List of top Questions asked in CAT

The expression \((x \mathbin{£} y) + (x \mathbin{@} y))^2 - 2(x \mathbin{£} y)\) will be equal to:
Given \( a \) and \( b = a - b \); \( a \) and \( b \) but \( c = a + c - b \); \( a \) or \( b = b - a \); \( a \) but not \( b = a + b \); find 1 or (2 but not (3 or (4 and 5 but (6 but not (7 and (8 or 9)))))).
Given that \( x \mathbin{@} y = x - y \), then find \( (x \mathbin{\$} y) + (x \mathbin{£} y) \).
In the following question, four different sentences are given. Choose the option that contains the grammatically incorrect sentence/s. I. He is feeling that this relocation is nothing but the kick upstairs.
II. Consensus is now emerging at our state and national levels.
III. A more and more rigorous circle is formed from which one is more and more unlikely to escape.
IV. It happened up on a system that worked.
Given below are sentences, each using the question word "happen" in different ways. Identify the sentence which uses the question word in a grammatically incorrect manner.
Given below are sentences, each using the question word "gut" in different ways. Identify the sentence which uses the question word in a grammatically incorrect manner.
Given below is a paragraph whose last line is missing. Choose the line which completes the paragraph most logically from the options given below.
The real change in corporate culture began with the personal computer. With the PC, any empolyee could have a computer of his or her very own and use if for real work. It simplified applications that were cumbersome with a mainframe even without taking into account the problem of gaining access. A mainframe required a skilled programmer to do things that a non-technical user eventually could easily do with a spreadsheet on a PC. The forms and macros required to solve problems on PCs were trivial compared to traditional programming in COBOL or other computer languages.
Given below is a paragraph whose last line is missing. Choose the line which completes the paragraph most logically from the options given below.
So the unpleasant shocks that used to affect other people now affect us. Few of us have not been touched on the shoulder lightly or, in some cases, heavily, by the hand of failure. A dozen or more years ago, failure was for the untalented, or the unlucky. Today, no one is safe.
Given below is a paragraph whose last line is missing. Choose the line which completes the paragraph most logically from the options given below. The remake the world (including Nature), Fourier mobilised: an intolerance (for civilisation), a form (classification), a standard (pleasure), an imagination (the ‘scene’), a discourse (his book), all of which pretty well define the action of the signifier or the signifier in action. This action continually makes visible on the page a glaring lack, that of science and politics, that is, of the signified.
Rekha drew a circle of radius 2 cm on a graph paper of grid 1 cm × 1 cm. She then calculated the area of the circle by adding up only the number of full unit-squares that fell within the perimeter of the circle. If the value that Rekha obtained was 4 sq cm less than the correct value, then find the minimum possible value of d.
what is the minimum possible value of \(d\)?
Rekha drew a circle of radius 2 cm on a graph paper of grid 1 cm × 1 cm. She then calculated the area of the circle by adding up only the number of full unit-squares that fell within the perimeter of the circle. If the value that Rekha obtained was 4 sq cm less than the correct value, then find the minimum possible value of \(d\).
Auto fare in Bombay is ₹2.40 for the first 1 km, ₹2.00 per km for the next 4 km, and ₹1.20 for each additional km thereafter. Find the fare in rupees for \(k\) km (\(k \geq 5\)).
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%?

In the figure, \(O\) is the centre of the circle and \(AC\) is the diameter. The line \(FEG\) is tangent to the circle at \(E\). If \(\angle GEC = 52^\circ\), find the value of \(\angle E + \angle C\).

In the figure, \(\triangle ABC\) is equilateral with area \(S\). \(M\) is the mid-point of \(BC\), and \(P\) is a point on \(AM\) extended such that \(MP = BM\). If the semi-circle on \(AP\) intersects \(CB\) extended at \(Q\), and the area of a square with \(MQ\) as a side is \(T\), which of the following is true?

Let \(S_n\) denote the sum of the squares of the first \(n\) odd natural numbers. If \(S_n = 533n\), find the value of \(n\).
One morning, Govind Lal the owner of the local petrol bunk, was adulterating the petrol with kerosene. He had two identical tanks—the first was full of pure petrol while the second was empty. First, he transferred an arbitrary amount of petrol from the first tank into the second and then replaced the petrol removed from the first tank with kerosene. He then repeated this process one more time but this time he ensured that by the end of the process the second tank was exactly full.
Which of the following can be the concentration of petrol in the second tank?
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?
There are two water drums in my house whose volumes are in the ratio \(1 : 5\). Every day the smaller drum is filled first and then the same pipe is used to fill the bigger drum. Normally by 1:30 pm the smaller drum would just be full. But today, I returned early and started drawing water manually. I poured one-third into the smaller drum and the rest into the bigger drum. I continued this till the smaller drum was full. Immediately after that, I shifted the pipe into the bigger drum. If today the bigger drum was filled 12 minutes earlier than the normal time, when was the smaller drum full?
Two cars \(A\) and \(B\) start from two points \(P\) and \(Q\) respectively towards each other simultaneously. After travelling some distance, at a point \(R\), car \(A\) develops engine trouble. It continues to travel at \(2/3\)rd of its usual speed to meet car \(B\) at point \(S\) where \(PR = QS\). If the engine trouble had occurred after car \(A\) had travelled double the distance it would have met car \(B\) at a point \(T\) where \(ST = SQ/9\). Find the ratio of speeds of \(A\) and \(B\).
Let \( f_{n+1}(x) = f_n(x) + 1 \) if \( n \) is a multiple of 3; otherwise, \( f_{n+1}(x) = f_n(x) - 1 \).
If \( f_1(1) = 0 \), then what is \( f_{50}(1) \)?
Mohan’s fixed commission is ₹560 per assignment. Cost = ₹\(2n^2\), where \(n\) = number of chairs made. If average cost per chair ≤ ₹68, then minimum and maximum values of \(n\) are:
On a plate in the shape of an equilateral triangle \(ABC\) with area \(16\sqrt{3}\) sq cm, a rod \(GD\), of height 8 cm, is fixed vertically at the centre of the triangle. \(G\) is a point on the plate. If the areas of the triangles \(AGD\) and \(BGD\) are both equal to \(4\sqrt{19}\) sq cm, find the area of the triangle \(CGD\) (in sq cm).
The values of the numbers \(2^{2004}\) and \(5^{2004}\) are written one after another. How many digits are there in all?
Rajat draws a \(10 \times 10\) grid with squares numbered 1 to 100. He places two identical stones on any two separate squares. How many distinct ways are possible?