BMT June - Examination 2017 BSCP Examination Mathematics J{UV. Paper - BMT. Time : 3 Hours ] [ Max. Marks :- 80

Size: px

Start display at page:

Download "BMT June - Examination 2017 BSCP Examination Mathematics J{UV. Paper - BMT. Time : 3 Hours ] [ Max. Marks :- 80"

Scot Bruce
5 years ago
Views:

1 BMT Jue - Eamiatio 7 BSCP Eamiatio Mathematics J{UV Paper - BMT Time : 3 Hours ] [ Ma. Marks :- 8 Note: The questio paper is divided ito three sectios A, B ad C. Write aswer as per the give istructios. {ZX}e : h àíz Ì "A' "~' Am a "g' VrZ IÊS>m {d^m{ov h & àë oh$ IÊS> Ho$ {ZX}emZwgma àízm Ho$ CÎma Xr{OE& Note: {ZX}e : Sectio - A 8 = 6 (Very Short Aswer Questios) Sectio A cotai 8 Very Short Aswer Type Questios. Eamiees have to attempt all questios. Each questio is of marks ad maimum word limit is thirty words. IÊS> - "A' (A{V bkw CÎmar àíz) IÊS> "E' 8 A{V bkwcîmamë H$ àý h, arjm{w m H$mo g^r àým H$mo hb H$aZm h & àë oh$ àý Ho$ A H$ h Am a A{YH$V eãx gr m Vrg eãx h & BMT / 3 / 6 () (P.T.O.)

2 ) (i) If z = ( 3, ) the fid the value of Z. {X z = ( 3, ) Vmo Z H$m mz kmv H$s{OE& d - (ii) Fid the value of ( cos ). d - ( cos ) H$m mz kmv H$s{OE& (iii) Write the defiitio of Idetity fuctio. VËg H$ $bz H$s [a^mfm {b{ie& (iv) If y = 3 log the fid the value of. {X y = 3 log hmo Vmo H$m mz kmv H$s{OE& cos( log ) (v) Fid the value of y cos( log ) y H$m mz kmv H$s{OE& 5 (vi) Fid the value of Itegratio y.. 5 g mh$bz y.. H$m mz kmv H$s{OE& (vii) Write the equatio of taget of parabola y = 4a at the poit (, y ). adb y = 4a Ho$ {~ÝXþ (, y ) a ñe aoim H$m g rh$au {b{ie& (viii)write the defiitio of parabola. adb H$s [a^mfm {b{ie& BMT / 3 / 6 () (Cotd.)

3 Note: {ZX}e : Sectio - B 4 8 = 3 (Short Aswer Questios) Sectio B cotai 8 Short Aswer Type Questios. Eamiees will have to aswer ay four (4) questios. Each questio is of 8 marks. Eamiees have to delimit each aswer i maimum words. IÊS> - ~ (bkyîmamë H$ àíz) IÊS> "~r' AmR> bkw CÎma àh$ma Ho$ àý h, arjm{w m H$mo H$sÝht ^r Mma (4) gdmbm Ho$ Odm~ XoZm h & àë oh$ àý 8 A H$m H$m h & arjm{w m H$mo A{YH$V eãxm àë oh$ Odm~ [agr{ V H$aZo h & + r ) Prove that: ( + i) + ( - i) = cos. 4 + r + i + - i = cos 4 {gõ H$s{OE ( ) ( ). 3) If f : R " R ad : g R " R are defied o the set of real umbers R, where f( ) = - 6! R ad g( ) = - 5, 6! R the fid (go f ) () ad (f o g) (). {X f : R " R VWm g : R " R dmñv{dh$ g» mam Ho$ g wàm R a [a^m{fv $bz h & Ohm± f( ) = - 6! R VWm g( ) = - 5, 6! R V~ (go f ) () Ed (f o g) () kmv H$s{OE& BMT / 3 / 6 (3) (P.T.O.)

