(A) 1 (B) 1 + (sin 1) (C) 1 (sin 1) (D) (sin 1) 1 (C) and g be the inverse of f. Then the value of g'(0) is. (C) a. dx (a > 0) is

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Download "(A) 1 (B) 1 + (sin 1) (C) 1 (sin 1) (D) (sin 1) 1 (C) and g be the inverse of f. Then the value of g'(0) is. (C) a. dx (a > 0) is"

Reynard Tyler
5 years ago
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1 [STRAIGHT OBJECTIVE TYPE] l Q. Th vlu of h dfii igrl, cos d is + (si ) (si ) (si ) Q. Th vlu of h dfii igrl si d whr [, ] cos cos Q. Vlu of h dfii igrl ( si Q. L f () = d ( ) cos 7 ( ) )d d g b h ivrs of f. Th h vlu of g'() is cos 7 7 o of hs Q.5 If, b d c r rl umbrs h h vlu of bc b c c Lim l ( si b) d quls bc c b Q.6 Th vlu of h dfii igrl ( d )( ) ( > ) is Q.7 L = ( si ) si d h Lim is qul o som fucio of. / / / Q.8 Th vlu of h dfii igrl )si ( )cos 8 ( d, is 8

2 Q.9 L C = si () d h Lim C () quls d Q. If sisfis h quio cos si d = ( < < ), h h vlu is ± si ± si ± si ± si Q. If f () = g() d d g() = h f () quls /7 quls quls co b drmid Q. A fucio f () sisfis f () = si + f '() ( si si ) d h f () is si si si cos cos si Q. Suppos h fucio g () = b ( N) sisfis h quio ( p q) g () d = for ll lir fucios (p + q) h = b = b = ; = = ; b = = ; b = Q. Th vlu of 5 r r Lim is qul o r r 5 Q.5 If F () = f () d whr f () = u u du h h vlu of F '' () quls 7 7 Q.6 L f () = 5 7 d d h () = f g() , whr g () is dfid for ll, g'() iss for ll, d g () < for >. If h'() = d g'() =, h h possibl vlus which g() c k

3 Q.7 Th vlu of > sisfyig h quio l d =, is 5 Q.8 L f b o-o-o coiuous fucio such h f () = d f (5) = 7. Giv h vlu of h dfii igrl f ()d quls 7 f () d = 7, h Q.9 L f () b fucio sisfyig f ' () = f () wih f () = d g b h fucio sisfyig f () + g () =. Th vlu of h igrl 5 f ()g() d is ( ) g() Q. L f () = d cos whr g () = ( si ) d. Also h() = d f () = si if d f () = h f ' quls l ' () h ' ( ) h ' ( + ) Lim cos si si( ) si Q. Lim d quls d Q. Th vlu of ( ) is co b vlud Q. Lim sc sc... sc ( ) hs h vlu qul o Q. For f () = +, l I = I f (cos )d d I = f (si )d h I / hs h vlu qul o

4 Q.5 If g () = cos d, h g ( + ) quls g () + g () g () g () g () g () [ g ()/g () ] / si Q.6 d is cos / / / / 6 / / / / 6 / / Q.7 L f b posiiv fucio. L I = f ( ) d ; I = ( ) Th I I is k k k / Q.8 If Lim d is qul o whr k N quls k 8 6 k k f d, whr k >. Q.9 Suppos h h qudric fucio f () = + b + c is o-giv o h irvl [, ]. Th h r udr h grph of f ovr h irvl [, ] d h -is is giv by h formul A = f ( ) + f () A = f f A = [ f ( ) f () f ()] A = [ f ( ) f () f ()] f () Q. If d = cos, h f ' (9) is qul o 9 is qul o is qul o is o is Q. L I () = miimum vlu is si d whr '' is posiiv rl. Th vlu of '' for which I () is is 6

5 / Q. L u = cos si d d v = Q. / cos si d, h h rlio bw u d v is u = v u = v u = v u = v d = / si d Q. L f () = d / si d / si d / si. If g () is h ivrs of f () h g'() hs h vlu qul o d Q.5 Domi of dfiiio of h fucio f () = is R R + R + {} R {} Q.6 Th s of vlus of '' which sisfy h quio ( log ) d = log is R R + < > Q.7 l( ) Lim d quls / / Q.8 Vribl d y r rld by quio = y y y d y y d Q.9 Th vlu of h dfii igrl ( )( ) is d y. Th vlu of is qul o d y y / / /8 /6 Q. If f & g r coiuous fucios i [, ] sisfyig f () = f ( ) & g () + g ( ) = h f ().g()d = d f ()d f ()d f ()d f ()d

