Page 2 : Shobhit’s father wants to construct a rectangular garden using a brick wall on one'side of the garden and wire, fencing for the other three sides as shown in figure. He has 200 ft of wire fencing., , Pot Tn es PPT, , , , Based on the above information, answer the following questions., , (i) To construct a garden using 200 ft of fencing, we need to maximise its, (a) volume (b) area (c) perimeter (d) length of the side, , (ii) If x denote the length of side of garden perpendicular to brick wall and y denote the length of side parallel, to brick wall, then find the relation representing total amount of fencing wire., , (a) x+2y=150 (b) x+2y=50 (c) y+2x=200 (d) y+2x=100, (iii) Area of the garden as a function of x, say A(x), can be represented as, (a) 200 + 2x? (b) x-2x (c) 200x- 2 (d) 200-x, (iv) Maximum value of A(x) occurs at x equals, (a) 50 ft (b) 30 ft (c) 26 ft (d) 31 ft, (v) Maximum area of garden will be, (a) 2500 sq. ft (b) 4000 sq. ft (c) 5000 sq. ft (d) 6000 sq. ft, , ¢—__—, , The Government declare that farmers can get 300 per quintal for their, onions on 1* July and after that,the price will be dropped by 2 3 per, quintal per extra day. Shyam’s father has 80 quintal of onions in the field, on 1“ July and he estimates that crop is increasing at the rate of 1 quintal, per day., , Based on the above information, answer the following questions., , (i) If x is the number of days after 1* July, then price and quantity of, onion respectively can be expressed as, , (a) % (300 — 3x), (80 + x) quintals (b) % (300 — 3x), (80 - x) quintals, (c) % (300 + x), 80 quintals (d) None of these, , , , (ii) Revenue R as a function of x can be represented as, (a) R(x) = 3x2 - 60x - 24000 (b) R(x) = -3x2 + 60x + 24000, (c) R(x) = 3x7 + 40x — 16000 (d) R(x) = 3x - 60x - 14000

Page 3 : (iii) Find the number of days after 1* July, when Shyam’s father attain maximum revenue., , (a) 10 (b) 20 (c) 12 (d) 22, (iv) On which day should Shyam’s father harvest the onions to maximise his revenue?, , (a) 11" July (b) 20" July (©) 12 July (d) 224 july, (v) Maximum revenue is equal to, , (a) % 20,000 (b) = 24,000 (c) % 24,300 (d) % 24,700, , _g—___—, An owner of an electric bike rental company have determined that if they charge, customers % x per day to rent a bike, where 50 < x < 200, then number of bikes (),, they rent per day can be shown by linear function m(x) = 2000 — 10x. If they charge =, 50 per day or less, they will rent all their bikes. If they charge ~ 200 or more per day,, they will not rent any bike., , Based on the above information, answer the following questions., , , , (i) Total revenue R as a function of x can be represented as, , (a) 2000x - 10x (b) 2000x + 10x, , (c) 2000 - 10x (d) 2000 - 5x?, (ii) If R(x) denote the revenue, then maximum value of R(x) occur when x equals, , (a) 10 (b) 100 (c) 1000 (d) 50, (iii) At x = 260, the revenue collected by the company is, , (a) 710 (b) %500 (c) 70 (d) % 1000, , (iv) The number of bikes rented per day, if x = 105 is, (a) 850 (b) 900 (c) 950 (d) 1000, , (v) Maximum revenue collected by company is, (a) % 40,000 (b) % 50,000 (c) % 75,000 (d) = 1,00,000, , 9, Mr. Sahil is the owner of a high rise residential society, having 50 apartments. When he set rent at ¥ 10000/month,, all apartments are rented. If he increases rent by = 250/, month, one fewer apartment is rented. The maintenance, cost for each occupied unit is ¥ 500/month., , Based on the above information answer the following, questions., , (i) If Pis the rent price per apartment and N is the number, of rented apartment, then profit is given by, (a) NP (b) (N-500)P (c) N(P-500) (d) none of these, , , , (ii) Ifx represent the number of apartments which are not rented, then the profit expressed as a function of x is, (a) (50- x) (38+x) (b) (50 + x) (38- x) (c) 250(50—x) (38+x) (d) 250(50 + x) (38 - x)

