Objective Mathematics

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Gyles Dennis
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1 . o o o o {cos 4 cos 9 si cos 65 } si 7º () cos 6º si 8º. If x R oe of these, the mximum vlue of the expressio si x si x.cos x c cos x ( c) is : () c c c c c c. If ( cos )cos cos ; 0, the vlue of 4. The vlue of t / t / Ojective Mthemtics Er.L.K.Shrm () 4 6.cos.cos.cos.cos () 5. If cos si c d cos si c, the 6. If t, t re the roots of qudrtic equtio x px q 0, the vlue of expressio si ( ) qcos ( ) psi( ).cos( ) p q q p q () p q q p 7. If t, the cos(8 ) p p p + p () p p oe of these 8. The vlue of {si 44º. si 08º. si7º. si6º} is equl to : 6 9. The vlue of () t 0 t 0 7 t 0 is : () 4 0. The vlue of oe of these 7 9 cos cos cos cos () 6 oe of these vlue of t. If cos A si A, m, the si B cos B si B () c m () m c m m [ 00 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm

2 Trigoometric Rtios d Idetities. If / / f ( ) ( cos si ) ( si cos ) the mximum vlue of f ( ) is : () ( ) 4 9. If f ( ) si si si ; the vlue of f 5 oe of these () t x. Let f ( x) d x or ; I, the t x itevl i which f (x) lies is : R, R, () R, R, If cos si K si ( ) ; 0, the vlue of K 4 () 4 8 o o o o 5. The vlue of cos 0 cos0.cos 50 cos 50 is : 4 4 () Ojective Mthemtics Er.L.K.Shrm 6. If A + B + C = 0, the vlue of the expressio {si A+cos C(cos A cos B cos C)+ cos B (cosa cosc cosb)} () 0 0. If cot A, cot B, cot C re i A.P. for ABC, the si A cos B si C is : t B sec B. Let, i i R si () si B cot B i,,. if for ll si i cos i i i si i.cosi i d si i cos i i i cos, the si i.cos i i. Let 4 4 si cos. () si cos si cos. si cos. cos A cos B cos B d si A si B si B, the si ( B ) is : 5 4 () Vlue of (t 40º + tº 0) is : cot 50º () cot 40º cot 0º cot 0º. Let for ll / x x x R, t, x x where 8. 8 o si (5 r) r 9 () 9 7 (0, ),, the vlue of ' ' c e : () 5 [ 0 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm

3 si x/ cos x/ 4. The miimum vlue of (8) (7) equl to : sec () t 8 si is cosec = = 5 = 0 () = = 0 0. Vlue of equl to : 6 r r o o ( t( r )). ( cot( r )) is r r Let, R d, the mximum vlue of {si si } () 04 0 () 0 0 r0 0 r0 0 C C r r 6. Let r f ( ) t. ( sec( )), the r f 6 () f 64 f 48 f Which of the followig re rtiol umers? si.cos si.cos 0 5 Ojective Mthemtics Er.L.K.Shrm ().cosec sec 9 9 si º. si 48º. si 54º 8. Solutio set {x, y} for the system of equtios 9. If x y = d cos ( x) si ( y) c e give y : 7 5, , m0 (),, 6 6 m si x.si x m cos x, where 0,,,... 6 re costts, the Followig questios re ssertio d resoig type questios. Ech of these questios cotis two sttemets, Sttemet (Assertio) d Sttemet (Reso). Ech of these questios hs four ltertive swers, oly oe of them is the correct swer. Select the correct swer from the give optios : Both Sttemet d Sttemet re true d Sttemet is the correct expltio of Sttemet. () Both Sttemet d Sttemet re true ut Sttemet is ot the correct expltio of Sttemet. Sttemet is true ut Sttemet is flse. Sttemet is flse ut Sttemet is true.. I trigle ABC with fixed se BC, t he A vertex A moves such tht cos B cosc 4si. If, d c deote the side legths of trigle opposite to the gles A, B d C respectively, the. Let Sttemet : locus of vertex poit A is ellipse ecuse Sttemet : I the give ABC,, d c form rithmetic progressio. 4 4 si cos, where R, the si cos Sttemet : Vlue of is equl to 7 4 sgl. log 0 0 ecuse Sttemet : Vlue of t. 7 [ 0 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm

