Page 1 Series : OSR/I *l*,. 6snt3 +s+t err-gk*,f *-W-gua T{ siErqq ffi r Candidates must write the Code on the title page of the answer-book. 1afr+o-av ait: Ioo I Maximum Marks : 100 riiri. Roll No. o ge-erqlqordt+'gq +Ekfrlps t r o rrsr-rr-jr { Erf6+ ilq ftt ek lqq rqqilsqq{*} om wc-gfiror *5e-Y*'n fui} r o ge'fi dqmdfm gsvFt-rrif zg strt r o Srrrft rFt ul utrfaqqrvJsur+ + v6d, gl':rul rqia rqvqftrd t o {n }rfi-wr si Wi + frq 15 flffie $T uttit fEqrrqr t r mq-.Ir or f+mor WRT { tO.tS q$ fuqr qr&n I 10.15 qq t 10.30 {q ird6-trFT !5qqT qfi-q{ q}+ 31Y{ gs erqtr + d{lr * str- EksTw*ttstnrdifudn I o Please check that this question paper contains 8 printed pages. o Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. o Please check that this question paper contains 29 questions. o Please write dovm the Serial Number of the question before attempting it. o 15 minutes time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. MATIISMATICS futifuâ‚¬rtzt : 3 w4 Time allowed: j hours l wqrqfrTtvr; (i) az,fr sfr erfuri t r (ii) qsyw-wilZg erlfiEiahazsiC f$rtfuifi; 4 dtwrv tu,0'â‚¬erif tO swf Fil?+ drdr Vqqaw* I urrsad 12 ev;rf,F77+ SrdF Errdqw * I soc sl7 Yfr Se# tsdrrl ;iawt r (iii) sâ‚¬ -rr f pr# mr+ # rar <ra Vm W qTqq swet snr dt afiq?zrqdr argcr fr<' tr smd' fr (iv) Wf sTa-wtfu?E?f rfurfiarriiotad t rY++ wn* efud;qrd'2 wif t amftrfu* r 0d srfryqitd+orqni Wdlfqaarermi I (v) *ffi?der# yqlrr*+ Wqfu %f+ t fle*zraarrglqr ewdylvralqsTvftinart* r 651u3 tP.T.O. Page 2 Series : OSR/I *l*,. 6snt3 +s+t err-gk*,f *-W-gua T{ siErqq ffi r Candidates must write the Code on the title page of the answer-book. 1afr+o-av ait: Ioo I Maximum Marks : 100 riiri. Roll No. o ge-erqlqordt+'gq +Ekfrlps t r o rrsr-rr-jr { Erf6+ ilq ftt ek lqq rqqilsqq{*} om wc-gfiror *5e-Y*'n fui} r o ge'fi dqmdfm gsvFt-rrif zg strt r o Srrrft rFt ul utrfaqqrvJsur+ + v6d, gl':rul rqia rqvqftrd t o {n }rfi-wr si Wi + frq 15 flffie $T uttit fEqrrqr t r mq-.Ir or f+mor WRT { tO.tS q$ fuqr qr&n I 10.15 qq t 10.30 {q ird6-trFT !5qqT qfi-q{ q}+ 31Y{ gs erqtr + d{lr * str- EksTw*ttstnrdifudn I o Please check that this question paper contains 8 printed pages. o Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. o Please check that this question paper contains 29 questions. o Please write dovm the Serial Number of the question before attempting it. o 15 minutes time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. MATIISMATICS futifuâ‚¬rtzt : 3 w4 Time allowed: j hours l wqrqfrTtvr; (i) az,fr sfr erfuri t r (ii) qsyw-wilZg erlfiEiahazsiC f$rtfuifi; 4 dtwrv tu,0'â‚¬erif tO swf Fil?