vt{fhkt 11. Jt;twoG (11) ðíkwo Lkku MÃkþof MÃkþo çkëwyu Ëkuhu rºkßþk MkkÚku... {kãklkku ¾qýku çklkkðu Au. (a) 30 (b) 60 (c) 45 (d) 90

Transkript

1 vt{fhkt. Jt;twoG () ðíkwo Lkku MÃkþof MÃkþo çkëwyu Ëkuhu rºkßþk MkkÚku... {kãklkku ¾qýku çklkkðu Au. 0 (b) 60 (c) 90 () P yu (O,) kt çknkhlkkt ¼køk{kt ykðu wt çkëw Au. P {ktúke ðíkwo Lku Ëkuhu ku MÃkþof ðíkwo Lku T {kt MÃkþuo Au. òu PT = 8 nkuþ, íkku OP =... 7 (b) (c) 7 () PA ylku PB Lku (O,r) Lku A ylku B MÃkþuo Au. òu m AOB = 80 nkuþ, íkku m OPB = (b) 0 (c) 0 00 () O fulÿeík ðíkwo Lkkt çknkhlkkt ¼køk{kt ykðu k çkëw P {ktúke ðíkwo Lku Ëkuhu ku MÃkþof ðíkwo Lku Q {kt MÃkþuo Au. òu OP = y u PQ = nkuþ, íkku ðíkwo Lkku ÔÞkMk =... Au. 76 (b) (c) 8 () ABC {kt AB =, BC = ylku AC = nkuþ, íkku rºkfkuýlke ºkýuÞ çkkswykulku MÃkþoíkk ðíkwo Lke rºksþk... Au. (b) (c) () O fulÿðk k ðíkwo Lku PQ y u PR ylkw {u A y u B çkëwyu MÃkþuo Au. òu m OPB = 0 ylku OP = 0 nkuþ, íkku ðíkwo Lke rºkßþk... nkuþ. (b) 0 (c) 60 0 (6) O fulÿðk k ðíkwo Lke çknkhlkkt çkëw P {ktúke ðíkow Lku Ëkuhu k MÃkþofkuLkkt MÃkþo çkëwyku A ylku B Au. òu m OPB = 0 nkuþ, íkku m AOB =... 0 (b) 60 (c) 90 0 (7) (O,) Lke yuf Sðk (O,) u MÃkþuo Au. íkku SðkLke tçkkr... nþu. 8 (b) 0 (c) 7 6 (8) ðíkwo Lkku MÃkþof ðíkwo Lku... AuËu Au. çku çkëwyku{kt (b) ºký çkëwyku{kt (c) [kh çkëwyku{kt yuf ylku {kºk yuf çkëw{kt (9) ðíkwo Lku çku r¼òk çkëwyku{kt AuËíke hu¾klku... fnuðkþ. rºkßþk (b) ÔÞkMk (c) [kãk AuËefk (0) ðíkwo Lkku MÃkþof MÃkþo çkëw{ktúke Ëkuhu... Lku tçk nkuþ Au. hu¾k (b) rºkßþk (c) rfhý hu¾k¾tz () (O,r) Lkk çknkhlkkt çkëw P {ktúke ðíkwo Lku PA ylku PB MÃkþofku Ëkuhu k Au, íkku... PA > PB (b) PA < PB (c) PA = PB PA = PB = r () AB yu yuf ðíkwo Lkku ÔÞkMk Au. A y u B çkëwykuyu MÃkþofku l y u l Ëkuhu k Au, íkku... l l (b) l l (c) l = l l < l () (P,) Lke çknkhlkkt çkëw A {ktúke Ëkuhu e MÃkþohu¾k ðíkwo Lku B çkëw{kt MÃkþuo Au. òu PA = nkuþ, íkku AB = (b) 7. (c) 0 () (O,) Lkk çkrn¼koøk{kt ykðu k çkëw P {ktúke Ëkuhu k MÃkþofku ðíkwo Lku A y u B {kt MÃkþuo Au. òu PA = 8 nkuþ, íkku PB =... (b) 8 (c) 6 (6) (O,8) Lkk çkrn¼koøk{kt ykðu çkëw P {ktúke ðíkwo Lku PM MÃkþof Ëkuhu ku Au. OP ðíkwo Lku N {kt AuËu Au. òu NP = nkuþ, íkku PM =... (b) 8 (c) 6 0 (7) (O,r) k çkrn¼koøk{kt çkëw P Au. P çkëw{ktúke PA y u PB MÃkþofkuì Ëkuhu k Au. òu m APB = 6 nkuþ, íkku m AOB =... 