GATE EC 2016 Question Paper (30-Jan-2016) (Shift 1)

A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?

In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong. Which of the following inference(s) is/are logically valid and can be inferred from the above passage?

(i) His friends were always asking him to help them.

(ii) He felt that when in need of help, his friends would let him down.

(iii)He was sure that his friends would help him when in need.

(iv) His friends did not help him last week.

Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does. Which one of the following statements must be TRUE based on the above?

If ${\mathrm{q}}^{-\mathrm{a}}=\frac{1}{\mathrm{r}}$ and ${\mathrm{r}}^{-\mathrm{b}}=\frac{1}{\mathrm{s}}$ and ${\mathrm{S}}^{-\mathrm{c}}=\frac{1}{\mathrm{q}}$, the value of abc is _______

P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?