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ICSE Pre-Prelims 2018 : Mathematics (Arya Vidya Mandir (AVM), Mumbai)

7 pages, 47 questions, 46 questions with responses, 205 total responses,

Aaryamonvikram Singh
Vasudev C. Wadhwa Arya Vidya Mandir (VCW AVM), Mumbai
1st to 10th

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A R Y A V D Y A M A N D IR G R O U P O F S C H O o L S S td X M a th D a te 1 1 1 2 2 0 1 7 PRE . . A - P R E L IM N A R Y R E V IE W C S M ATH EM AT 2017 - M a rk s T Im e 2 8 0 % h rs . n s w e rs to th is p a p e r m u st b e ritteri o n th e p a p e r p r o v id e d s e a r a te l p y a llo w e d to w rite d u rin g th e firs t 1 5 m in u te s T h is tim e is to b e s p e n t in re a d in g th e Q u e s tio n p a e r p T h e tim e g iv e n a t th e h e a d o f th is a e r is th e tim e a llo w e d fo r w ri p p tin . Yo u w ill n o t b e . A tte A ll w m pt a q u e s tio n s fro m includng o rk in g i D u gh S e c t io n a n d a n y fo u r fr o m A The g th e a n s w e rs S e c t io n B . . w o rlr m u s t b e c le a rly s h o w n a n d m u s t b e d o n e o n th e s a m e s h e e t a s th e re s t o f th e a n s w e r O . . m is s io n o f e s s e n tia l w o rk in i l re s u l! in th e lo s s o f m a rk s g w . in te n d e d m a rk s fo r u e s tio n s o r a ris o f u e s tio n s a re q p q g iv e n in b r a c k e ts [ ] 7 h s p a p e r c o n s is ts o f s e v e n p rin te d p a g e s , . S e c t io (A tte m Q a . u e s t io n F in d In atA - (4 0 l q u e s tio n s fr o pt a M a m rk s ) t h is s e c tio n ) 1 th e v a ue o f x a nd y L ] b n R . th e fig u re . L T A D B D is , L , 3 [1 A B C D is = 6EJ a c y c lic q u a d rila te ra l a n d P T th e d ia m e te r o f th e c irc le PA B a n d z C B D . L A B D - 3 0 a n is a ta n g e n t to th e c irc le d L C D B - ' 6 0 ' . D e te rm in e . . . . 2 Scanned by = l E u - T C o nt . . S td X M . . a th P re v ie w r R e re h m in a y P - - 20 17 . in e n u m b e r e e t o n th u tio n s o e n t th e s s re a n d re p in e c u a tio n v e th e g iv e n s o c -2+2X 9 +2X ; x w 3 3 F in d ' T he s u m a is in a n A p o f th re e n u m b e rs n u m b e rs - 12 36 ro d u c t is a n d th e ir p . m th e . 2 0 p a y in g 8 % co u n t o f R s re s a t a d is a h s 0 1 0 m o f R s 20 M r J o s h i in v e s te d s 4 8 0 0 0 o n a t a p re m iu ls th e s h a e s se d iv id e n d A t th e e n c o f th e y e a r , h e 3l . b . . . . . . F in d : i)T h e - a n n u a d iv id e n d ii)T h e p ro fit d u d in g h is d iv id e n e a r n e d in c " r H ' " g " th e h e x a g o n Q a . cm c . e c ir c u m s c b in g o n s tru c t a c irc q 40 . ' it a c c o u n t f 1:h e . i) T h e ii) T h e iii) T h e b a n k p a y s in te re s t a t t h e r a te s h e g e ts o n m s tra ig h t lin e p a s s c o o rd in a te 5 a d e p o s its R s 5 0 0 e v e ry m o n th fo r 3 y e a rs in a b a n k th e a m o u n t . u e s tio n 3 Reem de p o s A . o n of " " th ro ' a s a t u rity a n d c u r n g u m p e r a n n , fin d . u g h th e a x e s a t D o in t s A o f 12 % r e s p o in ts p ( B . M is th e - 2 5) , a n d Q (5 r 2 ) . It in te rs e c ts th e m id p o in t o f th e s e g m e n t A B . 3 F in d e q u a tio n o f lin e P Q r d i n a t e co o r d ir a te of A and B o f M . . Scanned by - C ont . . . S ld x M . a th p m 3 e w e v p re w n h a r y P 20 17 - 14 1 Q a . o n u e s t so 4 e n a n d G iv o w in g e q u a tio e fo l lv e fig u re s s ig n ific a n t 31 . x ii) W tw o o n e c l Io a n s w e r c h a t w il b e th e n e w c y e n e a c h f re q u m e a n w h e - axi i# d o u b le d ? Scanned by 4 - C o nt . . . S td X M . a th p re S e c t io C . is a rd s m a rk e d w it h n u m b e rs 1 d ra w n a t ra n d o m i)a p e rfe c t s q ii)d iv is ib le b y . w ha t . , m p t th is q u e s tio n o n g ra p h i) P o t A (2 5 ) ' ii) B is t h e im , . W a rk s ) , , . , . . . . . . . . . . . s e c t io n ) h is rd l s h u ffle d a n d a c a w e 2 0 a re is 5 A e rite 2 3 4 . u a re p rim e n u m b e r i )W 8 (4 0 M - 2 0 17 - o n th e c a rd th e n u m b e r is th e p ro b a b ility th a t ii) a o rig in lim in a ry R e v ie w m tio n s f r o m p t a n y fo u r q u e s (A tte a n - p re - . a