6 (b) (c) 70 (8) (O,r) k çkrn¼koøk{kt çkëw P Au. P çkëw{ktúke PA ylku PB MÃkþofku Ëkuhu k Au. òu m APB = 70 nkuþ, íkku m POB =... (b) 70 (c) 0 (9) (O,) k çkrn¼koøk{kt çkëw P Au. PA ðíkwo Lkku MÃkþof Au. òu m AOP = 0 nkuþ, íkku m OPA = (b) 0 (c) 90 (0) (O,8) k çkrn¼koøk{kt çkëw P Au. PA ðíkwo Lkku MÃkþof Au. òu m AOP = nkuþ, íkku AP =... (b) 9 (c) 6 8 () (O,r) Lkk çkrn¼koøk{kt çkëw P Au. PA ðíkwo Lkku MÃkþof Au. òu OP = 0 ylku AP = 8 nkuþ, íkku ðíkwo Lkku ÔÞkMk =... 8 (b) 6 (c) 9 () çku Mk{fuLÿe ðíkwo kulke rºkßþkyku ylkw {u y u Au. òu {kuxk ðíkwo Lke Sðk LkkLkk ðíkwo Lku MÃkþoíke nkuþ, íkku yk SðkLke tçkkr... nkuþ. 6 (b) (c) 8 () ABC {kxu a =, b = ylku c = Au. ABC Lke çkkswykulku ytëhlke MÃkþoíkk ðíkwo Lke rºkßþk... Au.. (b) 6. (c) 6

2 () PQR {kt Q fkx¾qýku Au. òu PQ = 8 ylku QR = nkuþ, íkku PQR Lke çkkswykulku ytëhúke MÃkþoíkk ðíkwo Lke rºkßþk... Au. 7 (b) 0 (c) 7 () ðíkwo Lkk çknkhlkk ¼køk{kt ykðu k fkur Ãký rçktëw{ktúke ðíkwo Lku ðä{kt ðäw... MÃkþof Ëkuhe þfkþ. yuf (b) çku (c) [kh ymktïþ (6) yuf ðíkwo ABC Lke çkkswyku AB, BC ylku CA Lku ylkw {u D, E ylku F {kt MÃkþuo Au. òu AB =, BC = ylku CA = nkuþ, íkku AD =... (b) (c) 0 (7) yuf [kuhmklke çkäe çkkswykulku (O,) ytëhúke MÃkþuo Au, íkku [kuhmklke Ãkrhr{rík... Au. (b) 0 (c) 0 0 (8) (P,r) yu m ABCD Lke çkäe çkkswykulku MÃkþuo Au, íkku ABCD yu... Au. [kuhmk (b) tçk[kuhmk (c) [ eþ [íkw»fkuý Mk{çkksw [íkw»fkuý (9) m ABCD yu [ eþ [íkw»fkuý Ãký Au. òu AB = ylku BC = nkuþ, íkku AC =... 0 (b) 8 (c) (0) (O,) y u (O,9) Mk{fuLÿe ðíkwo ku Au. (O,) Lke Sðk AB yu (O,9) Lku MÃkþuo Au, íkku AB =... 0 (b) 0 (c) () (O,7) y u (O,) Mk{fuLÿe ðíkwo ku Au. (O,7) Lke Sðk AB yu (O,) Lku MÃkþuo Au, íkku AB =... (b) 8 (c) 6 () ABCD Lke [khuþ çkkswykulku yuf ðíkwo MÃkþuo Au. òu AB = 6, BC = y u CD = nkuþ, íkku AD =... (b) 9 (c) 7 AP (b) AQ (c) AO AB () ABCD Lke [khuþ çkkswykulku ðíkwo ytëhúke MÃkþuo Au. òu ABCD {kt MkkiÚke {kuxe tçkkrlke çkksw AB nkuþ, íkku MkkiÚke LkkLke tçkkrlke çkksw... nkuþ. CD (b) BC (c) AD BC (6) ykf]rík{kt çkíkkôþk «{kýu AB, AC ylku PQ yu ðíkwo Lkk MÃkþofku Au. òu AB = 6 nkuþ, íkku APQ Lke Ãkrhr{rík... 6 (b) 9 (c) (7) ykf]rík{kt çkíkkôþk «{kýu PA y u PB yu (O,r) Lkk MÃkþofku Au. òu m PAB = 60 nkuþ, íkku m PBA =... 