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) p a id b y t h e fa c tu r e m an u 1s t h e c u s to m e o A p r o fit se d i t y t o i t s d i s t r ib u t o r fo r R s 2 2 , 000 i n c l u d i n g d it y t o , w ha t a r e ta i l e r fo r R s 2 5 , 000 p l u s ta x (u n d e r V A T ) w a s the the m a n u fa c tu r e r 7 r e ta 2 0 , 000 ; A i le r ? m ou n t of V AT = R s 300) Scanned by ( 1 6 ) T h e p r i n te d p r i c e o f to th e s h o p k e e pe r a n a r tic le T he c o s t t o th e s c (A c o st h o pk e e p e r i n c l u s i v to t h e c u s t o ( i ) R s 5 0 8 80 ns : l l s the se ha r g e d a t the ( i ) V A T p a i d b y t h e s h o p k e e p e r ( i ii ) t he 6 0 , 00 0 T h e s ho p k e e p e r s S a l e s t a x (u n d e r V A T ) i s ( i ) th e is R , to the i n c u s i v m er ( i i) R s 7 2 0 ; l lo w a dis c o u n t s a a r t ic l e t o t h e c u s t o m e r a t t h e r a te o e o ho e s a e r w f 6% t ev a e r y s ta f 2 0% o p r i n te d p r ic e ge F in d f ta x Gov e r nme nt e o f ta x ( i i i ) R s 6 3 6 00) ; , . 2 i n t e r e s t i s 1 0% p e r y e a r ; i e At th e t i m e o f c a lc u l a te m a tu r ity (A (2 ) M r R K N a i r g e t s R s 6 4 5 5 . R (3) e c u r r in A hm e g D e p o s it A ccou n a r e c u r r in d ha s a n s : BANK ING the a m q u en d f o on e j R a e s j a e sh w g d e po s i t accom ba n k t in a e o H w i t ge t (A en t r e c e iv e a il l = R t the e n in an n u m In s ta m e n , , o f 2 ye a r s , f 14% pe r n s: d 7 9 5 0) s d e p o s i t s R s 2 5 00 p e r e m a t u r it y f h a t th e r a te o year F i n d t h e m o n t il l y i n s t a m t I f h e g e t s R s 66 , 2 5 0 a t th e t i m 2 years th a t R am o u nt t th e n t th a t t = a R s 5 00 ) m o n t h tb r f in d ( i ) t h e i n t e r e s t p a i d by t h e b a n k (i i ) t h e r a te o (4 ) M o n i c a h a s th e m a tu r C D a it y fi n d t h e t i m f in te r e s t e A v a lu e o ( in cc o un t i n th e U f th i s accoun t y e a r s ) fo r w n io n is R h i c h th e s Bank o 24 9 30 , acc o u n f I n d ia an t w as an d th e h e ld d d e p o s i t e d R s 600 p e r r a te o m o n f i n t e r e s t i s 1 0% p e r (A n s : t h e t i m e - th {f an n u m 3 ye a rs ) Scanned by ' (6) M o ha n d e po s i t e d R s 8 0 p e r t he a m o u n t p a y a b l e to (A ns: him m o n o n m a t u r i ty , 6 2 5 0 in , R s 2 5 s h a r e s fo r R s 3 1 2 5 (A n s : i n c o m e s ha r e s o ac h , f s ix f i n t e r e s t i s 6% p e r r a te o ye a r s F in d an num at R s 2 0 pr e m iu m in F 2 00s h a r e s (A n s : m a r ke t v a lu e R s 2 4 , 000 ; - F i n d th e d i v i de n d d u e a t the e n d o d l v l d e n d $ 4% v a lu e o o f the b o u Bht 5 00 s h a r e s fi rst y e a r d i v ?d e n d f ro e m th e i n v e s tm an num f he b o u g h t ent R s 3 00) - m a r k e t v a lu e o d u r in g t he p a n y pa y i n g 6 % d i v i d e n d pe r a com fi n d h i s i n c o m ( i ) th e of fo r S H A R E S A N D DI VI DEI ) (2 ) M a n o j b u y s R s 1 00 s h a r e s m an a c o u n t , ( 1 ) R a v i i n v e s te d R s (4 ) A if t h e de po s it R s 6 8 1 1 2 0) 3 (3) t h i n a c u m u l a t iv e , e e r o n th e s h a r e s , ( i) h i s annua f a f th e s h a r e an nua l in c o m ye a r on c ha s e , e l in c o m e ; (i i i ) h i s pe r c e n t a g e i n c o m e R s 3 , 000 ; pe r c e n ta g e I n c o m e - o Rs 10 , - 1 2 5% ) l R s 50 e a c h i t t he h a l l y e w l y (A n s : d iv i de n d a t t he r e c e iv es F in d pa n y p a y i n g 1 5 % d i v i d e n d 2 50 s ha r e s e a c h o f fa c e v a l u e p. a c o rn , end o o f a c e r ta i n f t he y e a r bu s i n e s s R s 1 , 000 ) - c o nc e rn a nd R s 400 a s d iv ide n d o n hi s s h a r es n d th e m (A n s : R a t e o f d i v i d e n d , = 8% ) Scanned by ( S) M u k u l i n v e s t s R s 9 000 i n fa c e (A n s : A a t R s 1 50 h e n th e p r ic e r i s e s s ha r e s w (6) R s 1 00 s t a n d s v a lu e in an n ua com e (i) H o w h he m uc w a n ts bu y ? l A n (7 ) A pa n y co m f 1 5% o a lA l in r e c e iv e c h bu ys a M V n s (9 ) j a y ? I f he e l in c o m R s 5 0% a s o ha r e o F f hi s h i s g a i n i n t h i s tr a n s a c t i o n ? ann ua n R s I , 5 00 ) - b e i n g R s 1 00 ) v a lu e l in c o m ? e by R s 1 5 0 ho w e m an , 8 , 1 84 ; s in a l nom se he n ? annua v a lu e o d f d iv i d e r d p a i d b y t h e c o m e o on a R s f S a lm l y 1 0% on 4 0 s h a r e s in - R s l in c o m f Rs l lo eac e y e x t r a s ha r e s s R s 4 65 ; - h de c la r e s ho e x tr a s h a r e an an n ua u d he - 2 0) l d i v id e n d = an w 560 s ha r e s d i v id e n d a o o f s e s tm e n t 66 , 0 00 ; a com pa n y on , , w co m fi n d t h e p r i c e ann ua in c o m e o pa n y f S a lm an h is in v At e s tm e n t p a id f o r 1 , 4 52 ; pa i d s h a r e - h i c h h e p a y s 1 0% d iv i d e n d r a te o lA d iv id e n d th a t A f in t e r e s t ja y on ja y T h e fa c e m pa n y a w - eac h s ha r e R s 1 65) H e b u y s th e s h i u ha t p r i c e d i d he b u y t he s ha r e ? v a lu e o f eac h s h a r e is R s 2 5 T h e co m pa n y C a l c u la te f 9% ( i i ) th e . h o h o l d s 88 s h a r e s i n t h e h i s in v R pa n y co m 25) ( i ) th e d i v i d e n d th a t ! f o annu m w , o w n s de c la r e s ns f 6% pe r l in c o m R s 1 32 ( pa r at i l b e h is = p r i c e t h a t h i s p r o fi t i s 1 6% f L:L in v e s t e to th e a m o u n t o f d i v id e n d m an t su he ha v am o unt o an nu a ( i i i) I f h e ( 8) A l to ta T he (A n s : an nua o C a l c u l a te (i) T h e Oi ) w to in c r e a s e h i s a n n u a s n a t is W il a b l e ha t w , i t h 4 000 s h a r e s w av a to in v e s t e ( i i) f th e d iv i d e n d i s 7 5 % ( i i i) I f h e is h is n at , d i v i de n d a R s 36 0 ; M u k l u k g a i n i n t h i s t r a n s a c t i o - ill ha v w W R s 2 00 to bu y 62 s ha r e s m a n w a n ts t o pa n y p a y i n g a co m , w ill ge t h i s i n v e s tm w i ll ge t = ent R s , if A ja y l , 2 60 ; h a d p a id R r a te o s f i n te r e s t 30 fo r - eac h s ha r e 7 5% ) Scanned by ( 0) A d iv i de n d r et ur n f 9% o S 7 5% m a rke ( i i ) th e a m o unt (A M V n s : u e t va o f f th e o to be in v a s ha r e ( 12) A m an se in v in (A r R i f th e , c n s : l l s 60 , R 15 s ha r e s d G o pa l in v a sh a r e s a t R s 12 0 ; t he en t : s co m e s ns: (i ) ( 14 ) A s ho k an R l in c o R s o f h r e s A s h o k b u y s 7 5 ho R p r e m iu m t a o f d i v id e n d f the pr ic e r a te o f 8% r v e ste d R = 630 s s 8 4 00) , 90 ? at o f a a n o t he r co m d i v id e n d o pa n y a f 8 pe r cen t t R s 9 ea c h h R s 21 F in d t he c ha n g e in d iv id e n d , at ea c an d cent 4 0 80 l e s s ) 8 000 i n 7 % R s d in v e s te (i i ) d S a n d e e p in v a t t o be i n f R o pa n y p a y i n g 1 2 p e r a com d R in th e m e 7 00 ; s t 1 20 o a s , 1 00 s h a r e s at R s 8 0 A fte r a ye a r he d t h e p r o c e e d s ( i n c l u d i n g h i s d i v i d e n d ) i n 8% , so R s l d th e s e 25 yea r sec o n ( i i i ) th e p e r c e n t a g e i n c r e a s e i n h i s (A a t a c e r ta i n F in d 41 an n u a l i n s d iv id e n d a n an n ua am o un p a n y pa y s ( i ) h i s d i v i d e n d fo r t h e f i r s t (i i) h i s re se is be t te r ) 6 - an 1 2% ha re s s e ste t R s 75 each bt a in s in R secon to o R - ha n g e i n in c o m am d e s tm e n t t he p r o c e e d s e s ts com e ( 1 3) M s T h e fi r s t i n v n s: 1 00 s h a s s ha r e e s te ( 1 1 ) W h i c h i s be t te r i n v e s t m (A R o n c a l c u la t e , (i ) th e d e c la r e d w as o s s e sts 9 00 ; R s 1 00 s h a r e s f 2 0% r e c e iv e R I f b o th d ye a r r e tu r n o n ( i ii ) 1 8 , 0 00 at a l in v o r i g in a e s tm e n t 2 5% ) eac h in b u y in g s ha r e s dis c o u n t r e c e iv e e d by S a n de e p his (A n s : o f 2 0% , d q u a l d i v id e n R a te o w o f tw o d if f e r e n t co m pa n ie s h e r e a s S a n de e p b u y s R s 5 0 s h a r e s a t th e e n f d i v i de n d d o r e c e iv e f the y e a r , f i n d th e d by S a n d e e p - r a te 1 1 2 5% ) Scanned by ( 1 5 ) J o h n h a d 1 000 s h a r e s o f , He a so ld f the s e so m e o s ha r e s a t dis c o u n t a D iv id e R dis c o in ( 1 7) fa c e o v a lu e o n f 1 0% t a p r e m i u m o f 5 0% a n d p a y i n g 1 2 % d i v id e n d (A n s : N o th e n u m be r o f s h a