+ drdr Vqqaw* I urrsad 12 ev;rf,F77+ SrdF Errdqw * I soc sl7 Yfr Se# tsdrrl ;iawt r (iii) sâ‚¬ -rr f pr# mr+ # rar <ra Vm W qTqq swet snr dt afiq?zrqdr argcr fr<' tr smd' fr (iv) Wf sTa-wtfu?E?f rfurfiarriiotad t rY++ wn* efud;qrd'2 wif t amftrfu* r 0d srfryqitd+orqni Wdlfqaarermi I (v) *ffi?der# yqlrr*+ Wqfu %f+ t fle*zraarrglqr ewdylvralqsTvftinart* r 651u3 tP.T.O. General Instructions : (i) All questions are compulsory (ii) The question paper consists of 29 questions divided into three sections A, B and C. Section - A comprises of 10 questions of one mark each, Section - B comprises of 72 questions of four marks each and Section - C comprises of 7 questions of six marks each. (iii) All questions in Section - A are to be answered in one word, one sentence or as per the exact requirement of the question. (iv) There is no overall choice. However, internal choice has been provided in 4 questions offour marks each and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculators is not permitted. You may askfor logarithmic tables, if required. ,rffioi1o $F {qr 1 t 10 iro'qdq, sF r eis'sT t r Question numbers L to 10 carry 1 mark each. 1 *r[ ; 1 ].[ ; I ]=[ ; l ]*d(,-y)EFrrTr{vro+1tuq r [: 41 l-r vl I t ot If 2Ls , J*Lo i l=L ,o ,l,Rna(x-y). 2. frq etq5v$q.qor*)x*floqre*tfqq:, [x 1] Solve the following matrix equation forx:, [x I l- r 0l l-, o l=o' l- r 0l )l-r o.l=o' 3. qk lzx5l tt- l8 xl bc 5ll s ,l=l , write the value of x. i i l*d"rsf qrqfrtuq r 6 7 -2 3 4. (r^n . U)* sfr-srqsirq frfiqq r Write the antiderivative "t (rrF . 1f,) 65m3 Page 3 Series : OSR/I *l*,. 6snt3 +s+t err-gk*,f *-W-gua T{ siErqq ffi r Candidates must write the Code on the title page of the answer-book. 1afr+o-av ait: Ioo I Maximum Marks : 100 riiri. Roll No. o ge-erqlqordt+'gq +Ekfrlps t r o rrsr-rr-jr { Erf6+ ilq ftt ek lqq rqqilsqq{*} om wc-gfiror *5e-Y*'n fui} r o ge'fi dqmdfm gsvFt-rrif zg strt r o Srrrft rFt ul utrfaqqrvJsur+ + v6d, gl':rul rqia rqvqftrd t o {n }rfi-wr si Wi + frq 15 flffie $T uttit fEqrrqr t r mq-.Ir or f+mor WRT { tO.tS q$ fuqr qr&n I 10.15 qq t 10.30 {q ird6-trFT !5qqT qfi-q{ q}+ 31Y{ gs erqtr + d{lr * str- EksTw*ttstnrdifudn I o Please check that this question paper contains 8 printed pages. o Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. o Please check that this question paper contains 29 questions. o Please write dovm the Serial Number of the question before attempting it. o 15 minutes time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. MATIISMATICS futifuâ‚¬rtzt : 3 w4 Time allowed: j hours l wqrqfrTtvr; (i) az,fr sfr erfuri t r (ii) qsyw-wilZg erlfiEiahazsiC f$rtfuifi; 4 dtwrv tu,0'â‚¬erif tO swf Fil?+ drdr Vqqaw* I urrsad 12 ev;rf,F77+ SrdF Errdqw * I soc sl7 Yfr Se# tsdrrl ;iawt r (iii) sâ‚¬ -rr f pr# mr+ # rar <ra Vm W qTqq swet snr dt afiq?zrqdr argcr fr<' tr smd' fr (iv) Wf sTa-wtfu?E?f rfurfiarriiotad t rY++ wn* efud;qrd'2 wif t amftrfu* r 0d srfryqitd+orqni Wdlfqaarermi I (v) *ffi?der# yqlrr*+ Wqfu %f+ t fle*zraarrglqr ewdylvralqsTvftinart* r 651u3 tP.T.O. General Instructions : (i) All questions are compulsory (ii) The question paper consists of 29 questions divided into three sections A, B and C. Section - A comprises of 10 questions of one mark each, Section - B comprises of 72 questions of four marks each and Section - C comprises of 7 questions of six marks each. (iii) All questions