+2 MATH COME BOOK CREATIVE ONE MARK QUESTIONS

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1 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS COME BOOK CREATIVE ONE MARK QUESTIONS 1. The rk of the mtrix 1 CHAPTER I ( MATRICES AND DETERMINANTS) ) 1 ) ) 8 1. The rk of the mtrix 1 ) 9 ) ) 1. If A d B re mtries oformle to multiplitio the AB T ) A T B T ) T. 1 ) A equl to 1 A ). If Ar the whih of the followig orret? B T A T ) AB BA ) ll the miors of order r whih does ot vh ) hs tlest oe mior of order r whih does ot vh ) A hs tlest oe (r+1) order mior whih vhes T A ) A A 1 T ll (r+1) d higher order miors should ot vh 6. Whih of the followig ot elemetry trsformtio? ) Ri R j ) Ri Ri R j ) Ci C j Ci Ri Ri C j. Equivlet mtries re otied y ) tkig iverses ) tkig trsposes ) tkig d joits tkig fiite umer of elemetry trsformtios 8. I ehelo form, whih of the followig iorret? ) Every row of A whih hs ll its etries ours elow every row whih hs o-zero etry ) The first o-zero etry i eh o-zero row 1 ) The umer of zeroes efore the first o-zero elemet i row less th the umer of suh zeroes i the ext row Two rows hve sme umer of zeroes efore the first o-zero etry 9. If the the system ) Costet d hs uique solutio ) Costet d ifiitely my solutios ) Iostet Either ostet or iostet 1. I the system of lier equtios with three ukows, if d oe of x, or z o-zero the the system ) ostet ) iostet ) ostet d the system redues to two equtios ostet d the system redues to sigle equtio 11. I the system of lier equtios with three ukows, if, x, y, z d tlest oe x mior of the the system ) ostet ) iostet d ) ostet the system redues to two equtios ostet d the system redues to sigle equtio 1. I the system of lier equtios with three ukows, if d ll x miors of d tlest oe x mior of x or y or z o-zero the the system ) ostet ) iostet ) ostet d the system redues to two equtios ostet d the system redues to sigle equtio MATHS TIMES.COM Pge 1 y

2 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS 1. I the system of lier equtios with three ukows, if d ll x miors of, x, tlest oe o-zero elemet i the the system ) ostet ) iostet, re zeroes d ) ostet d the system redues to two equtios ostet d the system redues to sigle equtio 1. Every homogeeous system ) lwys ostet ) hs oly trivil solutio ) hs ifiitely my solutios eed ot e ostet A A, B the the system 1. If ) ostet d hs ifiitely my solutios ) ostet d hs uique solutio ) ostet iostet A A, B = the umer of ukows the the system 16. If ) ostet d hs ifiitely my solutios ) ostet d hs uique solutio ) ostet iostet A A, B the the system 1. ) ostet d hs ifiitely my solutios ) ostet d hs uique solutio ) ostet iostet A A, B the the system 18. I the system of lier equtios with three ukows 1 ) hs uique solutio ) redues to equtios d hs ifiitely my solutio ) redues to sigle equtio d hs ifiitely my solutio iostet 19. I the homogeeous system with three ukows, A ) oly trivil solutio ) redues to equtios d hs ifiitely my solutio ) redues to sigle equtio d hs ifiitely my solutio iostet umer of ukows the the system hs. I the system of lier equtios with three ukows, i the o-homogeeous system A A, B system ) hs uique solutio ) redues to equtios d hs ifiitely my solutio ) redues to sigle equtio d hs ifiitely my solutio iostet 1. I the homogeeous system A the umer of ukows the the system hs y z the the ) oly trivil solutio ) trivil solutio d ifiitely my o-trivil solutios ) oly o-trivil solutios o solutio. Crmer s rule pplile oly ( with three ukows ) whe ) ) ), x. Whih of the followig sttemet orret regrdig homogeeous system ) lwys iostet ) hs oly trivil solutio ) hs oly o-trivil solutios hs oly trivil solutio oly if rk of the oeffiiet mtrix equl to the umer of ukows x y z MATHS TIMES.COM Pge

3 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS CHAPTER II ( VECTOR ALGEBRA ) 1. The vlue of whe i j k d i j k ) 19 ) ) The vlue of whe j k d i k ) ) - ). The vlue of whe j k d i j k ) ) - ) 6. If m i j k d i 9 j k re perpediulr the m ) - ) 8 ) 1. If i 9 j k d m i j k re perpediulr the m ) ) ) If d re two vetors suh tht, d 6 the the gle etwee d ) 6 ) 6 ) MATHS TIMES.COM Pge. The gle etwee the vetors i j 6 k d i j 8 k ) os 1 ) si 1 ) si 1 os The gle etwee the vetors i j d j k ) ) ) 9. The projetio of the vetor i j k o i 6 j k 8 8 ) ) ) , whe i j k d 6 i j k ) ) - ) 11. If the vetors i j k d i j k re perpediulr to eh other, the ) ) 1. If the vetors i j 9 k d i m j k re perpediulr the m ) -1 ) 1 ) - 1. If the vetors i j 9 k d i m j k re prllel the m ) 1. If, ) ) ), re three mutully perpediulr uit vetors, the ) ) 9 ) 1. If 6, d d 6 the ) ) 1 ) Let u, v d w e vetor suh tht u v w

4 If u, v + MATH COME BOOK CREATIVE ONE MARK QUESTIONS d w the u v v w w u ) ) - ) 1. The projetio of i j o z x ) ) 1 ) The projetio of i j k o i j k ) ) ) 19. The projetio of i j k o i j k ) ) ) The work doe i movig prtile from the poit A, with positio vetor i 6 j k, to the poit B, with positio vetor i j k, y fore F i j k ) ) 6 ) 8 1. The work doe y the fore F i j k i movig the poit of pplitio from (1,1,1) to (,,) log strightlie give to e uits. The vlue of ) - ) )8-8. If u, v d 9 the ) ) 6 ) The gle etwee two vetors d if ). If, d ) ) i j 6 k ) ) 6 the the gle etwee d ) 6. The d..s of vetor whose diretio rtios re,-, -6 re 6 6 ),, ),, ) 6,, The uit orml vetors to the ple x y z re ) i j k 6,, ) i j k ) i j k i j k. The legth of the perpediulr from the origi to the ple r i j 1 k 6 )6 ) 6 / 169 ) 1 / r 8. The dte from the origi to the ple ) ) MATHS TIMES.COM Pge i j k ) 9. Chord AB dimeter of the sphere r i j 6 k 18 Is ) (1,,1) ) (-1,,-1) ) (-1,,1) (1,,-1). The etre d rdius of the sphere i j k r re with oordite of A s (,,-) The oordites of B