r e s s o ld b y Jo h n ( 1 6) w it h a pa n y a com 4 0 , 6 08 i n t o t w s u n t an co m es d th e o th e r p a r ts o (A n s : t h e t w o p a r ts a r e R A m an ha s c h o ic e to in s v e st e s tm e n ru il a b l e at a c o m pa n y B are av a i la b le a m u c h in , a ll , do e s he in v ( i) 3x (2 ) I f t h e p la c e m re 4 + re + lA ( i) 4 5 (i i) 8 en 24 t se t s o lu tio n s e t n s : {0 f f 1 0% su m T he n a tu r a 4x 2 f ho l e set o w 2 2x 4x = set o x i s th e Oi ) ? (A d th e R s 600) - i n 8% R v e ste d 1 00 s h a r e s s 8% p r e m i u m at fin d , 8% at the a n n u a l , o an an o co m pa n ie s A d i t p a y s 8% d i v id e n d d it p a y s 7 % d i v i d e n d f th e m an f tw in r et ur n he r e a s w , d B I f t he fr o m the m is R s 9 3 6 in v e sts an a ll = R s , S ha r e s s ha r es m an o o f f i n v e s ts f in d h o w 1 2 , 9 6 0) I NE OUA T I ONS i s th e en t set 16 p la c e m (i) 5x n s < e st an o s ha r e s o pe e f 2 0% o m dis c o u n t t a pa n ie s W ( 1 ) I f th e pr e m iu ld by J o h n i s R s 1 92 e qu a l in hu n dr e d a re a v a c o m are e , so 1 00 s h a r e s 5 d p a y i n g 8% d i v i d e n d h a n g e in h i s in c o m p a r t is in one R s 2 0 , 7 36 ) pa n y A q u a l l y in bo t h t h e t c f s ha r e s 1 9 , 87 2 & c om e h th a t i f an d in v e s te d t he p r o c e e d s i n R s 2 0 s h a r e s I f t he o p a r t i s in v e s te d i n 9 % R o m bo t h th e in v , su c an R s 40 , + l n u m n um (N ) f i n d t h e be r ( W ) , , f n d the s o lu t io n s e s o lu tio n se t o t o f f 10 1 , 2 , 3 4 } ; (ii ) , be r s s o lu t io n s e t - 10 , 1 , 2 , 3, 4 5 }) , Scanned by j) i. ? ! . I f t he r e p l a c e m e n t 0) Of lA 6x ( i) ns (4 ) F t h e re 1 9+ 3x e n (i i) (A n s : ( i ) S o l u t i o n ( i i) S o l u t io n (5 ) S o l v e : 2 (i) y (A {x : set - {x : x w he r e 4 , ( ) W h e n n s : ( i i) W h e n y rea 4 be r s (R ) , f in d t he 6 e e n an d 8 , fi n d t h e so i u t i tJ n se t 3 c (r e a n u m an an d d x x E R E R }) po s i t iv a 2y n {l n t e g e r s } E R be tw 3 n u m < be r s ) e o } dd in te ge ( A n s : S o l u t io n r set - ( I 3 5 }) . , y + 1 5 4y + 7 ; if be r s ) s o l u t io n s e t num l s o l u t io n s e t o 2x is x (r e a l E R l 2 > x i n g in e q u a t io y E > , o r , 8 + 3 2 2 8 ( I n te g e r s } (ii) y E , - 3 (6) S o v e t h e f o l l o w 3x z) (t , 3 4 , 5 6, 7 1 t se Jc 5 5 , 15 t s e t is the s e t o f l {2 - f i n te g e r s sc t o ( ii ) x s o l u tio n s e t pla c e m 0) 5 x > i s th e se t ( - 1, 0 1, 2 3 } 2, s o lu tio n s e t , b - , 2 s : 4 an d y 2 S x < 3) < v R j ) (7 ) S i m p l if y 2 3 G ( 8) ra ph L i s t th e se t o 3 @r il R x t h e v a l u e o f x o n th e r e a l n u m s o lu tio n s e t o b ta i n e d (9 ) S o l v e 1 an on a nu m d g r a p h the t 50 5) 3 (2x be r i n e (A ti o t o f s o u n 5 ns : - be r i n c ( A < 25 , g iv ns: en r e qu ir e d s o l u 2 1 2x 6 or s o l u ti o n th a t W A ls o x t io n s e t 2x + - - 17 , re pr e s e n t t h e } 8, 9, 5 Z 13; w s o l u t io n he r e x E R Scanned by ( 1 01 G i v e n p = Q = W he r e R {x 5 : {x { = d lA < x P ( l ) S o lv 2 e 2 \ lA ns ( 1 4 ) F in d 2 + ns Q R be r s } an d I R ; x Q lu e , f x . w 2 2 3 , sm a l le s t an u ir e an d d { in t e g e r s } = n um l s = be r lin e s x < 5 ; w W r i te d o w he r e n the e l e m e n t s i ; P x Q n = p n Q { 4 n 5 o I} x d i f e r e n t o n tw o 4 0, th r 23 4 2 3 s o lu t i o n s e t o n th e n u m v a < < + R} x , 4x s 6; f th e la r g e s t lA nu m the in e qu a t io ( 1 3) F i n d ti e o 3 h th e 2 re a an ns 1 5 11 1 5 3 R e pr e s e n t P = 2x < h ic h sa 5 2, ' E W x be r l in e t i s f y t h e in " G ra q a u t io n ph th e s o l u tio n s e t o n th e n u m be r lin e d 4) c on w o n e sn a u fi h lle s t t i v e w h o le ru m b e t s s u c o f the sm a l le s t i s c o n s e c u tiv e w h o le a h t h a t t h e d i f c e b e t we f o u r t h t le a s t 3 n um bers a re : 5 0, 5 an d 52 ) Scanned by s o v e + 2 ( ( 2 ) F i n d th e q u a d r a t i c e q u a t i o n (3 ) U s e t he (A n s b s t i t u t io n su (4 ) W i t h o u t I or , s o l v in x W it h o u t s o lv s the q u a d r a t ic IA o r not ( 6 ) F i n d th e (7 ) lf x m an ( 8) I f 2 = d ns x e q u a t io n I is - w x e s o v e q u a t io IA o r n ot f k fo r v a lu e o k ( n s in g = 2 or x s e s o l u t io n s e t l to + x fo r y l) is { , 2, 3 } i f 5 ( 3y (A )2 + ns: x 6( 3 y + z + x l 8 ) 6 = = 0 0) ! y ( r o o t) o f t h i s e q u a t i o n (5 ) n s ho w 3v - A z ns x 1 + x x = - 2 2x 1 is 2 is ro o t 1 = 0 w h e the r fi n d , w h e th e r f th e g i v e n 3 x a s o l u t io n o 0 ; fi n d = f th e g i v no t a roo t o h ic h 3 n x e n e q u a ti o n 1 is - x x + x l u t io 2x l 0) f th i s e q t a t io n = n 0) = (s o l u t i o n ) o f e q u a t i o n k c z a so z a ro o t o l 1 is - + 2x 3= 0 = an n o n e ro o d x - (A n s : t o 3 a r e r o o ts o m - 7 5 an f t h e qu a d r a t i c t h e o th e r r o o t IA n s d f the n - 3 e qu a ti o n 2 2m + 2n - 0 li n d t h e v a lu es o f 9) e q u a t io n th e o t h e r r o o t 2x - z + ? 6 = 0 is 2 , f i n d th e v a lu e o f a A ls { , l in d ) 2 Scanned by (9 ) S o l v e h ea c 2 (i) 5 f t h e fo l l o w i n s 3 2x s o lv ( 1 0) W i t h o u t (i ) 5 in g + 6x + 3 v a 3) x m ( 3 ) S o lv e ( i) x )x eac 2 d e c im 2 lu e 2 + o a h o f ' + f ' (m , 9 + g in a r y 2 + if t he , n s: i f th e 1)x + 1 = an r o o ts o p r o o ts o 9 5x + F t he e 0 0 = 2 = 0 d l ; ( iv ) T h e u n e qu a = q u a t io n s r o o ts a r e r a t i o n a l (r e a l ) a n d e q u a l r o o t s a r e r a t io n a l an d a t i c e q u a t io n a r e e q u a f t h e jEo l l o w i n g q u a ? u n equ a l) l 4) f t h e fo l l o w i n g q u a d r a t i c 0 IA n s f t h e fo l l o w i n g e q u a t i o n (iii) X 2 + 1 1 X + 6 + 6x i u la Oi) T h e - r o o ts o f th e 2 ; ir r a ti o n a l 0 (A = ' m a x g t h e tb m 77 m a tu r e o ( iv ) 3 im u s in 1 8x . 0 ' p 2 (i i ) r o o ts a r e 6x 2 + = x 0 = r o o ts a r e v a lu e o ( 1 2 ) F in d t he + in e th e 7 ( 1 1 ) F i n d t he (4 ex am + (i i i) T h e (p ( i i) 6x ( i ) t he n s , by e q u a t io n s 0 = 2 (i i i ) 2 x lA o s m fo r = x 5 an or m q u a t io n a re e qu a 3) = d Bi v e e , in eac h case . Yo u r a n s w e r c o r r e c t to l pla c e s 1 0x + 6 (A n s : ( i ) 9 3 6 . = an 0i ) 0 d 0 64 ; Oi ) 1 09 an 3x d z + 5x 9 = 0 2 76 ( 1 4 ) S o l v e t h e fo l l o w i n s e q u a t i o n x - (A n s : 8 2 6 G iv e y o or 2 2) u r a n sw er c o rr ec t t o tw o s i g n i f i c a n t fi g u r e s Scanned by ( 1 5 ) S o v e ( i) 2 ( 1 7 ) F i n d the (i) x E so ( 1 8) S o lv ( 2 0) S o l v (A e n a x x n set o x 1 a b 3 f th e , (A bx or e qu a t io n 3 1 x n s : a + + 2 Q (r a t io n a l E x 2 (i i ) ( x th e s o lu t io n s e t 25 _ 0 = (i i) E Z 3 )2 ( 2x e n s lu t io w ne : 2 + 5 (i n t e g e r s ) Z (A n s : 4 b a + o r x w he r e a + b - 3 n u m be r s ) - 2 (x 8x {3 } 4 x , = )2 3x 0 ; = ; W he n x ) 3x + w Q 6 = 0 , x E R he n , t he s o lu t i o n s e t - {3 , }) 1) b + O , b 0 ) Scanned by m s o V ?N G E R Q B m s @& ( I ) n d tw o n a tu r a n u m ( A n s : N u m be r (2 ) F i v e t i m e s F i n d the 6 are w and 9) b e r (A ( 3 ) D i v i de 8 i n to ho l e (A n s : R e q u i r e d p a r ts (4 ) F o r th e w o rk i n 1 3 ho u r s 2 0 (A n s : B a o n e w i l suc a re sa m e am o u n t o num be r i s R e q u ir e d ns: tw o p a r t s Q A I D R A T U A T I O N h i c h d i ff e r b y 3 be r s a c e r ta in w num Q fw h t ha t t h e 3 and o rk ho e T a k in g cm re p Fe s e n t s t he t h e t r i a n g ie ' a a s the fi n d h o w 30 h r s To e n gt h bo v e s t a te m ' x ' a s the l f th e ir com m uc o h tim p le t e the cm an f th e s h o r t e r tr ia n g l e m m o r e t ha n v a lu e o br e a d t h f t he be r n um be r i s 3 ) 15 ip r o c a l s i s re c ill B e w w ork I f t o g e t h e r th e y a lo n e - o f t h e tw o s cm ; p l e t e th e w o rk ta k e to c o m p le te th e d th e d i f fe r e n c e b e t w 5 com ) id e s e n t a n d a l s o s o l v e t he e q u a t i o n t o da h i s 3 v era n n u m e r ic a l to t h e ( i ) T a k in g ' num o 5) (A n s : O n e s i d e o f th e ( 6 ) T he l e n g t h o f a e qu a x ho s e s q u a r e s is 1 1 7 w to t h r e e l e s s t h a n t w i c e t h e s q u a r e su m o ( ) t h e h