**Joint Management Entrance Test (JMET)** was an admission exam used by some institutes in India as the first step in the admission to postgraduate programs in management. Institutes which used the exams included Indian Institute of Science (IISc) and the IIT Schools of Management. The results of JMET were used to short-list the candidates for subsequent part of the selection process. In 2011 JMET was discontinued and replaced by Common Admission Test (CAT)

**1**

A student pedals from his home to college at a speed of 10 km/hr and back from the college to his home at 15 km/hr. What is the average speed?

**2**

A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the card and so he had the last possible credit card number. He was afraid of forgetting his PIN. He wrote down number 123 in his diary to remember his PIN. He also wrote out the way to calculate 123: "Multiply the card number by PIN. Divide the product by 997. The remainder is 123" Once. Prafull saw his diary in which Pinaki wrote this number 123. Prafull did a lot of purchasing, as he now knows Pinaki??s PIN. What is Pinaki's PIN?

**3**

Ajay loses 20 % of his money. After spending 80 % of the remainder, he is left with Rs. 4500. How much money (in rupees) did he have initially?

**4**

Out of 6 ruling and 5 opposition party members, 4 are to be selected for a delegation.

In how many ways can this be done so as to include exactly one ruling party member?

**5**

Out of 6 ruling and 5 opposition party members, 4 are to be selected for a delegation.

In how many ways can this be done so as to include at least one opposition member?