# Recent questions tagged cat2022-set2

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Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio $5: 8: 10$. They accept a job which they can finish in $4$ days if they all work...

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Mr. Pinto invests one-fifth of his capital at $6 \%$, one-third at $10 \%$ and the remaining at $1 \%$, each rate being simple interest per annum. Then, the minimum numbe...

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Regular polygons $\mathrm{A}$ and $\mathrm{B}$ have number of sides in the ratio $1: 2$ and interior angles in the ratio $3: 4$. Then the number of sides of $\mathrm{B}$ ...

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The number of distinct integer values of $n$ satisfying $\frac{4-\log 2 n}{3-\log _{4} n}<0$, is

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The average of a non-decreasing sequence of $\mathrm{N}$ numbers $a_{1}, a_{2}, \ldots \ldots, a_{N}$ is $300$ . If $a_{1}$ is replaced by $6 a_{1}$, the new average beco...

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If $a$ and $b$ are non-negative real numbers such that $a+2 b=6$, then the average of the maximum and minimum possible values of $(a+b)$ is$3.5$$4.5$$3$$4$

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The length of each side of an equilateral triangle $\mathrm{A B C}$ is $3 \mathrm{~cm}$. Let $\mathrm{D}$ be a point on $\mathrm{B C}$ such that the area of triangle $\ma...

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The number of integers greater than $2000$ that can be formed with the digits $0,1,2,3,4,5$, using each digit at most once, is$1480$$1440$$1200$$1420$

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Let $f(x)$ be a quadratic polynomial in $x$ such that $f(x) \geq 0$ for all real numbers $x$. If $f(2)=0$ and $f(4)=6$, then $f(-2)$ is equal to$36$$12$$24$$6$

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Manu earns ₹$4000$ per month and wants to save an average of ₹$550$ per month in a year. In the first nine months, his monthly expense was ₹$3500$, and he foresees ...

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In an election, there were four candidates and $80 \%$ of the registered voters casted their votes. One of the candidates received $30 \%$ of the casted votes while the o...

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On day one, there are $100$ particles in a laboratory experiment. On day $n$, where $n \geq 2$, one out of every $n$ particles produces another particle. If the total num...

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There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first co...

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Five students, including Amit, appear for an examination in which possible marks are integers between $0$ and $50$ , both inclusive. The average marks for all the student...

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Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are $60 \mathrm{~km}$ apar...

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For some natural number $n$, assume that $(15,000) !$ is divisible by $(n !) !$. The largest possible value of $n$ is$5$$4$$6$$7$

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Suppose for all integers $x$, there are two functions $f$ and $g$ such that $f(x)+$ $f(x-1)-1=0$ and $g(x)=x^{2}$. If $f\left(x^{2}-x\right)=5$, then the value of the sum...

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In triangle $\mathrm{A B C}$, altitudes $\mathrm{A D}$ and $\mathrm{B E}$ are drawn to the corresponding bases. If $\angle \mathrm{B A C}=45^{\circ}$ and $\angle \mathrm{...

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The number of integer solutions of the equation $\left(x^{2}-10\right)^{\left(x^{2}-3 x-10\right)}=1$ is

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Let $r$ and $c$ be real numbers. If $r$ and $-r$ are roots of $5 x^{3}+c x^{2}-10 x+9=0$, then $c$ equals$4$$-4$$-\frac{9}{2}$$\frac{9}{2}$

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Consider the arithmetic progression $3,7,11, \ldots$ and let $A_{n}$ denote the sum of the first $\mathrm{n}$ terms of this progression. Then the value of $1^{25}, A$ is$...

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In an examination, there were $75$ questions. $3$ marks were awarded for each correct answer, $1$ mark was deducted for each wrong answer and $1$ mark was awarded for eac...

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Comprehension: A few salesmen are employed to sell a product called TRICCEK among households in various housing complexes. On each day, a salesman is assigned to visit on...

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Comprehension:Every day a widget supplier supplies widgets from the warehouse (W) to four locations - Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D)....

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Comprehension:The two plots below show data for four companies code-named $A, B, C$, and $D$ over three years - $2019, 2020$, and $2021$.The first plot shows the revenues...

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Comprehension:A speciality supermarket sells $320$ products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also ...

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