SECTION QA. Sol. (c); Let principle be x and time period is t months. Now, x + = 62100

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1 SECTION QA. Swam a SME enterprise borrowed a sum of money from a nationalized bank at 0% simple interest per annum and the same amount at 8% simple interest per annum from a microfinance firm for the same period. It cleared the first loan 6 months before the scheduled date of repayment and repaid the second loan just at the end of the scheduled period. If in each case it had to pay Rs. 600 as amount then how much money and for what time period did it borrow? (a) Rs. 5550, years (b) Rs.5500, years (c) Rs. 550,.5 years (d) Rs. 5550,.5 years Sol. (c); Let principle be and time period is t months. 0 (t 6) 8 t Then, + = + = On equating the first too, we get 0 (t - 6) = 8t Or 5t 0 = t t = 0 months i.e..5 years. 8 0 Now, + = = 550 Option (c).. A rectangular plank 0 metre wide, is placed symmetrically along the diagonal of a square of side 0 metres as shown in the figure. The area of the plank is: (a) 00( 0 ) sq. mt. (b) 00( 5 ) sq. mt. (c) 00 0 sq. mt. (d) None Sol. (a); A Q L P M B N S D AB = 0 AC = 0 OP = 0 O Area PQRS = 0 0 = 0 0 Required area = area PQRS area LAM R C

2 = = ( 0 ) = 0. Somesh, Tarun and Nikhil can complete a work separately in 5, 60 and 5 days. They started the work together but Nikhil left after 5 days of start and Somesh left days before the completion of the work. In how many days will the work be completed? (a) 5 (b) 50 (c) 5 5 (d) Sol. (a); M S T N S + T + N T S + T R T / W Total days = = 5. (+ 5 ) (+5) log e + (log e) (+ 5 ) + (log e) +!! (a) (b) (c) (d) 5 Sol. (b); e = !!! Or = e!!! The given series can be broken into two series log e (loge ) log...e e + + =!! = 5 log (5 log ) 5log + e + e +... = e e!! = 5 = = 0 + = Option (b). 5. If f() =, then find the value of f[f{f()}], at = 5 + (a) /9 (b) / (c) 5/ (d) 5/9 5 0 Sol. (b); f() = + 6 f = = f = = 6 + f (5) = 6

3 6. A Pharmaceutical company produces "two chemicals X and Y, such that X consists of 5% salt A and 0% salt B and Y consists of 0% salt A and6% salt B. For producing the chemicals X and Y, the company requires at least gm of Salt A and at least gm of Salt B. If chemical X costs Rs per gm and chemical Y costs Rs..80 per gm, what is the minimum cost at which the company can meet the requirement by using a combination of both types of chemicals? (a) Rs. 80 (b) Rs. 850 (c) Rs. 5 (d) None Sol. (a); Salt A Salt B X 5% 0% Y 0% 6% Let & y are the quantities of and y respectively. Then, 5 0y y And X+ y y 50 On solving, = 0 and y = 50 minimum cost required = = 80.. Sunte Company plans to manufacture a new product line of Razor net year and sell it at a price of Rs. per unit. The variable costs per unit in each production run is estimated to be 50% of the selling price, and the fied costs for each production run is estimated to be Rs. 50,00. "Based on their estimated costs how many units of the new product will company Y, Sunte need to manufacture and sell in order for their revenue to be equal to their total costs for each production run? (a) 500 (b) 00 (c) 800 (d) 00 Sol. (c); SP/unit = CP/unit = 6 (55% of SP) Let number of units be Then = Or = 800 Option (c). 8. In a certain sequence the term n is given by formula X n =5X n- - - X n- for n. What is the value of, if 0 = and (a) 6/ =? (b) / (c) / (d) None Sol. (a); n = 5n n Let n = = 5 0 = 5 = Let n = = 5 = 5 = 5 6 =

4 9. A mobile company that sells two models ACN-I and ACN-IT of mobile, reported that revenues from ACN-I in 06 were down % from 05 and revenue from ACN-II sales in 06 were up by 900 from 05. If the total revenues from sales of both the mobile models ACN-I and ACN-II in 06 were up by % froql05, what is the ratio of revenue from ACN-I sales in 05 to revenue from ACN-TI sales in 05? (a) 5: (b) :5 (c) : (d) None Sol. (b); ACN I ACN II Total y y y y From the given condition, 9y = or = + y y 5 ACN I in = = ACN II in If 06-8 is written as an integer in base 0 notation, what is the sum of digits in that integer? (a) 68 (b) 89 (c) 58 (d) 589 Sol. (d); 0 8 = 0 8 = = 99 and so on = 65 times Sum of digit = = 589 Option (d).. A flag pole on the top of a mall building is 5 m high. The height of the mall building is 5 m. To an observer at a height of00 m, the mall building and the pole subtend equal angle θ. 'If the horizontal distance of the observer from the pole is '', then what is the value of? (a) 0 0 m (b) 0 0 m (c) 5 5 m (d) None Sol. (d); A 5 B θ θ D 5 C θ E 5 In ADB, tanθ 00 & In CDE tanθ = tan θ Now, tanθ = tan θ 5 00 = 5

