# 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...

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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...

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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...

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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...

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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...

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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}$

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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 $\mathrm{A}$...

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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...

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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 ...

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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...

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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...

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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...

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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$

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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: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: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...

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