Recent questions tagged cat2025-set3

Anirbid, Chandranath, Koushik, and Suranjan participated in a puzzle solving competition. The competition comprised $10$ puzzles that had to be solved in the same sequenc...

Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different e...

Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different e...

Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different e...

Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different e...

Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different e...

For a $4$-digit number (greater than $1000$), sum of the digits in the thousands, hundreds, and tens places is $15 $. Sum of the digits in the hundreds, tens, and units p...

The average salary of $5$ managers and $25$ engineers in a company is $60000$ rupees. If each of the managers received $20\%$ salary increase while the salary of the engi...

The monthly sales of a product from January to April were $120,135,150$ and $165$ units, respectively. The cost price of the product was Rs. $240$ per unit, and a fixed m...

A triangle $\text{ABC}$ is formed with $\text{AB}=\text{AC}=50 \mathrm{~cm}$ and $\text{BC}=80 \mathrm{~cm}$. Then, the sum of the lengths, in $\mathrm{cm}$ , of all thre...

In $\triangle \mathrm{ABC}, \mathrm{AB}=\mathrm{AC}=12 \mathrm{~cm}$ and $\mathrm{D}$ is a point on side $\mathrm{BC}$ such that $\mathrm{AD}=8 \mathrm{~cm}$. If $\mathrm...

For real values of $x$, the range of the function $f(x)=\dfrac{2 x-3}{2 x^{2}+4 x-6}$ is$(-\infty, \dfrac{1}{4}] \cup[1, \infty)$$(-\infty, \dfrac{1}{4}] \cup [\dfrac{1}{...

The sum of all possible real values of $x$ for which $\log _{x-3}(x^{2}-9)=\log _{x-3}(x+1)+2$, is$\dfrac{3+\sqrt{33}}{2}$$\sqrt{33}$$3$$-3$

Rahul starts on his journey at $5$ pm at a constant speed so that he reaches his destination at $11$ pm the same day. However, on his way, he stops for $20$ minutes, and ...

The ratio of the number of coins in boxes $A$ and $B$ was $17:7$. After $108$ coins were shifted from box $A$ to box $B$, this ratio became $37: 20$. The number of coins ...

Let $\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$ be three natural numbers such that their sum is $900$, and $\mathrm{r}$ is a perfect square whose value lies between $150$ a...

$\text{ABCD}$ is a trapezium in which $\text{AB}$ is parallel to $\text{DC}$ , $\text{AD}$ is perpendicular to $\text{AB}$, and $\text{AB}=3 \text{DC}$. If a circle inscr...

Vessels $\text{A}$ and $\text{B}$ contain $60$ litres of alcohol and $60$ litres of water, respectively. A certain volume is taken out from $\text{A}$ and poured into $\t...

The rate of water flow through three pipes $\text{A}, \text{B}$ and $\text{C}$ are in the ratio $4: 9: 36$. An empty tank can be filled up completely by pipe $\text{A}$ i...

If $f(x)=(x^{2}+3 x)(x^{2}+3 x+2)$, then the sum of all real roots of the equation $\sqrt{\mathrm{f}(\mathrm{x})+1}=9701$ is$-3$$3$$-6$$6$

The sum of all the digits of the number $(10^{50}+10^{25}-123)$ is$221$$255$$324$$212$

If $(x^{2}+\dfrac{1}{x^{2}})=25$ and $x>0$, then the value of $(x^{7}+\dfrac{1}{x^{7}})$ is$44853 \sqrt{3}$$44850 \sqrt{3}$$44859 \sqrt{3}$$44856 \sqrt{3}$

If $12^{12 x} \times 4^{24 x+12} \times 5^{2 y}=8^{4 z} \times 20^{12 x} \times 243^{3 x-6}$, where $x$, $y$ and $z$ are natural numbers, then $x+y+z$ equals

Teams $\text{A}, \text{B}$, and $\text{C}$ consist of five, eight, and ten members, respectively, such that every member within a team is equally productive. Working sepa...

In a school with $1500$ students, each student chooses any one of the streams out of science, arts, and commerce, by paying a fee of Rs $1100$, Rs $1000$ , and Rs $800$ ,...

In an arithmetic progression, if the sum of fourth, seventh and tenth terms is $99$ , and the sum of the first fourteen terms is $497$, then the sum of first five terms i...

Ankita walks from $\text{A}$ to $\text{C}$ through $\text{B}$, and runs back through the same route at a speed that is $40 \%$ more than her walking speed. She takes exac...

In a class of $150$ students, $75$ students chose physics, $111$ students chose mathematics and $40$ students chose chemistry. All students chose at least one of the thre...