IAS 2023 — CSAT Maths

Three variables x, y and z take values 2, 3, 4 or 5 such that their values are always distinct. If M and N denote the largest possible value and the smallest possible value, respectively, for the expression \(\{(x \times y) + z\}\); then \(M - N\) is

Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to \(x^2\) and x is inversely proportional to z. For \(z = \dfrac{7}{25}\), the values of x and y are 5 and 50, respectively. If \(y = 98\), what is z equal to?

For \(\dfrac{1}{3} < x < y < 2\), which of the following statements is/are always correct? 1. \(x + \dfrac{1}{x} < y + \dfrac{1}{y}\) 2. \(\dfrac{\sqrt{1+y^2}}{y} < \dfrac{\sqrt{1+x^2}}{x}\) Select the answer using the code given below.

What is the minimum number of times one needs to measure to get 298 litres of water from a tank, if the measuring cylinders have capacities 1 litre, 6 litres, 25 litres and 100 litres?

In an objective type question paper, 5 marks are awarded for a correct answer and 2 marks are deducted for a wrong answer. A student attempted all the questions and got a score of 69. Had he been awarded 4 marks for a correct answer and 1 mark deducted for a wrong answer, he would have scored 84. How many questions were there in the question paper?