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					                                                                                                                CODE      CHANCH




                                          NARAYANA
                                           I      I      T              A       C        A        D       E        M        Y


                                     NARAYANA PART TEST – 04
                                               PAPER – I –:– Date: 12–12–10

 Ti m e : 3 ho ur s                                                                              M a xi m um m ar ks : 2 4 0
 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

                                                                              12.  Section I contains 8 multiple choice questions. Each
                     INSTRUCTIONS                                                  question has 4 choices (A), (B), (C) and (D), out of
A.   General:                                                                      which only one is correct.
     1.    This booklet is your Question Paper containing 60                  13. Section II contains 4 multiple correct answer type
           questions. The booklet has 20 pages.                                    questions. Each questions has 4 choices (A), (B), (C)
                                                                                   and (D), out of which one or more answers are
     2.    The question paper CODE is printed on the right hand
                                                                                   correct.
           top corner of this booklet.
                                                                              14. Section III contains 2 compression types (2
     3.    Blank papers, clipboards, log tables, slide rules,
                                                                                   compressions each with 3 questions).
           calculators, cellular phones, pagers, and electronic
           gadgets in any form are not allowed to be carried inside           15. Section IV contains 2 Matrix Match Type Questions.
           the examination hall.                                        D.    Marking Scheme
     4.    The answer sheet, a machine–readable Objective                     16. For each questions in Section I, you will be awarded 3
           Response Sheet (ORS), is provided separately.                           marks if you have darkened only the bubble
                                                                                   corresponding to the correct answer and zero mark if no
     5.    DO NOT TAMPER WITH / MUTILATE THE ORS OR
                                                                                   bubble is darkened. In case of bubbling of incorrect
           THE BOOKLET.                                                            answer, minus one (–1) mark will be awarded
B.   Filling the ORS                                                          17. For each question in Section II, you will be awarded 4
     6.    On the lower part of the ORS, write in ink, your name in                marks if you have darkened all the bubble(s)
           box L1, your Registration No. in box L2 and Name of the                 corresponding to the correct choice(s) for the answer,
           Centre in box L3. Do not write these anywhere else.                     and zero mark if no bubble is darkened. In all other
     7.    Write your Registration No. in ink, in the box L4 provided              cases, minus one (–1) mark will be awarded.
           in the lower part of the ORS and darken the appropriate            18. For each question in Section III, you will be awarded 4
           bubble UNDER each digit of your Registration No. with a                 marks if you darken the bubble corresponding to the
           good quality Blue or Black ball pen.                                    correct answer and zero mark if no bubble is darkened.
                                                                                   In all other cases, minus one (–1) mark will be
     8.    The ORS has a CODE printed on its lower and upper
                                                                                   awarded.
           parts.                                                             19. For each question in Section IV, you will be awarded 2
     9.    Make sure the CODE on the ORS is the same as that on                    marks for each row in which you have darkened the
           this booklet and put your signature in ink in box L5 on                 bubble(s) corresponding to the correct answer. Thus,
           the ORS affirming that you have verified this.                          each question in this section carries a maximum of 8
     10. IF THE CODES DO NOT MATCH, ASK FOR A                                      marks. There is no negative marking for incorrect
           CHANGE OF THE BOOKLET.                                                  answer(s) for this section.
C.   Question paper format:
     11. The question paper consists of 3 parts (Part I:
           Chemistry:, Part II: Mathematics, Part III: Physics).
           Each part has 4 sections.


                 Name of the Student                                                              Roll Number



     I have read all the instructions and shall abide by them                I have verified all the information filled in by the Candidate

       ……..………………………………………………………                                                    ………………………………………………………..
              Signature of the Candidate                                                Signature of the Invigilator
NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10



                                      PART I : CHEMISTRY
                                              PAPER – I
                                              SECTION – I
                                     Straight Objective Type
This section contains 8 multiple choice questions. Each question has 4 choices ((A), ((B), (C)and ((D), out
of which ONLY ONE is correct.


