Instructions

For the following questions answer them individually

Question 1

You travel by Delhi Metro every day from Botanical Garden, Noida to Hauz Khas, Delhi. At Hauz Khas metro station, you use an escalator to get out of the station. The escalator takes 80 seconds to get you down. One day, the escalator was not working and you walk up the escalator in 50 seconds. How many minutes does it approximately take you to walk up the working escalator?

Question 2

If $$x=8-\sqrt{32}$$ and $$y=2+\sqrt{2}$$, then $$\left(x+\frac{1}{y}\right)^2$$ is given by:

Question 3

If the co-ordinates of orthocentre and the centroid of a triangle ABC are (—5, 7) and (5, 5), then the circumcentre of the triangle ABC is :

Question 4

Consider a cuboidal underground tunnel of length 500 m whose cross-section is given in the figure. If $$1 m^3$$ of concrete costs 1000 rupees, find the amount of money needed to build the Tunnel.

Question 5

In $$\triangle MNL$$,line NP bisects the angle MNL. If NP : NL=2: 3 and angle MNL=$$120^\circ$$. Then NP: NL: MN is:

Question 6

A group of women in a society decided to execute interior and exterior decoration of the society in a week’s time. Since 11 women dropped out every day from the second day, the entire decoration was completed on $$12^{th}$$ day. How many women participated at the beginning ? (Answer to the nearest integer)

Question 7

Joseph is in a dilemma. He has been offered a job which would pay him ₹ 80,000 per month for first three years and ₹ 1,20,000 per month for the next three years, and ₹ 1,50,000 per month for the remaining four years. He has also been offered an MBA at a prestigious place and he is considering whether to accept the job or go for the MBA. The first year tuition fee for the MBA program is ₹ 16,00,000 and the second year tuition fee for the MBA program is ₹ 20,00,000. After MBA, he'll get a salary of ₹ 2,00,000 per month for the first four years and then ₹ 2,50,000 per month for the remaining four years. What will be the approximate percentage gain for Joseph in opting for the MBA instead of the job in the 10 years horizon considering no discounting of money ?

Question 8

AB is the tangent on the circle at point A. The line BC meets the circle at points C and E. Line AD bisects the angle EAC. If angle EAC = $$60^\circ$$ and angle BAC : angle ACB = 2: 5. Find angle ABC :

Question 9

KBC restaurant chain regularly conducts survey of its customers. The customers are asked to rate the food quality, service and price as Excellent, Good and Fair. Customers are also asked whether they would comeback. It was foundthat 76% of customers say that they will come back. Amongst those whosay that they will come back, 57% rate the restaurant as Excellent, 36% rate it as Good and remainderrate it as Fair. Of those whosay that they will not return, the respective values are 14%, 32% and 54%. What percentage of customers rated the restaurant as good ?

Question 10

Four couples are to be seated in a circular table such that each couple sits together. In how many ways they can sit such that two males sit to the right of their female partners and the other two males sit to the left of their female partners ?