6 Q. If f () d = + f ()d, h h vlu of h igrl f () d is qul o / / Q. Th vlu of h dfii igrl ( )d is qul o Q. If h vlu of dfii igrl h h vlu of '' quls [log ] d whr >, d [] dos h grs igr, is Q. l l( l ) ll( l ) d quls + Q.5 L f b coiuous fucios sisfyig f ' (l ) = dfid s f () = f () = if if if if for for f () = f () = d f () = h f () c b if if if if Q.6 Th vlu of 8 si d is qul o Q.7 Lim k k, > is qul o () () () () Q.8 Th irvl [, ] is dividd io qul sub-irvls by h pois,,,...,, whr = < < <... < =. If = i i for i =,,,... h qul o 8 6 Lim is i i

7 (si )d Q.9 Th bsolu vlu of ( 8 is lss h ) Q.5 L > d l f () is moooic icrsig such h f () = d f () = b h f ()d f quls + b b + b b + b Q.5 Lim (!) is qul o b () d l d Q.5 Th vlu of h limi, Lim d is quls / o is 7 Q.5 Th vlu of h dfii igrl } (si ) Q.5 If Q.55 9 { d whr { } dos h frciol pr fucio. 6 9 c o b drmid cos d = k d h 'k' quls f l d is qul o zro is qul o o is qul o Q.56 Th vlu of h dfii igrl d, is c o b vlud Q.57 Posiiv vlu of '' so h h dfii igrl d chivs h smlls vlu is 8 8

8 Q.58 Th vlu of r) r ( d quls k k! ( + )!! Q.59 Th vlu of h fucio f () = + + (l + l) d whr f ' () vishs is + Q.6 Lim ( ) d is qul o l l Q.6 + d is qul o ( N). ( )!!! ( )! Q.6 Th ru s of vlus of '' for which h iquliy (. ) d is ru is: [, ] (, ] [, ) (, ] [, ) Q.6 If h vlu of h igrl d is, h h vlu of d is : ( ) Q.6 If g () is h ivrs of f () d f () hs domi [, 5], whr f () = d f (5) = h h vlus of 5 f ()d g(y) dy quls Q.65 Which o of h followig fucios is o coiuous o (,)? f()= co h () = si 9 Q.66 If f () = si ; g () = cos for [, ] A = f () d ; B = g() d h g() = l () = si d si si(, ), A > ; B < A < ; B > A > ; B > A < ; B <

9 Q.67 Th vlu of d is udfid Q.68 l d = l 7 l l 5 l / Q.69 For < <, l ( cos ). d (si ) is qul o : / 6 si si si si Q.7 Th ru soluio s of h iquliy, 5 6 dz > si d is : R (, 6) ( 6, ) (, ) 5 Q.7 Th igrl, ( cos si si cos ) d hs h vlu qul o / / Q.7 Th vlu of h dfii igrl / si si si d is qul o : 7 6 co Q.7 If h vlu of h dfii igrl d, is qul o /6 + b / h ( + b) quls 6 si Q.7 For U = ( ) d ; V = ( ) d N, which of h followig sm(s) is/r ur? U = V U = V U = V U = V Q.75 L S () = l d ( > ) d H () = S ( ). Th H() is : coiuous bu o drivbl i is domi drivbl d coiuous i is domi ihr drivbl or coiuous i is domi drivbl bu o coiuous i is domi.

10 Q.76 L f () = si, h f () f d = f () d f () d f () d [REASONING TYPE] f () d Q.77 Sm- : If f() = ( f () ) d, h f () d = bcus Sm- : f() = + Sm- is ru, sm- is ru d sm- is corrc plio for sm-. Sm- is ru, sm- is ru d sm- is NOT h corrc plio for sm-. Sm- is ru, sm- is fls. Sm- is fls, sm- is ru. Q.78 Cosidr I = Sm-: I = bcus Sm-: d si f () d, whrvr f () is odd fucio Sm- is ru, sm- is ru d sm- is corrc plio for sm-. Sm- is ru, sm- is ru d sm- is NOT h corrc plio for sm-. Sm- is ru, sm- is fls. Sm- is fls, sm- is ru. Q.79 Sm-: Th fucio f () = d is odd fucio d g () = f ' () is v fucio. bcus Sm-: For diffribl fucio f () if f ' () is v fucio h f () is odd fucio. Sm- is ru, sm- is ru d sm- is corrc plio for sm-. Sm- is ru, sm- is ru d sm- is NOT h corrc plio for sm-. Sm- is ru, sm- is fls. Sm- is fls, sm- is ru. Q.8 Giv f () = si d P() is qudric polyomil wih ldig coffici uiy. Sm-: bcus Sm-: P () f ''() d vishs. f () d vishs Sm- is ru, sm- is ru d sm- is corrc plio for sm-. Sm- is ru, sm- is ru d sm- is NOT h corrc plio for sm-. Sm- is ru, sm- is fls. Sm- is fls, sm- is ru.

