**1**

Find the sum of the following series;

\({2\over 1!}+{3\over 2!}+{6\over 3!}+{11\over 4!}+{18\over5!}+....\)

**2**

How many positive integers 'n' can we form using the digits 3, 4, 4, 5, 6, 6, 7 if we want 'n' to exceed 6,000,000?

**3**

A Techno company has 14 machines of equal efficiency in its factory. The annual manufacturing costs are Rs. 42,000 and establishment charges are Rs. 12,000. The annual output of the company is Rs. 70,000. The annual output and manufacturing costs are directly proportional to the no. of machines. The share holders get 12.5% profit, which is directly proportional to the annual output of the company. If 7.14% machines remain closed throughout the year, then the percentage decrease in the amount of profit of the share holders would be:

**4**

Sun Life Insurance Company issues standard, preferred, and ultra-preferred policies. Among the company's policy holders of a certain age, 50% are standard with a probability of 0.01 of dying in the next year, 30% are preferred with a probability 0.008 of dying in the next year, and 20% are ultra-preferred with a probability of 0.007 of dying in the next year. If a policy holder of that age dies in the next year, what is the probability of the deceased being a preferred policy holder?

**5**

A metro train from Mehrauli to Gurgoan has capacity to board 900 people. The fare charged (in RS.) is defined by the function

*f = \({(54 - {x\over 32})^2}\)*

where 'x' is the number of the people per trip. How many people per trip will make the marginal revenue equal to zero?