SUMMER 17 EXAMINATION

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(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr jct Cod: Important Instructions to aminrs: ) Th answrs should b amind by ky words and not as word-to-word as givn in th modl answr schm. ) Th modl answr and th answr writtn by candidat may vary but th aminr may try to assss th undrstanding lvl of th candidat. ) Th languag rrors such as grammatical, splling rrors should not b givn mor Importanc (Not applicabl for subjct English and Communication Skills. ) Whil assssing figurs, aminr may giv crdit for principal componnts indicatd in th figur. Th figurs drawn by candidat and modl answr may vary. Th aminr may giv crdit for any quivalnt figur drawn. 5) Crdits may b givn stp wis for numrical problms. In som cass, th assumd constant valus may vary and thr may b som diffrnc in th candidat s answrs and modl answr. ) In cas of som qustions crdit may b givn by judgmnt on part of aminr of rlvant answr basd on candidat s undrstanding. 7) For programming languag paprs, crdit may b givn to any othr program basd on quivalnt concpt. 7 Q. wr Attmpt any TEN of th following: a) Find th point on th curv 8 whr th tangnt is paralll to X-ais y y 8 b) ta n g n t is p a ra ll l to X -a is P o in t is, y 8 -------------------------------------------------------------------------------------------------------------- Find th radius of curvatur of th curv y c at point c, c y c y Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 b) c) y d d a t c, c c d c y c c d c c R a d iu s o f c u rv a tu r c c c --------------------------------------------------------------------------------------------------------- E v a lu a t s in s in p u t s in t t lo g t c lo g s in d d t c d) ---------------------------------------------------------------------------------------------------- E v a lu a t Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 d).. c d c ) f) --------------------------------------------------------------------------------------------------- E v a lu a t ta n.d ta n d d ta n ta n d d. d ta n. ta n d ta n lo g c d ------------------------------------------------------------------------------------------------------------ E v a lu a t s in d s in d s in. s in d c o s s in d P u t c o s t w h n, t s in d d t w h n, t Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 f) t d t t t t d t OR g) s in s in s in c o s c o s 8. ------------------------------------------------------------------------------------------------------------ Find th ara of th rgion boundd by quadrant y, y, y and Y-ais in first A a b y y Pag /9

[ Q. (ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 g) 8 8 7 5 h) i) j) --------------------------------------------------------------------------------------------------------------------- Dtrmin th ordr and dgr of Ordr= Dgr= m y d d ----------------------------------------------------------------------------------------------------------------------- F o rm th d iff r n tia l q u a tio n y A 8 A y 8 y y if y A.W h r A is a rb itra ry c o n s ta n t ----------------------------------------------------------------------------------------------------------------------- A fair di is rolld. What is th probability that th numbr on th di is a prim numbr S,,,, 5, n s A,, 5 n A p o r.5 A n n A s ----------------------------------------------------------------------------------------------------------------------- Pag 5/9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 k) From mn and womn, prsons ar chosn at random to form a committ. Find th probability that th committ consists of at last on prson of ithr s. n S c n A c c c c p A o r 5.8 l) m). --------------------------------------------------------------------------------------------------------------------- A prson firs shorts at targt. Th probability that any shot will hit th targt is 5.Find th probability that th targt is hit actly 5 tims. G iv n : n, p, q p 5 5 5 5 n r n r p r c p q p 5 5 c5. 