n i B ( - a g e 2 o f B rite t h c o o 3) - . , w h e n I p a p e r: L s e iA in re f e c te d in R e e c rd in a te s o f B ' , a n 1c m 1 n it u th e x a x is to A o n b o th {3 } a xe ' - y a x is - d p Io , fo ow e d l sa m t th e e e c tio n in t h e b y a re f o n th e g ra p h r p a p e . ' th e g e o m e tric a n a m e o f t h e fig u re A A . B B . A m a n u fa c tu re r m a rk s a n a rt ic le f o r R s 7 5 o o H e s e ls it to th e w h o e s a e r a t a u n t o f 2 0 % o n th e m a rk e d p ric e a n d t h e w h o le s a le r s e lls it to th e re ta i e r a t a d is c o u n t o f 15 % o n th e m a rk e d s it to th e c o n s u m e r p ric e T h e re ta ile r s e l a t th e m a rk e d p r ic e a n d a t e a c h s ta e v A T is 5 % C a c u a te V A T re c e iv e d b g y th e G o v e r n m e n t o m . . d is c o [4 ] . i)th e ii)th e Q a . In w h o le s a le r re ta ile r u e s t io n 6 th e fi u re o , FEC S im ila r to trla n e A B C g G BD a nd L P . D E = z A E D . P ro v e th a t tr ia n e A D E g is . . . . 5 Scanned by C b fa b . (a C . . 2 60 30 ' , 2 + b F ro Q a ,c , d + c o nt . . . S td X M )(b 2 + c 2 2 + d ) (a b + = th e fo o t o f th e to w e r , m n a d fro fin d , u e s t io n A B C D is a . co - e th a t 2 u m n is a n g le o f e le v a t io n o f th e to p o f th e c o w h ic h ig h h is 1 0 m , th e a n g le o f e le v a tio n is . , y) B (5 8 ) C (4 7 ) a , , , , nd D (2 - , 3 4 ) F in d . o rd in a te s o f A [ n n th e fig u re Q p ro v , 20 17 - e q u a tio n o f d ia g o n a l B D t A B A is re lim in a ry R e v ie w ) w h e re A ( x o g ra m le p a ra [n - - c P - 7 Le = th e u m n th e h e ig h t o f th e c o ii) T h e . b c + c d th e to p o f th e to w e r , m T he b p ro p o rtio n a re in c o n tin u e d 2 a th P re . , . N d = B A B C D is p ro d u c e d . If z F in . d a m A E is ic q u a d rila te ra l a cy c . = A B C 9 2 s u c h th a t a tn x x a n d L F A E = 0 2 - B e to C D d ra w n p a ra l fin d , A X a nd L B C D u e s t io n 8 a d th e s e s o d iv id e n d ) in ii) H R s s h a re s a t 1 8 % , R s . 75 25 sh in c o m e r a n n u a iii) T h e p e . r c e n ta g e e in v e s te d t h e e a c h a nd s a re s a t R o n s h a re s e in c r e a s in . 4 1 F in . in th e d u d in g c e e d s ( in c p ro : - se c o n d rn h e r re t u he r o n th e in v e s tm o r ig in a l e n t . . . 6 Scanned by C b P ro , . . . S td X M . a th p re - p re lim in a ry R e v ie w 2 0 17 - v i t h t c o o c @ C ont co te c o e tc e + c o t o Tt rr T Q a A . u * tio n 9 o o lid a co m p o se d o f a c y in d e r w it h h e m is p h e ric a l e n d s f th e . w h o le l e n g th w U He g f a c to r th e o r e m , s h o w th a n c e fa c to r ia t (3 x + e th e 5 ) is e x re a fa c t p s s io n a o r o f co m 3 x + l e te l p y 2 5 , Q a . J U s in . u e s ti o n 10 F iv e y e a rs a g q a w o m an ii) T h e _ 9x - 15 . ' s a ge w as s q u a re o f he r s o n p re s e n t a g e o f th e w om a n ' s a . ge . Fo ur e y a rs [3 ] Scanned by C T he m i) o n t o d e o f a f th e in S td . . b u i d in g . X M m e t re s a th P re - P re lim in a r R e v ie w y 2 0 17 - is c o n s t r u c te d w ith s c a le fa c t o r 1 :5 0 0 h e ig h t o f t h e f th e ii) . m o d e is 5 0 c m , fin d th e 31 . a c t u a l h e ig h t o f th e b u ild in g . u m e o f a ta n k o n th e to p o f th e b u ild in g is 5 0 c m a c tu a l v o th e a fin d , v o lu m e o f th e m o d e . C = 4 0 X - 12 0 , Z T W n th e g iv e n fig u re , O is th e c e n t re o f th e c irc le X O Y E v a u a te th e fo llo w in g g iv in g s u ita b \e re a s o n s e to T Z a n d X Y is p a r a l . . 14 1 . . XZY i) ii) Z Y X Z iii) Z T Z Y a L T Q a u e s t io n 1 1 n t is 4 0 : 4 1 f a c o n ic a te rfa c e a re a o u s d e rv u c a s e a re a a n d T h e r a t io o f t h e b nt c ity o f th e te th e a ir c a p a d n i F m 8 1 If th e h e ig h t is . . . [3 ] 85 . ii . c h A A B C in w h i u s D ra w th e o c th e c . m s id e s B C - m A B 6 - . 2cm , BC = 4 1c . m o ve s t w h ic h m p o in o f a a n d a C A a nd C A = 4 6cm . . w a ys 2 a s o t h a t it . fro m 5cm B C iOn q otubt D u 5\ n j b Scanned by

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