5 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS ) (, -1, ) d ) (, 1, ) d ) ( -, 1, ) d 6 (, 1, - ) d r re 1. The etre d rdius of the sphere i j k ),,, ),, d ),,, 6,, d. The vetor equtio of ple pssig through poit where P, V d perpediulr to vetor ) r ) r ) r r. The vetors equtio of ple whose dte from the origi p d perpediulr to vetor ) r p ) r q ) r p r p. The o-prmetri vetor equtio of ple pssig through poit whose P. V d prllel to u d v )r, u, v ) r, u, v ) r,, u v, u, v. The o prmetri vetor equtio of ple pssig through the poit whose P. V s re, d prllel to, )r v )r v ) v r 6. The o-prmetri vetor equtio of ple pssig through three poits whose P. Vs re,, )r ) r )r. The vetor equtio of ple pssig through the lie of itersetio the ples r 1 q1 d r q )r 1 q1 r q ) r 1 r q1 q ) r 1 r q1 q r 1 r q1 q 8. The gle etwee the lie r t d the ple r q oeted y the reltio. ) os ) os ) si si q 9. The vetor equtio of sphere whose etre origi d rdius ) r ) r ) r r CHAPTER - III COMPLEX NUMBERS 1. The omplex umer form of ) i ) - i ) i i. The omplex umer form of ) i ) i ) i i. Rel d imgiry prts of i re ), ), ),,. Rel d imgiry prts of i re ), / ) /, ),,. The omplex ojugte of i ) i ) i ) i i MATHS TIMES.COM Pge

6 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS 6. The omplex ojugte of i 9 ) i 9 i ) 9 ) i 9 i 9. The omplex ojugte of ) ) ) i i i of i ( i) ) i ) i ) i i = 8 6i i the the vlues of d re 8. The stdrd form 9. If i ) 8, -1 ) 8, 1 ) 1, 9 1, -8 p i q i i the q 1. If ) 1 ) -1 ) -8 8 i i ) 8 i ) 8 i ) i i i re 11. The ojugte of 1. The rel d imgiry prts of 8 8 i ) -1, 8 ) -8, 1 ) 8, -1-8, The modulus vlues of d ), ), 1 ), 1 -, 1 d i ), ), ) 6, 1 1, 1. The modulus vlues of i 1. The ue roots of uity re ) i G.P. with ommo rtio ) i G.P. with ommo differee ) i A.P. with ommo differee i A.P. with ommo differee 16. The rgumets of th roots of omplex umer differ y ) i ) i 1. Whih of the followig sttemets orret? ) egtive omplex umers ext ) order reltio does ot ext i rel umers 1 i i meigless ) MATHS TIMES.COM Pge 6 ) order reltio ext i omplex umers 18. Whih of the followig re orret? i) Re( Z) Z ii) Im( Z) Z iii) Z Z iv) Z ) (i), (ii) ) (ii), (iii) ) (ii),(iii) d (iv) (i),(iii) d (iv) 19. The vlues of Z Z ) Re( Z ) ) Re(Z ) ) Im(Z ) Im( Z ). The vlue of Z Z ) Im( Z ) ) i Im( Z) ) Im(Z ) i Im(Z) 1. The vlue of Z Z ) Z ) Z ) Z Z. If Z Z1 = Z Z the the lous of Z ) irle with etre t the origi ) irle with etre t Z 1 ) stright lie pssig through the origi perpediulr etor of the lie joiig Z 1 d Z Z

7 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS. If ue root of uity the ) 1 ) 1 ) 1 1. The priipl vlue of rgz lies i the itervl ), ), ),,. If Z 1 d Z re y two omplex umers the whih oe of the followig flse ) Re( Z1 Z ) Re(Z1) Re( Z ) ) Im( Z1 Z ) Im(Z1 ) Im( Z ) ) rg( Z1 Z ) rg(z1) rg( Z ) Z1Z Z1 Z 6. The fourth roots of uity re ) 1 i, 1 i ) i, 1 i ) 1, i 1, 1. The fourth roots of uity form the verties of ) equilterl trigle ) squre ) hexgo retgle 8. Cue roots of uity re 1 i i 1 i 1 i ) 1, ) i, 1 ) 1, i, 9. The umer dtit vlues of q p os i si where p d q re o-zero itegers prime to eh other ) p ) q ) p+q p-q i i. The vlue of e e ) os ) os ) si si i i 1. The vlue of e e ) si ) si ) i si i si. Geometril iterprettio of Z ) refletio of Z o rel x ) refletio of Z o imgiry x ) rottio of Z out origi rottio of Z out origi through i lokwe diretio. If Z1 i, Z i the Z1 Z lies o ) rel x ) imgiry x ) the lie y = x the lie y = -x. Whih oe of the followig iorret? ) os i si os i si ) os i si os i si 1 ) si i os si i os os i si os i si. Polyomil equtio P(x)= dmits ojugte pirs of roots oly if the oeffiiets re ) imgiry ) omplex ) rel either rel or omplex 6. Idetify the orret sttemet ) Sum of the moduli of two omplex umers equl to their modulus of the sum ) Modulus of the produt of the omplex umers equl to sum of the moduli ) Argumets of the produt of two omplex umers the produt of their rgumets Argumets of the produt of two omplex umers equl to the sum of their rgumets. Whih of the followig ot true? ) z1 z z1 z ) z1z z1 z ) z z Re( z) 8. If Z 1 d Z re omplex umers the whih of the followig meigful? z z Im( z) i MATHS TIMES.COM Pge

8 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS ) Z1 Z ) Z1 Z ) Z1 Z Z1 Z 9. Whih of the followig iorret? ) Re( Z) Z ) Im( Z) Z ) Z Z Z Re( Z) Z. Whih of the followig iorret? ) Z1 Z Z1 Z ) Z1 Z Z1 Z ) Z1 Z Z1 Z Z1 Z Z1 Z 1. Whih of the followig iorret? ) Z the mirror imge of Z o the rel x r, ) The polr form of Z ) Z the poit symmetril to Z out the origi The polr form of Z r,. Whih of the followig iorret? ) Multiplyig omplex umer y i equivlet to rottig the umer outer lokwe out the origi through gle of 9 ) Multiplyig omplex umer y -i equivlet to rottig the umer lokwe out the origi through gle of 9 ) Dividig omplex umer y i equivlet to rottig the umer outer lokwe out the origi through gle of 9 Dividig omplex umer y i equivlet to rottig the umer lokwe out the origi through gle of 9. Whih of the followig iorret regrdig th roots of uity? ) the umer of dtit roots ) the roots re i G.P. with ommo rtio ) the rgumets re i A.P. with ommo differee produt of the roots d the sum of the roots 1. Whih of the followig re true? i) If positive iteger the os i si os i si ii) If egtive iteger the os i si os i si iii) If frtio the os i si oe of the vlues of os i si iv) If egtive iteger the os i si os i si ) (i), (ii), (iii), (iv) ) (i), (iii), (iv) ) (i), (iv) (i) oly ' O,, A z1, B Z, B z re the omplex umers i rgd ple the whih of the followig re orret? i) I the prllelogrm OACB, C represets z1 z ii) I the rgd ple E represets z z 1 where OE = OA.OB d OE mkes gle rgz1 rg z with positive rel x. iii) I the rgd prllelogrm OB DA, D represets z1 z z1 OA iv) I the rgd ple F represets where OF d OF mkes gle rgz1 rg z with positive rel z OB. If x. ) (i), (ii), (iii), (iv) ) (i), (iii), (iv) ) (i), (iv) (i) oly rg Z ) ) ) idetermite 6. If Z = the the MATHS TIMES.COM Pge 8

9 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS 1. The x of the prol y x CHAPTER IV ) x = ) y = ) x = 1 y = 1. The vertex of the prol y x ) (1,) ) (,1) ) (,) (,-1). The fous of the prol y x ) (,1) ) (1,1) ) (,) (1,). The diretrix of the prol y x ) y = -1 ) x = -1 ) y = 1 x = 1. The equtio of the ltus retum of y x ) x = 1 ) y = 1 ) x = y = The legth of the L.R. of y x ) ) ) 1. The x of the prol x y ) y = 1 ) x = ) y = x = 1 8. The vertex of the prol x y ) (,1) ) (,-1) ) (1,) (,) 9. The fous of the prol x y ) (,) ) (,-1) ) (,1) (1,) 1. The diretrix of the prol x y ) x = 1 ) x = ) y = 1 y = 11. The equtio of the L.R. of x y ) x = -1 ) y = -1 ) x =1 y = 1 1. The legth of the L.R. of x y ) 1 ) ) 1. The x of the prol y 8x ) x = ) x = ) y = y = 1. The vertex of the prol y 8x ) (,) ) (,) ) (,-) (,-) 1. The fous of the prol y 8x ) (,-) ) (,) ) (-,) (,) 16. The equtio of the diretrix of the prol y 8x ) y+ = ) x- = ) y - = x+= 1. The equtio of the ltus retum of y 8x ) y-= ) y+ = ) x - = x+ = 18. The legth of the ltus retum y 8x ) 8 ) 6 ) The x of the prol x y ) y = ) x = ) x = y =. The vertex of the prol x y ) (,) ) (,) ) (,) (,-) MATHS TIMES.COM Pge 9

10 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS 1. The fous of the prol x y ) (,) ) (,) ) (,) (-,). The equtio of the diretrix of the prol x y ) y- = ) x+ = ) x- = y+ =. The equtio of the ltus retum of the prol x y ) x- = ) y- = ) y+ = x+ =. The legth of the ltus retum of the prol x y ) ) 1 ). If the etre of the ellipse (,) oe of the foi (,) the the other fous ) (1,) ) (-1,) ) (1,-) (-1,-) 6. The equtios of the mjor d mior xes x y 1re 9 ) x =, y = ) x = -, y = - ) x =, y = y =, x =. The equtios of the mjor d mior xes of x y 1 re ) x, y ) x =, y = ) x, y y =, x = 8. The legths of mior d mjor xes of x y 1re 9 ) 6, ), ),6, 9. The legths of mjor d mior xes of x y 1 re ), ), ),,. The equtio of the diretries of x y 1re ) y ) x ) x y 1. The equtio of the diretries of x 9 y re ) x ) x ) y y. The equtio of the ltus retum of x y 1re 16 9 ) y ) x ) x y. The equtio of the L.R. of x 9y re ) y ) x ) y x. The legth of the L.R. of x y ) 9 / ) / 9 ) 9 / / 9. The legth of the L.R. of x 9y ) 9 / ) 18 / ) / 9 / The eetriity of the ellipse x y 1 9 ) 1 / ) / ) / /. The eetriity of the ellipse x y 1 9 ) ) ) / / MATHS TIMES.COM Pge 1