7 r 5 5 ----------------------------------------------------------------------------------------------------------------------- E v a lu a t 9 d O R 9 9 d = s in. c = s in c s in / ----------------------------------------------------------------------------------------------------------------------- d d c Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 n) E v a lu a t. lo g d. lo g d P u t lo g t w h n t lo g d d t w hn t log td t t ----------------------------------------------------------------------------------------------------------- Attmpt any FOUR of th following: a) E v a lu a t ta n d C o n s id rin g in d a s ta n ta n ta n d s c ta n d ta n s c ta n d ta n s c d ta n d In firs t in t g ra l, p u t ta n s c td t lo g s c c t lo g s c c ta n d d d t lo g s c c t Not: If studnt attmptd to solv th problm assuming any ind valu thn considr it and rward appropriat marks to it. ---------------------------------------------------------------------------------------------- Pag 7/9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr jct Cod: 7 Q. wr b) c) E v a lu a t lo g lo g lo g lo g lo g P u t lo g t d d t t t c o n s id r P u t t A P u t t B lo g t t A B t t t t t A t B t t t t t t t d t d t t t t t lo g t lo g t c lo g lo g lo g lo g c ------------------------------------------------------------------------------------------------------------ Find th quations of th tangnt and normal to th llips y 5 which is prpndicular to th lin y 7 S lo p o f lin y 7 is m y 5 y d y y Pag 8/9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 c) s lo p o f ta n g n t m y L in a n d ta n g n t a r p rp n d ic u la r m. m. y y y 5 5 if y p o in t is, if y p o in t is, E q u a tio n o f ta n g n t a t (, ) is y y 5 E q u a tio n o f ta n g n t a t (,) is y y 5 E q u a tio n o f n o rm a l a t (, ) y y E q u a tio n o f n o rm a l a t (,) is d) y y ----------------------------------------------------------------------------------------------------------------------- Find th radius of curvatur for th curv a c o s y a s i n d a c o s s in a s in c o s d d a co s, y a sin a t + Pag 9/9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 d) d d sc d d sc d d tan sc a t a s in c o s a c o s s in d a c o s s in ta n sc a a a c o s s in. a R a d iu s o f c u rv a tu r a a o r.5 a ----------------------------------------------------------------------------------------------------------------------- Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 ) A bullt is fird into a mud tank and pntrats t t mtrs in t sconds aftr impact. Calculat maimum dpth of pntration. y t t 7 t L t 7 t t 7 D p th is m a im u m. M a im u m d p th y m t r f) ----------------------------------------------------------------------------------------- E v a lu a t 5 8 5 5 C o n s id r 8 5 A B 5 A B P u t A P u t B 5 8 5 8 5 8 Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 f) I lo g lo g c ----------------------------------------------------------------------------------------------------------------------- Attmpt any FOUR of th following: a) E v a lu a t T h ird t rm 9. 9 9 ta n ta n ta n ta n --------------------------------------------------------------------------------------------------------------------- b) E v a lu a t c o t c o t Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 b) I d c o t c o s s in c o s s in I s in s in c o s d -------------------- I s in s in c o s d I s in s in c o s I c o s c o s s in d -------------------- a d d ( ) a n d ( ) s in c o s I I + d s in c o s c o s s in I s in I d I I I s in c o s d c o s Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 c) Find th ara of th rgion nclosd btwn parabola y and th lin [ y y a n & A r a b a y y d d d d d) ----------------------------------------------------------------------------------------------------------------------- S o lv. y y. y y y y d P u t y v v d v d d v dv d v v d v v v v d Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 d) ) f) v dv d v v v dv v v dv v d v v d d v d v d v d v ta n ta n v lo g c y lo g c ----------------------------------------------------------------------------------------------------------------------- S o lv c o s y c o s y P u t y v d v d d c o s d dv v c o s s o lu tio n is d s c d