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ICSE Class X Prelims 2023 : Mathematics (Smt. Sulochanadevi Singhania School, Thane)

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- SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE No. of printed Tfme Marks Class Date Subject sides 2 20mins 10 MathsMCQ 09.01.23 15 Exam ~ Prelfms Question 1 Choose the correct answers to the questions from the given options and write [ 15 marks ] in the main answer sheet: i. If x e W, then the solution set of the inequation 5 - 2x ~ 1 is b) {------,-2,-1,0,1,2} a) {0,1,2} d) {0,1,2,---} c) {2,3,4, } ,\( a) real & equal b) rationa~ c) irrational & unequal d) imagj.q~{1 cos 28 - m. \ .,'"\. , ...;i, \ "-4 ...... .,_ ~~ t , ... i~ ' . equal f"\;._ aj~~ .'~,, '~~ 2 J sec -1 = --tan 2 J ()!:_~ 'o a) sin 2 8 ~, \~~ c)-1 2 d) -sin B .,,..,,\,_"The mean proportiopai~ ~een ! and 128 is iv. ' <: ;!,;:ii -. . 'x' .__../'. ., , ' d) 8 .,,,.. .. 2 3 If ( x +f)"'is,.cffactor of (3x - x + kx - 4) then the value of k is \. . b) 32 , \: ,. c) 16 v. 2 ":: \ ~ a) 64 ~\v a)-8'~ :<Y""' b)- 6 ~~-~-;, d)O Ji~ vii. I 2 The roots of quadratic equation Sx + 20x +7 = 0 a~ ii. he centroid ~f triangle who_se vertices are (3, -7), (-8, 6) and ( 5, 10) is a) (0, 9) b) (0, 3) c) (1, 3) d) (3, 3) If [ 6 7] -A =[27 -5 6 ~1] + A, the matrix A is -2 a) [ 6 iJ b) [ 2 -4] 1 [!6 i] d) [!6 !1] c) - 6 1 The first four terms of an Arithmetic progression whose first term is 3 and common difference is(-6)are: Viii. a) 3, -9, -15, -21 b) 3, 9, 15, 21 c) 3, - 3, - 6, - 15 d) 3, -3, - 9, - 15 ix. The base radii of two circular cylinders of the same height are in the ratio 3 : 5. The ratio of their volumes is b)25:3 a)3:5 c.) 9: 25 d) 3: 8 @ x. 'O' is the centre of the circle. Points A, B, Clies on the circumference of the circle. If LABC = 110 , find LAOC. b) 220 a)70 1 c) 140 d) 55 . . ("~ \ r~) 0 A ,,o B C . x1. If the lines 2x + 3y = 5 and kx - 6y = 7 are P.a~ , then value of k 1s b),;:_li~ ' a) 4 c)~ q~ . ~~--..., 4 4 xii. If a rectangular sheet havin~J,iye'~sions 22cm x 11 cm is rolled along its shorter side to form a~\~1'er, then the curved surface area of the cylinder so formed is!-~ .., -~.,., a) 242cm2 b) 968cm2 . '1,,~ c) 424cm2 d) 121cm2 ""'' ~~ ~~ . ~ ,. s: ., ' '\:.... "\,: \ ... ' 30 , LC = 50 , BC = 6cm, AB = 5cm, c ,,.J ;C "'LlDFE, LA= xiii. Given..tha~ A8}sni,DF = 7.5cm, then which of the following is true. b) DE= 12cm, LF = 100 d) EF = 12cm, LD = 30 9cm, LF = 50 ,,. ~~aj' EF = 12cm, LF = 100 \.." ..-1a) EFI= '( ~ (~ .J .. xiv. The reflection of the point P(0, 3) in the line x = 0 is b) (0, -3) a) (0, 3) c) (-3, 0) d) (3, 0) xv. A dealer sold an oven to a customer in the same city at Rs. 28000. If CGST is Rs. 1680, the rate of GST is b)12% a)9% . d) 6% c) 18% ************************* 2 SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE - Exam Prelirns Class Subject 10 Maths Date Marks Time 09.01.23 65 2 hrs 10 mins No. of print ed sides 4 GENERAL INSTRUCTIONS : 1. Attem pt all ques tions from Section A 2. Attem pt any four ques tions from Section B. 3. All working, including rough work, must be clearly show n, and must be done on the same shee t as rest of the answer. 