Recent questions tagged cat2025-set1

Comprehension:A train travels from Station $\text{A}$ to Station $\text{E}$, passing through stations $\text{B, C}$, and $\text{D}$, in that order. The train has a seatin...

Comprehension:A train travels from Station $\text{A}$ to Station $\text{E}$, passing through stations $\text{B, C}$, and $\text{D}$, in that order. The train has a seatin...

Comprehension:Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either ...

Comprehension:Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either ...

Comprehension:Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either ...

Comprehension:Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either ...

A value of $c$ for which the minimum value of $f(x)=x^{2}-4 c x+8 c$ is greater than the maximum value of $g(x)=-x^{2}+3 c x-2 c$, is$2$$\dfrac{1}{2}$$-\dfrac{1}{2}$$-2$

Shruti travels a distance of $224$ $\mathrm{km}$ in four parts for a total travel time of $3$ hours. Her speeds in these four parts follow an arithmetic progression, and ...

In a $3$-digit number $\mathrm{N}$, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. T...

Let $3 \leq x \leq 6$ and $\left[x^{2}\right]=[x]^{2}$, where $[x]$ is the greatest integer not exceeding $x$. If set $\mathrm{S}$ represents all feasible values of $x$, ...

Stocks $\text{A, B}$ and $\text{C}$ are priced at rupees $120, 90$ and $150$ per share, respectively. A trader holds a portfolio consisting of $10$ shares of stock $\text...

For any natural number $k$, let $a_{k}=3^{k}$. The smallest natural number $m$ for which $\left\{\left(a_{1}\right)^{1} \times\left(a_{2}\right)^{2} \times \ldots \times\...

The number of distinct integers $n$ for which $\log _{\left(\frac{1}{4}\right)}\left(n^{2}-7 n+11\right)>0$, is$2$infinite$1$$0$

The number of distinct pairs of integers $(x, y)$ satisfying the inequalities $x>y \geq 3$ and $x+y<14$ is

At a certain simple rate of interest, a given sum amounts to Rs. $13920$ in $3$ years, and to Rs. $18960$ in $6$ years and $6$ months. If the same given sum had been inve...

A container holds $200$ litres of a solution of acid and water, having $30 \%$ acid by volume. Atul replaces $20 \%$ of this solution with water, then replaces $10\%$ of ...

In a class, there were more than $10$ boys and a certain number of girls. After $40 \%$ of the girls and $60 \%$ of the boys left the class, the remaining number of girls...

A cafeteria offers $5$ types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of $4$ breads and opt for either small or large sized sandwich....

In the set of consecutive odd numbers $\{1,3,5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the el...

Arun, Varun and Tarun, if working alone, can complete a task in $24,21$, and $15$ days, respectively. They charge Rs. $2160$, $2400$, and Rs $2160$ per day, respectively,...

Kamala divided her investment of Rs. $100000$ between stocks, bonds, and gold. Her investment in bonds was $25 \%$ of her investment in gold. With annual returns of $10 \...

If $a-6 b+6 c=4$ and $6 a+3 b-3 c=50$, where $a, b$ and $c$ are real numbers, the value of $2 a+3 b-3 c$ is$20$$14$$18$$15$

The $(x, y)$ coordinates of vertices $\mathrm{P}, \mathrm{Q}$ and $\mathrm{R}$ of a parallelogram $\mathrm{PQRS}$ are $(-3,-2),(1,-5)$ and $(9,1)$, respectively. If the d...

In a circle with center $\operatorname{C}$ and radius $6 \sqrt{2} \mathrm{~cm}, P Q$ and $S R$ are two parallel chords separated by one of the diameters. If $\angle P Q C...

The ratio of the number of students in the morning shift and afternoon shift of a school was $13: 9$. After $21$ students moved from the morning shift to the afternoon sh...

If the length of a side of a rhombus is $36$ $\mathrm{cm}$ and the area of the rhombus is $396$ $\mathrm{sq}. \mathrm{cm}$, then the absolute value of the difference betw...

The number of non-negative integer values of $k$ for which the quadratic equation $x^{2}-5 x+k=0$ has only integer roots, is

A shopkeeper offers a discount of $22 \%$ on the marked price of each chair, and gives $13$ chairs to a customer for the discounted price of $12$ chairs to earn a profit ...