CCE PR Revised & Un-Revised

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1 D CCE PR Revised & Un-Revised KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE S.S.L.C. EXAMINATION, JUNE, 08 : ] MODEL ANSWERS : 8-K Date : ] CODE NO. : 8-K Subject : MATHEMATICS / New Syllabus / Private Repeater / Kannada Version [ : 00 [ Max. Marks : 00 I.. A B n ( A ) 7, n ( B ) 6 n ( A B ) 5 n ( A B ) (A) (B) 6 (C) 4 (D) 5 (A) [ Turn over

2 8-K CCE PR. (A) 6 (C) 4 8 (B) (D) 4 6 (C) 4. (A) (B) (C) (D) (C) 4. f ( x ) x x x 6 f ( ) (A) 0 (B) 0 (C) 8 (D) 8 (D) 8 5. ABC 90º, BD AC, BD 8 AD 4 CD (A) 6 (B) 4 (C) 64 (D) (A) 6

3 CCE PR 8-K 6. sin( 90 cos ( 90 ) ) (A) sec (B) cot (C) tan (D) cosec (B) cot 7. (, ) ( 4, 7 ) (A) (, 5 ) (B) (, ) (C) (, 5 ) (D) ( 6, 0 ) (C) (, 5 ) 8. r (A) r (B) r (C) r (D) 4r (D) 4 r [ Turn over

4 8-K 4 CCE PR II S { HH, TT, HT, TH }

5 CCE PR 5 8-K. f ( x ) x + 5x + 6 ( x + ) x + 5x + 6 x + x + x + 6 x ( x + ) + ( x + ) ( x + ) ( x + ) ( x + ). x ) x 5x 6 ( x x x ( ) ( ) x + 6 x + 6 ( ) ( ) 0 ( x + ) 4. m m m m. [ Turn over

6 8-K 6 CCE PR III. 5. A {,, } B {,, 4, 5 } U {,,, 4, 5, 6, 7, 8 } ( A B ) l A l B l A B {, } ( A B ) l U ( A B ) {, 4, 5, 6, 7, 8 }... ( i) A l { 4, 5, 6, 7, 8 } B l {, 6, 7, 8 } A l B l {, 4, 5, 6, 7, 8 }... (ii) (i) (ii) ( A B ) l A l B l a, r, S? S a r

7 CCE PR 7 8-K 7. p q p, q z, q 0 p p q q q p q q 8. n C 4 n n ( n ) C 8 8 ( 8 ) C [ Turn over

8 8-K 8 CCE PR n n ( 8 ) n ( n ) , 5, 0, T n a + ( n ) d a 0, d 5, T 95 n ( n ) 5 ( n ) 85 5 n ( n ) 7 n 8 n S n [ a + ( n ) d ] S [ 0 + ( 8 ) 5 ] 9 ( ) 9 05 S 8 945

9 CCE PR 9 8-K n 8, a 0, l 95 S n S 8 n ( a l ) 9 8 ( 0 95 ) ( ) 5 ( 9 ) 5 ( 90 ) ,,, 4, n n n ( P ) 50 P 4-5 P P 4 P P P 4 4 [ Turn over

10 8-K 0 CCE PR P 4 4 ( n P ) 50 n P n ( n ) + 50 n ( n ) n n n n 4n n 50 n 50 n 5 n 5 n n ( s ) 6 A (, 6 ) ( 4, ) (, 5 ) ( 5, ) (, 4 ) ( 6, ) n ( A ) 6 A P ( A ) n ( A ) n ( S ) 6 6 6

11 CCE PR 8-K ( 5 ( 5 5 ) ( ) ) ( ) ( 0 ) 0.. ( ) ( 0 ). ( ) ( 0 ) ( ) ( ) ( 5 5 ) ( 5 ) 5 ( 5 ) 5 ( 5 ) ( ) 6 ( 5 ) [ Turn over

