided into strictly boys and strictly girls students sections. All the sections in the school has same number of students. What is the number of sections in the school? $27$ $36$ $39$ $23$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 3, 2020
by
Lakshman Bhaiya
13.7k
points
759
views
nielit2019feb-scientistd
quantitative-aptitude
algebra
0
votes
1
answer
18
NIELIT 2019 Feb Scientist D - Section D: 26
A dog at point $A$ goes in pursuit of a fox $30$ $m$ away. The dog makes $2$ $m$ and the fox, $1$ m long leaps. If the dog makes two leaps to the fox’s three, at what distance from $A$ will the dog catch up with the fox ? $100$ $m$ $110$ $m$ $105$ $m$ $120$ $m$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 3, 2020
by
Lakshman Bhaiya
13.7k
points
942
views
nielit2019feb-scientistd
quantitative-aptitude
algebra
0
votes
1
answer
19
NIELIT 2019 Feb Scientist D - Section D: 27
If $5$ spiders can catch $5$ files in $5$ minutes. How many files can $100$ spiders catch in $100$ minutes : $100$ $1000$ $500$ $2000$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 3, 2020
by
Lakshman Bhaiya
13.7k
points
571
views
nielit2019feb-scientistd
quantitative-aptitude
algebra
0
votes
1
answer
20
NIELIT 2016 MAR Scientist C - Section A: 12
The expression $(11.98\times 11.98 + 11.98 \times x +0.02 \times 0.02)$ will be a perfect square for $x$ equal to: $2.02$ $0.17$ $0.04$ $1.4$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 2, 2020
by
Lakshman Bhaiya
13.7k
points
501
views
nielit2016mar-scientistc
algebra
quadratic-equations
0
votes
1
answer
21
NIELIT 2016 MAR Scientist C - Section A: 15
The value of $\large\frac{(0.96)^3-(0.1)^3}{(0.96)^2+0.096+(0.1)^2}$ is : $0.86$ $0.95$ $0.97$ $1.06$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 2, 2020
by
Lakshman Bhaiya
13.7k
points
958
views
nielit2016mar-scientistc
algebra
0
votes
1
answer
22
NIELIT 2019 Feb Scientist C - Section D: 15
The simplified form of $\left[ \left ( \left( \dfrac{a+1}{a-1}\right)^2+3 \right)\div \left( \left( \dfrac{a-1}{a+1}\right)^2+3\right) \right] \div \left [\left( \dfrac{a^{3}+1}{a^{3}-1}\right)-\dfrac{2a}{a-1} \right]$ is: $a-1$ $1-a$ $-1$ $1$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 1, 2020
by
Lakshman Bhaiya
13.7k
points
709
views
nielit2019feb-scientistc
algebra
0
votes
2
answers
23
NIELIT 2019 Feb Scientist C - Section D: 23
Rs.$6500$ were divided among a certain number of persons. If there had been $15$ more persons, each would have got $Rs.30$ less. Find the original number of persons. $50$ $60$ $45$ $55$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 1, 2020
by
Lakshman Bhaiya
13.7k
points
996
views
nielit2019feb-scientistc
quantitative-aptitude
algebra
0
votes
1
answer
24
NIELIT 2019 Feb Scientist C - Section D: 30
A charitable trust donates $28$ different books of Maths, $16$ different books of science and $12$ different books of social science to poor students. Each student is given maximum number of books of only one subject of their interest and each student got equal number of books. Find the total number of students who got books. $14$ $10$ $12$ $15$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 1, 2020
by
Lakshman Bhaiya
13.7k
points
912
views
nielit2019feb-scientistc
quantitative-aptitude
algebra
0
votes
1
answer
25
NIELIT 2019 Feb Scientist C - Section C: 3
The factors of $(x^{2}+4y^{2}+4y-4xy-2x-8)$ are: $(x-2y-4)(x-2y+2)$ $(x-y+2)(x-4y-4)$ $(x+2y-4)(x+2y+2)$ None of these
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 1, 2020
by
Lakshman Bhaiya
13.7k
points
703
views
nielit2019feb-scientistc
algebra
1
vote
2
answers
26
NIELIT 2019 Feb Scientist C - Section C: 19
If $a^{x}=b, b^{y}=c$ and $c^{z}=a$, then $xyz$ equals: $abc$ $\dfrac{1}{abc}$ $1$ None
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Apr 1, 2020
by
Lakshman Bhaiya
13.7k
points
739
views
nielit2019feb-scientistc
algebra
1
vote
1
answer
27
CAT 2019 Set-2 | Question: 86
