List of top Questions asked in CAT

Let $x$, $y$, and $z$ be real numbers satisfying
\(4(x^2 + y^2 + z^2) = a,\)
\(4(x - y - z) = 3 + a.\)
Then $a$ equals ?
Suppose $x_1, x_2, x_3, \dots, x_{100}$ are in arithmetic progression such that $x_5 = -4$ and $2x_6 + 2x_9 = x_{11} + x_{13}$. Then, $x_{100}$ equals ?
The terms \(x_5 = -4\), \(x_1, x_2, \dots, x_{100}\) are in an arithmetic progression (AP). It is also given that \(2x_6 + 2x_9 = x_{11} + x_{13}\). Find \(x_{100}\).
In a group of 250 students, the percentage of girls was at least 44% and at most 60%. The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70% of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are
After two successive increments, Gopal's salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was
The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is
Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
An item is sold with a profit of \(40\%\). If the cost price is reduced by \(40\%\) and Rs. \(5\) are also reduced from it, then the profit will be increased to \(50\%\). Find the final cost price.
A bus leaves the bus stand at 9 am and travels at a constant speed of 60 km/h. It reaches its destination 3.5 hours later than its original time. The next day, it travels \( \frac{2}{3} \) of its route within \( \frac{1}{3} \) of its initial time and travels the rest of the route within 40 minutes. At what time does it reach its destination normally?
Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is
When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become
\( 10^{68} \) is divided by 13, the remainder is  is
Consider two sets A = {2, 3, 5, 7, 11, 13} and B = {1, 8, 27}. Let f be a function from A to B such that for every element b in B, there is at least one element a in A such that f(a) = b. Then, the total number of such functions f is
For any non-zero real number x, let\( f(x) + 2f\left(\frac{1}{x}\right) = 3x.\)Then, the sum of all possible values of x  for which f(x) = 3, is
Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is
A container has a mixture of acid and water. If 2 liters of water are added, the acid content reaches 50%. After adding 18 liters of acid, the acid content increases to 80%. What was the initial acid to water ratio in the container?
A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is
A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was
If \( x \) and \( y \) satisfy the equations
\(|x| + x + y = 15 \quad \text{(1)},\)
\(x + |y| - y = 20 \quad \text{(2)}.\)
Find the value of \( x - y \).
\(\sqrt{x + 6\sqrt{2}} - \sqrt{x - 6\sqrt{2}} = 2\sqrt{2}.\)
Find \( x \).
\(3^{3333}\) divided by 11, then the remainder would be?
The number of all positive integers up to 500 with non-repeating digits is
One direct question from the Number System was 10 to the power 100 divided by seven, candidates had to choose the correct answer for the problem.
For any natural Number 'n', let an be the largest number not exceeding \(\sqrt{n}\) , then a1 + a2 + a3... +a50 =
The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
John Cleese told Fox News Digital that comedians do not have the freedom to be funny in 2022. “There’s always been limitations on what they’re allowed to say,” Cleese said. “I think it’s particularly worrying at the moment because you can only create in an atmosphere of freedom, where you’re not checking everything you say critically before you move on. What you have to be able to do is to build without knowing where you’re going because you’ve never been there before. That’s what creativity is — you have to be allowed to build. And a lot of comedians now are sitting there and when they think of something, they say something like, ‘Can I get away with it? I don’t think so. So and so got into trouble, and he said that, oh, she said that.’ You see what I mean? And that’s the death of creativity.”