LIMITS MULTIPLE CHOICE QUESTIONS. (a) 1 (b) 0 (c) 1 (d) does not exist. (a) 0 (b) 1/4 (c) 1/2 (d) 1/8. (a) 1 (b) e (c) 0 (d) none of these
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1 DSHA CLASSES Guidig you to Success LMTS MULTPLE CHOCE QUESTONS Te value of + LEVEL (Objective Questios) (a) e (b) e (c) e 5 (d) e 5 (a) (b) (c) (d) does ot et (a) (b) / (c) / (d) /8 (a) (b) (c) (d). Te itig value of cos si as 7. c si cos or, a bg b c bg d + b g b g l + l K J + si + equal to b g (a) (b) e (c) (d) oe of tese (a) l (b) l (c) (l )/ (d) oe of tese 8. + si (a) (b) (c) (d) it does ot et 9.. Let a + a,,,,... ad a. Te a + (a) (b) (c) 5 (d) + + Te value of bg a bg b bg c bg d oe of tese 8 CENTAL MKT., ASHOK VHA - & OHN (SEC-9) 7, 7, 887, 75585
2 DSHA CLASSES Guidig you to Success.... ta K J bg a b e c e bg bg bg d S T K JU V W Te value of ta + (a) e (b) e (c) e (d) oe of tese a b e e si a si b a b b g (a) (b) (c) / (d) log c c (a) log e (b) log e (c) (d) 5. Give tat f (a), g(a), f (a), g (a), te value of f g a f a g a a (a) 5 (b) 5 (c) /5 (d) / e cos a bg b c bg d oe of tese H G K J b gta (a) / (b) + (c) / (d) + + (a) (b) / (c) log (d) oe of tese f f f ( ), f, te (a) (b) (c) (d) a a si t si t e dt e dt equal to were a z z y + y b a costatg bg bg si y si y a e b si y e c d oe of tese CENTAL MKT., ASHOK VHA - & OHN (SEC-9) 7, 7, 887, 75585
3 DSHA CLASSES Guidig you to Success. Let f : be a differetiable fuctio suc tat f (). Te te value of z f t dt (a) f () (b) f () (c) f () (d) oe of tese. f a, b, c, d are positive, te + (a) e d/b (b) e c/a a + b (c) e (c + d)/a + b (d) e ta ta. b cos g (a) (b) (c) ½ (d) /. Let f : be suc tat f () ad f (). Te 5. f (a) (b) e / (c) e (d) e (a) (b) ( + )/ (c) (d) + /. si cos + equal to ( e ) ( a) ( b) ( c) ( d) doesot et 7. cb g a ta si ( + 7)l( ) Limit ( 9) c + d ( a) 8 ( b) 8 ( c) 9 ( d) 9 b g f f + /, were ozero real umber, te a equal to 8. cos ( ) Limit + ( a) ( b) ( c) ( d) si( l ( + )) 9. Te value of Limit : l( + si ) ( a) ( b) / ( c) / ( d). Te value of Limit ta si + si + si + si + equal to:. + ( ) ( ) / H (a) / (b) / (c) / (d) /8 ( a) ( b) if eve: if odd ( c) ot et if eve: if odd ( d) + if eve; does ot et if odd K CENTAL MKT., ASHOK VHA - & OHN (SEC-9) 7, 7, 887, 75585
4 DSHA CLASSES Guidig you to Success... K J Limit cos si as te value equal to: ( a) / ( b) / ( c) / ( d) oe a Te it a K J ta a K J equal to a/ a/ / ( a) e ( b) e ( c) e ( d) Limit ( a) 5 ( b) ( c) ( d) zero ta Limit K Jc si 5. / + ta K Jb g ( a) ( b) ( c) ( d). Lim log + si( / ) si equal to ( a) ( b) ( c) ( d) LEVEL - 7. f f si,,, ±, ±, ±,... te g f S T, c oterwe ad g S T +,,, 5, (a) (b) 5 (c) (d) does ot et 8. f [ ] deotes te greatest iteger, te te value of (a) (b) (c) (d) oe of tese, Z ( set of itegers) f f Skc, Z te f ets we T (a) k (b) k (c) {} (d) does ot et s. Te value of si ([. ] deotes te greatest iteger fuctio) (a) does ot et (b) (c) (d) CENTAL MKT., ASHOK VHA - & OHN (SEC-9) 7, 7, 887, 75585
5 DSHA CLASSES 5 Guidig you to Success ae + be, e + e (a) (b) a (c) b (d) does ot et (a) / (b) / (c) (d) (a) /5 (b) / (c) / (d) oe of tese b g, iteger, for e were a b upto terms. 5. b g cos si cos K J (a) o value of (b) all values of (c) oly egative values of (d) oly positive values of m Te value of log, m, N + b g (a) (b) m/ (c) m (d) oe of tese Te value of log, > (a) (b) (c) / (d) /! Let f, te + (a) f (), for > (b) f () for < (c) f () ot defied for ay value of (d) f () for Te value of z cos t dt si (a) / (b) (c) (d) oe of tese si f f,, were [] deotes te greatest iteger less ta or equal to, te : (a) (b) (c) (d) oe of tese bcos gc cos e Te iteger for wic a fiite o zero umber (a) (b) (c) (d) cos si si a bg b c bg d f CENTAL MKT., ASHOK VHA - & OHN (SEC-9) 7, 7, 887, 75585