4 Trigoometric Rtios d Idetities. Let,, R, d cos, cos c c d cos, where the sides,, c of trigle ABC re i A.P. Sttemet : Vlue of t to ecuse t is equl Sttemet : p t d t p 4. Sttemet : For t rigle ABC, if si A si B si C, the trigle must e right gled ecuse Sttemet : I y trigle PQR, si P si Q si R ( 4 cos P.cos Q.cos R) 5. Cosider y trigle ABC hvig iterl gles, d, where,,. Sttemet : If Ojective Mthemtics Er.L.K.Shrm t t t 6 4x x for ll x R, the trigle ABC is essetilly cute gled trigle ecuse Sttemet : I y trigle except the right-gled, sum of the tget of iterl gles is lwys equl to the product of tget of iterl gles. [ 0 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm

5 Comprehesio pssge () ( Questios No. - ) Let ; where I, d cos si....() cos( ) si( ) O the sis of give reltio, swer the followig questios.. Usig the idetity 4 4 cos si cos, the vlue of t which is otied from the give reltio... () of pssge cos si cos si () cos si si cos. Usig the idetity si.cos cos si si cos, the vlue of t which is otied from the give reltio...() of pssge cos si x si cos () si cos x Ojective Mthemtics Er.L.K.Shrm si cos. If ' ' is elimited from reltio...() of pssge, the qudrtic i which is otied, cos 0 () si 0 cos 0 si 0 Comprehesio pssge () ( Questios No. 4-6 ) 9 Let vlue of t, where 4 > > 0, the swer the followig questios. 5. The vlue of () 4 4 cos(r ) r0 8 () o o o o 6. The vlue of t 6.t 4.t 66.t 78 is 7. If equl to : T si 4 6 T T 8. If si 4 9. If x cos () x, is equl to... t he vlue of is root of the cuic equtio 8x 4x 4x 0 d [.] represets the gretest iteger fuctio, the vlue of is equl to (r ) si, 4 the vlue of r is equl to The vlue of equl to : cos.cos.cos.cos is 0. Let 8, d e three sides of trigle, the lest possile itegrl vlue of ' ' is equl to... [ 04 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm

6 Trigoometric Rtios d Idetities. Let si si d cos cos, where, the mtch the followig colums (I) d (II). Colum (I) Colum (II) t t (p) ( ) 4 4( ) () cos.cos (q) ( ) cos 8 (r) ( ) 4 4 si( ) (s) ( ) (t). Mtch the followig colums (I) d (II). Colum (I) Ojective Mthemtics Er.L.K.Shrm Colum (II) If x,, the the output set of (p) (, ] si x si x f ( x) 4 4 coti the itervl(s) () If x, 0, the the output set of (q) [4, 5) 6 4 f ( x) si x si x 5si x cos x (r) (5, 9] coti the itervl(s) If x,, the the output set of (s) [, 4) f (x) = t 6 x + 4 t x + 5 coti the itervl(s) If x,, the output set of (t) [, 4) sec x sec x f ( x) 9 4() 5 coti the itervl(s) [ 05 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm

7 .. () Ex () (). (). (). () () 8. () 9. () 0. ().. () (,, c) 7. (,, c, d) 8. (, c d) 9. (,, c) 0. (, ).. () ().. 4. () 5. Ex ( 6 ) 8. ( 0 ) 9. ( 9 ) 0. ( 6 ). r. s () p () q, r, s t p, q, r, s, t q q Ojective Mthemtics Er.L.K.Shrm [ 06 ] Mthemtics for JEE-0 Author - Er. L.K.Shrm

EXERCISE a a a 5. + a 15 NEETIIT.COM

EXERCISE a a a 5. + a 15 NEETIIT.COM - Dowlod our droid App. Sigle choice Type Questios EXERCISE -. The first term of A.P. of cosecutive iteger is p +. The sum of (p + ) terms of this series c be expressed s () (p + ) () (p + ) (p + ) ()