What is the largest positive integer $n$ such that $\frac{n^{2}+7n+12}{n^{2}-n-12}$ is also a positive integer? $8$ $12$ $16$ $6$
go_editor
asked
in
Quantitative Aptitude
Mar 20, 2020
by
go_editor
13.8k
points
1.1k
views
cat2019-2
quantitative-aptitude
algebra
1
vote
1
answer
28
CAT 2019 Set-2 | Question: 97
If $5^{x}-3^{y}=13438$ and $5^{x-1}+3^{y+1}=9686$, then $x+y$ equals _______
go_editor
asked
in
Quantitative Aptitude
Mar 20, 2020
by
go_editor
13.8k
points
685
views
cat2019-2
quantitative-aptitude
algebra
numerical-answer
3
votes
1
answer
29
CAT 2018 Set-1 | Question: 69
Given that $x^{2018}y^{2017}=1/2$ and $x^{2016}y^{2019}=8$, the value of $x^2+y^3$ is $35/4$ $37/4$ $31/4$ $33/4$
go_editor
asked
in
Quantitative Aptitude
Mar 20, 2020
by
go_editor
13.8k
points
708
views
cat2018-1
quantitative-aptitude
algebra
2
votes
1
answer
30
CAT 2018 Set-1 | Question: 77
If $u^2+(u-2v-1)^2=-4v(u+v)$, then what is the value of $u+3v$ ? $1/4$ $0$ $1/2$ $-1/4$
go_editor
asked
in
Quantitative Aptitude
Mar 20, 2020
by
go_editor
13.8k
points
534
views
cat2018-1
quantitative-aptitude
algebra
1
vote
1
answer
31
CAT 2017 Set-2 | Question: 94
How many different pairs $(a,b)$ of positive integers are there such that $a\leq b$ and $1/a+1/b=1/9$ None of these $2$ $0$ $1$
go_editor
asked
in
Quantitative Aptitude
Mar 16, 2020
by
go_editor
13.8k
points
506
views
cat2017-2
quantitative-aptitude
algebra
2
votes
2
answers
32
CAT 2017 Set-2 | Question: 91
If $9^{\left ( x-1/2 \right )}-2^{\left ( 2x-2 \right )}=4^{x}-3^{\left (2x-3 \right )}$, then $x$ is $3/2$ $2/5$ $3/4$ $4/9$
go_editor
asked
in
Quantitative Aptitude
Mar 16, 2020
by
go_editor
13.8k
points
655
views
cat2017-2
quantitative-aptitude
algebra
1
vote
1
answer
33
CAT 2017 Set-1 | Question: 90
If $9^{2x-1}-81^{x-1}= 1944$ then $x$ is $3$ $9/4$ $4/9$ $1/3$
go_editor
asked
in
Quantitative Aptitude
Mar 13, 2020
by
go_editor
13.8k
points
565
views
cat2017-1
quantitative-aptitude
algebra
1
vote
1
answer
34
CAT 2017 Set-1 | Question: 88
If $x+1= x^{2}$ and $x> 0$, then $2x^{4}$ is $6+4\sqrt{5}$ $3+5\sqrt{5}$ $5+3\sqrt{5}$ $7+3\sqrt{5}$
go_editor
asked
in
Quantitative Aptitude
Mar 13, 2020
by
go_editor
13.8k
points
581
views
cat2017-1
quantitative-aptitude
algebra
1
vote
1
answer
35
CAT 2017 Set-1 | Question: 94
If $a, b, c$ and $d$ are integers such that $a+b+c+d=30$ , then the minimum possible value of $( a-b )^{2}+( a-c )^{2}+( a-d)^{2}$ is $1$ $2$ $5$ $6$
go_editor
asked
in
Quantitative Aptitude
Mar 13, 2020
by
go_editor
13.8k
points
424
views
cat2017-1
quantitative-aptitude
algebra
1
vote
1
answer
36
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 $y$? $2^{(1/3)}$ $2^{(2/3)}$ $2^{(1/4)}$ $2^{(3/4)}$
go_editor
asked
in
Quantitative Aptitude
Mar 11, 2020
by
go_editor
13.8k
points
506
views
cat2016
quantitative-aptitude
algebra
0
votes
1
answer
37
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. $\left (y ^{2} -z^{2}\right )$ is always negative.
go_editor
asked
in
Quantitative Aptitude
Mar 9, 2020
by
go_editor
13.8k
points
464
views
cat2015
quantitative-aptitude
algebra
2
votes
1
answer
38
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 $3$ $1$ $\frac{1}{3}$ $\frac{2}{3}$
go_editor
asked
in
Quantitative Aptitude
Mar 8, 2020
by
go_editor
13.8k
points
557
views
cat2019-1
quantitative-aptitude
algebra
0
votes
1
answer
39
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 $5$ but $(6$ but not $(7$ and $(8$ or $9) ) ) ) ) ).$ $9$ $-8$ $-11$ $17$
Krithiga2101
asked
in
Logical Reasoning
Mar 7, 2020
by
Krithiga2101
298
points
472
views
cat2011
logical-reasoning
algebra
0
votes
0
answers
40
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 positive difference of the squares of $x$ and $y.$ $x\&y$:gives the product of $ ... $ will be equal to $x₤y$ $x\$y$ $(x₤y)(x@y)$ Cannot be determined
Krithiga2101
asked
in
Logical Reasoning
Mar 7, 2020
by
Krithiga2101
298
points
289
views
cat2011
logical-reasoning
algebra
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