A. Activities : (1) From the following information, find n(MUPUC)', if n(X) = 100. Solution : (2) From the following representation, write (i) domain (ii) co-domain (iii) range of R (iv) the formula (Relation between x and y) where x € A = {1, 2, 3, 4, 5, 6} and ye A= {l, 2, 3, 4, 5, 6} Solution : -oy [s ae ‘| fink GB) WUe(¥lxreN tL sxs 12}, A= {1 4 7, 10}, B= {2, 4, 6, 7, 11, CO = {3,'5; 8,9, 12), complete the following activity Given : A = zy 24 n U B. Solve the following : Q 1. Ina hostel, 25 students take tea, 20 students take coffee, 15 students take milk, 10 student take both tea and coffee, 8 students take both milk and coffee. None of them take tea and milk and everyone takes at least one beverage. Find the number of students in the xT hostel. Solution; -+-+-bat. uSch..of ot sakQ 2. Write the domain and range of the following relations Q) {@b),ae Nias bandh 4) Gi) {abl abe Nat b= 12) am) {Q2. 4), Q. 5), 2.6), (2.7) Solution Cid Demstys Fi a sre a Fone > 1 ak GR Donen SLU EES ELE IG Povye - { Wed t, LES Be, 1% Q 3. IfA= {1, 2, 3}, B = {4, 5, 6}, which of the following are relations from A to B ? (i) Ry= (0, 4). C, 5), A, 6} (i) R, = {d, 5), @ 4), B, 6} (ii) R,= (1, 4). (1, 5), G, 6), 2, 6), GB, 4)} (iv) R= (4, 2), 2, 6), 6, D2, 4)} AVENE L(A) GS) 6% sepa gle felakin, Bais te 2 (C45) Bob)... Q26),.84N - i pee ma 3y.g.etdien dite Ae B Gv) {ee Gy, e453 72% ne : $ 2.) eta] bl Gori fr Ray tn al aeons Bo Ge) cha Fe a—~< 2. Partition Values 7 Activities : The height of the students of a college are given below. es - ST Toa Height of stu- | 160 -| 164 -| 168 - 172 -| 176 -| 180) 184 -| dents (in ems) | 163 | 167 | 171| 175 | 179 | 183 |_187_ No. ofstudents | 22 | 80 | 98 | 48 | 104| 43 | 5_ Calculate the height of student such that 75 % students have heights below it. To find [Q, _| Height of students CL f_| Less than Cy; 160-163 159.5 — 163.5 22 22 164-167 163.5 — 167.5 80 yor 168-171 167.5 - [3-5 98 200 172-175 fars)-(ass)| 48 jor-[248] + 176-179 ass ]- [tas || 4= 104 352 180-183 aes |-(ass | 43 345 184-187 183.5 — 85 5 400 Here N = 5 f=[4e0 re Q, = value of [3 =|) observation = value of | 3 (48°) | observation = value of 300® observation The required class is L= [i955 Cf =[24@ Lh=4 N=[4e0 }f=[lo4 h(3N Q=Lt (Bc. = 1755 + t](s00- Q = 1755 + SE l(a00 [zag] =|[t4e-5 | + 7 52) beg} 1755 +[ 22. Caleulate D, and BP), for the following Clr 295) 28-20] 30- 45) 35 20-25] | | i i +" 2 | s & | iP vess than | | | 2 ] | 1s | 29 oh I! ; (ad N=Xf=[50 i. D, = value of 1 (s) observation = value of |[/q |) =2.|| observation fc = value of 45 r observation AO AO AS AS 50) 50-55 w | 7 6 7 [44] 50 The required class is{ So |-| 55 Toot ie | hls 7 nine D,=L+ 2 10 of 5 = eo] + Ll 6 = 50 + ex 1 = 50 + | 0°33 = 50.83 a ii. P,, = value of |[13]| || observation loo 1h = value of nf = observation 100 = value of [5 }" observation The required class is (2s | - [39 - i~L2s] eas B. Solve the following : sticul 1. The number of ATM transactions per day te A a la6 _ location in a certain city are as follows, ‘is 0, 13, 65, 30, 75, 60, 49, 5. Calculate D,, Q, ant " . 0, 49, 58, 72, 55. Cale , eat cabin 34 5..5.%.,60.6S, FEAL Solution ; 2. Graphically find the values data. of Median, D, and P,, for the given“10 of oo. | 70 - | 80 - ]90 -| 100 - [110 - [120 - : Students | _ 69 79 Ro 99 109 Wo 129 No. of |, i § ZZ 3 a 4 | Students ' i : a a SCALE! : On fe drag 300 2 Gm = ley teil | lotta ue) tow je leep | DA ce aa fs rlhow Gorin. hy. ahh ods Mee Samtl ah seta. Got roms oy prtnend Meats 30, thy 3. Daily wages for a group of 100 workers are given below. If D, = 110, calculate the missing frequencies. Daily wages in] 0- | 50-] 100- | 7 | 200 - z so | 100 | 150 250 No. of workers | 7 | 2 | 2s | 30 | 2we ep te [ass ae] Woe low SF Jo bet BE. S85 405) [lo TAs. = > O23a-s4 => St A8- je = .G 28-99 Pbrnd [$4b= 389 a a E macaseng fatten are 19 4 20 A 4. Given below is the distribution of a sample of students appearing at a C.A. examination, Help C.A. board to decide cut off marks for qualifying the examination when 3% student pass the examination. Mois 0- | 100- | 200- | 300- | 400- | 500- 100 | 200 | 300 | 400 | 500 | 600 [No. of Students | 130 | 150_| 190 220 | 280 | 130 Solution : Jes mnie ened -meyke dae anlidgpng atest toto, : when... coplandendp-cpadp Oh haus de Big Pad + = ceases Sha Ska Bom cmbeben, Grape deot Bag] Sect \2e0 AZo ato | S42 E Ate=ed ~ - Wow eG co Rp SAE. : te cubation fe for: spratidgsng. 