1.      Which of the following bonds determines the secondary structure of proteins ?
        (A)Electrovalent bond                      (B)Covalent bond
        (C)Hydrogen bond                           (D)Coordinate bond

2.      The odd one amongst these on basis of structure is
        (A)Glycogen                                 (B) Amylopectin
        (C) Amylose                                 (D Cellulose

3.      Henry's law may be stated as
        (A)The mass of a gas dissolved per unit volume of a solvent is inversely
        proportional to the pressure of the gas in equilibrium with the solution at constant
        temperature.
        (B)The volume of a gas dissolved in a unit volume of solvent at a given temperature
        is independent of the pressure of the gas in equilibrium with the solution at constant
        temperature.
        (C)The mass of a gas dissolved per unit volume of a solvent is inversely
        proportional to the temperature of the gas in equilibrium with the solution at
        constant pressure.
        (D) The volume of a gas dissolved in solvent at a given pressure is independent of
        the temperature.

4.      A mixture of water and toluene is distilled under equilibrium conditions at 1 atm
        pressure. If the vapour pressure of pure water at the equilibrium temperature is 570
        torr, what is the mole fraction of toluene in the distillate.
        (A)0.5                                          (B)0.25
        (C)0.75                                         (D)Insufficient data

5.      How many unit cells are present in a cube– shaped ideal crystal of NaCl of mass
        1.00 g
        [Atomic masses: Na = 23. Cl = 35.5]
        (A)2.57 x 1021 unit cells                   (B)5.14 x 1021 unit cells
        (C)1.28 x 1021 unit cells                   (D)1.71 x 1021 unit cells
                                        Space for Rough Work                                             2
                                                              NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10



6.      2C6H6 (l) + 15O2         (g)  12 CO2(g) + 6H2O (l) H – U = ? (at 298 K)
        (A)+ 7.43 kJ                                        (B)+ 3.72 kJ
        (C) – 7.43 kJ                                       (D)–3.72 kJ

7.      The pyknometric density of sodium chloride crystal is 2.165 x 103 kg m–3 while its
        X–rays density is 2.178 x 103 kg m–3. The fraction of unoccupied sites in sodium
        chloride crystal is
        (A) 5.96 x 10–3                              (B) 5.96
                      –2
        (C) 5.96 x 10                                (D) 5.96 x 10–1

8.      The standard reduction potentials in acidic medium are 0.77V and 0.54V
        respectively for Fe3 / Fe2 and I 3 / I  . The equilibrium constant for the reaction
         2 Fe 3  3I    2 Fe 2  I 3      is    (antilog of 7.7834= 6.25 107 , antilog of
        9.9123= 8.168 109 , antilog of 4.5011= 3.171104 , antilog of 2.1602= 1.446 102 )
        (A) 6.25 107                                       (B) 8.168 109
        (C) 3.171104                                       (D) 1.446 102

                                              SECTION – II
                                Multiple Correct Answer Type
This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices ((A), ((B),
(C)and ((D), out of which ONE OR MORE is/are correct.

9.      Protein is present in :
        (A)Nail                                             (B)Hair
        (C)Wool                                             (D)DNA

10.     The base adenine occurs in :
        (A)DNA                                              (B)RNA
        (C)GTP                                              (D)ATP

11.     Which of the following is a non branched polymer ?
        (A)Low density polythene                   (B)Polyester
        (C)Nylon                                   (D)PVC
12.     Example of plasticizer is
        (A)di–n–butyl phthalate                    (B)di–n–octylphthalate
        (C)cresyl triphosphates                    (D)Styrene

                                           Space for Rough Work                                         3
NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10



                                         SECTION – III
                                   Linked Comprehension Type
This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice
questions have to be answered. Each question has 4 choices ((A), ((B), (C)and (D)out
of which ONLY ONE is correct.

                          Paragraph for Questions Nos. 13 to 15
        Redox reactions play a pivotal role in chemistry and biology. The values of SRP
        (E0) of two half–cell reactions decide which way the reaction is expected to
        proceed.
        A simple example is a Daniel cell in which zinc goes into solution and copper gets
        deposited. Given below are a set of half–cell reactions (acidic medium) along with
        their E0 (with respect to normal hydrogen electrode) values.
        Using this data.
                                I 2  2e   2 I  E 0  0.54
                                Cl2  2e   2Cl  E 0  1.36
                                Mn3  e   Mn 2 E 0  1.50
                                Fe3  e   Fe 2   E 0  0.77
                                O2  4 H   4e   2 H 2O E 0  1.23


13.     Among the following, identify the correct statement:
        (A) Chloride ion is oxidized by O2           (B) Fe2+ is oxidized by iodine
        (C) iodide ions is oxidized by chlorine      (D) Mn2+ is oxidisied by chlorine

