CAT 2022 Slot 1 Previous Year Questions with Detailed Solution

Let \(ABCD\) be a parallelogram such that the coordinates of its three vertices \(A, B, C\) are \((1, 1)\), \((3, 4)\) and \((-2, 8)\), respectively. Then, the coordinates of the vertex \(D\) are

The number of ways of distributing \(20\) identical balloons among \(4\) children such that each child gets some balloons but no child gets an odd number of balloons, is

A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio \(1 : 3\), then the ratio of lemon juice and sugar syrup in the new mixture is

For natural numbers \(x, y\), and \(z\), if \(xy + yz = 19\) and \(yz + xz = 51\), then the minimum possible value of \(xyz\) is

Let \(a, b, c\) be non-zero real numbers such that \(b^2 < 4ac\), and \(f(x) = ax^2 + bx + c\). If the set \(S\) consists of all integers \(m\) such that \(f(m) < 0\), then the set \(S\) must necessarily be

Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in \(10\) minutes while train B takes \(9\) minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

The average of three integers is \(13\). When a natural number \(n\) is included, the average of these four integers remains an odd integer. The minimum possible value of \(n\) is

Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is \(3 : 5\). If the total number of persons in the queue is less than \(300\), then the maximum possible number of persons standing ahead of Pinky is

Ankita buys \(4\) kg cashews, \(14\) kg peanuts and \(6\) kg almonds when the cost of \(7\) kg cashews is the same as that of \(30\) kg peanuts or \(9\) kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹\(1752\). She sells \(4\) kg of the mixture at this marked price and the remaining at a \(20\%\) discount on the marked price, thus making a total profit of ₹\(744\). Then the amount, in rupees, that she had spent in buying almonds is

The largest real value of \(a\) for which the equation \(|x + a| + |x - 1| = 2\) has an infinite number of solutions for \(x\) is