0 (b) (c) 60 7 (8) ykf]rík{kt AB, AC ylku PQ yu (O,r) k MÃkþofku Au. òu APQ e Ãkrhr{rík 6 nkuþ, íkku AB =... () PQRS [ eþ [íkw»fkuý Au. òu m P = 0 nkuþ, íkku m R =... 0 (b) 60 (c) 0 0 (9) (O,) k PA ylku PB MÃkþofku Au. òu OP = nkuþ, íkku PB =... (b) 0 (c) () ykf]rík{kt çkíkkôþk «{kýu AB,AC y u PQ yu (O,r) Lkk MÃkþofku Au. òu APQ Lke Ãkrhr{rík =... (b) (c) 8 6 (0) ÃkhMÃkh çknkhúke MÃkþoíkk çku ðíkwo kulku Mkk{kLÞ MÃkþof... Ëkuhe þfkþ. çku (b) ºký (c) [kh {kºk yuf s

3 Ans () Ans : () Ans : (b)() Ans : () Ans : (b)() Ans : (6) Ans : (7) Ans : (8) Ans : (9) Ans : (0) Ans : (b) () Ans : () Ans : (c)() Ans : () Ans : (c)() Ans : (b) (6) Ans : (c)(7) Ans : (8) Ans : (9) Ans : (b)(0) Ans : () Ans : (c)() Ans : (c)() Ans : () Ans : () Ans : (b) (6) Ans : (c)(7) Ans : (8) Ans : (9) Ans : (c)(0) Ans : () Ans : (c)() Ans : (c)() Ans : (c)() Ans : () Ans : (6) Ans : (c)(7) Ans : (c)(8) Ans : (c)(9) Ans : (c)(0) Ans : (b)... ydt;gtlte lttukdt vt{fhkt 09. r*tftuktrbtr;t () ABC {kt AC =, BC =, m A = 90, íkku tan B =... (b) () ABC {kt m C = 90 ylku tan (c) A=, íkku sin A =... (b) (c) () ABC {kt m C = 90 ylku cos B =, íkku cosec A =... (b) (c) () ABC {kt m A = 90, AB =, AC = ylku BC = Au. sin C+ cosc =... (b) 7 7 (c) () ABC {kt m B = 90, BC = ylku AC = Au, íkku tan A =... (b) (c) (6) cosec A = 0 íkku sin A =... (b) 0 (7) cos A = sin A, íkku tan A =... (c) 0 (8) 0 (b) (c) θ= íkku sin θ+ cos θ = sinθ cosθ... (b) (c) 6 9 tan, 7

4 (9) sec θ= íkku cos θ =... (b) (c) tan θ (0) òu cotθ=, íkku... = + tan θ 7 (b) (c) () fkuef θ (sþkt, 0 < θ < 90) {kxu Lke[uLkk Ãkife... MkíÞ Au. 7 a cosθ sinθ (0) cot θ=, íkku =... b cosθ+ sinθ a (b) b (c) a + b b a a b () sin 0cot 0 cos 60sec 0 =... a b a+ b (b) (c) 0 () òu ½wfkuý θ {kxu cos θ = sin θ nkuþ, íkku tan θ + sin θ + =... cos θ > q (b) cosec θ < (c) tan θ < 0 sec θ > () sin θ=, íkku θ =... 0 (b) (c) () cosθ= íkku θ =... 0 (b) (c) () tanθ= íkku θ =... 0 (b) (c) () cosec θ =, íkku θ =... 