Recent questions tagged cat2023-set1

Let $n$ be the least positive integer such that $168$ is a factor of $1134^{n}$. If $m$ is the least positive integer such that $1134^{n}$ is a factor of $168^{m}$, then ...

The number of integer solutions of equation $2|x|\left(x^{2}+1\right)=5 x^{2}$ is

The equation $x^{3}+(2 r+1) x^{2}+(4 r-1) x+2=0$ has $-2$ as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of $r...

Let $\alpha$ and $\beta$ be the two distinct roots of the equation $2 x^{2}-6 x+k=0$, such that $(\alpha+\beta)$ and $\alpha \beta$ are the distinct roots of the equation...

In an examination, the average marks of $4$ girls and $6$ boys is $24$. Each of the girls has the same marks while each of the boys has the same marks. If the marks of an...

The minor angle between the hours hand and minutes hand of a clock was observed at $8:48$ am. The minimum duration, in minutes, after $8.48$ am when this angle increases ...

A mixture $\mathrm{P}$ is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again remove...

Gita sells two objects $\text{A}$ and $\text{B}$ at the same price such that she makes a profit of $20 \%$ on object $\text{A}$ and a loss of $10 \%$ on object $\text{B}$...

Arvind travels from town $\text{A}$ to town $\text{B}$, and Surbhi from town $\text{B}$ to town $\text{A}$, both starting at the same time along the same route. After mee...

Anil invests Rs. $22000$ for $6$ years in a certain scheme with $4 \%$ interest per annum, compounded half-yearly. Sunil invests in the same scheme for $5$ years, and the...

A quadrilateral $A B C D$ is inscribed in a circle such that $A B: C D=2: 1$ and $B C: A D=5: 4$. If $A C$ and $B D$ intersect at the point $E$, then $A E: C E$ equals$2:...

In a right-angled triangle $\triangle A B C$, the altitude $A B$ is $5 \mathrm{~cm}$, and the base $B C$ is $12 \mathrm{~cm} . P$ and $Q$ are two points on $B C$ such tha...

For some positive and distinct real numbers $x, y$ and $z$, if $\frac{1}{\sqrt{y}+\sqrt{z}}$ is the arithmetic mean of $\frac{1}{\sqrt{x}+\sqrt{z}}$ and $\frac{1}{\sqrt{x...

A lab experiment measures the number of organisms at $8$ am every day. Starting with $2$ organisms on the first day, the number of organisms on any day is equal to $3$ mo...

Faculty members in a management school can belong to one of four departments - Finance and Accounting $\text{(F&A)}$, Marketing and Strategy $\text{(M&S)}$, Operations an...

Faculty members in a management school can belong to one of four departments - Finance and Accounting $\text{(F&A)}$, Marketing and Strategy $\text{(M&S)}$, Operations an...

Faculty members in a management school can belong to one of four departments - Finance and Accounting $\text{(F&A)}$, Marketing and Strategy $\text{(M&S)}$, Operations an...

Faculty members in a management school can belong to one of four departments - Finance and Accounting $\text{(F&A)}$, Marketing and Strategy $\text{(M&S)}$, Operations an...

Faculty members in a management school can belong to one of four departments - Finance and Accounting $\text{(F&A)}$, Marketing and Strategy $\text{(M&S)}$, Operations an...

The schematic diagram below shows $12$ rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are loca...

The schematic diagram below shows $12$ rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are loca...

The schematic diagram below shows $12$ rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are loca...

The schematic diagram below shows $12$ rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are loca...

The schematic diagram below shows $12$ rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are loca...

A visa processing office $\text{(VPO)}$ accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twen...

A visa processing office $\text{(VPO)}$ accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twen...

A visa processing office $\text{(VPO)}$ accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twen...

A visa processing office $\text{(VPO)}$ accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twen...

A visa processing office $\text{(VPO)}$ accepts visa applications in four categories - US, UK, Schengen, and Others. The applications are scheduled for processing in twen...

Five restaurants, coded $\text{R1, R2, R3, R4}$ and $\text{R5}$ gave integer ratings to five gig workers - Ullas, Vasu, Waman, Xavier and Yusuf, on a scale of $1$ to $5$....

Five restaurants, coded $\text{R1, R2, R3, R4}$ and $\text{R5}$ gave integer ratings to five gig workers - Ullas, Vasu, Waman, Xavier and Yusuf, on a scale of $1$ to $5$....

Five restaurants, coded $\text{R1, R2, R3, R4}$ and $\text{R5}$ gave integer ratings to five gig workers - Ullas, Vasu, Waman, Xavier and Yusuf, on a scale of $1$ to $5$....