Recent questions tagged cat2025-set2

Comprehension:The Sustainability Index $(\mathrm{SI})$ of a country at a point in time is an integer between $1$ and $100$. This question is related to $(\mathrm{SI})$ of...

Comprehension:The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs...

Comprehension:The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs...

Comprehension:The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs...

Comprehension:The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs...

Comprehension:The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs...

If $9^{x^{2}+2 x-3}-4\left(3^{x^{2}+2 x-2}\right)+27=0$, then the product of all possible values of $x$ is$1. 30$$2. 20$$3.5$$4.15$

The average number of copies of a book sold per day by a shopkeeper is $60$ in the initial seven days and $63$ in the initial eight days, after the book launch. On the ni...

The set of all real values of $x$ for which $(x^{2}-\mid x+9 \mid +x)>0$, is$(-\infty,-3) \cup(3, \infty)$$(-\infty,-9) \cup(3, \infty)$$(-9,-3) \cup(3, \infty)$$(-\infty...

An item with a cost price of Rs.$1650$ is sold at a certain discount on a fixed marked price to earn a profit of $20 \%$ on the cost price. If the discount was doubled, t...

If $m$ and $n$ are integers such that $(m+2 n)(2 m+n)=27$, then the maximum possible value of $2 m-3 n$ is

The sum of digits of the number $(625)^{65} \times(128)^{36}$, is

The equations $3 x^{2}-5 x+p=0$ and $2 x^{2}-2 x+q=0$ have one common root. The sum of the other roots of these two equations is$\dfrac{8}{3}-p+\dfrac{3}{2} q$$\dfrac{2}{...

If $\log _{64} x^{2}+\log _{8} \sqrt{y}+3 \log _{512}(\sqrt{y} z)=4$, where $x, y$ and $z$ are positive real numbers, then the minimum possible value of $(x+y+z)$ is$48$$...

Rita and Sneha can row a boat at $5 \mathrm{~km} / \mathrm{h}$ and $6 \mathrm{~km} / \mathrm{h}$ in still water, respectively. In a river flowing with a constant velocity...

Suppose $a, b, c$ are three distinct natural numbers, such that $3 a c=8(a+b)$. Then, the smallest possible value of $3 a+2 b+c$ is

Let $f(x)=\dfrac{x}{(2 x-1)}$ and $g(x)=\dfrac{x}{(x-1)}$. Then, the domain of the function $h(x)=f(g(x))+g(f(x))$ is all real numbers except$-1, \dfrac{1}{2}$, and $1$$\...

A loan of Rs $1000$ is fully repaid by two installments of Rs $530$ and Rs $594$, paid at the end of first and second year, respectively. If the interest is compounded an...

Two tangents drawn from a point $\text{P}$ touch a circle with center $\text{O}$ at points $\text{Q}$ and $\text{R}$. Points $\text{A}$ and $\text{B}$ lie on $\text{PQ}$ ...

The number of divisors of $\left(2^{6} \times 3^{5} \times 5^{3} \times 7^{2}\right)$, which are of the form $(3 r+1)$, where $r$ is a non-negative integer, is$36$$56$$24...

Let $\text{ABCDEF}$ be a regular hexagon and $\text{P}$ and $\text{Q}$ be the midpoints of $\text{AB}$ and $\text{CD}$, respectively. Then, the ratio of the areas of trap...

If $a, b, c$ and $d$ are integers such that their sum is $46$, then the minimum possible value of $(a-b)^{2}+(a-c)^{2}+(a-d)^{2}$ is

The ratio of expenditures of Lakshmi and Meenakshi is $2: 3$, and the ratio of income of Lakshmi to expenditure of Meenakshi is $6:7$. If excess of income over expenditur...

Let $a_{n}$ be the $n^{\text {th }}$ term of a decreasing infinite geometric progression. If $a_{1}+a_{2}+a_{3}=52$ and $a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{1}=624$, then th...

A mixture of coffee and cocoa, $16 \%$ of which is coffee, costs Rs $240$ per kg . Another mixture of coffee and cocoa, of which $36 \%$ is coffee, costs Rs $320$ per kg....

In a $\triangle \text{ABC}$, points $\text{D}$ and $\text{E}$ are on the sides $\text{BC}$ and $\text{AC}$, respectively. $\text{BE}$ and $\text{AD}$ intersect at point $...

Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after $20$ days. ...

A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received $20\%$ of the total amount and Meena received $40\%$ of the remaining amount. If Se...