Sunday, 31 March 2013

IIT JEE PAPER 2012 FULLY SOLVED

                                          

                                                                PAPER 1


Time: 3 Hours                                                                             Maximum Marks: 210


                       Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.


INSTRUCTIONS

A.    General:
       1.   This   booklet   is   your   Question   paper.   Do   not   break   the   seats   of  his   booklet   before   being   instructed  to   do   so   by   the
           invigilators.
       2.   The question paper CODE is printed on the right hand top corner of this page
and on the back page of this booklet.
       3.   Blank spaces and blank pages are provided in this booklet for your rough work. No additional sheets will be provided
           for rough work.
       4    Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers, and electronic gadgets are
           NOT allowed inside the examination hall.
       5.   Answers   to   the   questions   and   personal   details   are   to   be   filled   on   a   two-part   carbon-less   paper,   which   is   provided
           separately. You should not separate these parts. The invigilator will separate them at the end of examination. The upper
           sheet is machine-gradable Objective Response Sheet (ORS) which will be taken back by the invigilator.
       6.   Using a black ball point pen, darken the bubbles on the upper original sheet. Apply sufficient pressure so that the
           impression is created on the bottom sheet.
       7.   DO NOT TAMPER WITH /MUTILATE THE ORS OR THE BOOKLET.
  
    8.   On breaking the seals of the booklet check that it contains 28 pages and all 60 questions and corresponding answer
           choices are legible. Read carefully the instructions printed at the beginning of each section.
B.     Filling the Right Part of the ORS:
       9.   The ORS also has a CODES printed on its left and right parts.
       10.  Check that the same CODE is printed on the ORS and on this booklet. IF IT IS NOT THEN ASK FOR A CHANGE
           OF THE BOOKLET. Sign at the place provided on the ORS affirming that you have verified that all the code are
           same.
       11.  Write your Name, Registration Number and the name of examination centre and sign with pen in the boxes provided on
           the   right   part   of   the   ORS.  Do   not   write   any   of   this   information   anywhere   else.   Darken   the   appropriate   bubble
           UNDER each digit of your Registration Number in such a way that the impression is created on the bottom sheet. Also
           darken the paper CODE given on the right side of ORS(R4).
C.     Question paper format and Marking scheme:
       The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of three sections.
       12. Section I contains  10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which
           ONLY ONE is correct.
       13. Section II contains 5 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which
           ONE or MORE are correct.
       14. Section   III contains  5   questions.   The   answer   to   each   question   is   a single   digit   integer,   ranging   from  0   to   9   (both
           inclusive).
D.     Marking Scheme
       15.  For each question in  Section I, you will be awarded 3 marks if you darken the bubble corresponding to the correct
           answer ONLY and zero marks if no bubbles are darkened. In all other cases, minus one (−−1) mark will be awarded in
                                                                                                                  −−
           this section.
       16.  For each question in  Section II, you will be awarded 4 marks if you darken ALL the bubble(s) corresponding to the
           correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No negative marks will be awarded for
           incorrect answer in this section.
       17.  For each question in Section III, you will be awarded 4 marks if you darken the bubble corresponding to the correct
           answer ONLY.       In all other cases zero (0) marks will be awarded. No negative marks will be awarded for incorrect
           answer in this section.
                   Write your Name, Registration Number and sign in the space provided on the back page of this booklet.








 PAPER-1 [Code – 8] 
                    
                                                   IITJEE 2012 
                                            PART - I: PHYSICS  
                                  SECTION I : Single Correct Answer Type
This section contains  10   multiple choice questions. Each question   has   four choices (A), (B), (C) and (D) out of
which ONLY ONE is correct.
                                                            4MLg 
1.         In the determination of Young’s modulusY =            2   by using Searle’s method, a wire of length L = 2m
                                                             πld    
          and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire
          is   observed.   Quantities   d   and  l  are   measured   using   a   screw   gauge   and   a   micrometer,   respectively.   They
          have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to
          the maximum probable error of the Y measurement
           (A)  due to the errors in the measurements of d and l are the same.
           (B)  due to the error in the measurement of d is twice that due to the error in the measurement of l.
           (C)  due to the error in the measurement of l is twice that due to the error in the measurement of d.
           (D)  due to the error in the measurement of d is four times that due to the error in the measurement of l.
Sol.       (A)
                  0.5
          L.C. =      = 0.005 mm
                  100
          ∆Y     ∆l    2∆(d)
               =     +
           Y      l      d
          ∆l     0.005×10−3      1
              =               =
           l     0.25×10−3      50
            ∆(d)    2× 0.005×10−3       1
          2       =                  =
              d        0.5×10−3        50
2.         A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The
          mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed  ω. If the
                                                                                            r        r
          angular momentum of the system, calculated about O and P are denoted by  LO   and  LP   respectively, then
                  z
               P
               O        m
                     ω
                r        r
           (A)  LO   and  LP   do not vary with time.
               r                             r
           (B)  LO   varies with time while  LP   remains constant.
               r                             r
           (C)  LO   remains constant while  LP   varies with time.
               r        r
           (D)  LO   and  LP   both vary with time.
Sol.       (C)
     