yp o t e n u s e o f a r i g h t t r i a n g l e i s 1 3 7 f A ta k e s 6 h o u r s e s s t h a n B , m i n u te s ; ta k e w e qu a a n d th e s u m o , w r i te th e o t e r t w o a n e q u a t io n f i n d t h e tw o the r s i d e o i t s b r e a d th T h e een ' o u n lm o w n s f th e t r i a n g l e n u m e r ic a in id v a lu e o f i ts x ) area is is s th a t id e s cm 12 - ' o f f it s p e r i m e t e r o f the v eran da h , w r i te a n e q u a t i o n in ' x ' t h a t r e p r e s e n ts t h e a bo v e s t a te m e n t S o v e th e e q u a t i o nr (A n s : ( i ) x 2 x o b ta i n e d i n 6 = ( i) a bo v e a n d h e n c e fi n d t h e d i m 0 ; (i i) the l e n g t h o f v e ran da h = 6 m e n s io n s o f the ; its b r e a d th = v eran 3 m da h ) Scanned by (7 ) B y i n c r e a s i n g the s pe e d re (A d u c e d by 36 T he ns : (8) C a r A o r m in u te s i g in a l s by 1 0 k m /h r ca r F in d the pe e d k m fo tr a v e s x f a o o f the c a r litr e r e v e ry ig i n a o r o s the t im e o f j o u r n e y , pe e d f th e o fo r a d i s ta nc e o f 7 2 km is c a r 30 k m /h r - f pe tr o l , h i le w B tr a v car e s (x d c ar 5 ) k m fo + l it r e r ev e ry o f pe tr o l ( i ) W r it e d o w (i i) f A c ar q u a t io the (9 ) B y se ( 1 0) T h e in n x an j o u r n e y (A l l in g su m if t he o f l it r e s S o (A n s : d o f pe t r o l use d by / A c ar n B in c o v e r in re n u m be r o f l it r e s o f it r e s o f pe t r o l u se d by c ar A = N o o f l it r e s o f pe t r o l u se d by car B = f l it r e s o o R s 24 r ns: n a tu r a n s : be r is q u ir e d tw n suc o , l o f pe tr o l a tr a de r o s e s C P o nu m f the u se a r t ic e be r s i s g iv en car g a d i s ta n c e + is R s 60 b y th e u se r e la n an car B fo r d by l l itr e s ) = o r do w i tr e 5 c e n t a s th e c o s t h pe r w r ite l it r e 4 00 B , f pe t r o l x x d by as m uc o 4 00 o N g t h e 4 00 k m c o v e r in N R s pr ic e o f th e a i c le 4 0) t io n s ; S = n (n + 1 ) F in d n , 2 3) - h th a t t h e p r o d u c t t h e d i g it s i n te r c h a n T he B in m o r e tha n c a r it t o d e t e r m i n e t h e e p r i c e (A f fi r s t n um lv so fo i s 2 7 6 (A sum be r c o st f pe tr o l s o n s : a n a r t i c le t woi gi t n um 4 l it r e u ses C a lc u la t e th e (1 1) A be r f 4 00 k m o e n th e n u m g e th e ir p l a c e s d i g it num be r - o f its d i g its is 1 2 F i n d th e nu m W he n 36 is a dde d t o th i s be r 2 6) Scanned by ( 1 2 ) F iv e y e a n w a w o m a n ! a g e w a i th e r q u a r e o ' go , t w i c e \ ha t o i be ( i ) thc a g e ( i i ) th e pr o f t he so n e n l a ge o ( i ) T he a g e (A n f he r o ' on 1 a bo a t m o to r ba c k i r (A a to a T he ns : ( 4 ) A p ie c e s f th e f the pe e d f c l o th o ha t is th e ( 5) So m e o o l fa i e d l o j o in ho w y m an r a te pe F be r n t m o r igin a l co st o lA na x - a , f o - 5 ye a r s - 30 y e a r s ) i s 9 k m l h i n s ti l w a te r F i n d t h e s pe e d ge i f t he p i e c e w ou ld ha v e ? (A n s tr e a m a n d c o m e s o f t h e s tr e a m ns : w as 5 re m a in e d u n c le n g th o f t h e fo o d f o r f o r t h e p ic n i c be r co u o (A n s : e ac a n d ea c o n g e r m f th e c l o th h No m em o w as x , m f c o th : r a te p e r m R s 4 80 A s f s t u d e n ts f bo o k f o r R S 9 6 0 f t h c w r i te a ri e q u a m ete r o c o s ts c ig h t d R s 1 0) - o an f th e m be r in c r e a s e d b y R s 10 F i n d ld b e b o u g h t i b r R s 9 6 0 h bo o k o be R s 20 = h H o w lo n B i s th e p ie c e ha n g e d T h e b u d g e t f o r th e fo o d co st o a c e r ta i n n u m g o e s ] 2 k m do w , 3 k m /h r ) - m e te r f bo o k s t h a t eac a go w om a n p i c n ic t he s t u de n ts w e n t s s , t he f t he f th e p ie c e t h e pa r ty ( 16 ) A s h o p ke e p b u y s o R s 2 00 d e n ts p l a n n e d s tu 5 ye a rs so n f 3 ho u r s c o s ts o r i g in a a F i r d ge f th e s t r e a m cost o he r ce w om an s pe e d ho s e l t im e R s 2 e s s ; th e w w , T m y e a r hm ' so n 1 al e l i v e y e a r a 8o ( ii ) T h e pr e i e n t a g e ( 1 3) A f he r w o u w ho c o st w ent fo r p i c n i c pc r b o o k l d be 4 m ore w as - 1 6) Rs 8 T a k i n g th e t i o n i n x a n d s o v e i t 4 8) Scanned by ( \ ) ( i ) f 2x ( 2) r b d tA ns (3) T w 3y + 5 : 49 : 9) be r s fi n d t h e n u m in the are be r s I A (4 ) ( i) W n a t q u a n t ity 3 m es w o r k do + (6 ) W tl c 4 ) ? ys n th e t h e t ic lA ( h k e t fo 24 3 ( 6a : x y : 7b ) 6 8 is 5 : a dde d to ea c h num be r th e r a t io , be c 2 om es 3 d 4 0) an a d de d h to e a c g im fE c e r s 8i m r th e e l an e n f ra te r m o e th e r a t i o o b a t t le 6 d th e o O ; in ( 2 x m en j o t m y be c f f so b a n te I A e f the m eac n' d l + y by am e n um f f ic e r s n u bc r o b e fo r e ? O) i n t h e fa l e c r e as e 3 a c t e d fr o c )? = be r an r a t io 8 1 5 s o t h a t i t be an h te r m o f th e r a tio q u a to com es e b a it s o th a t ) d t he f a n a ir lin e r w a s w o rk do n e by IA n s x x ( 2x l) + m en in 6) - i n c r e a s e d i n th e r a t io R s 1 4 2 1 F i n d t h e i n c r e a s e i n t h e fi , 7 th e 5 c o st o f re R s 4 06 ) o f d 22 d ie r s ns ys v a lu e o t i o 3 : 1 0 F i n d th e a c e r ta i n jo u m bm su n s: 3) (x i n th e a re o be m ust by ne T h e in n s a re re r a t io d ? (A C : fa r e b a n te I n e o 8b ) + be 2 9 Fi n d 5 ? be c o (x \8 = ns m u st ( i i ) W n a t q u a n t it y (5 ) T h e 5y + Fi n d ( 5 o 3 = o nu m 3x : o f f ic to t h e n u m b e r l d ie r s so now T he rs no is 1 o f w ere f k i l le d T h e so ie rs r a t io be t w 1 3 F in d num be r o f o ff ic e r s o f fic e r s 21 ; no o f so 3 1 be fo r e a be r o e e n th e n u m : - 3 w as ld i e r s an - d so f ld i e r s i n t h e 2 1 7) Scanned by \ ( 8) I f b a b+ c + a c (A n s : h eac ( 9 ) F in d t h e ( i ) 3a Oi ) : 2b b a : a + ra t io b tr i p l ic a te F in d : b (a , d d 4x b )2 + ( 1 2 ) Qu a n t it i e s (A n s : a a an , b2 r a t io be r de r s an are c are 2 d b a 4 a m x eac h g iv is e n r a t io e qu a to 1 - b4 4 (A 3, 6 to are an re 5 r e q u ir e 6 , the : qu ir e d rec d com ip r o c a l po u n de d com po ra un d r at io l) I t i o o f 2 5 : 4 2 a n d t he r a t io - 1 f a : ) d 4 5 6 25 an d 1 8 c o n t in u e d in r a t io een l to 1 2 b 2 )2 b n y ; ( i i) : T he n s: 2 (a : an d O 16 p r o p o r t io n ; f i n d th e v a u e s o an d b 5 0) = su b t r a c t e d fr o (A in p r o p o r ti o n to e a c d p r o p o r tio n ) (a b + cd ) , d p r o p o r t io n a l b e tw h o u ld b e s an f th e d u p l i c a t e o t io o f 2 1 6 : 34 3 2, I O a n d b c o n tin u e 2 + d d 2 + de d ( 1 4 ) W h a t s h o u l d be a d d e d ( 1 5) I f ( a : a po m ean 04 - num r e m a in in 3y the th i r d p r o p o r tio n a ( i i i) are : po u n d u n - f c om c o m ra an O ; s ho w t h a t c 1) (i) t h e fo u r t h pr o p o r tio n a l (i i ) t he ( 1 3) W n a t : n r e qu ir e ( 1 0) F i n d t h e ( 1 1) 2m , b+ a + is r a tio s r a t io o po u n d d an b a + f th e g iv e n o com l A n s : (i ) su c = an h o (A n s : d (b 2 i n p r o p o r t i o n (A ns: + a 1 4x ns: f the , h m eac num an num d b e r s 1 3 , 17 q u ir e d d 2 num ) a r e in c f th e 84 - re b, o an d d be r x an - c o n t in u e a re b e r s 2 3 , 3 0, 5 7 - an d 7 8; so t h a t t he 6) d 22 s o t h a t t he r e s u t i n g num be r s 3) d p r o p o r t i o n pr o v in pr o p o r tio n e tha t a , b , c ) Scanned by ( 1 6) i r p q ( 1 7) If a * b p r o po If (A ( 1 9) I f an ' c a + c n s : ' = a , q is t he p 2 : r d r tio n a (A n s : ( 1 8) q p r o v e th a t p , l be t w i s t he b b, c m ean an an 2 + ' a an d b + d d r 2 _ a re q , pr o v e tha t 2 q : f r a t io o IA n s : a + c p d b+ an ) : r c pr o v , e t ha ' t c ' i s t he m ea n ' = , ' een and ' a e tha t a pr o v , b , ' c b ) ' a n d d a re i n p r o po r t io n in pr o po r tio n ) 4 p ( 2 0) I f z p r o p o r t i o n a b e tw d ' p r o p o r t io n a l b e t w m ean q een ' p - b i s t he d u p ic a t e a : m : r eac een p 2 h Biv q e n ra 2 tio a n + r , pr o v e t ha t r d d 2 an d is equ a l to Scanned by (2 2 ) 6 is the x an (2 3 ) I f (2 5 ) I f (2 6 ) I f P F i n d th e d y 8x + l 3y 8x 1 3y 8a 5b 8c p r o po r ti o m ea n " 7 8a x + 8c y ' + ' + x 5b 5b fi n d t h e ' e e n tw o n u m (A n s : be r s fin d , 5d = num 9 be t w n : pr o v v a lu e s o e tha t f : x an d y 2x 13 - y : are and 3 4 8 i s t h i r d p r o po r t i o n an o f d 12) 1) _ d b 2x p x t h e r e q u ir e d n o s (A n s : y be r s + p p + 2y 2y (A n s - 2) Scanned by (29 ) r x ( ) n e ac (A - ns ; h Rem ( 3 ) F i n d th e o f 5 a in v a l h e th e r ( x r e m a in F i n d th e c as e ( 2 ) F i n d th e w + de r o (A n s : k f f Q = if ( ' ' a de r he n w 2 ) is x a x ? 