12 8-K CCE PR 4. ( x x 7x 5 ) ( x ) f ( x ) x x 6x 0 ( x ) x + 7x f ( x ) x x 6x 0 ( x ) f ( x ) f ( ) 0 f ( x ) x x 6x 0 f ( ) ( ) 6 ( ) f ( ) 0 x x x 6x 0

13 CCE PR 8-K 5. ABC DE BC, AD DB 5 AE 4 AC ABC DE BC AD AE DB EC 4 5 EC EC AC AE + EC ABC DE BC AD AE AB AC 5 4 AC AC [ Turn over

14 8-K 4 CCE PR PQ P r 4 5 PQ 7 7. (, 4 ) ( 8, ) x y A (, 4 ) x y B ( 8, )

15 CCE PR 5 8-K d ( x x ) ( y y ) ( 8 ) ( 4 ) A B 5 A B x y x ( y ) xy 5 5 ( y ) y 5 y y 5 0 y 6y + 5y 5 0 y ( y ) + 5 ( y ) 0 ( y ) ( y + 5 ) 0 y y x 6 5 A 5 B [ Turn over

16 8-K 6 CCE PR 9. ABC (a) (b) (c) sin cos cosec (d) sec. a) sin BC AC b) cos AB AC c) cosec sin d) sec cos

17 CCE PR 7 8-K 0. 0 C 40 D B 60 E 0 0 A [ Turn over

18 8-K 8 CCE PR. P {,,, 4 }, Q {,, 4, 5, 6 } U {,,, 4, 5, 6, 7, 8, 9, 0 } ( P Q ) l. (a) n (b) a b ( a > b ). n ( n ) a) n ab b) ( H ) a b. (a) (b) 00 P 0 0 C. a) b) 00 P 0 0 C 0

19 CCE PR 9 8-K [ Turn over

20 8-K 0 CCE PR x 5x 0 a, b 5, c b 4ac ( 5 ) 4 ( ) ( ) > 0

21 CCE PR 8-K 7. ABCD 4AB AC BD AOB AB AO B 90 AO BO AO AC, BO BD AB AC BD AC BD 4 4 AC BD 4 4AB AC BD. 8. P ( x ) x x 5x 8 ( x ) P ( ) P ( ) ( ) ( ) 5 ( ) P ( ) 47 [ Turn over

22 8-K CCE PR 9. ( 8, 5 ) ( x, y ) x y ( x, y ) ( 8, 5 ) d ( 8 ) d cos 5 sin sin cos cos cos 5 AB AC ABC A B C 90 BC AC AB BC sin.

23 CCE PR 8-K sin cos sin cos IV T 5 T 5 a + 4d... (i) (i) (ii) a + 0d 5... (ii) a + 0d 5 a + 4d ( ) ( ) d d 6d 6 a + 4 ( ) a + a a 0 [ Turn over

24 8-K 4 CCE PR a 0 d T n a ( n ) d T 5 0 ( 5 ) 0 4 T 5 T 5 d T p T q p q T 5 T 5 T d a + 4 ( ) a + a 0 a 0 d T n a ( n ) d

25 CCE PR 5 8-K T 5 0 ( 5 ) 0 4 T 5 T ar... (i) T ar... (ii) ar ( r ) 96 ar ar r 96 r 8 r 8 r r a ( ) a r 4a a S n a ( r n ) r ( 9 ) S 9 ( 5 ) 5 S 5 9 [ Turn over

26 8-K 6 CCE PR 4. ( CI ) ( f ) A i 5 C.I. f x d x A i d f d f d N 5 f d 6 f d f d fd i N N ( )

27 CCE PR 7 8-K C.I. f x fx x f x N 5 fx 0 f f x f x N N x A C.I. f x d x A fd d f d N 5 fd 0 f d 550 [ Turn over

28 8-K 8 CCE PR f d f d N N C.I. f x fx d x x d f d N 5 fx 0 f x f x N d f d N

29 CCE PR 9 8-K 4. ( x + ) ( x ) + 0 x + px + q 0 4p 5q 0 ( x + ) ( x ) + 0 x ( x ) + ( x ) + 0 6x 4x + 9x x + 5x 4 0 a 6, b 5. c 4 x b b 4 ac a ( 4 ) x 4. [ Turn over