in Section - A are to be answered in one word, one sentence or as per the exact requirement of the question. (iv) There is no overall choice. However, internal choice has been provided in 4 questions offour marks each and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculators is not permitted. You may askfor logarithmic tables, if required. ,rffioi1o $F {qr 1 t 10 iro'qdq, sF r eis'sT t r Question numbers L to 10 carry 1 mark each. 1 *r[ ; 1 ].[ ; I ]=[ ; l ]*d(,-y)EFrrTr{vro+1tuq r [: 41 l-r vl I t ot If 2Ls , J*Lo i l=L ,o ,l,Rna(x-y). 2. frq etq5v$q.qor*)x*floqre*tfqq:, [x 1] Solve the following matrix equation forx:, [x I l- r 0l l-, o l=o' l- r 0l )l-r o.l=o' 3. qk lzx5l tt- l8 xl bc 5ll s ,l=l , write the value of x. i i l*d"rsf qrqfrtuq r 6 7 -2 3 4. (r^n . U)* sfr-srqsirq frfiqq r Write the antiderivative "t (rrF . 1f,) 65m3 5. {fr sin (ra-'}*.or-'r)= , t ni, $TrtFtirmeifqq I If sin (sin-t f * ,or-' ,) = ,, then find the value of x. O. q$ yf+ilqr6t{s{5qt3t*'qgffi d, qmr * goffi*rfr {kqr t *{-t a, b e R - {0} +kq a * b = $* rEf, t I qF( 2 *' (x * 5) = 10 t nt, $T qH ffa dkq r Let x be a binary operation, on the set of all non-zero real numbers, given by a * b = + forall a,b â‚¬ R- t0).Findthevalueof x, given that2 x (x * 5) = 10. 7. qtqvr I + 3j + ztor qk{r zi - :3 * of qtsq)q ffo +lflt{q r Find the projection of the vector i + :i + 7t on the vector Zi - li + Ot. g. s{r qrkrcr eT qlqvr {r+ffir {rer +tFre' qt t{S (a, b, c) t tlor qrer t Hsrt qtrtrcT ?.ti+3+tl=2*'qqimt r Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane ? . fi +i + t; = z. ril? g. qFT {rf, ftikq , I g(rin x - cos x) dx. 0 fi/2 f Evaluate : I er(sin.r - cos r) d,r. J 0 10. qi{vit A =2i*i-stst{ B =zi*i-zt+qtrmm+q$rTqs'qrf,m{rtffrflafuq r Write a unit vector in the direction of the sum of the vectors i = Zi * i * 5t and iAAA t5=2i+j-7k. 6sfit3 3 IP.T.O. Page 4 Series : OSR/I *l*,. 6snt3 +s+t err-gk*,f *-W-gua T{ siErqq ffi r Candidates must write the Code on the title page of the answer-book. 1afr+o-av ait: Ioo I Maximum Marks : 100 riiri. Roll No. o ge-erqlqordt+'gq +Ekfrlps t r o rrsr-rr-jr { Erf6+ ilq ftt ek lqq rqqilsqq{*} om wc-gfiror *5e-Y*'n fui} r o ge'fi dqmdfm gsvFt-rrif zg strt r o Srrrft rFt ul utrfaqqrvJsur+ + v6d, gl':rul rqia rqvqftrd t o {n }rfi-wr si Wi + frq 15 flffie $T uttit fEqrrqr t r mq-.Ir or f+mor WRT { tO.tS q$ fuqr qr&n I 10.15 qq t 10.30 {q ird6-trFT !5qqT qfi-q{ q}+ 31Y{ gs erqtr + d{lr * str- EksTw*ttstnrdifudn I o Please check that this question paper contains 8 printed pages. o Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. o Please check that this question paper contains 29 questions. o Please write dovm the Serial Number of the question before attempting it. o 15 minutes time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. MATIISMATICS futifuâ‚¬rtzt : 3 w4 Time allowed: j hours l wqrqfrTtvr; (i) az,fr sfr erfuri t r (ii) qsyw-wilZg erlfiEiahazsiC f$rtfuifi; 4 dtwrv tu,0'â‚¬erif tO swf Fil?