3a Bx f c t o r o f (A n s : k f Bc t o r i f ( he d iv i s io n ' bx e th a t : b x + = O , 4 is d i v i d e d b y 2 x + + 1 5 a a ls o a 5 ) is v a lue o 8 - o f a x x ' + 2 2 13 : (x - " 9x ' + kr 5 ) is + a , th t o r ) 10 by 4x H e n c e de te r m in e 10 + x + 8 i s d i v \d e d b y c 3 le a v e s a re m a in de r 2) (4 ) W n e n t h e p o y n o m i a 2 x i 6 1 4 F i n d t h v a l u e ( 5 ) T h e po l y n o m i a l s 3x w pr o v , he n d i v i{ k d b y x o ' lc r + ' f' k ' (A n s : k z a Jr + 5x 3 F i n d th e 3) ( 5k - 13 v a u e o x 2 th e , r e m a in de r 2) an f ' d (a a ' + 1) x (A n s : z Q 7x - + 5 l e a v e t he s a m e r e m a i n de r 5) Scanned by \ W f (x ) nen d iv id e d b y (A (7 ) n s : W ha t a be d iv id e d b y x ( 8) D e t e r m i n e w lA ( 9) I f n s 2 is x ( 1 0) G i v (A e n th a t x n s : a fa c to r o 7 - r o 2 + x fa c t o f an d an d b 3 a x f it F in d th e en ex ( 1 3 ) S ho w th a t 2 x ex + p r e s s io n c o m 7 is a IA . 6 5 f x rs o is d an b d zero as he n w ' f x + 3 + x x 3 re s u be r be to 2 x lt i n g p o l y n + x a 1 dd e d 3) = or n o t ia l i s om ? ia l) a c + (A n s : a b ; a - 5) c a l c u l a t e th e v a l u e s o f a a n d b ) 6 le a v ' ' a 3 f 2 2 3 + e s r e m a in an s h o w t ha t o x fi n d t h e , f a c to a re n s u s in o 2a + bx fa c t o r p le te l y f v a lu e o , ' a th e r e q u i r e d n u m n s : 7x 6 f tha t w h e n t he so m v a lu e o p r e s s io n (A x f t h e g i v e n po ly n o = ( 1 2 ) U s i n g th e F a c t o r T h e o r e m th e g i v fa c to r z + 3x + 3 2 + 3 4 r o x v a lu e s o i de r re m a n ) de r is 3 ? a 2 x 2 , th e x 3 0 F in d the d d e d to 2 1 is x not a 14 r e m a in , he the r a 8 i s d i v id e d b y de r is = ld b e 2 the fa c t o a ( 1 1 ) P o y n o m ia l a r sho u 1 is x d b an bx r e m a in , 7 2 x 1 t he x + - n u m 3 + x = d ' b (A ' (x 2 ) is 5x 2 5x g th e f a c t o r z w a - fa c t o r (x 1 lx ex 8 ns: a = th e o r e m ( 1 4 ) U s in g th e R e m a i n d e r T h e o r e m fa c t o r i s e th e de r IA h e n d iv i d e d b y 2 o an z f 3x 2 ) ( 3x d b l + 1 x an d 5x , ) en ns ( 2x ) n 2 3 + is 2 H e n c e fa c t o r i s e H e n c e fa c t o r i s e th e i v g pr e s s io 2 5) = 4 + x 7 x ) (x 2 2) 2x (x 1 + co m p le te ly Scanned by ( 1 5) F in d ( 1 6) th e (x + g iv en If lu e v a 5 ) it s fa as po l y n o (x 2 ) is ( i ) fi n d t h e Oi ) w ith t h e a f o ' lu e o ' r b ' the p le t e l y f 2 3 s o th a t th e v a lu (A z x f es o n s: a [ lu e s 2 x a v a b 2 B . 1 A = o f o - [ x ' a ' 13 - an d an b ' x ' , d b 3 + as o a x bx bta i n e d 31 ; = 2 + (x a bo 4 5 ha s v e 1) (x + , (x 1) an d f a c to r i s e t h e 9) (x + 5) 2 px f p fa c to r i s e t h e , a D M ( 1 ) F i n d th e p o y n o m ia l f p v a lu e o v a Fo c o m fa c t o r d an c to r s ia l m ' a , y , a an ] [ d b IA , n s bo v e ex p r e s s io n c o m p e t e ly ATRICE S if . - 2 , . - 3 , - 2 an d b = 4) Scanned by o) f A 4 = B (4 ) f po (A A A + m a tr i x A ss ib l e A n s : ,l ; t _ B + X [ = : ] ( i) A + A [ 1 3 B d c an _ . d B . . [ = ] Bt [: = Oi ) t ; fi n d B + ] B [ ', a _ ; f in d t' " SP. . . At , i . E s t A an d B t [f t " ; A " p o s s i b le no t an d B " " po ss i b le l a) 4 i 2 A [: ] = B + B' (i ) = ] C ]) fi n d , B 0l 1 (ii) X B : = , t he n s o lv e fo r 2 2 m a t r ix X suc h t ha t ; On x = A + B = t 5, ' Scanned by [ 5, ] ( 7 ) G iv e n ' " i ' " . (9 ) I F A (1 o) = L et A G iv = ] , , e a rea son (A n s . A B - d e v a l u a te ] [ - . n If ye s d B , = . . A 2 Tr i ' 3A [a , l , ] " + 2l, w ; n d . he r e l is . Tr i . X . . c h a M a u n t m a t r i x o f A o rde r . 2X = B 2 i s t h e p r o d u c t A B po s s ib l e ? fin d A B 12 1, Scanned by ( 3) If B an d C a r e tw o m a t r ic e s s u c t h e m a tr ix A s o t ha t B A ( 1 4 ) n d the W r ite do (A ns : m a tr i x w n : M suc . ( i ) th e the o r de r o f the 1 V e r (Q n Q i fy the 14 j eac ne r a h fo l lo w [: l " [ f th e = , m a t r ix X a x = ] ' X b ) [ - , 16 Oi ) t h e 2 = ] IA n s : m a tr ix M = [ 4 50 X 1 [ ] [:] = T o m a tr i x - m lA n s h th a t M rd e r o t h e m a tr ix x C = h t ha t B A r i t h m ? g P r Qm e r in g in m an s i o rm u ) A P an d th e n w he r e w r ite i ts g e n e r a l t e r m 13 W r i t e th e f i r s t t h r e e t e r m s o f the A P = 5, d = 3 Scanned by 3 ( 1 \ W n ic h te r m o f the A P 5 3 4 8 4 3 n ic h te o f the A P 3 , 1 0 1 7 , 4 W 5 F i n d th e 6 F in d 7 F i n d t h e \ 2 th t e 8 F in d k te r m s o 9 ' so , f , id d le t e m h e th e w ' rm r rm 5 5 is a te r m 2 o en m d o f the A P 4 k + 8, 2 k + 11 I f th e o su m 1 4 th t e r m i s su m o o f A p is an f th e 3rd z 6 3k + 6 + 37 0 4, 2, an ? rm r n o t d 3k 2 w h i c h te r m it i s 1 00 , . If y e s , f n d + 4k + 4 are th e t h r e e c o n s e c u tiv e an z ero d t h e 8t h an , d l th t e r m i s the n pr o v te r m s o e tha t f an 3 an 15 m o re tha n 1 1 th t e r m i t s 2 9 h t e r m i s tw i c e i t s 1 9 h t e r m A P is 7 a n d th e su m o f t h e 7 th an d th 3 , the n f i n d t h e 1 0 t e r m f thr e e n u m V n e I I (O n M m a (i) F i n d , te e t h a n i t s 1 3 h t e r m ? m o re f t h e A P 7 , 1 0, 1 3 , F i n d t h e A P i f t h e 6 1h t e r m i s 1 9 T he i l l b e 84 w . g a t iv ne A P a n I f th e 9 th t e r m 13 Is t h e f i r s t , f t h e A P 2 1 3 , 2 05 , 1 9 7 , o fr o rm th a t k 10 12 , the s u m o b e r s in A P i s n s (s ttw nr . d the ir pr o d u c t is 8 F in d th e num be r s )) f t h e f ir s t 2 4 t e r m s o fA P : 0 6 , 1 7 , 2 8, Scanned by J c i ) F in d t h e 14 How te r m 15 If a n 3 - f 17 F in d th e are 18 4n A P 1 5 F i n d th e 19 20 Y su m o d an su m an o u r an f in d o u sa v e 2 00 o g s t he n + 12 + 67 + e x t t h e 2 00 m 30 e pe c t iv re s f the l d be t a k e n s o t ha t the ir la s t s Fo r m a 3. an A P A l s o f in d s zo + 1 ) , th e n f n d t h e A P te r m s o gle s o n a tu r a n P f a an d R s 10 in n tn a r e s ta c , a 2: , f the f ir s t 1 7 a l l t he a 1 s ho u l f an A P ho w se 4 1h t e r m a n d 9 1h t e r m s y b e r s be t w n um 101 een an d 9 99 w h ic h a re d iv i s ib e d 5 R s 2 7 5 I f in 21 9 + (4 n n = E E ? c a t i o T he fo the n 7 : th e n s ho w t ha t a , if Sn , b y bo t h 2 Tym m f o m a n y te r m s o f t h e A P 5 4 5 1 4 8 , , . i s 5 \ 3 ? A l s o f i n d the s u m o f h t e te r m 16 an Su m ro b e a gj q u a d r i la t e r a l fo r m g le s t he fir s t w ee k o an A P I f th e co m m o n f t he y e a r t h e n i n c r e a s e d d if e r e n c e i s 1 5 w ee k ly sav t h e w e e k y o u r s a v i n g s be c o m e R s 5 9 5 F i n d n , k e d i n t h e fo o b o v e it 1 8 i n t h e , l o s s p la c e d an nex d ho w w in g t, a m a 2 0 o g s i n t h e b o tt o m m anner bo v e y o g s it an are d so o n [n h o w t h e r e i n th e t o p m an row y ro w , i n Bs b y , 19 in ro w a s a re ? Scanned by 22 A m an fo rm er pa y s R s 9 7 5 in by R s 5 T he a e n t ir e a m o u n t m o n t h ly T o u n 1 V 2 er i fy th a t r a eac in s t a l m e n ts , e ac f t r s t i n s ta l m e n t h in s ta l lm h T er m G E M E ? W r i t e th e f i r s t f i v C PR OG ? SS l O N (G U , e te r m s o G p an f the G p ho w an se n d the n th w r i t e t h e n e x t th r e e te r m s is te r m 5 2 3 4 5 F i n d t h e 7 th t e r m W h ic h te rm o o F in d 7 Pr o 8 T h e f i r s t te r m x v e so F in d th e 6 8 th , l l o f te r m 27 ' Is . th e e n d o f t he G P m th a t x + 9 h 1 n + l , f the G P t h a t 5 th , n f the G P 0 4 0 8 1 6 , . F in d t h e 5 t h t e r m f r o 6 be i n g e s s tha n the w h a t t i m e w i l l th e ) f th e fo l o w in g is o e nt is R s 1 oo n be p a i d ? 11 T y o e I ( OE n e t o , th x + 6 te r m s o a G P is 8 1 o f th e G P d 4 an f an a are G P d the ? 