28. ctrobeinalisn, a sis:A. a) (2) Activities : Consider the following geometrical representation 7 aT 2 2 “3; . 3 os —r 22 4 p07. > 46 ” 10 2 Where : A = {1, 2, 3, 4} B= (1-3, 5, 7 10) C = {-2, 6, 22, 46, 97, 100} and FS:ASB gi: BoC xeA, yeBzeC (i) The relation between x and y is Y= [e1 (ii) The relation between y and z is z= [yes seaees (iii)z = [22-7] -3 (Express z in terms of x) If fx) = = and g(x) = 8x + 5, find f [gx)] and gfftx)] by completing the following activity F tgeyj= 5 [bx+5-5 gx = = ae ~ Afx)] = 8 fx) + 5 8] + What can you conclude from f [g(x)] and AMx)] ? oe see corte Re de Comet. Sauntge,.Panckan,(3) Check whether the following relations are functions, (a) = Sree bOI Solution : Solution : ----- PM. ye eccceseeeeneeeeeseeresesesserssenieneeerteeaticeesgensesessesntesB. Solve the following : 1. Which sets of ordered pairs represent functions from A= {1, 2, 3, 4} to B= { -1, 0, 1, 2, 3}? Justify. (a) {(1, 0), @, 3), 2, -D, 4 D, @ 2} Solution Cn AD ee ee 7 coven Rte LRA are dpa gts (>) {(, 2), 2 -1), GD, 4 3} Solution : () (0, 3), 4 D, @ 2)} Solution : map Qaeg Re ye pyagaig eetWt DQ. QD. Dy Solution © xpd a ceeds fe feaforns | Samoa nnd wel fh hoa ts Te dA ed BURLY AIO de AL 2. Find x, if lx) = g(x) where M+ 28, gx) = 1? 3 Inter FS, xed, verify whether (fof) (x) = x yy Remy\ eS Activitic Find the Age No. of workers (f) 5 ; ae! Lessthanes. | 45 | 65 | 125 | 155 | 170 pst range and Q.D. for the following data. 1 95 | 30 40 | 45 (years) (x) 15 25 i, Largest value (L) = [ 45 Smallest value (S) = 20 Range = L-S=45 -[2e ]=[25 ] ii. For QD, we need to find Q and | Q, Q th = Value of (2 observation = Value of | \9¢ ay ® observation 2S jth Q, = Value of [ my observation QD =F a Value of qa re observation Q = [3as | Find the mean and variance of the first n natural numbersw i. Mean Mean (x) FF Zz @) - a 14+2434.40 _ n a)vy ’ ii, Variance Vw = —-(%) (set) froaa](2m+t) (nt) 6 (4) eye n+l) on) it peta 2 6 = (tn-1) _w-1 12esee2 The first group has 100 items with mean 45 and variance 49. If the combined group has 290 items with mean 51 and variance 130, find the mean and standard derivation of the second group. = (45 1 V,@) = 49 x =CS5) |V. = [130 a= VQ) = we + V,Q) = 49, 2 90) = (DF nx tnk m+n, 100/45 |+[156 |r, e\ |= 250 12450 |=[4500 |+ 150 | 3 36 } d2= 16 +d?) +n,(o3 +d?) 7 m+n; ts 44 ]+36)+150(03 + 6 }) ie Nn ae(32. Sem] = 100 (jag]) + 190.02 + [24% 00 | , “32800 = [Asa] ~ [2qun | = 1500 “21600 = 180 | «3? | . 9) = [rapa fo, © 12 B. Solve the following : ing ; 7 ie following data ; 1. Find an appropriate measure of dispersion for th 3 | 13-15 above] | Less 9 [MIB] ISI | ys 5-7 | 7-9 Income (®. Lakhs) “than 5 IL SS No.of persons | 14 3 8 . went fe TPR Chap gem by ee * A asfeoy Aaa chet2. The mean and variance of 12 items are 22 and 9 respectively, Later on it was found that an item 32 was wrongly taken as 23. Compute the correct mean and variance. Solution : Geye.. 22... Mer Oef the following continuous series are 31 and taking step deviation is as Mean and variance of 254 respectively. The distribution after t follows. 3 |-2] -1 | ° 1/2/3 f| 10 | 15{ 25 | 25 110 10] 5 rvals. Determine actual class inte olution : + Yyeyer ees (= eB 4Price of vo cities is as follows 4. Price of @ particular commodity in S years in two eilies 18 a8 follows. Determine which city shows more stability in price Price in City A} 10 | 22 | 19 | 28 | 26 Price in City B | 10 | 20] 18 | 12 | 15 (Given V30 = 5.4772, Vi76 = 4.1952) tig dete Solution: bed. Sa. dencke pees fy Clg Ah toys per}: