IIT JEE MATHS MATRICES AND DETERMINANTS
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1 IIT JEE MTHS MTRICES ND DETERMINNTS THIRUMURUGN.K PGT Mths IIT Trir Pg. Lt = 5, th () =, = () = -, = () =, = - (d) = -, = -. Lt sw smmtri mtri of odd th quls () () () - (d) o of ths. Th vlu of th third ordr dtrmit, th vlu of th squr of th dtrmit formd th Coftors will () () () 78 (d) o of ths. If = λ +Bλ + Cλ + Dλ +E, th vlu of E quls () () () (d) o of ths 5. If D d 9 D K, th quls () 8 () () 9 (d) 7. Lt = ( ) (- ) (-), th quls () - () () (d) - 7. Lt =, B = d C = dj + dj B, th dt C =? () () 5 () 8 (d) - 8. If = th qul () () - () - (d) 9. If = t t, th th vlu of ' () os () s () os (d). If =, th quls to () () () ull mtri (d) I. If th mtri 7 8 sigulr, th α = () () () 5 (d)
2 IIT JEE MTHS MTRICES ND DETERMINNTS os si. If = d dj () = si os th th vlu of () si os () () (d) os. If f ( ) si os si () 5 () () (d) 5. Th mtri 5 () ivolutr mtri () orthogol mtri () ilpott mtri (d) o of ths 5. If d B r squr mtri of ordr, th () dj (B) = - dj (B) + dj(b) () (+B) - = - +B - () B = or B (d) B = d B. Mimum vlu of si si si os os os si si si () () () (d) o of ths 7. If, B d C r th gls of o right gld trigl BC, th th vlu of t 8. If t B t C qul to () () () - (d) - os( ) os( ) os( ) f ( ) si( ) si( ) si( ) d f () 5, th f ( ) quls r si( ) si( ) si( ) () 5 () () (d) o of ths os os os 9. Th roots of th qutio os os os (si ) / si si THIRUMURUGN.K PGT Mths IIT Trir Pg (si ) / () si β, os β () si β, os β () si β, os β (d) siβ, os β 5 5. Lt = 5. If =5, th quls 5 () () 5 () 5 (d) 5. Cosidr th st of ll dtrmits of ordr with tris or. Lt, B th sust of ostig of ll dtrmits with vlu. Lt C th sust of ostig of ll dtrmits with vlu - th () C mpt () B hs s m lmts s C () = B UC (d) B hs twi s m lmts s C.. Lt,, th rl umrs. Th followig sstm of qutios i, d si
3 . If IIT JEE MTHS MTRICES ND DETERMINNTS,, hs () No solutio () uiqu solutio () ifiitl m solutios (d) fiitl m solutios. f ( ) ( ) ( ) th f () quls ( ) ( )( ) ( ) ( ) () () () (d) -. If th sstm of qutios - =, - =, +- = hs o-ro solutio, th possil vlu of r () -, (), (), (d) -, 5. Th o. of dtit rl roots of si os os os si os os os si = i th itrvl THIRUMURUGN.K PGT Mths IIT Trir Pg () () () (d). If th sstm of qutios + =, + = d = hs ifiit solutios, th th vlu of () - () () (d) o rl vlus 7.If = d =5 th th vlu of α () () () (d) 5 8. If =, - = + + d I, th (, d) () (-,) () (-,) () (,) (d) (,) p q p q 9. Giv tht q -pr <, p > th vlu of q p q r q r q r () Zro () positiv () gtiv (d) q + pr. If,, r itgrs i.p, lig tw d 9, d 5, d r thr digits umrs th th 5 vlu of 5 () + + () - + () (d) + +. I third ordr dtrmit ij dots th lmt i th ith row d th jth olum., i j If ij, i j th th vlu of th dtrmit, i j () () () - (d) o of ths i / i /. Th vlu of th dtrmit i / i / i / i / () () (+ ) () + (d) -
4 . If. IIT JEE MTHS MTRICES ND DETERMINNTS = f()- f () th f() qul to () ( α) ( β) (-γ) ( δ ) () ( α ) (-β) (-γ) (-δ) = whr λ, u,v r i.p () qutio whos ll roots r rl () qutio with ol o rl root 5. If,, r sids of trigl d. If 7. If ( ) ( ) () Δ BC quiltrl trigl () Δ BC osls trigl ( ) ( ) () (- α )( +β ) ( + γ) ( +δ) (d) o of ths () idtit i (d) o of ths ( ) ( ) =, th D d D 5, th quls K () ΔBC right gld osls trigl (d) No of ths () () () 8 (d) o of ths f ( ) ( ) ( ) th f () qul to ( ) ( )( ) ( ) () () () (d) - 8. Usig th ftor thorm it foud tht +, + d + r thr ftors of th dtrmit Th othr ftor i th vlu of th dtrmit () () () + + (d) o of ths os si os 9. If th dtrmit si os os os os os pdd i powrs of si th th ostt trm i th psio () () () - (d) - log ( / ) log ( / ) log ( / ). Th vlu of th dtrmit log ( / ) log ( / ) log ( / ) log ( / ) log ( / ) log ( / ) () () - () log (d) o of ths. If = i d ω o-rl u root of uit th vlu of THIRUMURUGN.K PGT Mths IIT Trir Pg
5 IIT JEE MTHS MTRICES ND DETERMINNTS i i i i qul to () () i () ω (d). If =, th hrtrti qutio of giv () + + I = () - + I = () - - I = (d) o of ths. If th vlu of th dtrmit >, th () > () > -8 () < -8 (d) > -. Lt f() = + + Ɐ,, R d th qutio f() = hs imgir roots α,β d γ,δ th roots of f ( f ( )), th vlu of () () purl rl () purl imgir (d) o of ths os si 5. If = si os = f(), th - = () f(-) () f() () f() (d) f(-) os si. Lt α = si os, th () () 7. If si =, th si os os si si os qul THIRUMURUGN.K PGT Mths IIT Trir Pg 5 () (d) o of ths () () / () / (d) o of ths 8. If d B r squr mtris of qul dgr, th whih o orrt mog th followig? () +B = B+ () +B = -B () -B =B- (d) B = B 9. If = d B =, th vlu of α for whih = B 5 () () - () (d) o. rl vlus 5. If D = () divil ut ot () divil ithr or for, th D () divil ut ot (d) divil oth d
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