2 : 27 2 I 9 2 , = 3 ' , 1 62 t h r e e s u c c e s s i v e te r m s o f a G p are th r e e squ a r e o s u c c e s s iv e t e r m s o f th e t h ir d te r m is f e qu a a n a n o the r G p l t o it s l s t te r m Scanned by 9 T he p r o d u c t o f t h r e e n u m b e r i s n a G P is 2 1 6 a n d th e n u m be r s k t i a e n n pa i r s is 1 5 6 , F in d t h e n u m b e r s 10 T h e t h ir d te r m e e f a I O n S u m O f n (i) 11 F in d t h e (i i ) 0 15 12 F in d th e 13 F in d 14 T he n + f J f + 0 0 15 + 0 00 1 5 3 + f o : F in d the p r o du c t a l 6 + 5 - , f the p r o d u c ts f it s f i r s t f i v e o f th e te r m s n To n t e r m s To 8 t e r m s + 12 a 3 4 + + + 1 536 + 320 - , r 2 - (2 " te r m s o f a pr o g r e s s io n is n o o T e r m s (S o d S n if o G P is 4 su m sum an su m o su m 1 ) S h o w th a t i t i s G P F i n d i ts a c o o n r a tio 15 G iv en a 16 T he sum F i n d th e T v 17 c A bo y G P it h w f thr e e o nu m n um m ds R P s 0 ne s ide o f cess w a s qu a r e be r s i n a T7 d - D e te r m in e d 5 7 64 G P is 2 1 an d th e sum f th e i r s q u o ro i s 1 89 are s b e m s ) m uc h i s 1 0c m , in w ee a l T he k, R w m s 4 5 in the i l l he s pe n i dp o in ts o d a f i ts sec o n t the s d en id e s w ee d ar e o k, R f 8 , w ho se m 1 3 5 in the s w ee j o in e d id p o i n t s a r e a g a i n j o i n e d t o f o r m o n e i s c o n t i n u e d t h r e e m o r e t i m e s F i n d t h e s u m o f th e a n o th e r s q u a r e T he pr o an 1 5 i n th e f i r s t t h i r d w e e k F in d ho 18 729 - be r s a s pe n a ks to fo r m qu a r e o f a l l s qu a r e s m o re s area s Scanned by CO T he t r ia n g le A A B C do (i) (2 ) an O , , t r ia n B , n s : P = re n e c te d in t he c o o r d i n a te s o d i n a te s (8 6) ; C o is re o x B , fl e c t e d i n Co f le c t e d i n t h e l in e 0 y th e o r i g i n o n t o tr i a n l e A g - f the i m ge a o o r d i n a te s o f p f th e i m o n to tr i a n g le B C ax is W te d C an is ax R E FL ECTIO N re f its i m a g e f P o r d in a te s o , O M E T RY d C (3 , 7 ) i s fi r s t a n ( i i) A co o r f d C an ( i) F i n d th e ( i i) F i n d t h e 4) , D g le A B C w n t he c o o r d in a t e s o A R ( \ 2 ) B (4 d the n A po in t P is (A - un ge a de r o re f p a re (8 f e c t i o n i n th e y u n de r re l l e c t io n 6) , ax is i n th e y - ( 8 6) , ( 3 ) P o i n t s ( 5 0 ) a n d (4 0 ) a r e i n v a r i a n t p o i n t s u n d e r r e f l e c t i o n i n t h e l i n e L ; p o i n t s ( O 6 ) a n d ( 0 5 ) a r e i n v a r i a n t o n r e fl e c t i o n i n t h e i n e L 2 ( a ) N a m e o r w r i t e e q u a t i o n s fo r t h e l i n e s L I a n d L 2 ( b ) W r i t e d o w n t h e i m a g e s o f P ( 2 6 ) a n d Q( 8 3 ) o n r e f l e c t i o n i n L N a m e t h e i m a g e s as " a n d Q r e s pe c t iv e y ( c ) W r i t e d o w n t h e i m a g e s o f P a n d Q o n r e fl e c t i o n in L z N a m e e i m a g e s a s P a n d Q , , . , , , p e c t iv e ly S ta t e o r de s c r ibe re s a s i n g l e t r a n s fo r m a t i o n t h a t m a p s Q (d ) O ( A n s : (a ) T h e i n e L r i s x a x i s w h o s e e q u a t i o n i s y o n to Q - , T h e i n e L 2 is y (b ) P (4 ) ( i ) F i n d t h e ( i i ) F i n d t he (A n s : ( i ) P (2 = , 6 ); re u e c t io re f le c tio n (5 , Q a x is , ho s e w e q u a t io n i s x ( 8 3) . , f t h e p o i n t P ( 1 3 ) in t he l i n e o f t h e p o i n t Q( 2 , 1 ) i n t h e l i n e y n o 3 ) ; (i i) Q , (2 O - , x + 2 a 3 = 0 7) Scanned by ( 5 ) T h e p o in t s P (5 , 1 ) im a (A ns: P e s and th e co Q an d Q( 2 2) a re re d Q r e s pe c , f p o in ts P d i o r n a te s o f P o an ( . - t i v e l y in i n e r - 2 U s e g r a p h p a p e r t o fi n d t h e 2 T a k e 2 c m e q u a l t o 2 u n i ts , a g r a p h p a p e f o r th i s q u e s t io n P l o t t h e p o i n t s P (3 2 ) a n d Q ( 3 , ( T a k e t w o d i v i s i o n 1 u n i t o n b o th t h e a x e s ) 2 ) F r o m P a n d Q dr a w e r e n d ic u a r s P M a d N n p p Q - , a x is x x 1 1) (6 ) U s e o n th e fl e c t e d l n l i n e (a ) W r i t e t h e c o o r d i n a t e s o f p o i n t s M a n d N ( b ) N a m e t h e i m a g e o f P o n r e tl e c t i o n i n th e o r i i n g (c ) A s s i g n t h e s p e c i a l n a m e t o g e o m e t r i c a l f i u r e p M Q N a n d fi n d i t s a r e a g (d ) W r i t e t h e c o o r d i n a t e s o f t h e p o i n t t o w h i c h M i s m a e d o n r e f l e c t i i on n pp ( i) x ? i s Oi ) y a x i s i i i i i ( ) or , (A C n s : Co g , o o r din a te s o o r d in a te s o fM fN (3 , 0) = ( = and 3 , 0) (7 ) U s e g r a p h p a p e r fo r t h i s q u e s t i o n T h e p o i n t s A ( 2 3 ) B (4 5 ) a n d C ( 7 2 ) a r e t h e v e r t i c e s o f A A B C ( i) W r it e do w n t he c o o r d in a t e s o f A B C i f A B C is t h e im a g e , , , , , re f e c t e d in th e n t h e c o o r d i n a te s o ( ii ) W r i t e d o w w (ii i) M he n en A BCC m ( 1 ) F in d t h e re o e c te d in the t i o n t he s p e c ia (2 . B l 3 ), B , is an , x ax th e r a t i o 1 : 2 (4 B :, C if A A B C i s th e im f t h e q u a d r i a te r a B C C B a nd f i n d it s , , 5) an dC . i s o s c e l e s tr a p e z iu m ; o n th e x (A w , he n ns: a ge o f AA B C , is nam e o _ fA (7 area o a x is w f q u a d r i la te r a l B C C B . on x 2 1 sq u n it ) MI P A MWF O R MU L A E h o s e d i s t a n c e s f r o m th e p o i n t s A ( 7 , 6 ) R e q u ir e d p o i n t s a rea 2) , c T I o N F O R M U L 1 CI po in ts ABC o r ig in a x is a r e : ( 9 0) , an d ( , an d B ( 3, 4) are in O) Scanned by (2 ) P o i n t P( x Ox (3) F i n d th e a re \ (4 , 8y - 21 c o o r din a te s 6) F i n d the r a t io 2 ( 5 ) F in d t h e lA (6 ) I n w n s: ha t , co n s : (0 (A 4) . an (A o in r a t io w f th e ( r a t io e o r d in a t e s o 3 ra re s pe c t i v e ly w 10 x - (A n s : t io in A ls o w an d th e re po in t s o lA n s the r e q u ir e d po i n t (4 o Pro v e t ha t 21 ) - c ir c u m c e n j o in t o f ho s e w v e r t ic e s A , B t r e o f th e g i v e n t r i a n g l e A (4 5) , a n d C an - (3 3) , d B (6 3) i n t h e , e j o in i n g p o in t s (2 ) , a n d (7 , 6 ) , 2) 5 ) d i v ide d by t h e d (3 , an x ax is ? A ls o , f in te r s e c ti o n q u i r e d p o in t j o in i n g the f in t e r s e c t i o n o f in t e r s e c t i o p o i n t s (4 , 6 ) f th e po i n t c o o r d in a te s o f in d t he - , the h ic h th e in e lin e y , 2) f th e p o in t 2 ; 5 - 4) ) 9 j o in in g d B (3 , f th e t r ia n g le A B C ; h ic h d i v i de s the , is 3 an 8y , i s t h e l in C a lc u la t e th e d th a t h i c h t h e p o i r t ( 5 4 ) d i v i d e s t h e l in r a t io r a t io ve p o i n t s A ( 2 , 0) c i r c u m c e n tr e o 3 q u ir e d T he pro f po in t P = the r e c o nc e d (6 , 2 ) p ns : He n s : o r d in a te s o 5 : f in d th e (A ) i s e q u i d i s ta n c e f r o m t h e y - ( , o n an ( - d ( , 5 , O) 4 ) i s d iv i d e d b y t h e f in te r s e c t io n 3) Scanned by ( 8) T h e o r i g in O , B ( 6 9) , the r a tio 1 : 2 (A (9 ) S ho th a t w (4 A F in d the p o in t P n s : 2) , ( 1 0) F i n d t h e (3 P an (1 1) (14 A c o ( 12) o r T he d in a te s m o f m i d po in t o f the d ( ( 4) A B C is C (A = (a n s: 1 ) , fi n d a f the l in v a lu e o f th e in th e n s j o i n in g ( 3 m 2 An d i d p o in t th e c o u la te A lso f ' e se e se gm (A ' m en t gm = ' 7 ; b a = ' an , s ho w th a t p q : BC = B C ) = en n s : t j o in m i n g th e p o i n t s 5) - j o in in g n o - v e r te x 6) , f th e p o in ts P (4 6) , an d F in d th e p a r a l l e lo g ra m A B C D (0 C d an a 2) , ) F i n d th e ( 4 3n ) i s ( 1 2 m , , O) f AB o r d i n a te s o Q (2 , f , 4) is v e r tic e s A m , id p o i n t B an f BC o d R ( 1 2 ) is an , d C P h c e n tr o i d o f t h e t r i a n g l e t r i a n g l e a n d G (4 , 3 ) i s t e a , m _ n o thr e e v e r ti c e s o lA C en t m s : 2 , 5) is ; a re , gm Q d 1 ) ; p o in t p Q , o an f t r i a n g l e O B C p o i n t p d i v id e s 0 8 i n 1) , (8 2 ) t h v e r te x C a lc f A C (1 u r e se (4 id p o i n t d D (A n n P , m = f p o in ts P fin d the a n f Th e l i n o I n tr i a n g l e A B C m 2) f th e fo a n o a r e v e r t ic e s o f tr i s e c t io o , M i d p o in t n s : i d p o in t v a lu e s o ( 1 3) , d i n a te s co or 3) , Q po i n t a ( 1 4) H e n c e 2 ), B (6 , , ) is 5 d 8 , ; po in t , m (12 o r din a te s o co ( 2 3) = , Q ( 2 4 ) (A d C an d ' b 5 ; BC F i n d