11 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS 8. The eetriity of the ellipse 16x y ) / ) / ) / / 9. Cetre of the ellipse x y 1 9 ) (,) ) (,) ) (,) (,). The etre of the ellipse x y 1 9 ) (,) ) (,) ) (,) (,) 1. The foi the ellipse x y 1re 9 ), ), ),,. The foi of the ellipse x y 1re 9 ), ), ),,. The foi of the ellipse16x y re ), ), ),,. The verties of the ellipse x y 1re 9 ), ), ),,. The verties of the ellipse x y 1re 9 ), ), ),, 6. The verties of the ellipse16x y re ), ), ),,. If the etre of the ellipse (,-) d oe of the foi (,) the the other fous ) (,6) ) (6,-) ) (,-6) (6,) 8. The equtios of trsverse d ojugge xes of the hyperol x y 1re 9 ) x = ; y = ) y = ; x = ) x = ; y = x = ; y = 9. The equtios of trsverse d ojugte xes of the hyperol16 y 9x 1 re ) y = ; x = ) x = ; y = ) x = ; y = y = ; x =. The equtios of trsverse d ojugte xes of the hyperol 1x y 6 re ) y = ; x = ) x = 1 ; y = ) x = ; y = x = ; y = 1 1. The equtio of trsverse d ojugte xes of the hyperol 8y x 16 re ) x ; y ) x ; y ) x = ; y = y = ; x =. The equtios of the diretries of the hyperol x y 1re ) y ) x ) y x The equtios of the diretries of the hyperol16 y 9x 1 re 9 9 ) x ) y ) x y MATHS TIMES.COM Pge 11

12 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS. The equtio of the L.R s of the hyperol x y 1re 9 ) y 1 ) y 1 ) x 1 x 1. The equtios of the L.R s of the hyperol16 y 9x 1 re ) y ) x ) y x 6. The legth of the L.R. of x y 1 9 ) / ) 8 / ) / 9 /. The eetriity of the hyperol y x 1 9 ) / ) / ) 8. The etre of the hyperol x 16y ) (,) ) (,) ) (,) (,) 9. The foi of the hyperol y x 1re 9 ), ), ),, 6. The verties of the hyperol x 16y re ), ), ),, 61. The equtio of the tget t (,-6) to the prol y 1 x ) x y ) x y ) x y x y 6. The equtio of the tget t (-,1) to the prol x 9y ) x y ) x y ) x y x y 6. The equtio of hord of ott of tgets from the poit ( -, 1) to the prol y 8x ) x y 1 ) x y 1 ) y x 1 y x 1 6. The equtio of hord of ott of tgets from (,) to he ellipse x y ) x y ) x y ) x y x y 6. The equtio of hord of ott of tgets from (,) to the hyperol x 6y ) 9x 1y 1 ) 1x 9y 1 ) 9x 1y 1 1x 9y The omied equtio of the symptotes to the hyperol 6x y 9 ) x 6 y ) 6x y ) 6x y x 6y 6. Fid the gle etwee the symptotes of the hyperol x 8y ) ) or ) 68. The poit of ott of the tget y mx d the prol y x ), ), ),, m m m m m m m m x y 69. The poit of ott of the tget y mx d the ellipse 1 ) m, ) m, ) m, m, x y. The poit of ott of the tget y mx d the hyperol 1 MATHS TIMES.COM Pge 1

13 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS ) m, ) m, ) m, m, 1. The true sttemets of the followig re i) Two tgets d orml e drw to prol from poit ii) Two tgets d orml e drw to ellipse from poit iii) Two tgets d orml e drw to hyperol from poit iv) Two tgets d orml e drw to R.H. from poit ) (i), (ii), (iii) d (iv) ) (i), (ii) oly ) (iii), (iv) oly (i), (ii), d (iii). If ' t1 ' ' t ' re the extremities of y fol hord of prol y x the t 1 t ) -1 ) ) 1 1 /. The orml t ' t1' o the prol y x meets the prol t ' t ' the t 1 t1 1 ) t ) t ) t1 t t x y. The oditio tht the lie lx my my e orml to the ellipse 1 l ) ) ) lm m l m l m l m x y. The oditio tht the lie lx my my e orml to the hyperol 1 l ) ) ) lm m l m 6. The oditio tht the lie my x ) l lm m ) l m l lx my e orml to the prol y x l m ). The hord of ott of tgets from y poit o the diretrix of the prol y x l m m l m psses through its ) vertex ) fous ) diretrix ltus retum x y 8. The hord of ottof tgets from y poit o the diretrix of the ellipse 1 psses through its ) vertex ) fous ) diretrix ltus retum x y 9. The hord of ott of tgets from y poit o the diretrix of the hyperol 1psses through its ) vertex ) fous ) diretrix ltus retum 8. The poit of itersetio of tgets t ' t 1' d ' t ' to the prol y x ) t1 t, t1t ) t1 t, t1 t )t, t t1 t, t1 t 81. If the orml to the R.H. xy t ' t1' meets the urve gi t ' t ' the t 1 t )1 ) )-1-8. The lous of the poit of itersetio of perpediulr tgets to the prol y x ) ltus retum ) diretrix ) tget t the vertex x of the prol x y 8. The lous of the foot of perpediulr from the fous o y tget to the ellipse 1 ) x y ) x y ) x y x MATHS TIMES.COM Pge 1

14 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS x y 8. The lous of the foot of perpediulr from the fous o y tget to the hyperol 1 ) x y ) x y ) x y x 8. The lous of the foot of perpediulr from the fous o y tget to the prol y x ) x y ) x y ) x y x x y 86. The lous of poit of itersetio of perpediulr tgets to the ellipse 1 ) x y ) x y ) x y x x y 8. The lous of poit of itersetio of perpediulr tgets to the hyperol 1 ) x y ) x y ) x y x 88. The oditio tht the lie lx my my e tget to the prol y x ) l m ) m l ) l m lm x y 89. The oditio tht the lie lx my my e tget to the ellipse 1 ) l m ) m l ) l m lm x y 9. The oditio tht the lie lx my my e tget to the hyperol 1 ) l m ) m l ) l m lm 91. The oditio tht the lie lx my my e tget to the retgulr hyperol xy ) l m ) m l ) l m lm 9. The foot of perpediulr from fous of the hyperol o symptote lies o the ) Cetre ) orrespodig diretrix ) vertex L.R. CHAPTER V 1. Let h e the height of the tk. The the rte of hge of pressure p of the tk with respet to height dh dp dh dp ) ) ) dt dt dp dh. If the temperture C of the erti metl rod of l meters give y l 1.. the the rte of hge of li m / C whe the temperture 1 C ).1 m C ). m C ).6 m C. m C. The followig grph gives the futiol reltioship etwee dte d time of movig r i m / se. The speed of the r x t dt ) m s ) m s ) m s t x dt m s. The dte time reltioship of movig ody give y y = F ( t ) the the elertio of the ody the ) grdiet of the veloity / time grph ) grdiet of the dte / time grph ) grdiet of the elertio / dte grph grdiet of the veloity / dte grph. The dte trveled y r i t seods give y x t t t 1.The the iitil veloity d iitil elertio respetively re ) m / s, m / s ) m / s, m / s ) (, ) 18.m / s, m / s 6. The gulr dplemet of fly wheel i rdius give y 9t t.the time whe the gulr elertio zero ). s ). s ) 1. s. s MATHS TIMES.COM Pge 1

