CAT 2022 Slot 2 Previous Year Questions with Detailed Solution

In triangle \(ABC\), altitudes \(AD\) and \(BE\) are drawn to the corresponding bases. If \(\angle BAC = 45^\circ\) and \(\angle ABC = \theta\), then \(\dfrac{AD}{BE}\) equals

Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio \(5 : 8 : 10\). They accept a job which they can finish in \(4\) days if they all work together for \(8\) hours per day. However, Anu and Tanu work together for the first \(6\) days, working \(6\) hours \(40\) minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is

Regular polygons \(A\) and \(B\) have number of sides in the ratio \(1 : 2\) and interior angles in the ratio \(3 : 4\). Then the number of sides of \(B\) equals

If \(a\) and \(b\) are non-negative real numbers such that \(a + 2b = 6\), then the average of the maximum and minimum possible values of \((a + b)\) is

Manu earns ₹\(4000\) per month and wants to save an average of ₹\(550\) per month in a year. In the first nine months, his monthly expense was ₹\(3500\), and he foresees that, tenth month onward, his monthly expense will increase to ₹\(3700\). In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be

There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is

On day one, there are \(100\) particles in a laboratory experiment. On day \(n\), where \(n \geq 2\), one out of every \(n\) particles produces another particle. If the total number of particles in the laboratory experiment increases to \(1000\) on day \(m\), then \(m\) equals

The average of a non-decreasing sequence of \(N\) numbers \(a_1, a_2, \ldots, a_N\) is \(300\). If \(a_1\) is replaced by \(6a_1\), the new average becomes \(400\). Then, the number of possible values of \(a_1\) is

Let \(r\) and \(c\) be real numbers. If \(r\) and \(-r\) are roots of \(5x^3 + cx^2 - 10x + 9 = 0\), then \(c\) equals

Suppose for all integers \(x\), there are two functions \(f\) and \(g\) such that \(f(x) + f(x - 1) - 1 = 0\) and \(g(x) = x^2\). If \(f(x^2 - x) = 5\), then the value of the sum \(f(g(5)) + g(f(5))\) is