5 On solving, we get = 0 0. Option (b).. Witre Brown, an E-comrnerce company gives home delivery of its valuable products after receiving final order on their website by different modes of transportation like bike, scooter, tempo and truck. The probabilities of using bike, scooter, tempo and truck are respectively /9, /9,9 and 9. The probabilities of his delivering the product late to the destination by using these modes of transport are /5, /5, /5, and /5. If the product reach to the destination in time, find the probability that he has used scooter to reach the office; (a) /0 (b) /5 (c) /5 (d) None Sol. (c); Bike Scooter Tempo Truck Vehicle /9 /9 /9 /9 On time /5 /5 /5 /5 The required probability = = 5 Option (c).. A pest control person uses a particular machine for. his job, it moves along the circumference of a circular hall of radius 9 metres in 8 minutes to finish the pest control. How many minutes more will it take him to move along the-perimeter of a heagon of side. 5 metres? (a).69 minutes (b).6 minutes (c).00 minutes (d).8 minutes Sol. (a); Let the time required in II case is T. T 6 5 Then = 8 9 T = m,n. Hence, etra time needed = =.69 m,n. A premier B-school, which is in process of getting an AACSB accreditation, has 60 second year students. To incorporate sustainability into their curriculum, it has offered new elective subjects in the second year namely Green Supply Chain, Global Climate Change & Business and Corporate Governance. Twelve students have taken all the three electives, and 0 students have taken Green Supply Chain. There are twice as many students who study Green Supply Chain and Corporate Governance but not Global Climate Change & Business, as those who study both Green Supply' Chain and Global Climate Change & Business but not the Corporate Governance, and times as many who study all the three. students study Corporate Governance. There are students who could not muster up the courage to take up any of these subjects. The group of students who study 'both Green Supply Chain and Corporate Governance but not Global Climate Change & Business is eactly the same as the group made up of the students who study both Global Climate Change & Business and Corporate governance. How many students study Global Climate Change & Business only? (a) 6 (b) 0 (c) 5 (d) 88

6 Sol. (b); GSC 0 a GCC B y CG As per the given condition, = or = Also = y + y = 6 only CG = 8 6 = 8 Now, 0 + a + y + 8 = 60 a = 0 Option (b). 5. Ramesh and Sohan start walking away from each other from a point P at an angle of 0. Ramesh walks at a speed of km/hour while Sohan walks at a speed of km/hour. What is the distance between them after 90 minutes? (a) 9.89 km (b) 0.56km (c) 9. km (d). km Sol. (c); A.5 B 0 o 6 C Distance traveled by Ramesh =.5 =.5 km and that by sohan =.5 = 6km 6 Cos 0 o.5 + =.5 6 On solving, = 9. km 6. A chord AB of length cm is drawn in a circle of radius cm. Find the area of the shaded portion APB. (a) π cm (b) π cm (c) 80 69π 60 cm (d) 60 69π 60 cm 80

7 Sol. (c); The required area = area of sector area of triangle = π() π 60cm 60 Option (c).. Two tangents are drawn from a point P on the circle with centre at 0, touching the circle at point Q and T respectively. Another tangent AB touches the circle at point S. If angle QPT=55, find the angle AOB=? (a) 5 (b) 6.5 (c) 9.5 (d) 95 Sol. (b); QOA = AOS ( the triangles are congruent) = and also SOB = BOT = y QOT = + y o Now in PQOT, y + 90 = 60 o Or + y = 6.5 Option (b). 8. The coordinates of a triangle ABC are A(, 5), B(-, ), and C(0--); find the equation of the median AD? (a) -y+8=0 (b) 5-y+5=0 (c) +y-6=0 (d) -y+9=0 Sol. (d); A (,5) B (-, ) D C (0, -)

8 0 Coordinates of D are, =, Equation of AD is 5 ( y 5) = ( ) Or - y + 9 = 0 Option (d). 9. The Drizzle Pvt. Ltd., a squash company has cans of juice. The first contains 5% water and the rest is fruit pulp. The second contains 50% water and rest is fruit pulp. How much juice should be mied from each of the containers so as to get litres of juice such that the ratio of water to fruit pulp is :5? (a) 6 litres, 6 litres (b) litres, 8 litres (c) 5 litres, litres (d) 9 litres, litres Sol. (a); Water 8 Or An overhead tank, which supplies water to a settlement, is filled by three bore wells. First two bore wells operating together fill the tank in the same time as taken by third bore well to fill it. The second bore well fills the tank 0 hours faster than the first.one and 8 hours slower than the third one. The time required by the third bore well to fill the tank alone is: (a) 9 hours (b) hours (c) 8 hours (d) 0 hours Sol. (b); The question can be easily solved using options; Check option B M III I II I + II R 5 T 0 0 W 60 60