List of top Questions asked in CAT

A mixture has milk and water in the ratio 4:1. If 5 liters of water is added, the ratio becomes 2:1. Find the original milk quantity.
Find the distance between points (2, 3) and (5, 7).
In how many ways can 5 distinct letters be arranged in a circle?
The sum of the squares of three consecutive integers is 194. Find the integers.
A pipe fills a tank in 8 hours, another empties it in 12 hours. If both are opened, how long to fill?
If $2x + 3y = 15$ and $xy = 6$, find $x^2 + y^2$.
A rectangle has a perimeter of 50 cm and an area of 150 cm². Find its length.
A number is increased by 25 and then decreased by 25. What is the net percentage change?
A can complete a task in 15 days, B in 20 days. Together, how many days?
A bag has 5 red and 7 blue balls. Two balls are drawn without replacement. What is the probability both are red?
Find the number of ways to arrange 6 distinct books on a shelf if 2 specific books must be adjacent.
The ratio of ages of A and B is 3:5, and their sum is 64. What will be their age ratio after 5 years?
In a seating arrangement, 5 people (A, B, C, D, E) sit in a row. A and B must sit together, and C cannot sit at the ends. How many arrangements are possible?
The HCF of two numbers is 12, and their LCM is 144. If one number is 48, find the other.
A train travels 360 km at a uniform speed. If the speed increases by 6 km/h, it takes 1 hour less. Find the original speed.
A shopkeeper sells two items at Rs. 1000 each. On one, he gains 25, and on the other, he loses 20. What is his overall profit or loss percentage?
The sum of the first $n$ terms of an arithmetic progression is $2n^2 + n$. Find the 10th term.
A and B run a 1200m race. A gives B a 120m head start. A runs at 5 m/s, and B at 4 m/s. Who wins, and by how much time?
If $x^2 - 7x + 12 = 0$, what is the value of $x^3 - 4x^2 + 3x$?
An aquarium of size 100 cm × 80 cm × 60 cm is tilted along the 80 cm edge. Water spills until the water line reaches 1/3 of the base width. Find the height of water reduced when box is restored.
If the angle bisector of \( \angle P \) meets \( QR \) at point \( M \), find the length of \( PM \).
TV company makes 2 models A and B. - A takes 4 hrs to make, B takes 2 hrs
- Max 1000 hrs available
- Profit per unit: A → ₹1200, B → ₹800
- Want to maximize profit under constraints
Let P, Q, S, R, T, U and V represent the seven distinct digits from 0 to 6, not necessarily in that order. If PQ and RS are both two-digit numbers adding up to the three-digit number TUV, find the value of V.
There are five cards in a row with numbers from 1 to 100. Each adjacent pair must not differ by a multiple of 4. The remainder when each number is divided by 4 is written on a sixth card, in that order. How many different sequences can be written on the sixth card?
What percentage of the total information stored on paper media is taken up by Newspapers, Books, and Periodicals? Assume equal space per unit of information.