11 Suppos [COMPREHENSION TYPE] Prgrph for Qusio Nos. 8 o 8 Lim ( d r p ) b si = l whr p N, p, >, r > d b. Q.8 If l iss d is o zro h b > < b < b < b = Q.8 If p = d l = h h vlu of '' is qul o 8 6 / Q.8 If p = d = 9 d l iss h h vlu of l is qul o / / / 7/9 Prgrph for Qusio Nos. 8 o 86 L h fucio f sisfis f () f ' ( ) = f ( ) f ' () for ll d f () =. Q.8 Th vlu of f () f ( ) for ll, is Q.85 d f () 5 hs h vlu qul o 7 Q.86 Numbr of roos of f () = i [, ] is Prgrph for Qusio Nos. 87 o 89 Suppos f () d g () r wo coiuous fucios dfid for. Giv f () = f () d d g () = g() d +. Q.87 Th vlu of f () quls Q.88 Th vlu of g () f () quls g() Q.89 Th vlu of quls g()

12 Q.9 Prgrph for Qusio Nos. 9 o 9 Cosidr h fucio dfid o [, ] R si cos f () = f () d quls if d f () = si () si () si () si () Q.9 Lim f () d quls / /6 / / Prgrph for Qusio Nos. 9 o 9 Suppos d b r posiiv rl umbrs such h b =. L for y rl prmr, h disc from h origi o h li ( ) + (b )y = b dod by D() h Q.9 Th vlu of h dfii igrl I = d D() is qul o b b b Q.9 Th vlu of 'b' which I is miimum, is Q.9 Miimum vlu of I is b + [5] [] [] [MULTIPLE OBJECTIVE TYPE] Q.95 Which of h followig dfii igrl(s) vishs / l (co )d si d / d ( l ) / Q.96 Th quio = hs ls o roo i (, ) ls o roo i (, ) ls wo roos i (, ) o roo i (, ) cos d

13 Q.97 Which of h followig r ru?. f (si ) d =. f (si ) d f ( ) d =. f ( ) d f cos d =. f cos Q.98 Th vlu of d is : ( ) b c d f ( c) d = b c f ( ) d + l + l l co + l + co / / / Q.99 Suppos I = cos( si ) d ; I = cos( si ) d d I = cos( si ) d, h I = I + I = I + I + I = I = I Q. If I = d ; N, h which of h followig sms hold good? I + = + ( ) I I = 8 I = I 8 = Q. If f() = d whr > h h vlu(s) of sisfyig h quio, f() + f(/) = is : Q. L f () = cos() d h which of h followig hold ru? f () is o dfid Lim f () iss d quls Lim f () iss d is qul o f () is coiuous = Q. Th fucio f is coiuous d hs h propry f f () = for ll [, ] d J = f ()d h f + f = h vlu of J qul o f f = si d (si cos ) hs h sm vlu s J

14 Q. L f() is rl vlud fucio dfid by : f() = + f ()d + f ()d h which of h followig hold(s) good? f ()d f() + f( ) = f ()d > f ()d f() f( ) = Q.5 L f () d g () r diffribl fucio such h f () + g () d = si (cos si ), d f '() + () g = h f () d g () rspcivly, c b cos si, si, cos si, si si, cos Q.6 L f () = si b c d whr,b, c r o zro rl umbrs, h Lim f () idpd of idpd of d b d hs h vlu quls o c. idpd, b d c. dpd oly o c. d Q.7 L L = Lim whr R h L c b is [MATCH THE COLUMN] Q.8 Colum I Colum II Suppos, f () = log () log () log (5)... log () h h sum f ( k ) quls (P) 5 k (B L f () = ( ) ( )( ) (Q) 55 h f ()d is (R) 5 (C I A.P. h sris coiig 99 rms, h sum of ll h (S) 59 odd umbrd rms is 55. Th sum of ll h 99 rms of h A.P. is Lim r ( r) quls