6 DSHA CLASSES Guidig you to Success 5. L O N Q bg bg S U T V W M + P 8 a b c d 9 5. f f( + ) f( ) + N ad f() > for all N te f() equal to f( ) (a) (b) - (c) / (d) oe of tese 5. Te value of z + t + tk J dt (a) (b) (c) (d) e 55. f α ad β are te root of te quadratic equatio a + b + c, te c c c ( a) ( b) ( c) ( d) Noe of tese α α β β α β αβ α β 8 α cos( c + b + a) ( α) L NM O QP si[ ] 5. Lt, were [. ] deotes greatest iteger fuctios [ ] (a) (b) (c) does ot et (d) si 57. f Lim te te costats a ad b are (were a > ) a+ ( b si ) (a) b, a (b) a, b (c) a, b (d) b, a e j si [ ] 58. Lim were [. ] deote te greatest iteger fuctio. (a) (b) (c) does ot et (d) Noe of tese 59.. Limit e f f( ) S T,, < te fid Lim f( g( ( ))) ( a) ( b) ( c) ( d) 8 / cos si, g( ) S T +, > ad ( ) +, ( a) ( b) ( c) ( d) does ot ets. a + b + c Let α, β be te roots of a + b + c, were < α < β. Te Lim te wic of te followig statemets icorrect a + b + c (a) a > ad < (b) a > ad > β (c) a < ad α < < β (d) a < ad < CENTAL MKT., ASHOK VHA - & OHN (SEC-9) 7, 7, 887, 75585
7 DSHA CLASSES Guidig you to Success 7. cos cos Te it equal to ( a) ( b) ( c) ( d). Te grap of te fuctio f( ) Lim cot t t o y (a) (b) (c) (d) H G K J o p /. 5. o f( ) f Lim f( ) et ad fiite & ozero ad if Lim f( ) + f ( ) te te value of Lim f( ) ( a) ( b) ( c) ( d) oe of tese Te value of a a, a> e j + a ( a) la ( b) e ( c) e ( d) oe of tese a /. f [ + l (+ b )] b si θ, b > ad θ (, ), te te value of θ (a) ± (b) 7. Te value of ( ) 8. / si ( ) ± (c) si + (+ ), were > ± (d) (a) (b) (c) (d) sec f(t) dt equal ± (a) 8 f() (b) f() (c) f f() 9. Let f : be a positive icreasig fuctio wit f() f() Te f() (d) f() (a) (b) (c) (d) 7. Let f be a real-valued fuctio defied o te iterval (, ) suc tat for all (, ), ad let f be te iverse fuctio of f. Te e f() + t + dt, (f )() equal to (a) (b) (c) (d) e CENTAL MKT., ASHOK VHA - & OHN (SEC-9) 7, 7, 887, 75585
8 DSHA CLASSES Guidig you to Success 8 More ta oe. 7. cos cos Let f( ), te ( a) Lim f( ) si ( b) Limf( ) si ( c) Lim f( ) cos ( d) Limf( ) cos Let f( ) + ( a) f( ) ( b) f( ) ( c) f( ) ( d) f( ) 8. f Limit (cos + a si b) / e, te te possible value of a & b (a) a b (b) a, b (c) a, b / (d) a /, b 9. f Lim ( + a cos ) b si + a cos b l si, were l, te ( a) ( a, b) (, ) ( b) a & b are ay real umbers ( c) l ( d) l 7. si + a si f Limit p ( fiite), te ( a) a ( b) a ( c) p ( d) p 7. ( a + ) + A ( a) a if N ( b) if Z & a A ( c) if ( d) a if Z, A & a + A a a 7. Let L, a > f L fiite, te (a) a (b) a (c) L (d) L CENTAL MKT., ASHOK VHA - & OHN (SEC-9) 7, 7, 887, 75585
9 DSHA CLASSES Guidig you to Success 9 Aswers : Limits LEVEL (Objective Questios) b 8 d 5 b a 9 d a c 9 b a c c a a 7 c c a b d 8 b 5 d b 5 d b 9 a c c a d a 7 c d 7 a d c 8 b 5 c LEVEL & More ta Oe 7 c B 5 d 58 b 5 a 7 a,b 8 c 5 a 5 d 59 c d 9 b a 5 a b 7 c a 7 a, b 5 c d 8 a d 8 b 55 a c 9 d b 9 d 5 c c 7 b D 5 c 57 a a 7 ab CENTAL MKT., ASHOK VHA - & OHN (SEC-9) 7, 7, 887, 75585
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