14.     While Fe3+ is stable, Mn3+ is not stable in acid solution because:
        (A) O2 oxidises Mn2+ to Mn3+                   (B) O2 oxidises both Mn2+ and Fe2+
        (C) Fe3+ oxidises H2O to O2                    (D) Mn3+ oxidises H2O to O2

15.     The standard reduction potential values of three metallic cations, X, Y, Z are 0.52, –
        3.03 and –1.18V respectively. The order of reducing power of the corresponding
        metal is :
        (A) Y > Z > X                                (B) X > Y > Z
        (C) Z > Y > X                                (D) Z > X > Y




                                        Space for Rough Work                                4
                                                      NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10




                       Paragraph for Questions Nos. 16 to 18

      2 liter of 1 molar solution of a complex salt CrCl3 .6H 2O (mol. wt 266.5) shows an
      osmotic pressure of 98.52 atm at 300K. The solution is now treated with 1 liter of 6
      M AgNO3

16.   Weight of AgCl precipitated is
      (A)861 gm                                     (B)143.5 gm
      (C)287.0 gm                                   (D)574.0 gm

17.   Osmotic pressure of the clear solution that is obtained after removing precipitate is..
      (A)54.28 atm                                  (B)65.68 atm
      (C)75.45 atm                                  (D)95.80 atm


18.   The van't Hoff factor i is :
      (A)1                                          (B)2
      (C) 3                                         (D)4




                                     Space for Rough Work                                      5
NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10


                                              SECTION – IV
                                         Matrix Match Type

 This section contains 2 questions. Each question contains statements given in        p   q   r   s   t
 two columns, which have to be matched. The statements in Column I are            A   p   q   r   s   t
 labeled A, B, C and D, while the statements in Column II are labelled p, q, r,       p   q   r   s
                                                                                  B                   t
 s and t. Any given statement in Column I can have correct matching with
 ONE OR MORE statement(s) in Column II. The appropriate bubbles                   C   p   q   r   s   t
 corresponding to the answers to these questions have to be darkened as               p   q   r   s   t
                                                                                  D
 illustrated in the following example:
 If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s
 and t; then the correct darkening of bubbles will look like the following:


19.     Match the column I and II
                                Column – I                                        Column – II
                                  (Solute)                                  (Van’t Hoff factor, i)

         A     AlCl3 if   0.8                                   P    i = 3.4

         B     BaCl2 if   0.9                                   Q    i = 2.8

         C     Na 3 PO 4 if   0.9                               R    i = 3.8

         D     K4 Fe  CN 6  if   0.7
                                                                S    i = 3.7



20.     Consider the reduction reactions:
                                                                i) Sn2  2e  Sn; ESRP  0.14V
                                                                                     0


                                                                ii) Sn4  2e  Sn2 ; ESRP  0.13V
                                                                                         0




                Column I                                                     Column II
                  0
       A         Esn4 / sn                                             P    –0.005V

       B        Standard oxidation potential of Sn to Sn4+              Q + 0.005V

       C        Disproportionation of Sn2+                              R    Spontaneous
       D        Oxidation of Sn to Sn4+ (1 M)                           S    Non–spontaneous


                                         Space for Rough Work                                             6
                                                               NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10



                                   PART II : MATHEMATICS
                                    Straight Objective Type
This section contains 8 multiple choice questions. Each question has 4 choices ((A), ((B), (C)and ((D), out
of which ONLY ONE is correct.



                                                                  BC       BA       BI
21.     Let I be the incentre of the triangle ABC, where                             then the diameter
                                                                  BC       BA       k
        of the circumcircle of the triangle is
       (A) k(cos A/2 + cos C/2)                              (B) k(sin A/2 + sin C/2)
       (C) k(cot A/2 + cot C/2)                              (D) k (tan A/2 + tan C/2)

22.     The reciprocal of the distance between two points, one on each of the lines
        x 2 y 4 z 5          x 1 y  2 z  3
                          and            
          3      2      5         2     3      4
        (A) cannot be less than 9                            (B) having minimum value 5 3
        (C) cannot be greater than 78                        (D) cannot be 2 19

                                                     x y z
23.                                                      and perpendicular to the
       Equation of the plane containing the straight line
                                                     2 3 4
                                           x y z       x y z
        plane containing the straight lines   and   is
                                           3 4 2       4 2 3
       (A) x + 2y – 2z = 0                       (B) 3x + 2y – 2z = 0
       (C) x – 2y + z = 0                        (D) 5x + 2y – 4z = 0

