# Recent questions tagged cat2022-set2

1
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...
2
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...
3
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 $\mathrm{B}$ ...
4
The number of distinct integer values of $n$ satisfying $\frac{4-\log 2 n}{3-\log _{4} n}<0$, is
5
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...
6
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$$4 0 answers 7 The length of each side of an equilateral triangle \mathrm{A B C} is 3 \mathrm{~cm}. Let \mathrm{D} be a point on \mathrm{B C} such that the area of triangle \ma... 0 answers 8 The number of integers greater than 2000 that can be formed with the digits 0,1,2,3,4,5, using each digit at most once, is1480$$1440$$1200$$1420$
9
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$$6 0 answers 10 Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees ... 0 answers 11 In an election, there were four candidates and 80 \% of the registered voters casted their votes. One of the candidates received 30 \% of the casted votes while the o... 0 answers 12 On day one, there are 100 particles in a laboratory experiment. On day n, where n \geq 2, one out of every n particles produces another particle. If the total num... 1 answer 13 There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first co... 0 answers 14 Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50 , both inclusive. The average marks for all the student... 0 answers 15 Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 \mathrm{~km} apar... 0 answers 16 For some natural number n, assume that (15,000) ! is divisible by (n !) !. The largest possible value of n is5$$4$$6$$7$
17
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...
18
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 $\angle \mathrm{... 0 answers 19 The number of integer solutions of the equation$\left(x^{2}-10\right)^{\left(x^{2}-3 x-10\right)}=1$is 0 answers 20 Let$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}$0 answers 21 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$...
22
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...
23
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...
24
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...
25
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...
26
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...
27
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...
28
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)....
29
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)....
30
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)....
31
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)....
32
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)....
33
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...
34
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...
35
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...
36
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...
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...
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 ...
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 ...
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 ...