t h e e n g th ' = 5 u n it s o If A = (1 , 3) , B = (4 b ) , an d f s i de B C ) Scanned by Oa u i (t h s i \ H n A B f we q m - \ B DE 3 A a d A D (i m B D l u a r e AC A B c is a A B D is 3 6 = c m a n i m i a s d CD p er m d ic n a u k a g le r ight a n o d b ) Bc r m u k M e AD gle d a t v e n e x & c A D r oo 6 4 i u c M r ia n a pe 4 = is a l t i t hat \ R , D E m m e f pn ) a ti w / ; f i n d t h e e n th o f AD g c m / A ls lA (4) In e se A PO B d A B C DE = n s: 3 r e , gm 120 = P o in ts o n (A D E n s lin (& f in d , t he fig u th e (5 ) In o , an A B r - A D E) (a A B C ) l 5 = g iv m cm 2 , d A C 54 u 9 0 c m = 6 (t r r A r (A A D E) a p e z iu AB , = A area o rc - 6 d an c m area o r e s p e c t iv e a te t he 2 A g s id e , p B f in d t he = d L \ BCED) m ) a o n g le B a n c m a n A B If PO ent C a c c m area A \ = em su c an 9 p e r p e n d i c u la rs d f cm 2 ) d AC h tha t f ABc cm are an are a o QO A (A n s : 2 7 0 12 ly QO , f A QA an an = 15 cm 2 d th e n t h e ) D cm g le A E D to = an 90 are a o dE an are d f & ADE ! Y Scanned by . r (6 The scale o f ma p is 5e 000 In the map i) , m \ ar a lr i p ot ABC o f lan d ha s the fo low n g dtmen sio n s i l ABC = 90P AB = 2 cn , BC - 3 5 u n and angl e c a lcu a e ii ihe le n @ o f s ide bc in km . . o f the land i O875 sq Km ) (ii) tbe area o f he plot in Km IAns (i) l 75 km ; (i ) C ' m A re x an gje tank has len gth = 4 m , w idth = 3 m and e\ tan k is ma de w itl ca \ 3 h ity 30m A sma ll m ode o f t e - ity 240c m 3 Find fi) d e dim ens ions o f the mo de . i (ii) dbe ra io betwee the total m r f e air ea o f the tan k and ts lAns (i) 8cm x 6c m x 5 cm . , an gle RpT and an gle PRQ= ang e PTS R and PST ar e s im ilar (i) pro v e d at u iangles PQ (ii) If PT ST 3 = . (ii) 2500 1) (81 In the f gure giv en a longs ide An gle Qps = m ode / . \ 4 ; fin d the ratio betwee QR : Pk Scanned by in t p ( i v ) M a r k h p o A # tr * n * k c o n {u c l io n s tr a ( i) ig h t l i n e a lw a y s we \ i d \# w \c e a nd fo e q u I n m i t d f PB t h e \e n * th o f BC O e po in t P ( ii ) p i e q a i di a ( 5) A hi c h i d f e c o rd M (4) C o n m w f n m A B , l c w iM A B 8cm . a nd a n g le M L - M) " \ n e Mt by h t ha t *w AB m 7c m B L - and D ra w A B i s 8c m \o n * hc a ru l r o t d t B c M e a s u re t he l o c u s a n d de s c r i be o \c n g t h f P \ t a i n t w h ic h i s 4 c m fr o m t h e l i m A B M a r k t h e tw o po i n t s x and Y, w hic h a re 4 cm fr o m A B a n d equ i d i # t n n c e fr o m A and B Y D e s c r ib e th e gu n A X B 2c m - \ u e s ti o n T a ke i h s t f r o q r e h a a (6 ) u * g r p p p 7 \ b ( 5 , 3 ) a n d C (2 , ) i p o t t he po i n t s A ( 1 ) () ( ii ) c s of o n s t r u c t th e l o u ( i i i ) c o n s tr u c t i tp ( i v ) L o c a te t h e p o n ( v ) M e a s u re bo t h t h e ax es , , the lo c u s u n it o n of su c i d i s ta n c e p o i n t s e qu fr o m A a nd B d AC ta n c e fr o m A B a n po i n t a e qu idi s AB u id i s t a n c e f r o m i h th a t pA - p B a n d P s e q h a n d r ec o r d t e l e n g th P A i n and AC cm Scanned by ( 7) C o n s tr u c t a (i) C n g le B C P g i B C v e n t he r e c ta n P s e q u id i s ta n c e fr o m A B (b ) P i s e q u id i s ta n c e fr o m C e a s u r e a n o m (a ) i J) ia tr p l e te M d g le A B C D d t h e le r e c o r n g 5 p o in t E a t a c (2 ) fi g e th m e e ts A E (A (3 ) A o c f le n s : ho n r d c m o f th e c g n t E C D e p in O c e n tr e is h th a t s u c g le p B C 4 5 " c e h E r a a t s ) h ic h w s u c d iu d C D o r e te r m a t te r s e c ts tha t r o v e d ia a A B fin d th c m a n C IR C L E S C h o rd A B n s : id s ith w d f A B g le A E D a n (A lo a h th f th o is dr t a e c ir c le ) C g th 4 8 e n t c m is a t a w n in th e d is ta n c e s a n e c o ir f 1o th e c e n tr e o o m f in d it s d is t a le c fr c m n c e fr o m s o f th e c ir c le th e c e n A tr e o n o f th th e r c ho rd e ir c le c jo in i n g th e in id p o m ts o f t w o p a r a l e l c ho r d f a c ir c le p a o p po s s e s th r o u g h th e it r o v e a n e c ts le c a n ) gm (5) C h o r ds A B n c m c m c m s e e p c e n tr e f le o a ir c I f C E is 3 c m 1 4 r e n d A B o r 4 g th 2 0 (4) T h e in 42 h c a h o rd C D g iv u r e B E l An s 24 c e n tr e c e f o I f O E b is h o rd A B f n th d C D a n c m d D a n 1 6 ( J) C h o r d A B 4 a t d B C a n th o B P c m h th s u c d C D i r c le ; fi n d th e r a o f a c If A B d iu s o i r c le = l th e a re a 36 c c m i r c le p , ar a C D (A le ] t o = n s : e a c 48 R c m = h o the r a n a n 30 d l ie d the d is ta c m a n n c e b e tw s it e e e n s id e th e c s o f th e ho r d s is ) Scanned by (6 ) A B d C D a n tT A B a r e tw o e d CD a n th e c i r c c pr o (? ) T w , be in g o n v e tha t o c ir c e s w i th Pr tw o u n e (9 ) I n t h e L lA n s : A DC F in d B A c r a n ho r d s o hn ith w (b ) p l n J p Q pe r w Th e n o u \ h id * n pl ) = h rse c t e a c a c i r c e c e n tre t \ 1ln t P M eet nt d B i n te f lr c c n c pC - c o m m o n c ( 2 ) I n th e AB = ( i) L L C a en , an an A BC lA figu re th e r \t w In t p d ic hig ge r u a r ly ( A ho H is ns : D EC d L O A PQ , PR = If L C an d L PR Q = BAC L ( ii ) L = 1 18 DAB {) p rtw e th a t th e u n \r \ h lq e c \s p 9 t to th e c e n tr e 1 6 th e c \ r c \e 7 0 t h r o u gh t he po in ts 67 ; A C is re A ED = c a lc u la te (iii) 350 r e s h o w s a c ir c l e d D an (i i i) \ 1 o = n n c \o s e r 40) n s d j o i n i n g fi g u BC g le A o c ( ii ) 1 2 5 ; QA R g iv , d jo i n i n g fi u g a L fi gure (i i) ( i) 5 5 ( 1 0) I n t h e , (a ) p A qu a l d j o in i n g a ( i) A nj s n it ov e ( 1 1 ) T he \m c pmduc e d c e n tr e l in e A B b is e c ts th e (8) O u t o qua , a f n d : d ia m L DBC e te r o + L f th e DC B c i r \e C a l c u l a te lA n s ( i ) 2 8 ( i i ) 73) Scanned by \\ t\ L \ \ \ in f t he Ptw k \ t s l n the Gi\ re c in ABC L d ( i) A ( 1 6) I f o an ( i) 2 5 n o s th e r m id e s s id e s 17 ( I ) A B C is a r i ght a n O is th e = c e n tr e e n tr e o f tr i a n g e I F a n g \e B A C f the 5 0 = Fi n d an g l e I C D ( i i i) an gle B C D ( i i i ) t 5) y i c l i c q u a d r i l a l ie r a l a re e C A 60 m e e t s t h e c i r c u m c i r te o t ii ) a c e te r 1 40 = ( i i) 5 5 f n m I is the in c 7 0 = ' o r po in t D g le B C D ns a gk A O C re a t g le A B C an is F in d 5 n mgs i p n c le A B C an n 2L y fig u m t t n a m i a n : g i\ th a t A t w 1 1 4 1 n t \e g u u * rh 5V e pa r a lle l are , pr o v e th a t t h e qu a l T A N G E F T S A M ) I N T E R S E C T I N G C H O R D S g l e d tr i a n g l e w ith A B = 6 c m an d Scanned by (2 ) A , B an n \ e e ts d C t h r e e p o i n ts a re B A pr o du c e d 48 by A B f th e (3) T w o c d ir e c t (4 ) T h e a t c e n tre o i r c le ith s w c e n te r s o t h e tr a n s f tw d Qc (A (6 ) I n ns : f ( i) ( i) I t h e g iv C ho r d ta a re v a lu e s o o f ii 25 Be n t o c ir c e s an 12 e n n e n a lo n f g u r e 68 , c m a n d 9 (A n s : w ith (ii ) an O If x at an o + R fig u en D ia = = x , s m e te r g le S P R 2y re h th a t P T to Q an w d n t a t c = 36 a n g e su bte d de d n to = g le c m ns 6 QR , ith e a c a n d 2 c m ) o the r h ext er nal l y F in d the le n g th o the le f the ) c m IA h u c a n g le R O c e n tr e are c m QP c a , = lc u IO 6 8 c m , a pa r t C a lc u la te n g th o f PC a te th e Qc p ) a n A t C in te r s e c t s A B p r o d u c e d ( ) I n t h e g i v ge g le A T C c Ln A B is th e d ia m a c ir c e s u c ta n 96 ) d ii 6 ra pQ , a n 30 ta n ge n t g e Q o p ( i i) n s : t o th e c i r c l e w ge n ts ; (A gs ide T he n tha t a n l a te t h e c ir c e v e rse c o m m o n ( 5 ) I n t h e f i g r r e g i v an G iv e c a lc u ' rad c o m m o n ta n T a t tha t a n g e A C T ir c e o n a c u c g le B A C a t D he s g le 3 0o T h e ta n g e n t = Pro QR P = i th m e e ts y BC th a t v e a c ir c le w he n pr o d u c e d an d A C is the e te r a n , cen PT s ho w = BD A [ tr e at P th a t 9 0 R Scanned by (8) I n th c g iv PA AM = fi 8 u en P ro (9) in a r PB X ( 1 0) A B C i s m Pro an A B C i n s c r i be d I n Pr o a ta n v e th a t to u c ir c le e te r o he s th e g i v e n f ( 13) F r o m e tha c ir c le a t (i) t :a n g e p o a n e x te r io r p o i n ts A na s d Q = p o in t P d B lie d ia m e t e r i s d r a w as A C = n to i