24.    The distance between the plane x – 2y + z –6 = 0 and the plane containing the sets of
       points
       (1 + 2, 2 + 3, 3 + 4) and (2 + 3, 3 + 4, 4 + 5), where ,  are parameters, is
       (A)    3/ 2                                          (B)    6

       (C) 12                                               (D) 2 6

25.    Three numbers a, b, c are choosen randomly from the set of natural numbers. The
       probability that 'a2 + b2 + c2' is divisible by 7 is
       (A) 1/3                                            (B) 1/4
       (C) 1/5                                            (D) 1/7


                                        Space for Rough Work                                             7
NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10



26.    If the equation z2 + z +  = 0 has a purely imaginary root and  lies on the circle |z| =
       1 then the imaginary part of that root, is (are)
       (A)  2                                                             (B) 0
                                                                                     5 1
       (C)  2  2                                                         (D)       2
27.    Let z (, ) = cos + ei sin (, R, i =                          1 ) then the exaustive set of values of
       modulus of z(, 2), as  varies, is
       (A) [0, 1]                                                          (B) [0, 2 ]
       (C) [1, 2]                                                          (D) [ 2 , 2]

28.    If |z| = 1 and z  1 then one of the possible values of arg(z) – arg (z + 1) – arg (z –
       1), is
       (A) –/6                                       (B) /3
       (C) –/2                                       (D) /4

                                                             SECTION – II
                                        Multiple Correct Answer Type
This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices ((A), ((B),
(C)and ((D), out of which ONE OR MORE is/are correct.


                                            n
                                                             Cr 2r 1
                                                             n
        Let for nN, f (n)    1
                                                    r
29.                                                                       then
                                        r 0             r  1 r  2 
        (A)f(2n) = f(2n + 1)                                               (B) f(n) = f(n + 1)
        (C) f(2n) = f(2n – 1)                                              (D) f(2011) = f(2012)

30.     Let k1, k2 be two integers such that (n – a)! = (n – b)!, 2a + b + 1 = k1n + k2  n
        where a  b  n and a, b, n  N . Let P and Q be two points on the curve
         y  log1/2  x  k 2 / 2  log2    4x  4k x  k  k  Point P also lies on the circle x
                                                2
                                                         2       l   2 .
                                                                                                        2
                                                                                                            + y2 = k13

        – 2k2, however Q lies inside the circle such that its abscissa is an integer then
        (A)The values of k1 and k2 are respectively 2 and –1
        (B) maximum value of OP.OQ is 7
        (C) minimum value of PQ is 1

        (D) minimum value of OP . OQ is 3

                                                    Space for Rough Work                                            8
                                                                        NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10




31.   Let OABC be a tetrahedron whose four faces are equilateral triangles of unit side.
      Let OA  a , OB  b and OC  c , then
             1
             3
                  
      (A) c  a  b  2 2 a  b                      1
                                              (B) c  a  b  2 3 a  b
                                                       2
                                                                                                    
                                        1                      1
      (C) volume of the tetrahedron is        (D) a b c  
                                                         
                                       2 3                      2



32.                                                              
      If a, b, c, d are unit vectors such that a  b . c  d  1 and a.c                  1
                                                                                            2
                                                                                              then

      (A) a, b, c are non coplanar                                     (B) b, d are non parallel
      (C) b, c, d are coplanar                                         (D) a, d are parallel and b, c are
                                                                           parallel

                                  SECTION – III
                            Linked Comprehension Type
This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice
questions have to be answered. Each question has 4 choices ((A), ((B), (C)and (D)out
of which ONLY ONE is correct.
                         Paragraph for Questions Nos. 33 to 35
                                                                          1 x 
      Consider a G.P. with first term 1  x  ,  x  1 , common ratio 
                                              n
                                                                                 and number
                                                                          2 
      of terms (n+1). Let ‘S’ be sum of all the terms of the G.P., then

33.   ‘S’ equals
                                                           m
           1
      (A) n  2n 1 1  x   1  x   . lim           x
                            n          2n 1                      k

           2                                 m        k 0
                                                            m
             1  n 1
                   2 1  x   1  x   . lim          x
                             n 1       2n
       (B)     n 
                                                                   k

             2                              m           k 0
                                                           m
             1  n
                   2 1  x   1  x   . lim          x
                             n 1       2n 1
      (C)      n 
                                                                  k