IITJEE-2012-Paper 1-PCM-3
                       r
                       L
                        P
               r
              L
                O
                O        m
                      ω
3.         A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of
          the first lens is 1.5 and that of the second lens is 1.2. Both the curved surface are of the same radius of
          curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be
              n = 1.5             n = 1.2
                      R = 14 cm
           (A) −280.0 cm                  (B) 40.0 cm                   (C) 21.5 cm                   (D) 13.3 cm
Sol.        (B)
                           1                        1      0.5    0.2     1
            P  = (1.5 −1)      − 0  + (1.2 −1)   0 −         =      +     =
             T                                         
                          14                      −14       14    14     20
            f = +20 cm
            1     1      1
              −       =
            v   −40     20
            1     1     1     1
              =     −     =
            v    20    40    40
            ∴ v = 40 cm
4.         A thin uniform rod, pivoted at O, is rotating in the horizontal plane with                   z
          constant angular speed  ω, as shown in the figure.          At time t = 0, a small
          insect starts from O and moves with constant speed v, with respect to the                        ω
          rod towards the other end.      It reaches the end of the rod at t = T and stops.
          The angular speed of the system remains ω throughout.             The magnitude of                          v →
                         r
          the torque (| τ |) about O, as a function of time is best represented by which
                                                                                                      O
          plot?
            (A)                                                                (B)
                      r                                                                     r
                     | τ |                                                                 | τ |
                         O                                    t                                O                                    t
                                       T                                                                    T
            (C)                                                                (D)
                      r                                                                     r
                     | τ |                                                                 | τ |
                         O                                    t                                O                                    t
                                       T                                                                    T
Sol.        (B)
                 dI       d          2 2
          τ = ω      = ω    (C + mv  t   )
                 dt      dt
                   2
            = mωv  2t.
IITJEE-2012-Paper 1-PCM-3
                       r
                       L
                        P
               r
              L
                O
                O        m
                      ω
3.         A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of
          the first lens is 1.5 and that of the second lens is 1.2. Both the curved surface are of the same radius of
          curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be
              n = 1.5             n = 1.2
                      R = 14 cm
           (A) −280.0 cm                  (B) 40.0 cm                   (C) 21.5 cm                   (D) 13.3 cm
Sol.        (B)
                           1                        1      0.5    0.2     1
            P  = (1.5 −1)      − 0  + (1.2 −1)   0 −         =      +     =
             T                                         
                          14                      −14       14    14     20
            f = +20 cm
            1     1      1
              −       =
            v   −40     20
            1     1     1     1
              =     −     =
            v    20    40    40
            ∴ v = 40 cm
4.         A thin uniform rod, pivoted at O, is rotating in the horizontal plane with                   z
          constant angular speed  ω, as shown in the figure.          At time t = 0, a small
          insect starts from O and moves with constant speed v, with respect to the                        ω
          rod towards the other end.      It reaches the end of the rod at t = T and stops.
          The angular speed of the system remains ω throughout.             The magnitude of                          v →
                         r
          the torque (| τ |) about O, as a function of time is best represented by which
                                                                                                      O
          plot?
            (A)                                                                (B)
                      r                                                                     r
                     | τ |                                                                 | τ |
                         O                                    t                                O                                    t
                                       T                                                                    T
            (C)                                                                (D)
                      r                                                                     r
                     | τ |                                                                 | τ |
                         O                                    t                                O                                    t
                                       T                                                                    T
Sol.        (B)
                 dI       d          2 2
          τ = ω      = ω    (C + mv  t   )
                 dt      dt
                   2
            = mωv  2t.
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