+ drdr Vqqaw* I urrsad 12 ev;rf,F77+ SrdF Errdqw * I soc sl7 Yfr Se# tsdrrl ;iawt r (iii) sâ‚¬ -rr f pr# mr+ # rar <ra Vm W qTqq swet snr dt afiq?zrqdr argcr fr<' tr smd' fr (iv) Wf sTa-wtfu?E?f rfurfiarriiotad t rY++ wn* efud;qrd'2 wif t amftrfu* r 0d srfryqitd+orqni Wdlfqaarermi I (v) *ffi?der# yqlrr*+ Wqfu %f+ t fle*zraarrglqr ewdylvralqsTvftinart* r 651u3 tP.T.O. General Instructions : (i) All questions are compulsory (ii) The question paper consists of 29 questions divided into three sections A, B and C. Section - A comprises of 10 questions of one mark each, Section - B comprises of 72 questions of four marks each and Section - C comprises of 7 questions of six marks each. (iii) All questions in Section - A are to be answered in one word, one sentence or as per the exact requirement of the question. (iv) There is no overall choice. However, internal choice has been provided in 4 questions offour marks each and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculators is not permitted. You may askfor logarithmic tables, if required. ,rffioi1o $F {qr 1 t 10 iro'qdq, sF r eis'sT t r Question numbers L to 10 carry 1 mark each. 1 *r[ ; 1 ].[ ; I ]=[ ; l ]*d(,-y)EFrrTr{vro+1tuq r [: 41 l-r vl I t ot If 2Ls , J*Lo i l=L ,o ,l,Rna(x-y). 2. frq etq5v$q.qor*)x*floqre*tfqq:, [x 1] Solve the following matrix equation forx:, [x I l- r 0l l-, o l=o' l- r 0l )l-r o.l=o' 3. qk lzx5l tt- l8 xl bc 5ll s ,l=l , write the value of x. i i l*d"rsf qrqfrtuq r 6 7 -2 3 4. (r^n . U)* sfr-srqsirq frfiqq r Write the antiderivative "t (rrF . 1f,) 65m3 5. {fr sin (ra-'}*.or-'r)= , t ni, $TrtFtirmeifqq I If sin (sin-t f * ,or-' ,) = ,, then find the value of x. O. q$ yf+ilqr6t{s{5qt3t*'qgffi d, qmr * goffi*rfr {kqr t *{-t a, b e R - {0} +kq a * b = $* rEf, t I qF( 2 *' (x * 5) = 10 t nt, $T qH ffa dkq r Let x be a binary operation, on the set of all non-zero real numbers, given by a * b = + forall a,b â‚¬ R- t0).Findthevalueof x, given that2 x (x * 5) = 10. 7. qtqvr I + 3j + ztor qk{r zi - :3 * of qtsq)q ffo +lflt{q r Find the projection of the vector i + :i + 7t on the vector Zi - li + Ot. g. s{r qrkrcr eT qlqvr {r+ffir {rer +tFre' qt t{S (a, b, c) t tlor qrer t Hsrt qtrtrcT ?.ti+3+tl=2*'qqimt r Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane ? . fi +i + t; = z. ril? g. qFT {rf, ftikq , I g(rin x - cos x) dx. 0 fi/2 f Evaluate : I er(sin.r - cos r) d,r. J 0 10. qi{vit A =2i*i-stst{ B =zi*i-zt+qtrmm+q$rTqs'qrf,m{rtffrflafuq r Write a unit vector in the direction of the sum of the vectors i = Zi * i * 5t and iAAA t5=2i+j-7k. 6sfit3 3 IP.T.O. ,rffio*1, ym riqr rr t zz H*r*oqm I oi+.qr t r Question numbers ll to 22 carry 4 marks each. 11. fritt+{qRvri a, B, A+fuqfuq*leqiq, [a * u', E' * ?, ? * ?] = zfi,B, A] 3IW{t n+J nRvr ?, u' aqr ? tS tfu' ? * B + ? = d aqr I ? I = 3, I ts' | - s ireTr I ? I = z t r ? nqr B ++qorqiqaraqfr&q r Prove that, for any three vectors ?, bt, ? [? * B, B * ?, ? * ?] =zli,ts, ?] OR vectors ?, b' ana d ur. such that ? * B + ? = d ano l?l = 3, lBl = 5 ano l?l = z. Find the angle between ?anO Ut. FTq â‚¬rqsm qfurur *t co +lfuq, (*'*t)*.r*=*. Solve the following differential equation : .) -.dv 2 (x- - t) -.o* Zry = il t. qnnrnsliqq, [W* J Sm-x. cos-.r qelitt qFT Ern *1iqq , ! A- :;1ffi, - rs a, Evaluate' [W* J slnir. cos._r OR ?