             2                                 m       k 0
                                                    m
             1  n
                   2 1  x   1  x   . lim   x
                             n          2n
      (D)      n 
                                                            k

             2                              m   k 0


                                          Space for Rough Work                                                   9
NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10


34.      The coefficient of xn in 'S' is
        (A) 2n                                            (B) 2n+1
        (C) 22n                                           (D) 22n+1

                         r
          n
                   1
35.      Cr  2  equals
         r 0
              nr

                    
                 n
        (A) (3/4)                                         (B) 1
        (C) 2n                                            (D) 3n
                             Paragraph for Questions Nos. 36 to 38
        All the 52 cards of a well shuffled pack of playing cards are distributed equally or
        unequally among 4 players named P1, P2, P3 & P4 .
        For i = 1, 2, 3, 4, let
        i = number of ace(s) given to Pi
        i = number of black card(s) given to Pi
        i = number of red card(s) given to Pi
        i = number of diamond(s) given to Pi

36.     The probability that i  1  i = 1, 2, 3, 4, is
                    4!
        (A) 13C4 × 13
                    4
              24
        (B) [2 + 3 × 212 – 313 – 1]/224
        (C) [134 – 4C1 124 + 4C2 114 – 4C3 104 + 4C4 94]/134
        (D) 1 – 4(3/4)13 – 6 (1/2)13 – (1/4)12

37.     If i + i = 13  i = 1, 2, 3, 4 then the probability that i = 1  i = 1, 2, 3, 4, is
                                                                    133
        (A) 54 72 /134                                    (B)
                                                                17  7 2  52
                                                              7 3  32
        (C) 34 132 /174 27                                (D)
                                                                134
38.     If i + i = 13  i = 1, 2, 3, 4 then the probability that |i – i| = 1 i = 1, 2, 3, 4, is
                              2                                                    2
             26!   52!                                     (26!) (4!)   52! 
        (A)      2    2
                               4
                                                          (B)      2    2    2
                                                                                      4
             (6!) (7!)   (13!)                             (6!) (7!) (2!)   (13!) 
                                    2                                                  2
                      26!        52!                                26!        52! 
        (C) 4!      2    2    2
                                       4
                                                          (D) 4!      2     2          4
                (6!) (7!) (2!)   (13!)                        (6!) (7!) (2!)   (13!) 
                                        Space for Rough Work                                           10
                                                                NPT-4_Paper-I_(CODE: CHANCH) Ex Dt:12-12-10


                                             SECTION – IV
                                         Matrix Match Type
 This section contains 2 questions. Each question contains statements given in        p   q   r   s   t
 two columns, which have to be matched. The statements in Column I are            A   p   q   r   s   t
 labeled A, B, C and D, while the statements in Column II are labelled p, q, r,       p   q   r   s
                                                                                  B                   t
 s and t. Any given statement in Column I can have correct matching with
 ONE OR MORE statement(s) in Column II. The appropriate bubbles                   C   p   q   r   s   t
 corresponding to the answers to these questions have to be darkened as               p   q   r   s
                                                                                  D                   t
 illustrated in the following example:
 If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s
 and t; then the correct darkening of bubbles will look like the following:


39.     Match the following
                      n
                                 2k             n 1
                                                                           2k   
        Let f (n)   n C k cos       and g(n)             n 1
                                                                   Ck cos         , then
                    k 0         n               k 0                    n     


              Column –I                                      Column –II
       (A) f(n) is                                    (p) A rational number
       (B) f(6) is                                    (q) An irrational number
       (C) g(6) is                                    (r)    –27
       (D) g(8) is                                    (s)    2g(n + 2)
                                                      (t)    2g(n)


40.     Let n(P) represents the number of points P() lying on the rectangular hyperbola
        xy = 15!, under the conditions given in column I, match the value of n(P) given in
        column II.
               Column –I                                     Column –II
        (A)  ,   I                                  (p) 32
        (B)     ,   I and HCF ( ,  )  1         (q) 64

        (C)     ,   I  and  divides              (r)   96

        (D)  ,   I and HCF ( ,  )  35           (s)   4032

                                                       (t)   8064


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                                         PART III : PHSICS


                                              SECTION – I
                                     Straight Objective Type
This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C)and ((D), out of
which ONLY ONE is correct.



