Instructions

For the following questions answer them individually

Question 1

Find the sum of the following series;

$$\frac{2}{1!}+\frac{3}{2!}+\frac{6}{3!}+\frac{11}{4!}+\frac{18}{5!}+...$$

Question 2

How many positive integers â€˜nâ€™ can we form using the digits 3, 4, 4, 5, 6, 6, 7 if we want â€˜nâ€™ to exceed 6,000,000?

Question 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 shareholders get 12.5%Â of the total profit which is equal to the total output minus the total cost. If 7.14% of machines remain closed throughout the year, then the percentage decrease in the amount of profit of the shareholders would be:

Question 4

Sun Life Insurance Company issues standard,preferred, and ultra-preferred policies. Amongthe companyâ€™s policy holders of a certain age,50% are standard with a probability of 0.01 ofdying in the next year, 30% are preferred with aprobability 0.008 of dying in the next year, and20% are ultra-preferred with a probability of0.007 of dying in the next year. If a policy holderof that age dies in the next year, what is theprobability of the deceased being a preferredpolicy holder?

Question 5

A metro train from Mehrauli to Gurgoan has capacity to board 900 people. The fare charged (in RS.) is defined by the function $$f=(54-\frac{x}{32})^{2}$$ where â€˜xâ€™ is the number of the people per trip.How many people per trip will make the marginal revenue equal to zero?

Question 6

If each $$\alpha,\beta$$ and $$\gamma$$ is a positive acute angle such that $$Sin(\alpha+\beta-\gamma)=\frac{1}{\sqrt{2}},Cosec(\beta+\gamma-\alpha)=\frac{2}{\sqrt{3}}$$ and $$tan(\gamma+\alpha-\beta)=\frac{1}{\sqrt{3}}$$. What are the values of $$\alpha,\beta,\gamma$$?

Question 7

Shyam, Gopal and Madhur are three partners in a business. Their capitals are respectively Rs 4000,Rs 8000 and Rs 6000. Shyam gets 20% of total profit for managing the business. The remaining profit is divided among the three in the ratio of their capitals. At the end of the year, the profit of Shyam is Rs 2200 less than the sum of the profit of Gopal and Madhur. How much profit, Madhur will get?

Question 9

The area of a triangle is 6, two of its vertices are (1, 1) and (4, -1), the third vertex lies on y = x + 5. Find the third vertex.

Question 10

A small confectioner bought a certain number of pastries flavoured pineapple, mango and black-forest from the bakery, giving for each pastry as many rupees as there were pastry of that kind;altogether he bought 23 pastries and spent Rs.211; find the number of each kind of pastry that he bought, if mango pastry are cheaper than pineapple pastry and dearer than black-forest pastry.