15 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS. Food pokets were dropped from heliopter durig the flood d dte flle i t seods give y 1 y gt g 9.8 m / s. The the speed of the food poket fter it hs flled for seods ) 19.6 m / se ) 9.8 m / se ) 19.6 m / se 9.8 m / se 8. 1 A ojet dropped from the sky follows the lw of motio x gt g 9.8 m / s.the elertio of the ojet whe t = ) 9.8 m se ) 9.8 m se ) 19.6 m se 19.6 m se 9. A msile fired from groud level res x metres vertilly upwrds i t seods d x t 1 1. t mximum height rehed y the msiles ) 1m ) 1 m ) m m 1. A otiuous grph y = f ( x ) suh tht f ' x s x x1,t 1, y 1 The y = f ( x ) hs ) vertil tget y x1 ) horizotl tget x x1 ) vertil tget x x1 horizotl tget y y1 11. The urve y = f ( x ) d y = g ( x ) ut orthogolly if t the poit of itersetio ) slope of f ( x ) = slope of g ( x ) ) slope of f ( x ) + slope of g ( x ) = ) slope of f ( x ) / slope of g ( x ) = -1 [ slope of f ( x ) ] [ slope of g ( x ) ] = The lw of the me lso e put i the form ) h f hf ' h 1 f h f hf ' h 1. x 1 l Hopitl s rule ot e pplied to s x euse f x x 1 d g x x re x ) ot otiuous ) ot differetile ) ot i the i determie form s x i the i determie form s x. The the f ) 1 ) f h f hf ' h 1 f h f hf ' h 1 1. If gx 1. lim x x f g( x g lim x x t x d f otiuous t x = the ) lim g f ( x f lim gx ) lim f g( x f lim gx x x x x f lim x ) lim f lim f g( x gx x x lim )1 ) - 1 ) 16. f rel vlued futio defied o itervl I R ( R eig the set of rel umers iresed o l. The f wheever x x x1 x I f x1 f x wheever x1 x x1, x I f 1 x wheever x1 x x1, x I f x1 f x wheever x1 x x1, x I 1. If rel vlued differetile futio y = f ( x ) defied o ope itervl l iresig the dy dy dy dy ) ) ) 18. f differetile futio defied o itervl I with positive derivtive. The f ) iresig o I ) deresig o I ) stritly iresig o I stritly deresig o I 19. The futio f x x ) x1 f x ) x f x 1, ) ) iresig ) deresig ) stritly deresig stritly iresig. If the grdiet of urve hges from positive just efore P to egtive just fter the P ) miimum poit ) mximum poit ) ifletio poit dotiuous poit MATHS TIMES.COM Pge 1

16 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS f x x hs 1. The futio ) mximum vlue t x = ) miimum vlue t x = ) fiite o. of mximum vlues ifiite o. of mximum vlues f x x hs. The futio ) solute mximum ) solute miimum ) lol mximum o extrem. If f hs lol extremum t d if f ( ) exts the ) f ( ) < ) f ( ) > ) f ( ) = f ( ) =. I the followig figure the urve y = f ( x ) ) ove upwrds ) ovex upwrd ) hges from ovity to ovexity hges from ovexity d ovity. The poit tht seprtes the ovex prt of otiuous urve from the ove prt ) the mximum poit ) the miimum poit ) the ifletio poit ritil poit 6. f twie differetile futio o itervl I d if f ( x ) > for ll x i the domi I of f the f ) ove upwrd ) ovex upwrd ) iresig deresig. x = x root of eve order for the equtio f ( x ) = the x = x ) mximum poit ) miimum poit ) ifletio poit ritil poit 8. If x the x - oordite of the poit of ifletio of urve y = f ( x ) the (Seod derivtive exts) ) f x ) f ' x ) f " x f " x 9. The sttemet If f otiuous o losed itervl [, ] the f tt solute mximum vlue f ( ) d solute miimum vlue f( t some umer d d i [, ] ) The extreme vlue theorem ) Fermt s theorem ) Lw of Me Rolle s theorem. The sttemet : If f hs lol extremum (miimum or mximum ) t d if f ( ) exts the f ( ) = ) the extreme vlue theorem ) Fermt s theorem ) Lw of Me Rolle s theorem 1. Idetify the flse sttemet: ) ll the sttiory umers re ritil umers ) t the sttiory poit the first derivtive zero ) t ritil umers the first derivtive eed ot ext ll the ritil umers re sttiory umers. Idetify the orret sttemet: i) otiuous futio hs lol mximum the it hs solute mximum ii) otiuous futio hs lol miimum the it hs solute miimum iii) otiuous futio hs solute mximum the it hs lol mximum iv) otiuous futio hs solute miimum the it hs lol miimum ) (i) d (ii) ) (i) d (iii) ) (iii) d (iv) (i), (iii) d (iv). Idetify the orret sttemets. i) Every ostt futio iresig futio ii) Every ostt futio deresig futio iii) Every idetity futio iresig futio iv) Every idetity futio deresig futio ) (i), (ii) d (iii) ) (i) d (iii) ) (iii) d (iv) (i), (iii) d (iv). Whih of the followig sttemet iorret? ) Iitil veloity mes veloity t t = MATHS TIMES.COM Pge 16