41.                                                                            ˆ
        In region x > 0, a uniform and constant magnetic field B1  2B0 k exists.
                                                                      ˆ
        Another uniform and constant magnetic field B2  B0 k exists in region
        x < 0. A positively charged particle of mass m and charge q i s crossing
        origin at time t = 0 with a velocity u  u 0 ˆ . The particle comes back to
                                                         i
        its initial position after a time : (B 0 , u 0 are positive constants)
                  3 m
        (A)
                  2 q B0
                  2 m
        (B)
                  q B0
                  3m
        (C)
                  q B0
        (D)      Particle does not come back to its initial position.

42.     In the circuit shown the capacitor has charge Q. At t = 0 sec the key K is closed to
        complete the circuit. The charge on the capacitor at the instant potential difference
        across the inductor L1 is zero.




                                                                   Q
        (A) Q                                                (B)
                                                                   3
              2Q
        (C)                                                  (D) 0.
               3




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43.   In the ideal oscillating circuit, the capacitance of the capacitor is 25 F
      and has initial charge of 30 C. The inductance of coil is 0.04 H. The
      maximum magnitude of current in the circuit, after closing the switch K
      is




      (A) 10 mA                                     (B) 30 mA
      (C) 60 mA                                     (D) 3 mA

44.   A parallel beam of light of intensity I and cross section area S is incident on a plate
      at normal incidence. The photoelectric emission efficiency is 100%, the frequency
      of beam is  and the work function of the plate is  (h > ). Assuming all the
      electrons are ejected normal to the plane and with same maximum possible speed.
      The net force exerted on the plate only due to striking of photons and subsequent
      emission of electrons is
           S 2h
                                                       2S h
                                                                           
      (A) h    2m(h  )                      (B) h    2m(h  ) 
                                                                         
          S  h                                        2S h
                                                                          
      (C) h    2m(h  )                      (D) h    m(h  ) 
                                                                        

45.   Electrons in a sample of gas containing hydrogen like atom (Z=3) are in
      fourth excited state. When photons emitted only due to transition from
      third excited state to second excited state are incide nt on a metal plate
      photoelectrons are ejected. The stopping potential for these
      photoelectrons is 3.95 eV. Now, if only photons emitted due to transition
      from fourth excited state to third excited state are incident on the same
      metal plate, the stopping potential for the emitted photoelectrons wil l be
      approximately equal to
      (A) 0.85 eV                             (B) 0.75 eV
      (C) 0.65 eV                             (D) None of these




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                                                                            
46.     A point object Q moves along line BA with velocity u towards focus F of the
        concave mirror. AD is line parallel to the principal axis OP and the shown angle  is
        very small. If  is the image of the point object Q at the shown instant, then the
        velocity vector of image  is given by




                                                                                             
        (A)   v1                     (B)   v2          (C)   v3                           (D)   v4 .

47.     A pendulum of length ‘’ is free to oscillate in vertical plane about point
        O. An observer is viewing the bob of the pendulum directly from above.
        The pendulum is performing small oscillations in water (refractive index
        is µ) about its equilibrium position. The equation of trajectory of bob as
        seen by observer is :




                                                                   x2        y2
        (A) µ 2 x 2 + y 2 = 2                                (B)        +        =1
                                                                    2
                                                                            µ2 2
                                                                                      2
              x2           y2                                                 
        (C)        +                =1                       (D) x 2 + y 2 =  
                          
               2                2
                                                                             µ
48.     While measuring length of an object, it was observed that the zero of the
        vernier lies between 1.4 and 1.5 of the main scale and the fifth vernier
        division coincides with a main scale division. If the length of the object
        measured is , then the value of (– 1.4) in terms of the least count C of
        the instrument is
        (A) C                                   (B) 1.45 C
        (C) 4 C                                 (D) 5 C.

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                                    SECTION II
                               Multiple Correct Choice Type
This section contains 5 multiple correct answer(s) type questions. Each question has 4
choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct.

49.    A beam of light having frequency is incident on an initially neutral
       metal of work function (h > ). Then
       (A) all emitted photoelectrons have kinetic energy equal to (h  – ).
       (B) all free electrons in the metal, that absorb photons of energy h 
           completely, may not be ejected out of the metal.
       (C) after being emitted out of the metal, the kinetic energy of
          photoelectrons decreases continuously as long as they are at a finite
          distance from metal.
       (D) the emitted photo electrons move with constant speed after being
           ejected out of metal.



