# Recent questions tagged cat2022-set1

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Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the q...

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The largest real value of $a$ for which the equation $|x+a|+|x-1|=2$ has an infinite number of solutions for $x$ is$2$$-1$$0$$1$

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The average of three integers is $13$. When a natural number $n$ is included, the average of these four integers remains an odd integer. The minimum possible value of $n$...

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Let $A$ be the largest positive integer that divides all the numbers of the form $3^{k}+4^{k}+5^{k}$, and $B$ be the largest positive integer that divides all the numbers...

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In a village, the ratio of number of males to females is $5: 4$. The ratio of number of literate males to literate females is $2: 3$. The ratio of the number of illiterat...

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Let $\text{A B C D}$ be a parallelogram such that the coordinates of its three vertices $\text{A, B, C}$ are $(1,1),(3,4)$ and $(-2,8)$, respectively. Then, the coordinat...

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Alex invested his savings in two parts. The simple interest earned on the first part at $15 \%$ per annum for 4 years is the same as the simple interest earned on the sec...

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The average weight of students in a class increases by $600 \mathrm{gm}$ when some new students join the class. If the average weight of the new students is $3 \mathrm{~k...

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A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio $1: 3$, then the ratio...

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Amal buys $110 \mathrm{~kg}$ of syrup and $120 \mathrm{~kg}$ of juice, syrup being $20 \%$ less costly than juice, per kg. He sells $10 \mathrm{~kg}$ of syrup at $10 \%$ ...

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$\mathrm{A}$ trapezium $\mathrm{ABCD}$ has side $\mathrm{AD}$ parallel to $\mathrm{BC}, \angle \mathrm{BAD}=90^{\circ}, \mathrm{BC}=3 \mathrm{~cm}$ and $\mathrm{AD}=8 \ma...

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All the vertices of a rectangle lie on a circle of radius $R$. If the perimeter of the rectangle is $P$, then the area of the rectangle is$\frac{P^{2}}{16}-R^{2}$$\frac{P...

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Let $a, b, c$ be non-zero real numbers such that $b^{2}<4 a c$, and $f(x)=a x^{2}+b x+c$. If the set $S$ consists of all integers $m$ such that $f(m)<0$, then the set $S$...

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Let $a$ and $b$ be natural numbers. If $a^{2}+a b+a=14$ and $b^{2}+a b+b=28$, then $(2 a+b)$ equals$8$$9$$7$$10$

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In a class of $100$ students, $73$ like coffee, $80$ like tea and $52$ like lemonade. It may be possible that some students do not like any of these three drinks. Then th...

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Trains $\text{A}$ and $\text{B}$ start traveling at the same time towards each other with constant speeds from stations $\text{X}$ and $\text{Y}$, respectively. Train $\t...

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Ankita buys $4 \mathrm{~kg}$ cashews, $14 \mathrm{~kg}$ peanuts and $6 \mathrm{~kg}$ almonds when the cost of $7 \mathrm{~kg}$ cashews is the same as that of $30 \mathrm{...

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For natural numbers $x, y$, and $z$, if $x y+y z=19$ and $y z+x z=51$, then the minimum possible value of $x y z$ is

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Let $0 \leq a \leq x \leq 100$ and $f(x)=|x-a|+|x-100|+|x-a-50|$. Then the maximum value of $f(x)$ becomes $100$ when $a$ is equal to$0$$25$$100$$50$

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For any real number $x$, let $[x]$ be the largest integer less than or equal to $x$. If $\sum_{n=1}^{N}\left[\frac{1}{5}+\frac{n}{25}\right]=25$ then $N$ is

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For any natural number $n$, suppose the sum of the first $n$ terms of an arithmetic progression is $\left(n+2 n^{2}\right)$. If the $n^{\text {th }}$ term of the progress...

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The number of ways of distributing $20$ identical balloons among $4$ children such that each child gets some balloons but no child gets an odd number of balloons, is

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Comprehension:Given above is the schematic map of the metro lines in a city with rectangles denoting terminal stations (e.g. A), diamonds denoting junction stations (e.g....

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Comprehension:The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in...

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Comprehension:Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individuall...

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Comprehension:There are $15$ girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a $1$-day event, or a $2$...

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