n te r s e c t s t h e h y p o te n s id e B c c i r c le th r o u g h B to A id e A B in p o i n t p h th a t A B c ir c le a t a c i r c le w to t h e c i r c l e t h r o u h A a n g Pro v su c g e n t to t h e ith a b it h A B w D E i s p a r a l l e l to B C ( j 2 ) A B i s t h e d ia m an S ho w th a t A B uc = he s 4 x s ide A c at u s e it A p is o s c e le s t r ia n l e g w s an a c w g e n t a t p , b i s e c ts the d i n te r s e c t s ( ] I ) 7 e g i v e n fi u r e s h o g I f D A E is i r c le a c v e t ha t t h e ta n i d d le p o i n t D ir c e c P i s o s c e e s tr ia n le g an g e n t to the z i g h t t r ia n g l e a b c A C in P a ta n sc e e s MB = P M is , v e th a t ( i ) P M B is is o ( ii ) PA re ns : it h cen p o in t R d B at pQ in t A (A an d E A C = , he n c e pr o v e d ) tr e 0 an e pQ t he ta n g e n t s c u ts p o in ts P A l in d Q r e s pe c t iv e ly 9 0 , a ta n ge n t P T o n th e c ir c u m fe r e n c e an o d a sec a n f t he t P A B a r e U a w n to a iv e n c ir c e g c ir c le , pr o v If e th a t t r i a n g l e s P A T a n d P B T a r e s i m i la r ( i i) P A PB = PT 2 Scanned by & C O NW U I Q EI t c l r s ) ( ) D c i r c le e a c h (2) D r a w a n ts g iv e n c k pn i n i r c le fm m dism t a n c e t h is e x te r io r f n c m po in t M o in m e a s u re th e c e n t r e n f th e th c e n g th f n n t ir c e o is 6 0 o n s tr u c t a c f d iu ra i a te in a n sc i r c e i n A b in g o n s tr u c t a r e g u a r (7) D r a w th e a c ir c le c e n tr e e n g th 4 5 s ra D c m ra w tw o ta n g e n ts t o t h i s c i r c l e s o th a t th e a n g e M tr i a n g c A B C w o f C o f ra sc r ib in g i r c le c he x d iu s a o go 3 5 f a n e ith s id e 6 Dr cm f s id e 4 M c m o n s tr u c t t w o ta r o n e ta n gu a r he a re n o q u i a tc r a t r ia n g e a c ir c le c ir c u m s c r a w w ee n the ib i n g t h e f the is l l o c m lA H n s c ur v e F in d = 40 cm C c m k a go f n o w s i t h s id e 5 id e 5 8 o n s tr u c t a c po in t P o u ts t o th e giv c m c m irc le i d e th e en 6 c ir c u m s c r c c ir c ir c le le M a t a ib in B t he he d is t a n ea s u re a n c e o d w r x a f 6 go c m i te d o n fr o w n m th e ge n t C O NE ? (S a rea o ar x a g e n ts f o m P 19 ( I ) The a r ia n g k A B C (5 ) D r a w (6 ) C c M te r 1 2 c m m e t a n 8 c n ts t o t h c ra w ge f d ia o n s t r u c t a n e u r (4 ) C D ta n ta n g e (3) C a c i r c c o ra w : d s u r fa c e o ( i ) t h e h e i h t ; v o u m e - u r f t a e A a c o w El y l i n d e r i s 4 , 4 00 f the 3 8 5 00 , SPH E R E c y l in d e r cm ] cm l Oi ) th e an d th e v o lu c ir c u m m e o f th e fe r e n c ce o f it s b a s e y l in d e r ) Scanned by r (2 ) T he ba rr e o t fu l ba rre l o f i n k in t h e pe m an y w o r (A (3 ) A y l i n d r ic is I 2 c m the m e ta (4 ) T h e ra ha a n d 63 m lA n s m e le t in , s a n t o f o c m c an v as he ig ht f th e m ; a rea 2 c o s m e o ta e , - o v e r y w he f id t h i s l IA a te r n a C c m 3 06 2 n s H ge o w litr e ? a in Th e is 0 4 re o n a n av e ra A m e te r ds ) w o r in d ia m m l dia m a lc u 3 ) c m 7 c m a n e te r o f th e tu be t e th e v o l u m n e o a d 24 re s c m pe c t iv e f ly c o n e ) re c o s m e ta f o d 5 ds w o r c ir c u a r c o n e a r e f the 2 c m l i n d th e de ig h t a r nRh o n an g n g 3 10 4 5 00 n s : lo c m n w r it in f d e c im c e o f is 7 ta i n i n g c o n m a 7 04 w he d s is q u i r e d to t o f the c m a ke a n v a s a a c o n ic a l te n t 1 2 t t h e r a te o f R s in dia m m 5 pe ete r r m e te r R s 8 , 9 1 0) q u ir e d to c a n v a s re w ha pe (A p a - in m t p u s u r fa c e a r e a o A s o ; e n o ne s ds ) T he c m in f in k d the he ig ht 3 d w o r b o t h th e d t h e to ta l 5 94 = a n o 00 c o r r e c t to a u se bo tte a at n 1232 - g th n a re a 2 0% o f the c an v as u se (i) c a a so l i d (A d i n fo ld s an ly l id cm n s : c is c a n v a s 9, 42 8 p a c i ty he ig ht 24 so pe o m e a n le n g th r e s p e c tiv e ( 8) F r o m il be n w p u y i n d r ic c , ke m a a c o n ic a l te n t 1 4 h ig h m a n d 96 in d ia m m e te r e n th a t n s (7 ) T h e n d its e n g th is 2 lu lu v o ( 6 ) F i n d th e lA u se f the ba s e s o v o w ( i i) l t u be a a n d iu n s : ( 5 ) F in d (i) ld w o u l in t he tu be F in d the G iv in pe u n ta s n w e r c o r r e c t to th e n e a r e s t c (A ds fo a 4 7 2 m u se a n ; d d i n fo l d s s (i i) d th e b a s e t it c h i n g i s W 7 a rea o f a r F in d th e c u rv e y l in d e r f h e i g h t 36 o is dr i l le d v o lu m e - o ut d s t it c 2 0% 2 i g ht o cm an c m 2 h in g f th e 9 , 05 1 _ c u rv e 3 m 1 d ra f the v o lu m e a n area v e s se d iu s 1 4 d s u r fa c e a r e a o l cm l v esse IA n s , 4 7 96 cm l 9 85 6 a re 2 2 00 a c o n ic a d the t o ta l 2 f th e t e n t 2 c ir c u la r c o n i c a s u r fa c e a r e a o F i n d the 2 09 4 4 d an l cm cm 2 an d 6 16 cm 2 ) c a v it y o s u r fa c e a r e a o 3 f r a diu s f th e 7 cm r e m a in in an d g ) Scanned by ( 9 ) f th e fa su r c e ( O) T h e i nt er nn re s lA pe c tiv e n s ly ( 1 ) A B i r l n i ls the bu ket c th e ( i i) t he lA c m r y lin d r ic ( \3) T he ra L c o s o u n ( 1 5) A ra ( 1 6) pp e r i fo m e ta d iu s llic A ho llo i n to r o 3 5 w a a n ho lo a ls o its d he w o u a c o n ic lu 2 an d su r v e s s e fa c e l n s f a d s o s f the phe re is 9 w ire in f d ia an G iv 43 3 32 9 8 = yo e 42 ar e : ) c m a n d 45 s c m a re a d 18 o c m f the in ra s a n d d iu ith s w sa n d F th e h e i gh t S he e m f th e o pt ie c o n s \c a \ se tw o so It is c m ra d iu c m IA an o 10 5 s d he ight 3 o n e a r e a l s o th e a m e an e te r d 8 an d l e n g th 8 ess o c m d dr a w 97 2 n s pla c e o f de c im a \ l c u l a t e th e s la n t ir e e te r c a he ight o f is m e i n to n cm w lte d n u m is dra w n ir e TA n s an d th e n be r o f in to 15 rec as c o n es d ext er nal d i a m e t e r s 4 c m a w f d ia m o 2 F in d m m ) m f the F in d th e c m f i nt er nal f b a s e d ia m l id s m e te F in d th e t h i c k n f t to ) c m 1 u r a n sw e r c o rrec ) c m m e te rs m e te r re o phe r e a c o n e o = l phe cm s c m 3 ) l hea p a e \437 n s is ph e r e m c m IA m e te r c u r v in he ight c m kes m a v o 32 5 3 2 5 a r ea e s o th i c k n e s s rm ] lu m t h e le n g t h o f th e ( 1 4) A d an f th e h e a p o c m IA d iu d f m e te r s o it y N n d its d e n t h a t th e v o th e c o n e cm 2 m l b u c k e t 32 a gr o u n he ight 36 - c is 6 \6c n d , s a n s la n t n s G iv a c pa c a 1 9 , 4 04 - re l d ia te r n a F in d its d iu ra phe a s e x o n the h e a p is 24 (i) d a n p a c ity c a f a re a o F in d th e h e i gh t o cm f e a w ire c m ) o t i n to s m a H c o n M u s fo r m an f l e n g th \ 8 d 8 cm e d res IA m e s ea c ns o f h o f 1 2 61 p e c t iv e l y \s m e \t e d co ne Scanned by i s i n t h e fb r ( 7 ) A to d ia i n d tA 4 14 4 8 c m c i nder w 8 a r ea n s : m c m (A w fi n d F in d t h e 3 o a pe s pn n u m 6 s 5 " f o u o area in an s ho ts Cm ( i i) ( 1 (i ) (3) V e t h a i (i) Oi ) c os ta n 4 s in A + cot 4 A s + A )7 ta i in A 1 + co s A 2 + = c o s A A + 1 + cos A 1 d iL a n i sa m e he igh t is 8 ra d iu D c m The s e te r \ in e th e ) d rad iu Fi n d in in g so is 6 s c m , the v o lu m e o a c o n ic f th c re m a a c a v i ty in in o f h e i ght so l id id ) t s h e i gh t i s \ 1 i th w w a a re dro te r u p p pe o nD p p e d i n t o t h e ( l ) P r o \ e t h e i t y t a n A+ C Ot A (i ) , an o u t c o ne It i s fi l e d it h t h e c m t o th e r i m \n to v e s s e d th e a n W M e v e sse IA l n s n en 2 5 ra d iu le a d s o f i ts t o p sho ts Ot tne w ate r Ea c h o \0 W 5 f u u \ 44 0) T W G O N O M E T R I C A L I D I # l l aH 20 (2 ) p r o v e th a d ' c m c m d c m w re 3 4) - re m a c Tn 7 v e r te e w f the 3 603 - R isphe m is 2 7 53 6 - i s h o o c m c m f e a d o m e I he a n he ig h t i s 8 s e o i r & u S U Z ) e re be r ho o n r thc \o v o a r ea r m Is n m e o d i c a po r t io c o n s u r fa c e ! c m ? u \ o d iu ra se i n t h e fo ic h i s s thc the to ta 603 v es s e u H f ba a r J o n s - l id m a A tm w ti r e s e o m o u n te c o n e s u r fa c e a r e a a n ( 18) F ro ( 9) A f the ba e te r o wr a m = (1 A = = sec 2 c o s c o t sec 4 A 2 c o se c l A A )? A = A (c o s e c A = 2 sec 1 + c o s A s in + A 2 cot c o sec 2 A A c osec A 2 A )? Scanned by ( iil ) (4) Pro v e t ha i CO S A c o t 1 s in A A s e c : v e th a t : A c 1 (i) th a t v e s ta n A (ii) ( 1 (7 1 I f ta n A + ( 8) K . ' ' s in A A ' m = an s A ) d ta B, y ca s - o f th e s ha d o w e le v a t io n o n t h e s u N (2 ) T h e an h o r iz g le o n ta o f lA e l e v a t io n o p la n e i s fo un + A c o s 2 in tn A ( A c o s c o s A + A + in z s in A - s n A s in b - A . in B . A Pro n d s tha t v e . - . A i m Ia n A n + A G l s h. . 