17 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS ) Iitil elertio mes elertio t t = ) If the motio upwrds, t the mximum height, the veloity ot zero If the motio horizotl, v = whe the prtile omes to rest. Whih of the followig sttemets re orret ( m1 d m re slopes of two lies) i) If the two lies re perpediulr the m 1m 1 ii) If m1m 1 the the two lies re perpediulr iii) If m1 m the the two lies re prllel 1 iv) If m1 m the the two lies re perpediulr ) (ii), (iii) d (iv) ) (i), (ii) d (iv) ) (iii) d (iv) (i) d (ii) 6. Oe of the oditios of Rolle s theorem ) f defied d otiuous o (, ) ) f differetile o [, ] ) f ( ) = f ( ) f differetile o (, ). If d re two roots of polyomil f ( x ) = the Rolle s theorem sys tht there exts tlest ) oe root etwee d for f ( x ) = ) two roots etwee d for f ( x ) = ) oe root etwee d for f ( x ) = two roots etwee d for f ( x ) = 8. A rel vlued futio whih otiuous o [, ] d differetile o (, ) the there exts t lest oe i ) [, ] suh tht f ( ) = ) (, ) suh tht f ( ) = f f f f ) (, ) suh tht (, ) suh tht f ' 9. I the lw of me, the vlue of stfies the oditio ) ) ) 1 1. Whih of the followig sttemets re orret? i) Rolle s theorem prtiulr se of Lgrges lw of me ii) Lgrges lw of me prtiulr se of geerlized lw of me ( Cuhy) iii) Lgrges lw of me prtiulr se of Rolle s theorem. iv) Geerlized lw of me prtiulr se of Lgrges lw of me. ) (ii), (iii) ) (iii), (iv) ) (i), (ii) (i), (iv) CHAPTER VI 1. For the futio y x x the vlue of dy whe x = d =.1 ) 1 ) ) u. If U x y x y x y the x ) x 6xy 6xy ) x 6x y xy ) x 6x y 6xy x 6x y xy. If u = f ( x, y ) the with usul ottios, u xy u yx if ) u otiuous ) u x otiuous ) u y otiuous u, u x, u y re otiuous. If u = f ( x, y ) differetile futio of x d y ; x d y re differetile futios of t the du f x f y du f t y du f f dy u f x f y ) ) ) dt x t y t dt x dt y t dt x dt y dt t x t y t f f. If f ( x, y ) homogeeous futios of degree the x y x y ) f ) f ) ( - 1 ) f ( + 1 ) f MATHS TIMES.COM Pge 1

18 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS 6. If u x y u, x y x y x y the x y ) 1xy 6x ) 1xy 6x ) 1x y 6x 1xy 6x. If u x y u, x y x y x y the y x ) 1xy 6x ) 1xy 6x ) 1x y 6x 1xy 6x u 8. If u x, y x y x y x y the x ) y 6x y x ) 6y 6x ) 1x y 6x 1x 6y 6y u 9. If u x, y x y x y x y the y ) 6y 6x ) 1xy 6x ) 1x y 6x y 6x y x 1. The differetil o y of the futio y x 1 1 ) x ) x ) x 11. The differetil of y if y x ) x ) x ) x x 1. The differetil of y if y x x ) x x ) x x 1 x x 1 1 ) 1 1 x x 1 1 x x 1 x x x 1. The differetil of y if y x 1 ) ) ) x x x x 1. The differetil of y if y = si x ) osx ) osx. ) osx. osx. 1. The differetil of x t x ) x se x t x ) x se x t x ) x x x se x t x u 16. If u x, y x y x y x y the y ) y 6xy x ) y 6xy x ) y 6x y x y 6x y x 1. The urve y x 1 x defied oly for ) x d x ) x 1 d x 1 ) x 1 d x 1 x 1 d x 1 y x 1 x symmetril out 18. The urve se ) x-x oly ) y-x oly ) d y xes oly x, y xes d the origi y x 1 x hs 19. The urve ) oly oe loop etwee x = d x = 1 ) two loops etwee x = -1 d x = ) two loops etwee x = -1 d ; d 1 o loop y x 1 x hs. The urve ) symptote x = -1 ) symptote x = 1 ) two symptotes x = 1 d x = -1 o symptote MATHS TIMES.COM Pge 18

19 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS 1. The urve y x x 6 x exts for ) x 6 ) x 6 ) x 6 x 6 y x x 6 x. The x-iterept of the urve ) ) 6, ) - y x x 6 x. The symptote to the urve ) x = ) x = - ) x = 6 x = -6 y x x 6 x hs. The urve ) oly oe loop etwee x = d x = 6 ) two loops etwee x = d x = 6 ) oly oe loop etwee x = - d x = 6 two loops etwee x = - d x = 6 y x 1 x defied oly for ) x 1 ) x 1 ) x 1 x 1 y x 1 x symmetril out. The urve 6. The urve ) y-x oly ) x-x oly ) oth the xes origi oly y x 1 x hs. The urve ) symptote y = ) symptote x = 1 ) symptote y = 1 o symptote y x 1 x hs 8. The urve ) oly oe loop etwee x = -1 d x = ) oly oe loop etwee x = d x = 1 ) two loops etwee x = -1 d x = 1 o loop y x x, d does ot ext fro ) x ) x = ) x x = 9. The urve y x x. The urve symmetril out ) origi oly ) y-x oly ) x-x oly oth x d y-x y x x, d hs 1. The urve ) symptote x = ) s symptote x = ) symptote y = o symptote y x x, d hs. The urve ) loop etwee x = d x = ) two loops etwee x = d x = ) two loops etwee x = d x = o loop y 1 x x 1 x defied for ) 1 x 1 ) 1 x 1 ) 1 x 1 1 x 1 y 1 x x 1 x symmetril out. The urve. The urve ) oth the xes ) origi oly ) y-x oly x-x oly y 1 x x 1 x. The symptote to the urve ) x = 1 ) y = 1 ) y = -1 x = -1 y 1 x x 1 x hs 6. The urve ) loop etwee x = -1 d x = 1 ) loop etwee x = -1 d x = ) loop etwee x = d x = 1 o loop y x x defied for ) x d x ) x d x ) x d x x d x. The urve 8. The urve y x x symmetril out ) x-x oly ) y-x oly ) oth the xes oth the xes d origi y x x hs 9. The urve ) symptote x = ) symptote x = - ) symptote x = o symptote MATHS TIMES.COM Pge 19