15 T Q.9 L Lim (si si ) d = L h T T Colum I Colum II for =, h vlu of L is (P) for = h vlu of L is (Q) / for = h vlu of L is (R) R {,, } h vlu of L is (S) Q. Colum I Colum II cos Th fucio f () = is o dfid =. si (P) Th vlu of f () so h f is coiuous = is d Th vlu of h dfii igrl whr d b r igrs h ( + b) quls quls + b l (Q) sc Giv d = h h vlu of () is qul o (R) / L = () d d b = si () d h (S) Lim b hs h vlu qul o Q. Colum I Colum II g() cos d If f () = whr g () = ( si ) d (P) h h vlu of f ' If f () is o zro diffribl fucio such h (Q) f ()d = f () for ll, h f () quls (R) b If ( ) d is mimum h ( + b) is qul o (S) si b If Lim = h ( + b) hs h h vlu qul o

16 Q. Colum-I Colum-II Lim si l( ) ( y) y dy quls (P) Lim ( ) quls (Q) L f () = Lim h Lim f () quls (R) k k (S) Q. L f () = ( si ) d d g () = ( cos) d whr [, ]. Th quiy f () g() i h irvl giv i colum-i, is Colum-I,,, 7 Colum-II (P) (Q) (R) giv posiiv o giv 7,, (S) o posiiv Q. Colum-I Colum-II 8 (8) 8 Th vlu of h dfii igrl d Lim...( )... d quls (P) + l d is qul o (Q) / quls (R) / (S)

17 Q.5 Colum-I Colum-II si (si ) cos (cos ) d (P) d si (Q) si cos d quls (R) (S) Q.6 Colum-I Colum-II L f () = si cos si h h vlu of f () is cos L g () = (cos ) l d d f = (P) riol d d g () = (Q) irriol h h vlu of g is (R) igrl If rl umbrs d y sisfy ( + 5) + (y ) = () h h miimum vlu of ( y ) is (S) prim L k () = of k ( ) is ( ) d 6 d k ( ) = h h vlu

18 Q. C Q. A Q. B Q. C Q.5 A Q.6 A Q.7 A Q.8 A Q.9 D Q. D Q. A Q. B Q. B Q. C Q.5 C Q.6 C Q.7 A Q.8 C Q.9 D Q. C Q. D Q. B Q. A Q. C Q.5 A Q.6 D Q.7 D Q.8 C Q.9 D Q. A Q. A Q. A Q. C Q. B Q.5 D Q.6 B Q.7 A Q.8 B Q.9 B Q. B Q. C Q. A Q. A Q. A Q.5 D Q.6 D Q.7 C Q.8 B Q.9 C Q.5 D Q.5 A Q.5 B Q.5 B Q.5 A Q.55 A Q.56 B Q.57 A Q.58 D Q.59 D Q.6 B Q.6 C Q.6 D Q.6 B Q.6 A Q.65 D Q.66 A Q.67 C Q.68 A Q.69 A Q.7 D Q.7 A Q.7 D Q.7 A Q.7 C Q.75 B Q.76 A Q.77 C Q.78 D Q.79 C Q.8 A Q.8 D Q.8 A Q.8 B Q.8 B Q.85 A Q.86 A Q.87 A Q.88 A Q.89 B Q.9 A Q.9 B [SINGLE OBJECTIVE TYPE] Q.9 C Q.9 D Q.9 B Q.95 ABC Q.96 ABC Q.97 ABCD Q.98 ACD Q.99 ABC Q. AB Q. CD Q. CD Q. ABD Q. BD [MULTIPLE OBJECTIVE TYPE] [MATCH THE COLUMN] Q.5 CD Q.6 AD Q.7 ABC Q.8 S; R; S; Q Q.9 Q; S; P; R Q. R; P; S; R Q. S; R; R; Q Q. S; R; P; Q, R Q. Q; R; S; P Q. S; P; Q Q.5 Q; S; Q Q.6 Q; P; P, R; P, R, S ANSWERS

EXERCISE - 01 CHECK YOUR GRASP

EXERCISE - 01 CHECK YOUR GRASP DEFNTE NTEGRATON EXERCSE - CHECK YOUR GRASP. ( ) d [ ] d [ ] d d ƒ( ) ƒ '( ) [ ] [ ] 8 5. ( cos )( c)d 8 ( cos )( c)d + 8 ( cos )( c) d 8 ( cos )( c) d sic + cos 8 is lwys posiiv f() d ( > ) ms f() is