v v ta n v c ta n y c v d v ---------------------------------------------------------------------------------------------------------------------- S o lv y ta n ta n y d C o m p a rin g w ith P y Q Pag 5/9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 f) ta n P, Q In t g ra tin g fa c to r P d - ta n y. IF Q. IF d ta n ta n ta n y d y ta n ta n d P u t ta n t O R Put - ta n t ta n d d t. d d t ta n t t ta n y d t d t y td t t ta n y c y - ta n - ta n ta n ta n ta n y c y c t c ----------------------------------------------------------------------------------------------------------------------- Attmpt any FOUR of th following: a) E v a lu a t 7 7 L t I d --------------------( ) I 7 7 7 7 d I 7 A d d in g ( ) a n d ( ) d ----------------------( ) I 7 7 I Pag /9

[ Q. (ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 a) I 7 d b) 7 I d I I 7 I I 7 ---------------------------------------------------------------------------------------------------------------------- E v a lu a t. s in. s in d d s in s in. d. d d s in.. d d. s in. s in. s in. s in s in s in. s in s in. s in s in. Pag 7/9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 b) 8 8 c) ----------------------------------------------------------------------------------------------------------------------- Find th ara of th rgion in th first quadrant nclosd by th X-ais th lin y and th circl y, y 8 8 8 y 8 d) In firs t q u d ra n t to b A y y d a A 8 d 8 A 8 s in 8 8 A 8 s in 8 A A ------------------------------------------------------------------------------------------------------------ S o lv y. s c d y ta n s c y C o m p a rin g w ith M d N c M y. s c N = y ta n s c y M y y s c N y s c M y N Pag 8/9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr jct Cod: 7 Q. wr d) D.E. is a c t ) S o lu tio n is y. s c d s c y c y ta n ta n y c ---------------------------------------------------------------------------------------------------------------------- S o lv y P u t y v d v d d d v d d dv v v dv v v dv v v v s o lu tio n is d v d v v d v d v d v v v v tan v c d v d d y ta n y c y ta n y c f) ---------------------------------------------------------------------------------------------------------------------- Vrify that y m sin is a solution of diffrntial quation m y d d Pag 9/9

[[[[[ Q. (ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 C onsidr y m sin m s in. m m y m y S q u a rin g, m y m y d d d d m y d d d d m y d d m y d d OR m y d d C o n s id r y m sin m sin. m m y m y m m m y d d d m d d d d d Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 m y d d m y d d 5 a) ---------------------------------------------------------------------------------------------------------------------- Attmpt any FOUR of th following: A Card is drawn at random from a wll shuffld pack of 5 playing cards. A=vnt that th card drawn is not a spad. B=vnt that th card drawn is king. V rify th at vn ts A an d B ar in d p n d n t. 5 n s C 5 9 n A C n B C p p A B 9 n A 9 n s 5 n B n s 5 C o n s id r p A p B = 5 A B E v n t th a t th c a rd d ra w n is a k in g o f h a rt o ro f d ia m o n d o r o f c lu b n A B C n A B p A B n s 5 p A B p A p B A a n d B In d p n d n t v n ts. b) A s s u m in g th a t th p ro b a b ility o f a fa ta l a c c id n t d u rin g th y a r is. C a lc u la t th p ro b a b ility th a t in a fa c t o ry m p lo yin g w o rk rs th r w ill b a t l a s t tw o fa ta l a c c id n ts in a y a r.. 5.7 7 8 8 G iv n n, p m n p. 5 a t l a s t tw o fa ta l a c c id n ts p p p Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 5 b) p. 5. 5. 5. 