List of top Questions asked in CAT- 2015

A and B can complete a task in 12 days, B and C in 15 days, A and C in 20 days. How many days will A alone take?
The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other number?
What is the remainder when \(3^{100}\) is divided by 7?
Four people A, B, C, D form two teams of two. A and B cannot be together, C and D cannot be together. Who is in the same team as A?

What is the probability of getting a sum of 7 when two dice are rolled? 
 

A bag contains 4 red, 3 white, and 2 blue balls. Two balls are drawn at random. What is the probability that both are red?
If \( \sin \theta + \cos \theta = \sqrt{2} \), what is \( \sin \theta \cos \theta \)?
A number when divided by 7 leaves a remainder of 4. What is the remainder when the square of the number is divided by 7?
A and B start a business with investments of Rs. 4000 and Rs. 6000. If the profit after 1 year is Rs. 5000, what is A’s share?
If \( 2x + 3y = 12 \) and \( x - y = 1 \), what is the value of \( x \)?
What is the sum of the first 20 terms of the arithmetic sequence 3, 7, 11, …?
A pipe can fill a tank in 6 hours, and another pipe can empty it in 8 hours. If both are opened together, how many hours will it take to fill the tank? (Enter the answer as a fraction or decimal.)
In a class, 60% of students are boys, and 40% are girls. If 30% of boys and 20% of girls passed an exam, what percentage of the class passed?
A man can row at 6 km/h in still water. If the river flows at 2 km/h and it takes him 1 hour to row to a place and return, what is the distance to the place?
If \( x^2 - 5x + 6 = 0 \), what is the sum of the roots?
The ratio of two numbers is 3:4. If their sum is 70, what is the larger number?
A train travels 360 km in 4 hours. What is its speed in km/h?
If \( \log_2 x + \log_2 (x - 2) = 3 \), what is \( x \)?
The area of a circle is 154 cm². What is its radius? (Use \( \pi = \frac{22}{7} \))
A car travels from A to B at 60 km/h and returns at 40 km/h. What is the average speed for the round trip?
The sum of the ages of a father and son is 50 years. Five years ago, the father’s age was four times the son’s age. What is the father’s current age?
A rectangle has an area of 60 cm² and a perimeter of 32 cm. What is the length if it is greater than the width?
A sum of Rs. 10,000 is invested at 5% per annum compound interest for 2 years. What is the total amount?
A shopkeeper sells an item at a 20% profit. If the cost price is increased by 10% and the selling price by Rs. 10, the profit percentage becomes 15%. What is the original cost price?
Course Enrollment
In a college, 120 students are enrolled in three courses: Math (M), Physics (P), and Chemistry (C).

- 70 take Math
- 60 take Physics
- 50 take Chemistry
- 30 take both Math and Physics
- 20 take both Physics and Chemistry
- 15 take both Math and Chemistry
- 10 take all three courses