4 4) Eamie the cotiuity of the fuctio: si, f( ) = *!, = at = gmvë Vm H$s Om±M H$s{OE& si, f( ) = *,! = at = 5) If si y = si (a + y) the prove that BMT / 3 / 6 (4) (Cotd.) {X si y = si (a + y) hmo Vmo {gõ H$s{OE {H$ 6) Fid the value of lim " ( cosec ) log e 7) Fid the value of lim " ( cosec ) y log e H$m mz kmv H$s{OE& r/ a cos + b si a cos + b si r/ y H$m mz kmv H$s{OE& si ( a + y) =. si a si ( a + y) = si a 8) Fid the equatio of the hyperbola whose co-ordiates of the foci are (6, 4), ( 4, 4) ad eccetricity is. Cg A{Vadb H$m g rh$au kmv H$s{OE {OgH$s Zm{^ (6, 4), VWm ( 4, 4) h VWm CËHo$ZÐVm h & 9) Fid the agle betwee the plae 3 - y + z + 7 = ad 4 + 3y - 6z - 5 =. g Vb 3 - y + z + 7 = Ed 4 + 3y - 6z - 5 =. Ho$ Ü H$moU kmv H$s{OE&

5 Note: Sectio - C 6 = 3 (Log Aswer Questios) Sectio C cotai 4 Log Aswer Type Questios. Eamiees will have to aswer ay two () questios. Each questio is of 6 marks. Eamiees have to delimit each aswer i maimum 5 words. IÊS> - g (XrK CÎmar àíz) {ZX}e : IÊS> "gr' 4 {Z~ÝYmË H$ àý h & arjm{w m H$mo H$sÝht ^r Xmo () gdmbm Ho$ Odm~ XoZo h & àë oh$ àíz 6 A H$m H$m h, arjm{w m H$mo A{YH$V 5 eãxm àë oh$ Odm~ [agr{ V H$aZo h & ) (i) If a + b, a - b ad a + b are the positio vector s of poits A, B ad C i parallelogram, the fid the positio vector of D. g mýva MVw^w O ABCD {~ÝXþAm A, B, C Ho$ pñw{v g{xe H«$ e a + b, a - b Ed a + b h & {~ÝXþ D H$m pñw{v g{xe kmv H$s{OE& (ii) If y = a cos( log ) + bsi( log ) the prove that e + + y + ( + ) y + ( + ) y =. {X y a cos( loge) bsi( loge) y + ( + ) y + ( + ) y =. e = + hmo Vmo {gõ H$s{OE {H$ + + ) (i) Prove that ( a # b ) = a b - ( a - b). {gõ H$s{OE {H$ ( a # b ) = a b - ( a - b). BMT / 3 / 6 (5) (P.T.O.)

6 (ii) If a movig particle i a straight lie at the distace a - havig v from the origi is proportioal to, the fid the acceleratio law. {X gab aoim J{V mz H$U H$s yb {~ÝXþ go Xÿar a doj a -, Ho$ g mzwmvr h Vmo ËdaU H$m {Z kmv H$s{OE& ) (i) A particle is throw vertically from the groud with the rate of m/sec. Fid the distace attaied by the particle i secod. EH$ H$U H$mo rq>a à{v goh$ês> H$s Xa go YamVb go D$Üdm Ya D$a $H$m OmVm h & goh$ês> H$U Ûmam V H$s JB Xÿar ³ m hmojr? (ii) If z is a comple umber the prove that: 3 cos 3z = 4 cos z - 3 cos z. {X z EH$ g { l am{e h, V~ {gõ H$s{OE cos 3z = 4 cos z - 3 cos z. 3) (i) Fid the value of mz kmv H$s{OE y a 3 a a - + (ii) Fid the value of: mz kmv H$s{OE lim. / 3 " 3 = c + me + oe + o e + o G BMT / 3 / 6 (6)

MT-03 December - Examination 2016 B.A. / B.Sc. Pt. I Examination Co-ordinate Geometry & Linear Programming Paper - MT-03

MT-03 December - Examination 2016 B.A. / B.Sc. Pt. I Examination Co-ordinate Geometry & Linear Programming Paper - MT-03 MT-03 December - Examination 06 B.A. / B.Sc. Pt. I Examination Co-ordinate Geometry & Linear Programming Paper - MT-03 Time : 3 Hours ] [ Max. Marks :- 66 Note: {ZX}e : Note: {ZX}e : The question paper