Page 4 : (iii) If P= 10500, then N=, , (a) 47 (b) 48 (c) 49 (d) 50, (iv) If P = 11,000, then the profit is, (a) % 4,83,000 (b) %5,00,000 (c) %5,05,000 (d) %6,50,000, , (v) The rent that maximizes the total amount of profit is, (a) 11000 (b) 711500 (c) 715800 (d) 716500, , ——, , Western music concert is organised every year in the stadium that, can hold 36000 spectators. With ticket price of % 10, the average, attendance has been 24000. Some financial expert estimated, that price of a ticket should be determined by the function, , p(x) =15- so where x is the number of tickets sold., , Based on the above information, answer the following questions., , , , (i) The revenue, R as a function of x can be represented as, , , , x x x, a ss 5-—_ c) 15x- ee, (a) 15x 5000 (b) 1 3000 (c) 15x 5 (d) 15x 5000, (ii) The range of x is, (a) [24000, 36000] (b) [0, 24000} (c) [0, 36000] (d) none of these, (iii) The value of x for which revenue is maximum, is, (a) 20000 (b) 21000 (c) 22500 (d) 25000, (iv) When the revenue is maximum, the price of the ticket is, (a) %5 (b) 75.5 (c) 27 (d) 77.5, , (v) How many spectators should be present to maximize the revenue?, (a) 21500 (b) 21000 (c) 22000 (d) 22500, , , , ye, , A tin can manufacturer designs a cylindrical tin can for a company making sanitizer and, disinfector. The tin can is made to hold 3 litres of sanitizer or disinfector., , Based on the above in formation, answer the following questions., , (i) Ifrcm be the radius and h cm be the height of the cylindrical tin can, then the surface, area expressed as a function of ras, , (a) 2nr (b) 2nr +6000 (c) 2nr+ a (d) 2nr+ a, r r, , , , (ii) The radius that will minimize the cost of the material to manufacture the tin can is, , (a) 3 “ cm (b) , a cm (co), , , , cm (d) ./— cm, rT

Page 5 : (iii) The height that will minimize the cost of the material to manufacture the tin can is, , (a) 9 cm (b) 311500 ( pa (d) 2, 1500, TT rT rT wT, , - ~ 1500, (iv) If the cost of material used to manufacture the tin can is = 100/m? and 3 =z = 7.8, then minimum cost is, , approximately, (a) 711.538 (b) 712 (c) 713 (d) 714, (v) To minimize the cost of the material used to manufacture the tin can, we need to minimize the, (a) volume (b) curved surface area, (c) total surface area (d) surface area of the base, , _Q—___—, A poster is to be formed for a company advertisement. The, top and bottom margins of poster should be 9 cm and the, side margins should be 6 cm. Also, the area for printing the, advertisement should be 864 cm’., , Based on the above information, answer the following, questions., , (i) Ifacm be the width and b cm be the height of poster,, then the area of poster, expressed in terms of a and b, is, given by, (a) 648+ 18a+12b (b) 18a+12b, (c) 584+ 18a+12b (d) none of these, , , , (ii) The relation between a and b is given by, , , , , , , , , , 648+12b 12b 12b, =—_—_ b) a= = d f th, , (a) a bu18 (b) pin (c) a bai8 (d) none of these, , (iii) Area of poster in terms of b is given by, 126? 648b +126" 648b +1267 1267, ———— ee d, , @) b-18 ©) b-18 © b+18 @) b+18, (iv) The value of b, so that area of the poster is minimized, is, , (a) 54 (b) 36 (c) 27 (d) 22, (v) The value of a, so that area of the poster is minimized, is, , (a) 24 (b) 36 (c) 40 (d) 22, , ——_—_, , Nitin wants to construct a rectangular plastic tank for his house that can hold, 80 ft? of water. The top of the tank is open. The width of tank will be 5 ft but the, length and heights are variables. Building the tank cost 20 per sq. foot for the, base and @ 10 per sq. foot for the side., , Based on the above information, answer the following questions.