GATE CS 2024 Set 2 Q4 — General Aptitude

For positive real numbers $S$ and $K$, the function $H_{K}(S)$ is defined as: $H_{K}(S)=\max (S-K, 0)$. The max function is defined as: $$\max (a, b)=\left\{\begin{array}{ll} a, & \text{ when } a>b \\ b, & \text{ when } a \leq b \end{array}\right.$$ The graph below shows the plot of a function $N(S)$ versus $S$. $N(S)$ can be …

An unbiased six-faced dice whose faces are marked with numbers $1,2,3,4,5$, and $6$ is rolled twice in succession and the number on the top face is recorded each time. The probability that the number appearing in the second roll is an integer multiple of the number appearing in the first roll is $\_\_\_\_$

A day can only be cloudy or sunny. The probability of a day being cloudy is $0.5$, independent of the condition on other days. What is the probability that in any given four days, there will be three cloudy days and one sunny day?

The values of Stock $\text{A}$ and Stock $\text{B}$ on a particular day are Rs. $50$ and Rs. $80$, respectively. An investor invests Rs. $100$ in Stock $\text{A}$ and Rs. $80$ in Stock $\text{B}$. He sells all the stocks the next day when the value of Stock $\text{A}$ is Rs. $55$ and Stock $\text{B}$ is Rs. $70$. The profit made by …

Figures $\text{(i)}$ and $\text{(ii)}$ represent intercity highway systems. The black dots represent cities and the line segments between them represent intercity highways. A salesperson needs to make a trip. She needs to start from a city, visit each of the remaining cities exactly once, and finally return to the same city from which she started. Which …

An unbiased six-faced dice whose faces are marked with numbers $1,2,3,4,5$, and $6$ is rolled twice in succession and the number on the top face is recorded each time. The probability that the sum of the two recorded numbers is a prime number is $\_\_\_\_\_\_\_$