20 . The urve y x x + MATH COME BOOK CREATIVE ONE MARK QUESTIONS hs ) loop etwee x = d x = - ) two loops etwee x = - d x = ; x = d x = ) two loops etwee x = d x = o loop y x 1 x ot defied for ) x 1 ) x ) x x 1 1. The urve y x 1 x symmetril out. The urve ) oth x d y-x ) x-x oly ) y-x oly oth the xes d origi y x 1 x hs. The urve ) symptote x = 1 ) symptote x = ) two symptotes x = 1 d x = o symptote y x 1 x hs. The urve ) two loops etwee x = d x = ) oe loop etwee x = d x =1 ) oe loop etwee x = 1 d x = o loop 1. I si x the I ) si x os x I ) si x os x I. f x f x if ) f x f x ) f x f x. f x if f x f x f x f x CHAPTER VII ) si x os x I 1 1 si 1 x os x I ) f x f x f x f x ) ) ) f x f x f x f x. If f ( x ) odd futio the f x ) f x ) f x. f x f x ) f x 6. If f ( x ) eve the f x ) f x ) f x ) ) f x ) f x. f x ) f x 8. f x ) f x ) f x f x f x ) f x f x MATHS TIMES.COM Pge

21 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS ) f x ) f x ) f x f x 9. If positive iteger the x x e! 1! 1!! ) ) ) If odd the os x 1 1 ) ) 1 1 ) If eve the si x 1 1 ) ) 1 1 ) If eve the os x 1 1 ) ) 1 1 ) If odd the si x 1 1 ) ) 1 1 ) f x ) f x ) f x ) f x f x o o 1. The re ouded y the urve x = g ( y ) to the right of y - x d the two lies y = d y = d give y d d d ) x ) x dy ) y dy x dy 16. The re ouded y the urve x = f ( y ), y-x d the lies y = d y = d rotted out y-x. The the volume of the solid d ) x d dy ) x d ) y d y dy 1. The re ouded y the urve x = f ( y ) to the left of y-x etwee the lies y = d y = d d ) x dy ) d d x dy ) y d y 18. The r legth of the urve y = f (x ) from x = to x = dy d ) 1 ) dy dy 1 ) y 1 y dy 1 MATHS TIMES.COM Pge 1

22 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS 19. The surfe re otied y revolvig the re ouded y the urve y = f ( x ), the two ordites x =, x = d x-x, out x-x dy d ) 1 ) dy dy 1 ) y 1 y dy 1. x x e 6! 6! ) ) 6 1. e mx x m!! ) ) m m. 6 x x e 6! 6! ) ) 6. I os x the I ) os x si x I ) os x si x I )! 6 m! ) m1!! 8 m ) 6 6! 6! 1 1 ) os x si x I os x si x I CHAPTER VIII d y 1. The order d degree of the differetil equtio d y dy y re ), 1 ) 1, ),, dy. The order d degree of the differetil equtio re y x dy ), 1 ) 1, ) 1,, d y dy. The order d degree of the differetil equtio re ),1 ) 1, ),, 1 y' y'. The order d degree of the differetil equtio re ),1 ) 1, ), 1,1 dy. The order d degree of the differetil equtio re y x ) 1,1 ) 1, ),1,1 6. The order d degree of the differetil equtio re y' y x ),1 ) 1,1 ) 1,,1. The order d degree of the differetil equtio y ' ' y' y re ), ),1 ) 1,,1 MATHS TIMES.COM Pge

23 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS d y dy 8. The order d degree of the differetil equtio re x y ),1 ) 1, ), 1 /, d y 9. The order d degree of the differetil equtio re dy d y y ), ), ),, 1. The order d degree of the differetil equtio re y' ' y y ' ), ), ),, y' y" x y" 11. The order d degree of the differetil equtio re ) 1,1 ) 1, ),1, y' y" x x y" 1. The order d degree of the differetil equtio re ), ),1 ) 1, 1,1 dy 1. The order d degree of the differetil equtios re x x dy ), ),1 ) 1, 1, si x dy os x dy 1. The order d degree of the differetil re ) 1,1 ), ) 1,,1 1. The differetil equtio orrespodig to xy where ritrry ostts ) xy + x = ) y = ) xy + y = xy -x= mx 16. I fidig the differetil equtio orrespodig to y e where m the ritrry ostt, the m ) y y' ) y y' ) y y 1. The solutio of lier differetil equtio Px Q where P d Q re futios of y, dy ) yi. F I. F Q ) xi. F I. F Q dy ) y I. F I. F Q dy xi. F I. F Q dy 18. The solutio of the lier differetil equtio Py Q where P d Q re futios of x ) yi. F I. F Q ) xi. F I. F Q dy ) y I. F I. F Q dy xi. F I. F Q 19. Idetify the iorret sttemet ) The order of differetil equtio the order of the highest derivtive ourrig i it. ) The degree of the differetil equtio the degree of the highest order derivtive whih ours i it (the derivtives re free from rdils d frtios) dy f1 x, y ) the first order first degree homogeeous differetil equtio f x, y dy x xy e lier differetil equtio i x. CHAPTER IX 1. Whih of the followig re sttemets? MATHS TIMES.COM Pge

