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    For More Study Material & Test Papers: Manoj Chauhan Sir (Iit-Delhi) Ex. Sr. Faculty (Bansal Classes)

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    For More Study Material & Test Papers: Manoj Chauhan Sir (Iit-Delhi) Ex. Sr. Faculty (Bansal Classes)

    Uploaded by

    jaspreet singh

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    MANOJ CHAUHAN SIR(IIT-DELHI)


    EX. SR. FACULTY (BANSAL CLASSES)
    EXERCISE–III
    x tan 2x  2x tan x
    Q.1 Lim is : [ JEE '99, 2 (out of 200) ]
    x 0 (1  cos 2x)2
    1 1
    (A) 2 (B)  2 (C) (D) 
    2 2
    x
     x  3
    Q.2 For x  R , Lim
    x   = [ JEE 2000, Screening]
     x  2
    (A) e (B) e 1 (C) e 5 (D) e5
    sin(  cos2 x)
    Q.3 Lim equals [ JEE 2001, Screening]
    x 0 x2

    (A) – (B)  (C) (D) 1
    2

    atanx  asin x
    Q.4 Evaluate Lim , a > 0. [REE 2001, 3 out of 100]
    x 0 tan x  sin x

    (cos x  1)(cos x  e x )
    Q.5 The integer n for which Lim is a finite non-zero number is
    x 0 xn
    (A) 1 (B) 2 (C) 3 (D) 4
    [JEE 2002 (screening), 3]
    sin(n x)[(a  n)n x  tan x]
    Q.6 If Lim  0 (n > 0) then the value of 'a' is equal to
    x 0 x2
    1 n2  1
    (A) (B) n2 + 1 (C) (D) None
    n n
    [JEE 2003 (screening)]

    2 1  1  
    Q.7 Find the value of Lim  (n  1) cos  n   n .
    n  
    [ JEE ' 2004, 2 out of 60]
       

    x2
    a  a2  x 2 
    Q.8 Let L  lim 4 , a > 0. If L is finite, then [JEE' 2009, 3]
    x 0 x4
    1 1
    (A) a = 2 (B) a = 1 (C) L  (D) L 
    64 32

    1/ x
    Q.9 If lim 1  x ln(1  b 2 )   2b sin2 , b  0 and   ( , ], then the value of  is [JEE' 2011]
    x 0

       
    (A)  (B)  (C)  (D) 
    4 3 6 2

    Q.10 Let (a) and (a) be the roots of the equation [JEE' 2012]

     3
    1  a  1 x2   1 a  1 x    6

    1  a  1  0 where a > – 1

    Then lim (a) and lim (a) are


    a 0 a 0

    ETOOS Academy Pvt. Ltd. : F-106, Road No. 2, Indraprastha Industrial Area, End of Evergreen Motors 2
    (Mahindra Showroom), BSNL Office Lane, Jhalawar Road, Kota, Rajasthan (324005)
    5 1 7 9
    (A)  and 1 (B)  and 1 (C)  and 2 (D)  and 3
    2 2 2 2

     x2  x  1 
    Q.11 If lim   ax  b   4, then [JEE' 2012]
    x 0
     x 1 
    (A) a = 1, b = 4 (B) a = 1, b = – 4 (C) a = 2, b = – 3 (D) a = 2, b = 3

    (1  cos 2x)(3  cos x)


    Q.12 lim is equal to : [IIT Mains 2013]
    x 0 x tan 4x

    1 1
    (A) 2 (B)  (C) (D) 1
    4 2

    sin(  cos2 x)
    Q.13 lim is equal to : [IIT Mains 2014]
    x 0 x2

    (A)  (B) (C) 1 (D) – 
    2

    1 x
     ax  sin(x  1)  a 1 x 1
    Q.14 The largest value of the non-negative integer a for which lim    is
    x 1
     x  sin(x  1)  1  4
    [JEE Advanced 2014]

    EXERCISE–III
    Q.1 C Q.2 C Q.3 B Q.4 lna Q.5 C
    2
    Q.6 C Q.7 1 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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