# Recent questions tagged cat2022-set1

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$$1 1 answer 3 The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n... 0 answers 4 Let A be the largest positive integer that divides all the numbers of the form 3^{k}+4^{k}+5^{k}, and B be the largest positive integer that divides all the numbers... 1 answer 5 In a village, the ratio of number of males to females is 5: 4. The ratio of number of literate males to literate females is 2: 3. The ratio of the number of illiterat... 0 answers 6 Let \text{A B C D} be a parallelogram such that the coordinates of its three vertices \text{A, B, C} are (1,1),(3,4) and (-2,8), respectively. Then, the coordinat... 0 answers 7 Alex invested his savings in two parts. The simple interest earned on the first part at 15 \% per annum for 4 years is the same as the simple interest earned on the sec... 0 answers 8 The average weight of students in a class increases by 600 \mathrm{gm} when some new students join the class. If the average weight of the new students is 3 \mathrm{~k... 0 answers 9 A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1: 3, then the ratio... 0 answers 10 Amal buys 110 \mathrm{~kg} of syrup and 120 \mathrm{~kg} of juice, syrup being 20 \% less costly than juice, per kg. He sells 10 \mathrm{~kg} of syrup at 10 \% ... 0 answers 11 \mathrm{A} trapezium \mathrm{ABCD} has side \mathrm{AD} parallel to \mathrm{BC}, \angle \mathrm{BAD}=90^{\circ}, \mathrm{BC}=3 \mathrm{~cm} and \mathrm{AD}=8 \ma... 0 answers 12 All the vertices of a rectangle lie on a circle of radius R. If the perimeter of the rectangle is P, then the area of the rectangle is\frac{P^{2}}{16}-R^{2}$$\frac{P... 0 answers 13 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$S$... 1 answer 14 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$$10 0 answers 15 In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then th... 0 answers 16 Trains \text{A} and \text{B} start traveling at the same time towards each other with constant speeds from stations \text{X} and \text{Y}, respectively. Train \t... 0 answers 17 Ankita buys 4 \mathrm{~kg} cashews, 14 \mathrm{~kg} peanuts and 6 \mathrm{~kg} almonds when the cost of 7 \mathrm{~kg} cashews is the same as that of 30 \mathrm{... 0 answers 18 For natural numbers x, y, and z, if x y+y z=19 and y z+x z=51, then the minimum possible value of x y z is 0 answers 19 Let 0 \leq a \leq x \leq 100 and f(x)=|x-a|+|x-100|+|x-a-50|. Then the maximum value of f(x) becomes 100 when a is equal to0$$25$$100$$50$0 answers 20 For any real number$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$is 0 answers 21 For any natural number$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... 0 answers 22 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 0 answers 23 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.... 0 answers 24 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.... 0 answers 25 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.... 0 answers 26 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.... 0 answers 27 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.... 0 answers 28 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... 0 answers 29 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... 0 answers 30 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... 0 answers 31 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... 0 answers 32 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... 0 answers 33 Comprehension:Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individuall... 0 answers 34 Comprehension:Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individuall... 0 answers 35 Comprehension:Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individuall... 0 answers 36 Comprehension:Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individuall... 0 answers 37 Comprehension:Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individuall... 0 answers 38 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$2$... 0 answers 39 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$2$... 0 answers 40 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\$...