Recent questions tagged cat2022-set3

1 votes
1 answer
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$-60$ $-50$ $60$ $-70$
2 votes
1 answer
3
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4
2 votes
1 answer
7
1 votes
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8
Let $r$ be a real number and $f(x)=\left\{\begin{array}{cl}2 x-r & \text { if } x \geq r \\ r & \text { if } x<r\end{array}\right.$. Then, the equation $f(x)=f(f(x))$ hol...
1 votes
1 answer
11
The minimum possible value of $\frac{x^{2}-6 x+10}{3-x}$, for $x<3$, is$-2$$2$$\frac{1}{2}$$-\frac{1}{2}$
1 votes
1 answer
13
If $\left(\sqrt{\frac{7}{3}}\right)^{2 x-y}=\frac{875}{2401}$ and $\left(\frac{4 a}{b}\right)^{4 x-y}=\left(\frac{2 a}{b}\right)^{y-6 x}$, for all non-zero real values of...
1 votes
0 answers
17
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18
The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in $1421$, including itself, is$2442$$3333$$2592$$2222$
1 votes
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19
The lengths of all four sides of a quadrilateral are integer valued. If three of its sides are of length $1 \mathrm{cm}, 2 \mathrm{cm}$ and $4 \mathrm{cm}$, then the tota...
1 votes
0 answers
22
The average of all $3$-digit terms in the arithmetic progression $38,55,72, \ldots$, is
1 votes
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23
Comprehension:In the following, a year corresponds to $1^{\text {st }}$ of January of that year.A study to determine the mortality rate for a disease began in $1980$. The...
1 votes
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24
Comprehension:In the following, a year corresponds to $1^{\text {st }}$ of January of that year.A study to determine the mortality rate for a disease began in $1980$. The...
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25
Comprehension:In the following, a year corresponds to $1^{\text {st }}$ of January of that year.A study to determine the mortality rate for a disease began in $1980$. The...
1 votes
0 answers
26
Comprehension:In the following, a year corresponds to $1^{\text {st }}$ of January of that year.A study to determine the mortality rate for a disease began in $1980$. The...
1 votes
0 answers
27
Comprehension:In the following, a year corresponds to $1^{\text {st }}$ of January of that year.A study to determine the mortality rate for a disease began in $1980$. The...
1 votes
0 answers
28
Comprehension:Pulak, Qasim, Ritesh, and Suresh participated in a tournament comprising of eight rounds. In each round, they formed two pairs, with each of them being in e...
1 votes
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29
Comprehension:Pulak, Qasim, Ritesh, and Suresh participated in a tournament comprising of eight rounds. In each round, they formed two pairs, with each of them being in e...
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30
Comprehension:Pulak, Qasim, Ritesh, and Suresh participated in a tournament comprising of eight rounds. In each round, they formed two pairs, with each of them being in e...
2 votes
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31
Comprehension:Pulak, Qasim, Ritesh, and Suresh participated in a tournament comprising of eight rounds. In each round, they formed two pairs, with each of them being in e...
1 votes
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32
Comprehension:Pulak, Qasim, Ritesh, and Suresh participated in a tournament comprising of eight rounds. In each round, they formed two pairs, with each of them being in e...
1 votes
0 answers
33
Comprehension:All the first-year students in the computer science (CS) department in a university take both the courses (i) $\mathrm{Al}$ and (ii) $\mathrm{ML}$. Students...
1 votes
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34
Comprehension:All the first-year students in the computer science (CS) department in a university take both the courses (i) $\mathrm{Al}$ and (ii) $\mathrm{ML}$. Students...
1 votes
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35
Comprehension:All the first-year students in the computer science (CS) department in a university take both the courses (i) $\mathrm{Al}$ and (ii) $\mathrm{ML}$. Students...
1 votes
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36
Comprehension:All the first-year students in the computer science (CS) department in a university take both the courses (i) $\mathrm{Al}$ and (ii) $\mathrm{ML}$. Students...
1 votes
0 answers
37
Comprehension:All the first-year students in the computer science (CS) department in a university take both the courses (i) $\mathrm{Al}$ and (ii) $\mathrm{ML}$. Students...
1 votes
0 answers
38
Comprehension:There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto. During the onset of a pandemic, the number of new cases of a dise...
1 votes
0 answers
39
Comprehension:There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto. During the onset of a pandemic, the number of new cases of a dise...
1 votes
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40
Comprehension:There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto. During the onset of a pandemic, the number of new cases of a dise...