0 (b) (c) (6) sec θ =, íkku θ =... 0 (b) (c) (7) sin 60 sin + cos 60 cos =... + (b) (8) + sin 60+ cos0 =... + sin 0+ cos 60 (c) 6+ (b) (c) (9) sin x= sin 60 cos0 cos 60 sin 0, íkku x =... 0 (b) 0 (c) 60 (b) 7 (c) 7 () 0 < θ < 90 {kxu θ Lke f{ík 0 Úke ðäelku 90 íkhv òþ íku{... Lke f{ík ðäu Au. cos θ (b) sin θ (c) cosec θ cot θ () sin (90 - θ) =... cos θ (b) sec θ (c) cosec θ tan θ () sec (90 - θ) =... cos θ (b) cosec θ (c) tan θ cot θ (6) tan (90 - θ) =... tan θ (b) cot θ (c) sec θ cosec θ (7) cos =... cos (b) sin (c) sec cosec (8) cosec 0 =... sin 0 (b) sec 0 (c) cot 0 sin 0 (9) sin 70 = cos θ, íkku θ = (b) 90 (c) 0 0 (0) cos0 + sin =... sin 0 cos 7 0 (b) (c) () tan tan tan 8tan 67 =... (b) (c)

5 () òu sec A = cosec (A - 0) sþkt, A yu ½wfkuýLkwt {kãk Au, íkku A Lke rf{tík... Au. (b) 70 (c) 0 A+ B () òu A + B + C = 80 nkuþ, íkku tan =... A B cot + C C A (b) cot (c) sec sin () cos (0 - θ) - sin (0 + θ) =... sin 0 (b) sin 0 (c) 0 () + + cos 0 cos 0 sin 0 sin 0 =... (b) (c) 0 (6) sin 8sec + cos 8cosec =... (b) (c) 0 cos(90 A)sin(90 A) (7) Lkwt MkkËwYÃk... Au. tan(90 A) sin A (b) cos A (c) sin A (8) òu θ yu ½wfkuýLkwt {kãk nkuþ íkúkk sin θ = cos (θ - 6) nkuþ, íkku θ Lke f{ík... 6 (b) 6 (c) 9 8 (9) òu ½wfkuý {kãk θ {kxu sin θ = cos 0 nkuþ, íkku tan θ - =... (b) (c) 0 (0) òu tan A= cot B, íkku A + B =... 0 (b) 60 (c) () A yu ½wfkuýLkwt {kãk Au íkúkk sec A = cosec(a - ) nkuþ, íkku A Lke f{ík... (b) (c).. () 0 < θ < 90 ylku sec θ = cosec 60 nkuþ, íkku cos θ - Lke f{ík... Au. b () cos θ= ; sþkt, 0 < θ < 90 íkku sin θ =... a + b a (b) a (c) b ab a + b b a a + b (6) òu ½wfkuýLkwt {kãk nkuþ ylku b sin θ = a cos θ, íkku a sin θ b cos θ =... a sinθ+ b cosθ a + b a b (b) (c) a + b a b a b a + b a b a+ b (7) fkuef θ (sþkt, 0 θ< 90 ) {kxu Lke[uLkk Ãkife... Mkk[wt Au. sec θ > (b) sec θ = (c) secθ= 0 < cosθ cosecθ sec θ (8) òu tan θ=, íkku... = cosecθ+ sec θ (b) (c) 8 (+ sin θ)( sin θ) (9) òu tan θ=, íkku Lke f{ík... Au. 7 ( cos θ )(+ cos θ) 7 (b) 8 (c) cosθ sinθ (0) òu cot θ=, íkku Lke f{ík... Au. cosθ+ sinθ 7 (b) 7 () òu cosec A = (c) ylku A + B = 90, íkku sec B = (b) (c) () sin θ + sec θ + cot θ + cos θ - tan θ - cosec θ =... (b) (c) () cosec θ = íkku tan θ Lkwt {qõþ... Au. (b) (c) (b) (c) 7 () òu θ ½wfkuýLkwt {kãk nkuþ ylku sinθ= cos θ, íkku θ =... 0 (b) (c) 60 90

