MANOJ CHAUHAN SIR(IIT-DELHI)EX. SR. FACULTY (BANSAL CLASSES)
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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
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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
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