List of top Questions asked in CAT

What is the remainder when $7^{100}$ is divided by 8? 
 

A vessel has a milk solution in which milk and water are in the ratio 4:1. By addition of water to it, milk solution with milk and water in the ratio 4:3 was formed. On replacing 14 L of this solution with pure milk, the ratio of milk and water changed to 5:3. What is the volume of the water added?
Arrange the sentences to form a coherent paragraph:
A. It also fosters innovation.
B. Education empowers individuals.
C. It enables critical thinking.
D. Society benefits from educated citizens.
Find the incorrect usage of the word “TIME”.
The company's ___ approach led to success.
Choose the correct word: The policy had a ___ effect on growth.

What is the sum of the series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots$? 
 

In the figure below, \( \angle MON = \angle MPO = \angle NQO = 90^\circ \), \( OQ \) is the bisector of \( \angle MON \), and \( QN = 10 \), \( OR = 40/\sqrt{7} \). Find \( OP \).

A man invests Rs. 5000 at 6% simple interest per annum. How much interest will he earn in 3 years? 
 

What is the value of $\sqrt{50 + \sqrt{50 + \sqrt{50 + \ldots}}}$? 
 

If \( \log_x(a - b) - \log_x(a + b) = \log_x\left(\frac{b}{a}\right) \), find \( \frac{a^2 + b^2}{b^2 + a^2} \)

What is the sum of digits of $2^{10}$? 
 

The side of an equilateral triangle is 10 cm long. By drawing parallels to all its sides, the distance between any two parallel lines being the same, the triangle is divided into smaller equilateral triangles, each of which has sides of length 1 cm. How many such small triangles are formed?

A number when divided by 7 leaves a remainder of 4. What is the remainder when its square is divided by 7? 
 

What is the probability that a leap year has 53 Sundays? 
 

\( A, B, C \) can independently do a work in 15, 20, and 30 days respectively. They work together for some time after which \( C \) leaves. A total of ₹18000 is paid for the work and \( B \) gets ₹6000 more than \( C \). For how many days did \( A \) work?
Which sentence is grammatically incorrect?

A bag contains 4 red and 5 blue balls. Two balls are drawn without replacement. What is the probability that both are red? 
 

A solid sphere of radius 12 inches is melted and cast into a right circular cone whose base diameter is \( \sqrt{2} \) times its slant height. If the radius of the sphere and the cone are the same, how many such cones can be made and how much material is left out?
Identify the error: "The team are planning a meeting."
What is the antonym of "prolific"?

The sum of the first $n$ natural numbers is 55. What is $n$? 
 

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? 
 

Choose the grammatically correct sentence:

The ratio of ages of A and B is 3:4. After 6 years, their ages will be in the ratio 4:5. What is A's current age?