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  MANOJ CHAUHAN SIR(IIT-DELHI)EX. SR. FACULTY (BANSAL CLASSES) For More Study Material & Test Papers Visit : www.mathsiit.com  EXERCISE–III Q.1 x0 Lim  2 xtan2x2xtanx(1cos2x)   is :[ JEE '99, 2 (out of 200) ](A) 2(B)    2(C) 12 (D)    12 Q.2For x   R   , x Lim   x x3x2     =[ JEE 2000, Screening](A) e(B) e    1 (C) e    5 (D) e 5 Q.3 22x0 sin(cosx)Limx    equals[ JEE 2001, Screening](A) –   (B)  (C) 2  (D) 1Q.4Evaluate tanxsinxx0 aaLimtanxsinx   , a > 0.[REE 2001, 3 out of 100]Q.5The integer n for which xnx0 (cosx1)(cosxe)Limx     is a finite non-zero number is(A) 1(B) 2(C) 3(D) 4[JEE 2002 (screening), 3]Q.6If 2x0 sin(nx)[(an)nxtanx]Lim0x     (n > 0) then the value of 'a' is equal to(A) 1n (B) n 2  + 1(C) 2 n1n  (D) None[JEE 2003 (screening)]Q.7Find the value of n Lim  1 21(n1)cosnn           .[ JEE ' 2004, 2 out of 60]Q.8Let 2224x0 xaax4Llimx     , a > 0. If L is finite, then[JEE' 2009, 3](A) a = 2(B) a = 1(C) 1L64  (D) 1L32  Q.9If 1/x22x0 lim1xln(1b)2bsin,b0and(,],              then the value of   is[JEE' 2011](A) 4  (B) 3  (C) 6  (D) 2  Q.10Let  (a) and  (a) be the roots of the equation[JEE' 2012]       236 1a1x1a1x1a10           where a > – 1Then a0a0 lim(a)andlim(a)are       ETOOS Academy Pvt. Ltd. : F-106, Road No. 2, Indraprastha Industrial Area, End of Evergreen Motors(Mahindra Showroom), BSNL Office Lane, Jhalawar Road, Kota, Rajasthan (324005) 2  (A) 5and12  (B) 1and12  (C) 7and22  (D) 9and32  Q.11If 2x0 xx1limaxb4,x1          then[JEE' 2012](A) a = 1, b = 4(B) a = 1, b = – 4(C) a = 2, b = – 3(D) a = 2, b = 3Q.12 x0 (1cos2x)(3cosx)limxtan4x     is equal to :[IIT Mains 2013](A) 2(B) 14  (C) 12(D) 1Q.13 22x0 sin(cosx)limx    is equal to :[IIT Mains 2014](A)  (B) 2  (C) 1(D) –  Q.14The largest value of the non-negative integer a for which 1x1xx1 axsin(x1)a1limxsin(x1)14            is [JEE Advanced 2014]  EXERCISE–III  Q.1 C  Q.2 C  Q.3 B  Q.4  l na  Q.5 C Q.6 C  Q.7  21  Q.8 A, C  Q.9 D  Q.10 B Q.11 B  Q.12 A  Q.13 A  Q.14 0
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