# Recent questions tagged cat2022-set3

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A donation box can receive only cheques of ₹$100$, ₹$250$, and ₹$500$. On one good day, the donation box was found to contain exactly $100$ cheques amounting to a t...
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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$-60$ $-50$ $60$ $-70$
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If $(3+2 \sqrt{2})$ is a root of the equation $a x^{2}+b x+c-0$, and $(4+2 \sqrt{3})$ is a root of the equation $a y^{2}+m y+n – 0$, where $a, b, c, m$ and $n$ are inte...
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Suppose the medians $\mathrm{BD}$ and $\mathrm{CE}$ of a triangle $\mathrm{ABC}$ intersect at a point $\mathrm{O}$. If area of triangle $\mathrm{ABC}$ is $108$ $\mathrm{s... 0 answers 5 Bob can finish a job in$40$days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the f... 0 answers 6 A glass contains$500 \mathrm{cc}$of milk and a cup contains$500 \mathrm{cc}$of water. From the glass,$150 \mathrm{cc}$of milk is transferred to the cup and mixed th... 1 answer 7 Consider six distinct natural numbers such that the average of the two smallest numbers is$14$, and the average of the two largest numbers is$28$. Then, the maximum pos... 1 answer 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... 0 answers 9 Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port formed an equilateral triangle with sides of length$24 \...
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Nitu has an initial capital of ₹ $20,000$. Out of this, she invests ₹$8,000$ at $5.5 \%$ in bank $\mathrm{A}$, ₹$5,000$ at $5.6 \%$ in bank $\mathrm{B}$ and the rem...
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The minimum possible value of $\frac{x^{2}-6 x+10}{3-x}$, for $x<3$, is$-2$$2$$\frac{1}{2}$$-\frac{1}{2} 0 answers 12 In an examination, the average marks of students in sections \mathrm{A} and \mathrm{B} are 32 and 60, respectively. The number of students in section \mathrm{A}... 1 answer 13 If \left(\sqrt{\frac{7}{3}}\right)^{2 x-y}=\frac{875}{2401} and \left(\frac{4 a}{b}\right)^{4 x-y}=\left(\frac{2 a}{b}\right)^{y-6 x}, for all non-zero real values of... 1 answer 14 A group of \mathrm{N} people worked on a project. They finished 35 \% of the project by working 7 hours a day for 10 days. Thereafter, 10 people left the group ... 0 answers 15 Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator i... 0 answers 16 In a triangle \mathrm{A B C, A B=A C}=8 \mathrm{cm}. A circle drawn with \mathrm{BC} as diameter passes through \mathrm{A}. Another circle drawn with center at \ma... 0 answers 17 Suppose \mathrm{k} is any integer such that the equation 2 x^{2}+k x+5=0 has no real roots and the equation x^{2}+(k-5) x+1=0 has two distinct real roots for \math... 0 answers 18 The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is2442$$3333$$2592$$2222$
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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...
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Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take $1.5$ hours if they travel towards each other, ...
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A school has less than $5000$ students and if the students are divided equally into teams of either $9$ or $10$ or $12$ or $25$ each, exactly $4$ are always left out. How...
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The average of all $3$-digit terms in the arithmetic progression $38,55,72, \ldots$, is
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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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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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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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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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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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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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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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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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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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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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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...
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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...
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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...
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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...
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...