6 () òu () òu tan A=, íkku (sin A + cos A) sec A Lktw {qõþ... Au. tan θ=, íkku (b) 7 sinθ + sinθ (c) 7 Lke f{ík... Au. 7 (b) (c) 9 6 () ABC {kt òu m ABC= 90, m ACB= ylku AC = 6 íkku ABC Lkwt ûkuºkv =... 8 (b) 9 (c) 6 9 (6) òu cos - cos 0 = x cos sin, íkku x =... (b) (c) (7) òu A ylku B fkxfkuý nkuþ, íkku sin A sec B =... (b) 0 (c) - (8) tan 0 tan tan tan 6 tan 70 =... - (b) (c) 0 (9) òu 7θ ylku θ ½wfkuýkuLkk {kãk nkuþ íkúkk sin 7θ = cos θ íkku sin θ tan θ=... (b) 0 (c) - (60) òu A + B = 90, íkku cot A cot B + cot A tan B =... sin A sec B cosec A (b) cot A (c) tan A B+ C (6) ABC {kxu sin =... A sin (b) sin A (c) A cos cos A (6) òu tan θ tan θ=, íkku θ =... 7 (b) (c) 0 9 (6) òu ½wfkuýLkk {kãk A ylku B {kxu... 0 (b) (6) sin θ=, íkku tan θ =... tan A= ylku (b) (6) secθ=, íkku tan θ Lke f{ík... Au. (c) (c) = íkku cos (A + B) = sin B, (b) (c) (66) =... cos θ cot θ (b) 0 (c) cos θ (67) ( + tan θ) ( - cos θ) =... cot θ (b) tan θ (c) 0 (68) a sin θ = ylku a cos θ = nkuþ, íkku a =... (sþkt, a > 0) (b) (c) (69) òu sin θ = cos θ íkku θ Lkwt {qõþ... Au. 0 (b) 9 (c) 8 (70) cosθ= nkuþ, íkku cosec θ + cot θ Lkwt {qõþ... Auu. 7 (b) 7 7 (c) 7 8 (7) tan θ + cot θ =... (b) sin θ (c) cos θ cosec θ. sec θ (7) (sinθ+ cos θ ) + (sinθ cos θ ) =... sinθ+ cosθ (b) (c) 0

7 (7) tanθ= nkuþ, íkku cos θ =... (b) (c) 6 (7) òu A = 0 nkuþ, íkku cos A Lkwt {qõþ... Au. (b) 0 (c) (7) tan ylku... Lke f{ík Mkh¾e Au. cot (b) cot 7 (c) sec tan 7 (76) sin + cos θ = nkuþ, íkku θ =... (b) (c) 70 0 (77) sin + cos θ = nkuþ, íkku θ =... (b) (c) 70 0 (78) sinθ cos(90 θ ) =... tan θ (b) sin θ (c) cos θ sin θ. sec θ (79) tan θ = sin θ + cos θ nkuþ íkúkk 0 < θ < 90 nkuþ, íkku θ Lkwt {qõþ... Au. 0 (b) (c) 60 7 (80) sin (x + 0) + cos (x + ) = nkuþ, íkku x =... 