41 1l i i M aE H E IG HT S A ND DISTAN c Es 2 ( 1 ) T h e l e n g th 1 + s in A s + ta n z + 1 A n A ta n A + 1 s e c ta n A 1 A A c o t A + ta s e c A A c o s e c se c s e c A c o se c _ \n A A + ta n ( i) + t A o 1 + s tn A (ii) (6 1 Pr o ta n A c o s e c (S) Pn A o ns f a v e r t ic a to w er ti m e s h s h e i ght is F in d M e a n g e o f 30) f th e t o p o d t o b e 3 0 f a to w er a t a d i s ta i c e F in d th e he i gh t o o f th e f 1 2 0m f r o m i ts f o o to w er IA ns t o n a 69 2 8 m ) Scanned by (3 ) A g u a r d le v e To ( i) C a c u w w e r ( i i ) A fte r bse o be o f 70 o Pe o p e ( 5 ) T he e n th g a h itu d e n o de pr e s h ip s bs e r v , i f th e s IA o s (ii) On th e o p o s i t e i p s de s to 4 5 ( 8) T h e an an g le th e la id e to p o i n g d i r e c t l to y co m 3 o n t he o g le ho , o f w f n s o f 25 45 m i f r l to a t w ar o o c l i f iF f th e d s it o s s io n pe o p le in c a s tr a f m ) a m b v e se a m the fo m i g h t in e w e y f th e t h e fo o t o m o t o f the ; ( ii) 4 I it h i t o o bse bs e r r v a t io n v a t io n 59 th e a n g e s m ea s u re F t he he i g h t o f the is to w e r 9 1 3 8m ) gr o u n a l c u la te t h e d in by o c reas es he ig h t o f the m to w e r w , he th e n c o rre c t to ) 2 oo m an a bo d 3o i f (A n s : bs e r v a t i o n w i l l t he m v e the s e a re s pe c ti v (i) 1 46 4 le v e y e l , o bs e th e a n r v es F in d th e d i s ta m ; (ii) 54 6 4 to w e r o b s e r v es a c ar m o i n u t e s fo c ar reac a s ta t io n a r y c lo u re f 1 8o o gle s o be t w n c e f th e e e n , c o he iBh t ( i) 32 5 pe c tiv n s v e fr o a t fr o m n s res TA e w er o n f the bo FA d 5o a n to 3 o I f i t ta k e s 1 2 f te r t h i s f its 50 l to w e r a t a is 2oo to w e r a n c e o bo f de pre id e a v e r t ic a f a c tha t the o r v a t io n d i s ta e e n th e t w o 1 3 66 m a v e r ti c a e le v a ti o n ke le v e l IA f the bse o f 29 o w e r as n s f the o so o n a f ? p r e s s io n o an are the s a m e s g e m n , d h ip s t o be 4 5 o n n an w the to p o hip s an h a n g e s fr o ( i) ( 7) A b e tw n c e es f th e tw rv e f th e to o ha do su n c l p a c s bse o o n the sa m e s f t h e to p e r m s s io n o i t is , d in g f th e o f the o tw o d e c i m a (6 ) A s ta n f n d th e d is t a , fr o , f d e p r e s s io o a l c u la t e t h e n e w e e v a t i o n o m a t to t h e n e a r e s t m e te r s o m e tim e C y bo e n e m g le a t a n a n a te to w e r (4 ) T w rv e s a n r h t he ) in g a v a u n i fo th e a n le o f d s e pr e s s io n to c o b s e r v a t i o n t lo w d fr o m p o i n t 2 5 f le c t i o n in th e l k a e i s 6o m rn a bo v e a er ? lA n s la k e is 3 o M[ h a t i s t h e h i e gh t of r u s pe e d han ge f o m 1 6 39) an d th e th e c l o u d a b o v e Scanned by t9 ) F r o be m a h th a s \K lA \ e r t ic \ p o e a the a n g le o f o m v at i the of f th e m w e ( 2 ) F i n d th e w a n e le lk in g 5 o th e t o v a tio n o f t h e to p to w a r d s th e m s fo w e ri w o n s u nd to be a v e r t ic a f o th e ta n m w c r . l lo i nd t he he i i w gen gh t of t o f r und f \he the m n w Io \ r , l rva ean p o f th e o f t he to S M E DM ) to w e r , is 6o \e v an gr o e d the u n a n i f the h e i g h t w e r g \e o Fro d o m t h e t l p o f th e p o l e f de p re s s io n o f t h e p o \ e i q 2 1) m f the (A ns # f)m ) ND M O DE) Qu A R 1 L E S A 7 35 , 7 1 57 f 5 pe r s o n s a r e 3 6 \ kg) ts I A n s i o f th e i r w e g h , o , an d 45 f 6 85 ) c a s s in M , a r it h m e t i c m m m e an o to m e w e r a r e o n the s a ( in k i o w m e a l o F r e q f the to F i n d th e h e i g ht is 30 ( 3 ) F d t h ie lA ns of a v e r t ic a d an e e v a t io n i gh F i n d th e lA O t op (M E A N ( l ) T he is n t ge f o 2 0m l n s 1 0) A ta n g e Th e a n th e g r o u n d o n i t e \e or k g n p o in t t f 10 O o . & ' 41 L 20 10 6 2 0 30 8 1 30 40 \2 \ L 50 40 5 ' Scanned by F (4 ) F m d lA o t h e fo l o Y n s (5 ) k m e a n la 1 m e a n f t h e fo o o I 1 te r v a n in g s h o r t u t u s w 30 6 i n g d i s tr i b u t i o 30 T 10 40 Y 1 50 f t he ? lo o w i n g d i s tr i b u t i o n 50 1 8 49 6) the m m d q is 7 5 , 60 60 f in d t h e to ta l be n u m 5 0 F in d t h e ass \ u e n c ( 8) F i n d t h e (9) T he 1 W in 1 c m U a lc w e n e a re s t u c u l a te d ia n i g h ts o o f 45 kg) y c m e i s s i n g fi e u e n c i es q l 20 I 24 ) ? , , n in T a n 1 / . i n g d i s tr i b u t i o w l 40 12, 15 6 2 0 8 4 , h ildr e w e d i a n fo d ia n is 2 6) m i n t h e fo l o , a c la s s w e r e 7 5 n s f e r v a ti o n s an d 10 d n ta b le is 1 2 o a l2 60 60 IA r ec or d n s M e d ia d th e ir l I 32 n f, n - t o th e n e a r e s t is m e a n 80 00 9) kg as , fo l l o w s th e m e d ia n m e f 1 ! e n ( 1 0) F i n d t h e lA m e bs 20 = 80 9 Y o v a lu e s o 10 1 17 t Fre qu e n c y f r o 70 5 is s in g f r e q m 70 l 12 (? ) T he n 40 r 6 m e tho V 45 46) - Fre qu e n c y lA n s M e a n (6 ) I f 40 7 F in d th e in 40 25 m e an ss i n g d is t r i b u t io w r ig ht 8 lA ns M e d ia n t h e fo l l o w i n g 1 ' 12 w e \ + 2 ig ht 55 di s but i on 7 10 [ 8 \ 5 Scanned by ? 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( ]i ) A1 a T Ii e U s in g a b t a i n e d ks gw p h p a pe r dr a ) by 2 00 s t u d e n t s i n w O g iv an fo e a n ex a m t h e a bo r i n a ti o n a re d is t r i b t t i o v e ( i) t h e m ( i i) t h e n u m b e r o f s t u d e n t s w h o o b t a i n e d m o r e t h a n 8 0% ( i i i) th e n u m b e r o f s t u d e n t s w h o d i d n o t p a s s i t h e p a s s g iv U n be lo e n yo se w : O g iv u r e d ia n m arks s c a e a s U s e t he (A n s : M e d ia n T h e d a i ly ( 1 2) w R a e es n - w a I s 2c m 2c m 57 ; no ge s o 10 - o , the p e r c e n ta (A n s : m e ( 1 3 ) F in d d ia n lo w th e 1 7 13 7 , , f s t u d e n ts g iv o w o r fo e m o r e tha n 30 r Th e a bo v C 1 (A n s : L o w ( 1 5 ) U s in g No 20 ; = g iv are 40 40 no en 50 o f s t u de n t be o w : l 60 50 no d is tr ibu tio n s 45 ore da y a tha n R s 4 5 da y a 3 0% ) q u a r t i l e , u p p e r q u a r t i le a n d i n t e r q u a r t i l e r a n g e f o r t h e d a ta : 9 1 1 1 5, 19, L o w e r q u a r tile 9 ; u p pe r q u a r ti l e ns : 1 7 ; i n t e r q u a r t i le r a n e 8) g , - , - - 10 q u a r t i e 10 l - 15 4 ta b le 15 l , fin d (i i i) I n te r q u a r t i l e 20 20 1 1 5 5 ; U pp e r q u a r t i l e - 25 9 2 5 5 ; I n t e r q u a r t i le ra n ge 1 25 1 ra n 30 \ - L a 36 ; N o 10 o f s t u de n t s 20 s c o r in g 25 m a rks a bo 15 v e 65 = 1 30 35 1 7 1 0) a - 7o 34 ) - er (A 3 f s tu de n t s M e d ia n t pa s s ii g r a p h p a p e r , d r a w a n o g i v e f o r t h e f o l l o w i n g d i s t r ib u t i o n w h i c h s h o w o b ta i n e d i n t h e G e n e r a l K n o w le dg e p a e r b y 1 00 s t u d e n t s p M a rks o i o lm 2o l 3o 1 3 o 4 o 1 4 o 5o 6o o lA n s er 8 0% g e o f th e w o r k e r s w h o e a m m o r e tha n R 35 ; the p e r c e n t o f w o r k e r s w h o e a m m 5 30 e d n a n 35 w as ker s ( 14 ) F r o m th e f o l l o w i n g fr e q u e n c y d i s t r i b u t i o n (i ) L o w e r q u a r t i l e Oi ) U pp e r q u a r t i e Fr equ e nm 1 i n a t io is b u i d i n g p r o j e c t a l 20 an in d ge e x a m d o the r a x th e on s c o re w o rke rs 1 0 O o n e a x is a n k s O ri 2 0 s tu d e n ts f 1 60 U s in g t h e g r a p h p a p e r d r a w u s e y o u r o g i v e to e s t i m a t e ( i ) t h e m e d ia n w a g e o f t h e (i i) m a r i n t he p e r c e n ta , e t o e s t i m a te 12 s th e m a rks 1 6o 7 o 1 8 l E l= a 1 8) Scanned by ( 1) A ba g s iz e the in c o n ta M o ba l d r a b a s a h i t ta k e is w n c k ba l (i) a re d ba ll re ba ll fr o s o u t a the m a n d ba l ? a s in g e th r o w o f (3! 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