_ Evaluate , ) @- l1@rs o* 12. 13. 65t1t3 Page 5 Series : OSR/I *l*,. 6snt3 +s+t err-gk*,f *-W-gua T{ siErqq ffi r Candidates must write the Code on the title page of the answer-book. 1afr+o-av ait: Ioo I Maximum Marks : 100 riiri. Roll No. o ge-erqlqordt+'gq +Ekfrlps t r o rrsr-rr-jr { Erf6+ ilq ftt ek lqq rqqilsqq{*} om wc-gfiror *5e-Y*'n fui} r o ge'fi dqmdfm gsvFt-rrif zg strt r o Srrrft rFt ul utrfaqqrvJsur+ + v6d, gl':rul rqia rqvqftrd t o {n }rfi-wr si Wi + frq 15 flffie $T uttit fEqrrqr t r mq-.Ir or f+mor WRT { tO.tS q$ fuqr qr&n I 10.15 qq t 10.30 {q ird6-trFT !5qqT qfi-q{ q}+ 31Y{ gs erqtr + d{lr * str- EksTw*ttstnrdifudn I o Please check that this question paper contains 8 printed pages. o Code number given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. o Please check that this question paper contains 29 questions. o Please write dovm the Serial Number of the question before attempting it. o 15 minutes time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. MATIISMATICS futifuâ‚¬rtzt : 3 w4 Time allowed: j hours l wqrqfrTtvr; (i) az,fr sfr erfuri t r (ii) qsyw-wilZg erlfiEiahazsiC f$rtfuifi; 4 dtwrv tu,0'â‚¬erif tO swf Fil?+ drdr Vqqaw* I urrsad 12 ev;rf,F77+ SrdF Errdqw * I soc sl7 Yfr Se# tsdrrl ;iawt r (iii) sâ‚¬ -rr f pr# mr+ # rar <ra Vm W qTqq swet snr dt afiq?zrqdr argcr fr<' tr smd' fr (iv) Wf sTa-wtfu?E?f rfurfiarriiotad t rY++ wn* efud;qrd'2 wif t amftrfu* r 0d srfryqitd+orqni Wdlfqaarermi I (v) *ffi?der# yqlrr*+ Wqfu %f+ t fle*zraarrglqr ewdylvralqsTvftinart* r 651u3 tP.T.O. General Instructions : (i) All questions are compulsory (ii) The question paper consists of 29 questions divided into three sections A, B and C. Section - A comprises of 10 questions of one mark each, Section - B comprises of 72 questions of four marks each and Section - C comprises of 7 questions of six marks each. (iii) All questions in Section - A are to be answered in one word, one sentence or as per the exact requirement of the question. (iv) There is no overall choice. However, internal choice has been provided in 4 questions offour marks each and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of calculators is not permitted. You may askfor logarithmic tables, if required. ,rffioi1o $F {qr 1 t 10 iro'qdq, sF r eis'sT t r Question numbers L to 10 carry 1 mark each. 1 *r[ ; 1 ].[ ; I ]=[ ; l ]*d(,-y)EFrrTr{vro+1tuq r [: 41 l-r vl I t ot If 2Ls , J*Lo i l=L ,o ,l,Rna(x-y). 2. frq etq5v$q.qor*)x*floqre*tfqq:, [x 1] Solve the following matrix equation forx:, [x I l- r 0l l-, o l=o' l- r 0l )l-r o.l=o' 3. qk lzx5l tt- l8 xl bc 5ll s ,l=l , write the value of x. i i l*d"rsf qrqfrtuq r 6 7 -2 3 4. (r^n . U)* sfr-srqsirq frfiqq r Write the antiderivative "t (rrF . 