1.
In each of the questions given below which one of the five answer figures on the right should come after the problem figures on the left, if the sequence were continued ?

2. Which of the following is true?

3.

4. Find the sum of the following series;
$$\frac{2}{1!}+\frac{3}{2!}+\frac{6}{3!}+\frac{11}{4!}+\frac{18}{5!}+...$$

5. 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?

6. 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% 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 shareholders would be:

7. Sun Life Insurance Company issues standard,preferred, and ultra-preferred policies. Amongthe company’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?

8. 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 ‘x’ is the number of the people per trip.How many people per trip will make the marginal revenue equal to zero?

9. 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 $$\alpha,\beta,\gamma$$?

10. 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?

11. In how many ways can four letters of the word ‘SERIES’ be arranged?

12. 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.

13. 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.

14. Find the root of the quadratic equation $$bx^{2}-2ax+a=0$$

15. Three Professors Dr. Gupta, Dr. Sharma and Dr. Singh are evaluating answer scripts of a subject. Dr. Gupta is 40% more efficient than Dr. Sharma, who is 20% more efficient than Dr. Singh. Dr. Gupta takes 10 days less than Dr. Sharma to complete the evaluation work. Dr. Gupta starts the evaluation work and works for 10 days and then Dr. Sharma takes over. Dr. Sharma evaluates for next 15 days and then stops. In how man days, Dr. Singh can complete the remaining evaluation work.

16. If [x] is the greater integer less than or equal to ‘x’, then find the value of the following series $$[\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+[\sqrt{4}]+....+[\sqrt{360}]$$

17. What is the value of $$\sqrt{\frac{a}{b}}$$, If $$\log_{4}\log_{4}4^{a-b}=2\log_{4}(\sqrt{a}-\sqrt{b})+1$$

18. Three pipes A, B and C are connected to a tank. These pipes can fill the tank separately in 5 hours, 10 hours and 15 hours respectively. When all the three pipes were opened simultaneously, it was observed that pipes A and B were supplying water at 3/4th of their normal rates for the first hour after which they supplied water at the normal rate. Pipe C supplied water at 2/3rd of its normal rate for first 2 hours, after which it supplied at its normal rate. In how much time, tank would be filled.

19. The minimum value of $$3^{sinx}+3^{cosx}$$ is

20. In a B-School there are three levels of faculty positions i.e. Professor, Associate Professor and Assistant Professor. It is found that the sum of the ages of all faculty present is 2160, their average age is 36; the average age of the Professor and Associate Professor is 39; of the Associate Professor and Assistant Professor is $$32\frac{8}{11}$$; of the Professor and Assistant Professor is $$36\frac{2}{3}$$; Had each professor been 1 year older, each Associate Professor 6 years older, and each Assistant Professor 7 years older, then their average age would increase by 5 years. What will be the number of faculty at each level and their average ages?

21. $$\log_{5}{2}$$ is

22. In a square of side 2 meters, isosceles triangles of equal area are cut from the corners to form a regular octagon. Find the perimeter and area of the rectangular octagon.

23. The smallest perfect square that is divisible by 7!

24. A survey shows that 61%, 46% and 29% of the people watched “3 idiots”, “Rajneeti” and “Avatar” respectively. 25% people watched exactly two of the three movies and 3% watched none. What percentage of people watched all the three movies?

25. In a triangle ABC the length of side BC is 295. If the length of side AB is a perfect square, then the length of side AC is a power of 2, and the length of side AC is twice the length of side AB. Determine the perimeter of the triangle.

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