4. Omission of essen tial work ing will resul t in loss of "\' .., marks. .. ~. .,._'-it,~ ....\ SECTION A .,,; ~~ ,- , .,, , .,_.. t.._ .. l ~ .... n ( Attem pt all ques tions from this secti on ) -~")..\._ ... '\ Question 2 i. ( ...... ' , ',.. . . Rajesh depo sits a certa in sum of mone y every ~ rii~iltB in a Recurring Depo sit Account for 2 years . If the bank pays 't ~ ~st at 10% p.a. and Rajesh recei ves Rs. 6625 0 as the matu rit,t~ajiJ"of the accou nt, what sum of mone y did he pay every mont *~fo, find the inter est paid by the bank . ..._"'~'--: [ 4] ~ . ,. '.,,..~.1-- .., _,. Prov e the following identi!}l.~ ~.../' ., 0 ( 1 + cot 0 - cosec 0) ( k ,: ,F t~n + sec 0) = 2 [4] -f>"''' '\ ,_ ..~ ..... The line 4x - 3y +..J-~ 'j~ meet s x-axis at A. )l.;: ~ a Find the co-=,_o ~~~a tes of A b. Find the ee:iuation of a line passi ng throu gh A and perp endic ular to the .. .:,> \ line tx..-:: )Y + 12 = 0. [ 4] ' ,.f"'"' ~ ii. iii. ,,.... ... .. Questi _,,.on"3..,."' ' +-b \ ,( cone of radiu s 6 cm is full of wate r. Whe n 32 sphe rical marb les each of ...;;.~,;,. ~ ~ 1 r ,."Ct radiu s 0.5cm are drop ped into the cone, 18 of the wate r overflows. Find the heig ht of the cone. ii. [4] The weig hts of 50 apple s were recor ded as given below : Weig hts 80-8 5 85-9 0 90-9 5 95 -100 100- 105 105 -110 110- 115 in gram s No. of 5 8 10 12 8 4 3 apple s Calcu late the mean weig ht, to the near est gram , by Shor t Cut Meth od takin g assu med mean as 97 .5 [ 4] 1 t ~ . I ' II iii. Use gra ph pap er for this question. Plot P(2, 4), Q(- 2, 1) and R (- 2, 0). . a. Reflect P and Qin x-axis to get P, an d Q' w te the co- ord ina tes 0 f p' n and Q' b. Reflect poi nt R in the line PP' to get R' c. Give a geometrical nam e to the figu re PQQ'P'R' d. Find the are a of the figure so form [S] ed. Section B ( Attempt any four complete questions from this section ) '\Au est ion 4 \ i. ,...~, ... A ma nuf actu rer sells binoculars for Rs. 375 0 to a wholesaler, w~ ~~ )'}s' it to a reta iler at a profit of 12%. The retailer sells it to the Cl:\~ '-V)r at a pro fit of Rs. 600. If the rate of GST is 18% and all sales are Jiiti a~'state, find \. "'-. .:'\ , '. a. the GST pai d by the wholesa ler to the Central G~~ 13, ~en t b. The tota l GST received by the State Governmertt' \J c. The pric e pai d by the customer. ,,,..\~ ~ ~ ii. ,.. ~, - ~""-~ Solve the qua dra tic equation x 2 to thre e significant figures. - [3] 8 ~ ~nct give you r ans wer cor rec t \~~ [3] . . .- ~-' ~ ~'''" Use gra ph pap er for this ques{,-1.i 1w The daily poc ket expens ~_s'of)f udents in a school are given below : Pocket exp ens es 25 - 30 .\3'0 .:. 3 5 3540 40- 45 45 - so 50- 55 ~, (in Rs.) ' "' ' \ No. of stu den ts , , ' ,1S ~ 33 ,. 29 40 35 . 12 Dra w a his t,?~{am taking 2 cm = 5 uni ts on bot h the axes and estimate the mo ? ( , i lso 'sta te the modal class. [ 4] ' ~ii . ~ , i. . .. -.. """ uestion"'~~ -~ , r ~-1Jo.37 ,~s~i ! ][; : ]+3x~[ ~; 36 38 'l- ~ ] find the matrix ~ 3G !.i:2..'1 " ' [ 3] B ii. '2..1 Chords BA and CD are ext end ed to mee t at P. If AB = 5cm, AP = 3cm, PC =4cm, find CD. [3] .. m. Using the rem aind er and factor the ore m, factoris e the following polynomial completely: x 3 - 3x 2 - 4x + 12 2 [ 4] -. 