24 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS i.chei the pitl of Tmil Ndu. iii.rose flower ii.the erth plet. iv.every trigle oseles trigle ) ll ) (i) d (ii) ) (ii) d (iii) (iv) oly. Whih of the followig re ot sttemets? i. Three plus four eight ii. The su plet iii. Swith o the light iv. Where re you goig? ) (i) d (ii) ) (ii) d (iii) ) (iii) d (iv) (iv) oly. The truth vlues of the followig sttemets re i. Ooty i Tmildu d + = 8 ii. Ooty i Tmildu d + = iii. Ooty i Kerl d + = iv. Ooty i Kerl d + = 8 ) F,T,F,F ) F,F,F,T ) T,T,F,F T,F,T,F. The truth vlues of the followig sttemets re i) Chei i Idi or iteger. ii) Chei i Idi or irrtiol umer iii) Chei i Chi or iteger iv) Chei i Chi or irrtiol umer ) T F T F ) T F F T ) F T F T T T F T. Whih of the followig re ot sttemets? i. All turl umers re itegers. ii. A squre hs five sides iii. The sky lue iv. How re you? ) (iv) oly ) (i) d (ii) ) (i) (ii) d (iii) (iii) d (iv) 6. Whih of the followig re sttemets? i. + < 1 ii. The set of rtiol umers fiite iii. How eutiful you re iv. Wh you ll suess. () (iii) (iv) ) (i), (ii) ) (i), (iii) (ii), (iv). The truth vlues of the followig sttemets re i. All the sides of rhomus re equl i legth ii irrtiol umer iii. Milk white iv. The umer hs four prime ftors. ) T T T F ) T T T T ) T F T F F T T T 8. The truth vlues of the followig sttemets re i) Pr i Fre ii) six eve futio iii) Every squre mtrix o-sigulr iv) Jupiter plet ) T F F T ) F T F T ) F T T F F F T T 9. Let p e Kml goig to shool d q e There re twety studets i the lss. Kml ot goig to shool or there re twety studets i the lss stds for ) p q ) p q ) ~ p ~ p q 1. If p stds for the sttemet Sit likes redig d q for the sttemet Sit likes plyig. Sit likes either redig ot plyig stds for ) ~ p ~ q ) p ~ q ) ~ p q p q 11. If p true d q ukow the ) p p ~ p ~ true ) flse ) p ~ p true p q true 1. If p true d q flse the whih of the followig sttemets ot true? ) p q flse ) p q true ) p q flse p q true 1. Whih of the followig ot true? i) Negtio of egtio of sttemet the sttemet itself MATHS TIMES.COM Pge

25 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS ii) If the lst olum of its truth tle oti oly T the it tutology iii) If the lst olum of its truth tle ot oly F the it otrditio iv) If p d q re y two sttemets the p q tutology 1. Whih of the followig re iry opertio o R? mi, * mx, iii) * iv) * i) * ii) ) ll ) (i), (ii) d (iii) ) (ii), (iii) d (iv) (iii), (iv) 1. + ot iry opertio o Q ) N ) Z ) C iry opertio o ) N ) Q ) 1. iry opertio o R Z ) N ) R ) Z C 18. I ogruee modulo, x Z / x k, k Z represets ) ) ) ) ) 1 ) ) 1 ) 8 ) 1. I the group (G,. ), G 1, 1, i, i, the order of 1 ) -1 ) 1 ) G 1, 1, i, i, the order of i. I the group (G,. ), ) ) ) 1,, ( where ue root of uity). I the group (G,. ), G, the order of ) ) 1 ) Z, order of. I the group, ) 1 ) ) ot e determied. I the group, Z, ) ) ) 1 S, o, xoy x, x, y the o 6. I s ) oly ssoitive ) oly ommuttive ) ssoitive d ommuttive either ssoitive or ommuttive N,, x y x, y, x, y N N,. I mx the ) oly losed ) oly semi group ) oly mooid ifiite group 8. The set of positive eve itegers, with usul dditio forms ) fiite group ) oly semi group ) oly mooid ifiite group 9. The set of positive eve umers, with usul dditio forms ) fiite group ) oly semi group ) oly mooid ifiite group. I Z the order of, ) ) ) G 1, 1, i, i, the order of 1 1. I the group (G,. ), ) ) ) 1 G 1, 1, i, i, the order of i. I the group (G,. ), MATHS TIMES.COM Pge

26 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS ) ) ) 1,,. I the group (G,. ), G, ue root of uity the ) ) 1 ) 1,, 1. I the group (G,. ), G, ue root of uity the ) ) 1 ) 1. I the group, Z, ) 1 ) ) ot e determied 6. I the group, Z, ) 1 ) ) ot e determied. I Z the order of, ) ) ) 8. I Z the order of, ) ) ) 9. I 1 Z the order of, ) 1 ) ) CHAPTER X 1. A drete rdom vrile tkes ) oly fiite umer of vlues ) ll possile vlues etwee erti give limits ) ifiite umer of vlues fiite or outle umer of vlues. A otiuous rdom vrile tkes ) oly fiite umer of vlues ) ll possile vlues etwee erti give limits ) ifiite umer of vlues fiite or outle umer of vlues. If X drete rdom vrile the P X ) P X ) 1 P X ) 1 P X. If X otiuous rdom vrile the P X ) P X ) 1 P X ) P X 1 P X 1. If X otiuous rdom vrile the P X P X P X P X ll the three ove ) ) ) 6. A otiuous rdom vrile X hs p.d.f. f(x) the ) f x 1 ) x f ) f x 1 f x 1. A drete rdom vrile X hs proility, mss futio p(x), the ) p x 1 ) x x p ) p 1 p x 1 8. Me d vrie of iomil dtriutio re ) q, pq ) p, pq ) p, p p, pq 9. Whih of the followig or re orret regrdig orml dtriutio urve? i) Symmetril out the lie X ( me ) ii) Me = medi = mode iii) Uimodl iv) Poit of iflextio re t X ) (i), (ii) oly ) (ii), (iv) oly ) (i), (ii), (iii) oly ll 1. For stdrd orml dtriutio the me d vrie re ), ), ),1 1,1 11. The p.d.f of the stdrd orml vrite Z z ) 1 1 z e ) 1 z e ) 1 1 z MATHS TIMES.COM Pge 6 e z e

27 + MATH COME BOOK CREATIVE ONE MARK QUESTIONS 1. If X drete rdom vrile the whih of the followig orret? ) F x 1 ) F d F 1 X x F x F x 1 F x ostt futio ) P 1. If X otiuous rdom vrile the whih of the followig iorret? ) F ' x f x ) F 1 ; F P x F F P x F F ) 1. Whih of the followig re orret? i) EX EX iii) ii) ' 1' vrie iv) vr X vr X )ll ) (i), (ii), (iii) ) (ii), (iii) (i), (iv) 1. Whih of the followig ot true regrdig the orml dtriutio? ) skewess zero ) Me = medi = mode ) the Poits of ifletio re t X mximum height of the urve 1 MATHS TIMES.COM Pge