1f,) 65m3 5. {fr sin (ra-'}*.or-'r)= , t ni, $TrtFtirmeifqq I If sin (sin-t f * ,or-' ,) = ,, then find the value of x. O. q$ yf+ilqr6t{s{5qt3t*'qgffi d, qmr * goffi*rfr {kqr t *{-t a, b e R - {0} +kq a * b = $* rEf, t I qF( 2 *' (x * 5) = 10 t nt, $T qH ffa dkq r Let x be a binary operation, on the set of all non-zero real numbers, given by a * b = + forall a,b â‚¬ R- t0).Findthevalueof x, given that2 x (x * 5) = 10. 7. qtqvr I + 3j + ztor qk{r zi - :3 * of qtsq)q ffo +lflt{q r Find the projection of the vector i + :i + 7t on the vector Zi - li + Ot. g. s{r qrkrcr eT qlqvr {r+ffir {rer +tFre' qt t{S (a, b, c) t tlor qrer t Hsrt qtrtrcT ?.ti+3+tl=2*'qqimt r Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane ? . fi +i + t; = z. ril? g. qFT {rf, ftikq , I g(rin x - cos x) dx. 0 fi/2 f Evaluate : I er(sin.r - cos r) d,r. J 0 10. qi{vit A =2i*i-stst{ B =zi*i-zt+qtrmm+q$rTqs'qrf,m{rtffrflafuq r Write a unit vector in the direction of the sum of the vectors i = Zi * i * 5t and iAAA t5=2i+j-7k. 6sfit3 3 IP.T.O. ,rffio*1, ym riqr rr t zz H*r*oqm I oi+.qr t r Question numbers ll to 22 carry 4 marks each. 11. fritt+{qRvri a, B, A+fuqfuq*leqiq, [a * u', E' * ?, ? * ?] = zfi,B, A] 3IW{t n+J nRvr ?, u' aqr ? tS tfu' ? * B + ? = d aqr I ? I = 3, I ts' | - s ireTr I ? I = z t r ? nqr B ++qorqiqaraqfr&q r Prove that, for any three vectors ?, bt, ? [? * B, B * ?, ? * ?] =zli,ts, ?] OR vectors ?, b' ana d ur. such that ? * B + ? = d ano l?l = 3, lBl = 5 ano l?l = z. Find the angle between ?anO Ut. FTq â‚¬rqsm qfurur *t co +lfuq, (*'*t)*.r*=*. Solve the following differential equation : .) -.dv 2 (x- - t) -.o* Zry = il t. qnnrnsliqq, [W* J Sm-x. cos-.r qelitt qFT Ern *1iqq , ! A- :;1ffi, - rs a, Evaluate' [W* J slnir. cos._r OR ?_ Evaluate , ) @- l1@rs o* 12. 13. 65t1t3 14. Td itiil{m TId d&qFH+ Erm f(x) = 3# - 4x3 - t2* + 5 (a) frtnt *iqn t r (b) ffirarnqmi r qelt[f Effr .r = a sin30 irerr y = a cos30 +fu+ e = f, wwt tor mn qftdq *qdwrrr am ffi; intervats in which the tunction f(r) = 3# - +f - tz*r- 5 is (a) strictlyincreasing (b) srictly decreasing OR Find the equations of the tangent and normar to the curve x = a sin30 and y = a cos30 at It o =2. qHr A = {1, 2, 3,....., 9l iTen A x A { R gs-lirisr t, * e x A ii 1a, b), (c, d) *.kq (a, b) R (c, d) qk a + d = b + c Enr qlqqrfrd t r fqqsliqqm n f'oWar ffu t' I EEflr q,i' [(2, ,] rfl aro *1&q r Let A = {1, 2, 3,....., 9I and R be the relation in A x A defined by (a, b) R (c, d) if a + d = b + c for (a, b), (c, d) in A x A. Prove that R is an equivalence relation. Also obtain the equivalence class t(2, 5)1. 15. 16. =|;*. (o,f) =|; *. (0,'; irrâ‚¬ft1iw tr 2 tan-t (f) *,..-, ffi + 2 ,un-t(,l = f Provethatcorll'@ Wl +sinx-{l-sinx Prove that2,"r-, Gl + sec-r (9 + 2 ,un-tGl = t 17. qky =,r t, Hrftradriqqio # +eI-I= o. rry -rl, prove tnoff-i(#-I= o. 6snt3 5 OR lP.T.O.Read More

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