30 8-K 0 CCE PR x px q 0 a, b p, c q m n m 4n m + n b a 4n + n p 5n p n mn a c p 5... (i) 4n n q 4 n q... (ii) (i) (ii) p 4 q 5 4p 5 q 4p 5q 4p 5q 0

31 CCE PR 8-K 44. A B BP BQ BP BQ AP, AQ AB APB AQB A P B AQ B AB AB AP AQ APB AQB BP BQ [ Turn over

32 8-K CCE PR 45. ABC AB AC, PN AC PM AB BC P MB. CP NC. BP ABC DE BC, DE BC ABC 8 cm ADE 6 cm ABC AB AC BMP B C B M P M B P CNP P N C N C P MBP ~ NCP MB NC BP MP AA - CP NP MB. CP BP. NC.

33 CCE PR 8-K ADE DE BC A D E D A E DE BC ABC A B C B AC ADE ~ ABC ADE ABC DE BC ADE ADE 9 6 cm 46. ( + cot A cosec A ) ( + tan A + sec A ) 0 0º 60º cos A sin A sin A sin A cos A cos A sin A cos A cos A sin A sin A cos A ( sin A cos A ) sin A cos A sin A cos A sin A cos A sin A cos A [ Turn over

34 8-K 4 CCE PR sin A cos A sin A cos A sin A cos A sin A cos A sin A cos A BED D B E 0 DE tan 0 BE x 0 BE BE ( x 0 ) ABC AC B 60 AB tan 60 AC 0 ( x 0 )

35 CCE PR 5 8-K ( x 0 ) 0 x 60 0 x 80 x V. 47. x x 6 0 y x + x 6 0 x + x 6 x 0 4 y x + x 6 0 y y x x, y 6 x x 0 y y 6 x x 0 y [ Turn over

36 8-K 6 CCE PR

37 CCE PR 7 8-K [ Turn over

38 8-K 8 CCE PR R 4, r R r 4 d 9 EF 8 8

39 CCE PR 9 8-K AB M C, C, C DB EF ABC, A B C 90 AC AB BC BD AC ABC ABD A B C B AC A D B B A D BAC ~ DAB BA AC AA DA AB AB AC. AD... (i) [ Turn over

40 8-K 40 CCE PR ABC BDC A B C B DC AC B B C D BCA ~ DCB BC AC DC BC AA BC AC. DC... (ii) (i) (ii) AB BC AC AD + AC DC AC ( AD + DC ) AD + DC AC AB AC AC BC AC cm 0

41 CCE PR 4 8-K 5 7 7, 4, ( ) l rl rh r r ( l + h + r ) 7 ( ) [ Turn over

42 8-K 4 CCE PR h 4 l 5 rl rh r ( )

43 CCE PR 4 8-K r h r c.c. h 5 r + h 7 4 r h r r ( h r ) ( 4 6 ) r 6 h 5 r h 4 r [ Turn over

44 8-K 44 CCE PR r h r h r 6 ) 4 ( 5 ) 6 (

KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE G È.G È.G È.. Æ fioê, d È 2018 S. S. L. C. EXAMINATION, JUNE, 2018

KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE G È.G È.G È.. Æ fioê, d È 2018 S. S. L. C. EXAMINATION, JUNE, 2018 CCE RR REVISED & UN-REVISED O %lo ÆË v ÃO y Æ fio» flms ÿ,» fl Ê«fiÀ M, ÊMV fl 560 00 KARNATAKA SECONDARY EDUCATION EXAMINATION BOARD, MALLESWARAM, BANGALORE 560 00 G È.G È.G È.. Æ fioê, d È 08 S. S. L.

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