5 a t l a s t tw o fa ta l a c c id n ts!! =.7788.7788.5 =.5 c) ------------------------------------------------------------------------------------------------------------------- In c rta in a m in a tio n 5 stu d n ts a p p r rd.m a n sco r is 8 w ith S.D 8.F in d th n u m b r o f stu d n ts sco rin g i) l ss th a n 5 ii) m o r th a n G iv n 8, 8 i) w h n 5 z.5 ii) w h n 5 8 8 z 8 8 d) NOTE : As th aras for th abov problm ar not givn, th studnts cannot solv th problm compltly. If studnts attmptd to solv th problm and calculatd upto valu z. Full marks to b rwardd. ---------------------------------------------------------------------------------------------------------------------- E v a lu a t 5 s in 5 s in P u t ta n t, d d t, s in t t t t t 5 t Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 5 d) t t t t t t 5 t 5 t lo g c 5 t lo g t c t lo g ta n c ta n O R 5 s in P u t ta n t, d d t, s in t t t t t 5 t t t t t t t 5 t 5 t 5 5 Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 5 d) 5 t 5 t lo g 5 t t lo g t ta n lo g ta n ) ---------------------------------------------------------------------------------------------------------------------- E v a lu a t s in s in s in s in s in c o s s in P u t s in t w h n t c o s d d t w h n t td t t c o n s id r, t t t t t t A B t t t t t A t B t p u t t A p u t t B Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 5 ) f) td t t t t t t lo g lo g lo g lo g lo g lo g lo g lo g s in s in s in c o s s in P u t s in t O R w hn t c o s d d t w h n t td t t td t t lo g t lo g lo g lo g lo g ----------------------------------------------------------------------------------------------------------------------- S o lv lo g y d y c o m p a rin g w ith M d N M lo g y N = y M, N y y y + M y N g iv n D.E. q u a tio n is a c t Pag 5/9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 5 s o lu tio n is y cons ta n t trm s fr from y c o n s ta n t M d N c lo g y d c lo g y y c lo g y y c a) Attmpt any FOUR of th following: A H u s b a n d a n d w if a p p a r d in a n in t rv i w fo r tw o v a c a n c i s in a n o ffic T h P ro b a b ility o f h u s b a n d 's s l c tio n i s a n d th a t o f w if 's s l c tio n is 7 5 F in d th p ro b a b ility th a t i) b o th o f th m a r s l c t d. b) ii) o n ly o n o f th m is s l c t d. G iv n p H p W 7 5 ' ' p H p H a n d p W p W 7 5 i ) p H W p H p W 7 5 5 ' ' ' ' ii ) p H W p H W p H p W p H p W = 7 5 7 5 7 ------------------------------------------------------------------------------------------------------------ A company manufacturs lctric motors. Th probability that an lctric motor is dfctiv is.. What is th probability that a sampl of lctric motors will contain actly 5 dfctiv motors? G iv n n, p. m n p. P 5. 8 5 5!. 9 8 Pag /9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 c) In a tst of lctric bulbs it was found that th lif of particular mak was normally distributd with avrag lif of hrs. and S.D.of hrs. Estimat th numbr of bulbs likly to burn for (i) btwn 9hrs. and hrs. (ii) mor than 5 hrs. G iv n th a t A. 7 7 A.8., i) 9, z 9 z P ( B tw n 9 h rs. a n d h rs.) A A. 7 7. 7 7.9 5 N u m b r o f b u lb s h a v in g lif b tw n 9 h rs. a n d h rs..95 9 8.8 9 9 ii) 5 z 5.8 S. D P M o r th a n 5 h rs..5 A.8.5.. N u m b r o f b u lb s h a v in g lif m o r th a n 5 h rs.. 7. 7 d) F in d th m a im u m a n d m in im u m v a lu s o f y Pag 7/9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 d) o r o r fo r d y y is m in im u m a t ) y m in m a 7 fo r y is m a im u m a t y 5 ----------------------------------------------------------------------------------------------------------------------- F in d th q u a tio n o f th ta n g n t a n d th n o rm a l to th c u rv y y 8 a t, y y 8 a t, y y d d y y d d d y y a t, s lo p o f ta n g n t E q u a tio n o f ta n g n t is y y y s lo p o f n o rm a l E q u a tio n o f n o rm a l is Pag 8/9

(ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr wr jct Cod: 7 ) f) y y 9 y ------------------------------------------------------------------------------------------------------------ F in d b y in t g ra tio n th a r a o f th lli p s 9 y 9 y y 9 y 9 9 y A r a b a y d d 8 d 8 s in 8 s in 8 9 s in 8 9 Important Not In th solution of th qustion papr, whrvr possibl all th possibl altrnativ mthods of solution ar givn for th sak of convninc. Still studnt may follow a mthod othr than th givn hrin. In such cas, first s whthr th mthod falls within th scop of th curriculum, and thn only giv appropriat marks in accordanc with th schm of marking. ------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------ Pag 9/9

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