0 (b) (c) 0 60 (8) sin 60 - tan + cos 0 - cot 90 =... (b) (c) (8) tan (6 + θ) - cot( - θ) - sec( - θ) + cosec( + θ) =... (sþkt, 0 < θ < ) (b) (c) 0 (8) 8 sin - tan 60 + cot 0 - cos. (b) 6 (c) (8) =... cos θ sin θ (b) cot θ (c) tan θ cosec θ (8) =... sin θ cos θ (b) cot θ (c) tan θ sec θ (86) tan θ sec θ=... - (b) (c) cot θ sin θ (87) sec θ+ tan θ= nkuþ, íkku sec θ - tan θ Lkwt {qõþ... Au. (b) (c) (88) òu tan θ = nkuþ, íkku sin θ. cos θ =... (b) (c) (89) sec θ =... secθ+ tan θ (b) sin θ (c) cosec θ cos θ + sinθ cosecθ+ + cosθ (90) cotθ tan θ=... cot θ + tan θ (b) 0 (c) sin θ. cos θ (9) òu θ yu ½wfkuýLkwt {kãk nkuþ íkúkk cos θ = sin θ nkuþ, íkku θ Lke f{ík... Au. (b) 0 (c) 0 (9) sin 0- tan + cos 60 - cot 90 Lke f{ík... Au. (b) (c) (9) òu tan 7θ tan θ= nkuþ, íkku θ Lkwt {qõþ... Au. 0 (b) 8 (c) 9 (9) tan tan tan tan 6 tan 8 Lke f{ík... Au. (b) (c) 0 (9) sin + sin 7 =... (b) 0 (c) 6

8 (96) sin + sin + sin 87+ sin 89 =... 0 (b) (c) (97) 7cos θ+ sin θ=, íkku tan θ =... (b) 7 (c) 7 (98) sin θ = cos θ nkuþ, íkku tan θ =... (b) (c) (99) + =... tan θ cosec θ (b) sec θ (c) cot θ cos θ sin θ cos θ (00)... = sin θ cos θ (b) 0 (c) sin θ cos θ (0) ½wfkuý A ylku B {kxu tan A = ylku sin B =, íkku cos (A + B) =... 0 (b) (c) (6) Ans : (c)(6) Ans : (c)(6) Ans : (b)(6) Ans : (6) Ans : (c) (66) Ans : (67) Ans : (b)(68) Ans : (69) Ans : (b)(70) Ans : (c) (7) Ans : (7) Ans : (b)(7) Ans : (c)(7) Ans : (c)(7) Ans : (b) (76) Ans : (77) Ans : (b)(78) Ans : (b)(79) Ans : (b)(80) Ans : (b) (8) Ans : (8) Ans : (8) Ans : (b)(8) Ans : (c)(8) Ans : (b) (86) Ans : (87) Ans : (b)(88) Ans : (c)(89) Ans : (90) Ans : (9) Ans : (c)(9) Ans : (9) Ans : (9) Ans : (c)(9) Ans : (96) Ans : (c)(97) Ans : (98) Ans : (c)(99) Ans : (00) Ans : (0) Ans :... ydt;gtlte lttukdt Ans () Ans : (b)() Ans : (c)() Ans : () Ans : () Ans : (6) Ans : (b)(7) Ans : (8) Ans : (c)(9) Ans : (c)(0) Ans : () Ans : () Ans : () Ans : (b)() Ans : (c)() Ans : (c) (6) Ans : (7) Ans : (c)(8) Ans : (9) Ans : (b)(0) Ans : () Ans : (b)() Ans : () Ans : (b)() Ans : () Ans : (b) (6) Ans : (b)(7) Ans : (b)(8) Ans : (b)(9) Ans : (c)(0) Ans : (c) () Ans : () Ans : () Ans : (b)() Ans : () Ans : (c) (6) Ans : (7) Ans : (8) Ans : (c)(9) Ans : (0) Ans : (c) () Ans : () Ans : () Ans : () Ans : (b)() Ans : (6) Ans : (b)(7) Ans : (b)(8) Ans : (9) Ans : (0) Ans : (b) () Ans : (c)() Ans : () Ans : (c)() Ans : () Ans : (b) (6) Ans : (c)(7) Ans : (8) Ans : (9) Ans : (b)(60) Ans :