List of top Questions asked in CAT

A rectangle is drawn such that none of its sides has length greater than ‘\( a \)’. All lengths less than ‘\( a \)’ are equally likely. The chance that the rectangle has its diagonal greater than ‘\( a \)’ (in terms of %) is:
\( p \) is a prime and \( m \) is a positive integer. How many solutions exist for the equation \[ p^5 - p = (m^2 + m + 6)(p - 1)? \]
A certain number written in a certain base is 144. Which of the following is always true?
If \( (a^2 + b^2), (b^2 + c^2) \) and \( (a^2 + c^2) \) are in geometric progression, which of the following holds true?
If \( x \) is a real number and \( \lfloor x \rfloor \) is the greatest integer \( \leq x \), then \[ 3\lfloor x \rfloor + 2 - \lfloor x \rfloor = 0 \] Will the above equation have any real root?
If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \[ x^2 - 10x + 15 = 0, \] then find the quadratic equation whose roots are \( \left( \alpha + \frac{\alpha}{\beta} \right) \) and \( \left( \beta + \frac{\beta}{\alpha} \right) \).
What is the sum of all the 2-digit numbers which leave a remainder of 6 when divided by 8?
Let \( P = \{2, 3, 4, \ldots, 100\} \) and \( Q = \{101, 102, 103, \ldots, 200\} \). How many elements of \( Q \) are there such that they do not have any element of \( P \) as a factor?
Find the remainder when \( 2^{1040} \) is divided by 131.
If the roots of the equation \[ (a^2 + b^2)x^2 + 2(b^2 + c^2)x + (b^2 + c^2) = 0 \] are real, which of the following must hold true?
Choose the grammatically correct sentence:
Arrange the following sentences to form a coherent paragraph:
A. The startup grew rapidly in its first year.
B. It offered innovative tech solutions.
C. A young entrepreneur founded the startup.
D. Investors were impressed by its potential.
Choose the grammatically correct sentence:
A train travels 240 km in 4 hours. What is its speed in km/h?
The values of the numbers \(2^{2004}\) and \(5^{2004}\) are written one after another. How many digits are there in all?
If a = 2b and b = 3c, what is the ratio a:b:c?
A man works 8 hours a day for 5 days to earn Rs. 4,000. What is his hourly wage?
Vaibhav wrote a certain number of positive prime numbers on a piece of paper. Vikram wrote down the product of all the possible triplets among those numbers. For every pair of numbers written by Vikram, Vishal wrote down the corresponding GCD. If 90 of the numbers written by Vishal were prime, how many numbers did Vaibhav write?
If the sum of three consecutive integers is 24, what is the middle integer?
If the concentration of petrol in the second tank is 75% and the cost price of kerosene is half that of petrol, then what is Govind Lal's net profit percentage on selling the contents of the second tank given that he claims to sell the petrol at a profit of 25%?
A sum of Rs. 12,000 is lent at 6% simple interest for 4 years. What is the interest?
A car travels 300 km at an average speed of 60 km/h. How long does it take?
A sum of Rs. 5,000 is invested at 10% compound interest annually for 2 years. What is the total amount?
Choose the word closest in meaning to "Mundane":
Among the given five players, who scored the least number of runs in the 3rd match?