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Recent questions tagged cat2018-1

2 votes
1 answer
12
CAT 2018 Set-1 | Question: 67
Let $x, y, z$ be three positive real numbers in a geometric progression such that $x < y < z$. If $5x$, $16y$, and $12z$ are in an arithmetic progression then the common ratio of the geometric progression is $3/6$ $3/2$ $5/2$ $1/6$
Let $x, y, z$ be three positive real numbers in a geometric progression such that $x < y < z$. If $5x$, $16y$, and $12z$ are in an arithmetic progression then the common ...
2 votes
1 answer
14
CAT 2018 Set-1 | Question: 71
If $\log_2(5+\log_3a)=3$ and $\log_5(4a+12+\log_2b)=3$, then $a+b$ is equal to $67$ $40$ $32$ $59$
If $\log_2(5+\log_3a)=3$ and $\log_5(4a+12+\log_2b)=3$, then $a+b$ is equal to$67$$40$$32$$59$
3 votes
1 answer
16
CAT 2018 Set-1 | Question: 69
Given that $x^{2018}y^{2017}=1/2$ and $x^{2016}y^{2019}=8$, the value of $x^2+y^3$ is $35/4$ $37/4$ $31/4$ $33/4$
Given that $x^{2018}y^{2017}=1/2$ and $x^{2016}y^{2019}=8$, the value of $x^2+y^3$ is$35/4$$37/4$$31/4$$33/4$
2 votes
1 answer
17
CAT 2018 Set-1 | Question: 73
In a circle, two parallel chords on the same side of a diameter have lengths $4$ cm and $6$ cm. If the distance between these chords is $1$ cm, then the radius of the circle, in cm, is $\sqrt{12}$ $\sqrt{14}$ $\sqrt{13}$ $\sqrt{11}$
In a circle, two parallel chords on the same side of a diameter have lengths $4$ cm and $6$ cm. If the distance between these chords is $1$ cm, then the radius of the cir...
2 votes
1 answer
19
CAT 2018 Set-1 | Question: 79
While multiplying three real numbers, Ashok took one of the numbers as $73$ instead of $37$. As a result, the product went up by $720$. Then the minimum possible value of the sum of squares of the other two numbers is _________
While multiplying three real numbers, Ashok took one of the numbers as $73$ instead of $37$. As a result, the product went up by $720$. Then the minimum possible value of...
2 votes
1 answer
20
CAT 2018 Set-1 | Question: 78
If $x$ is a positive quantity such that $2^x=3^{\log_52}$, then $x$ is equal to $1+\log_3\dfrac{5}{3}$ $\log_58$ $1+\log_5\dfrac{3}{5}$ $\log_59$
If $x$ is a positive quantity such that $2^x=3^{\log_52}$, then $x$ is equal to$1+\log_3\dfrac{5}{3}$$\log_58$$1+\log_5\dfrac{3}{5}$$\log_59$
3 votes
1 answer
23
CAT 2018 Set-1 | Question: 74
If among $200$ students, $105$ like pizza and $134$ like burger, then the number of students who like only burger can possibly be $93$ $26$ $23$ $96$
If among $200$ students, $105$ like pizza and $134$ like burger, then the number of students who like only burger can possibly be$93$$26$$23$$96$
2 votes
1 answer
24
CAT 2018 Set-1 | Question: 77
If $u^2+(u-2v-1)^2=-4v(u+v)$, then what is the value of $u+3v$ ? $1/4$ $0$ $1/2$ $-1/4$
If $u^2+(u-2v-1)^2=-4v(u+v)$, then what is the value of $u+3v$ ?$1/4$$0$$1/2$$-1/4$
2 votes
1 answer
27
CAT 2018 Set-1 | Question: 82
$\log_{12}81=p$, then $3\bigg (\frac{4-p}{4+p}\bigg)$ is equal to $\log_416$ $\log_68$ $\log_616$ $\log_28$
$\log_{12}81=p$, then $3\bigg (\frac{4-p}{4+p}\bigg)$ is equal to $\log_416$$\log_68$$\log_616$$\log_28$
2 votes
1 answer
31
CAT 2018 Set-1 | Question: 88
Let $\text{ABCD}$ be a rectangle inscribed in a circle of radius $13$ cm. Which one of the following pairs can represent, in cm, the possible length and breadth of $\text{ABCD}?$ $24,10$ $25,9$ $24,12$ $25,10$
Let $\text{ABCD}$ be a rectangle inscribed in a circle of radius $13$ cm. Which one of the following pairs can represent, in cm, the possible length and breadth of $\text...
2 votes
1 answer
37
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 ________
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 ________
2 votes
1 answer
38
CAT 2018 Set-1 | Question: 92
The number of integers $x$ such that $0.25 < 2^x < 200$, and $2^x +2$ is perfectly divisible by either $3$ or $4$, is _______
The number of integers $x$ such that $0.25 < 2^x < 200$, and $2^x +2$ is perfectly divisible by either $3$ or $4$, is _______
2 votes
1 answer
39
CAT 2018 Set-1 | Question: 91
How many numbers with two or more digits can be formed with the digits $1,2,3,4,5,6,7,8,9$, so that in every such number, each digit is used at most once and the digits appear in the ascending order?
How many numbers with two or more digits can be formed with the digits $1,2,3,4,5,6,7,8,9$, so that in every such number, each digit is used at most once and the digits a...
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