1G Question 6 i. If the sum of th . fl d e first 14 terms of an A.P. is 1050 and its first term 1s 10, n the 20th term. [ 3] ii. Prove: iii. The line through P(S, 3) intersects y-axis at Q and makes an angle of 45 with x-axis. Find : a. the equation of line PQ. b. the co-ordinates of Q. c. the value of m, if PQ passes through the point R(m-1, 5 - m) cos9 cosec8+l cos0 + cosec0 -1 = 2 tan0 Question 7 [3] . "~~;~["4] -~ "- ~~\ "" Q f;J~ v \ The given figure represents a solid consisting hemisphere surmounted by a corie. The ~~r of their bases is 14 cm each and the surface afe"a of the solid is 660 cm2, find the slant height of t\~~t, . [3] i. -~~\ (~:s: ii. A jar contains some marbl~s~ ~e, green and white colour. The green and white marbles toget~'rl?e 36 in number. The probability of .... \ 1'\ selecting a blue ma(b!e:-Tu~ and the probability of selecting a green , ,v 3 marble is~ . Ho:~ ~l ~y marbles are there of each colour? 9 iii. '~"' 'I\,_ '" 4' ' f''-'1''\ . : PQRS ista cy..i;:Jic quadrilateral in the circle wi:4, ~~J 0. MN is tangent to the circle at Q; If b12$W=50 , LPOQ = 68 . ~~d i PQR, LPRQ, LPQM. [ 4] [3] __s_...._ (~~ .. ~ ,4uestion 8 i. Solve the following inequation and graph the _solution on real line: 14 3x + - 3 ii. 4x >- -2 3 2: 2x - 5, x E R. [ 3] In what ratio does the line x = 3 divide the join of A(l, 2) and B(7, 5) .. Also, find the co-ordinates of the point of intersection. [3] 3 p- iii. B In MBC, LB = 90 , PQ l AC. a. Prove MBC "' MQ P b. If AB = 15 units, AQ = 6 units, AP = 3x +4 and QC = lOx -1, find the value ofx and PQ. C A [4] Question 9 i. The sum of ages of a mot her and her dau ghter is 40 years. Five yea rs ago, the mot her 's age was squ are of her daughter's age. Taking the dau ght er's pre sen t ages as 'x' years, fram e an equation in x and solve for x. Hence, find thei r pre sen t ages. ~] ii. Use gra ph pap er for this question. The tabl e sho ws scores obtained by 200 shooters in a shoo~ ~v competition 6] ,1,V-. Scores 010- 20- 30- 40- 50- 60- 7'8,-' 80- 90obt aine d 10 20 '\~ 30 40 50 60 J.f\ l,eo 90 100 No. of 5 11 14 26 29 25 '\ ~~- 33 22 10 ' # sho oter s Draw an ogive for the given distributi~ - ~n g 2cm = 10 scores on one axis and 2cm = 20 shooters on the ~ ~s. From the graph find: a. the med ian ~' ~.... b. The upp er quartile ,~<~ c. The num ber of sho oter~l~ 'c'ored mor e than 65% scores. \'-. """} ~\ ~~ "'x"' [ f' "1 t'' \' J,Question 10 i. ~ ) ( _::;:,.~ .~ ~ . Construct LlD~ ~11 uE = 6cm, LFDE = 60 and LFED =45 . Circumsc~JJ;>~~ ~cle abo ut the triangle. Measure and reco rd the radius of the c~J .licircle. [ 3] ...... ...), ~~ ra = ,., ii. ~ ?2 t!.. .,9a +27 . ,.~~"' 63 62 , using the properties of proportion solve for a. [ 3] iii.: rrw o lam p pos ts of equal heights are standing opposite to each oth er on eac h side of a roa d which is 80in wide. From a poi nt between them on the road, the angle of elevation of the top of the lamp pos ts are 60 and 30 respectively. Find the height of the lamp posts and the distance of the poi nt from the lamp posts. [ 4] 4

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