50.    Pick up the correct statements :
       (A) Due to the time varying magnetic field in a certain region an induced
           electric field may be produced in a region where that magnetic field
           is not present.
       (B) A uniform magnetic field increasing at constant rate, induces an
           electric field which is constant and non conservative.
       (C) Non zero force exerted by uniform and constant magnetic field on a
           moving charged particle does no work but always changes
           momentum of the particle.
       (D) All the above statements are wrong.




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51.     A conducting rod of length     is moved at constant velocity ‘v 0 ’ on two
        parallel, conducting, smooth, fixed rails, that are placed in a uniform
        constant magnetic field B perpendicular to the plane of t he rails as
        shown in figure. A resistance R is connected between the two ends of the
        rail. Then which of the following is/are correct :


                                         R    XB        V0
                                                      X
                                              x

        (A) The thermal power dissipated in the resistor is equal to rate of work
           done by external person pulling the rod.
        (B) If applied external force is doubled than a part of external power
           increases the velocity of rod.
        (C) Lenz’s Law is not satisfied if the rod is accelerated by external force
        (D) If resistance R is doubled then power required to maintain the
           constant velocity v 0 becomes half.


52.     A point object 'O' is placed at focus of a diverging lens of focal length ' f
        '. When a converging lens of focal length (f/2) is placed in between
        object and lens at distance f/2 from diverging lens then:

        (A) The final image will be found at second focus of the converging lens
        (B) Final image will be formal on the object itself.
        (C) Final image is real.
        (D) Final image is virtual




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                                   Section III
                               Comprehension Type
This section contains 2 groups of questions. Each group has 3 multiple choice questions
based on a paragraph. Each question has 4 choices (A), (B), (C) and (D) out of which
ONLY ONE is correct.
                        Paragraph for Question Nos. 53 to 55
       A particle (1) having positive charge q and mass m is moving along
                                     ˆ
       x–axis with a velocity v  v 0 i in space having uniform and constant
                         
                         B  B0 ˆ
                                i
       magnetic field         , where v 0 and B 0 are positive constants. At
       time t = 0 second, the moving particle (1) strikes another stationary
       uncharged particle (2) of mass m lying at origin, as shown in figu re
       (i). The collision is perfectly elastic and the uncharged particle (2)
       after collision moves along a straight line (in x –y plane) making an
       angle 45° with positive x–axis, as shown in figure (ii). Assume that
       there is no transfer of charge between the p articles during
       collision.




53.    The time period of revolution of charged particle (after t = 0
       second) is
             2 m                                            2 2 m
       (A)                                         (B)
              qB                                               qB
              m
       (C)                                         (D) None of these
              2q B
54.    The minimum time after t = 0, at which the charged particle
       touches x–axis is
                                                           2 2 m
              m                                             qB
       (A)                                         (B)
              2q B
             2 m
       (C)
              qB
       (D) After t = 0 charged particle does not touch x –axis.

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55.     The minimum time after t = 0, at which velocity of both particles
        are parallel is
            m                                     2 m
        (A)                                 (B)
            qB                                     qB
              m
        (C)
            2 2q B
        (D) Velocities of both cannot be parallel.

                             Paragraph for Question Nos. 56 to 58
        The radionuclide 56 Mn is being produced in a cyclotron at a
        constant rate P by bombarding a maganese target with deutrons.
        56 Mn has a half life of 2.5 hours and the target contains large
        number of only the stable maganese isotope 55 Mn. The reaction
        that produces 56 Mn is :
        55 Mn + d  56 Mn + p
        After being bombarded for a long time, the activity of      56 Mn
        becomes constant equal to 13.86 × 10 10 s –1 . (Use ln2 = 0.693;
        Avogadro No = 6 × 10 23 ; atomic weight 56 Mn = 56 gm/mole)

56.     At what constant rate P, 56 Mn nuclei are being produced in the
        cyclotron during the bombardment ?
        (A) 2 × 10 11 nuclei/s            (B) 13.86 × 10 10 nuclei/s
        (C) 9.6 × 10 10 nuclei/s          (D) 6.93 × 10 10 nuclei/s

57.     After the activity of 56 Mn becomes constant, number of 56 Mn
        nuclei present in the target, is equal to
        (A) 5 × 10 11                         (B) 20 × 10 11
        (C) 1.2 × 10 14                       (D) 1.8 × 10 15

58.     After a long time bombardment, number of 56 Mn nuclei present in
        the target depends upon
        (a) the number of 56 Mn nuclei present at the start of the process.
        (b) half life of the 56 Mn
        (c) the constant rate of production P.

        (A) All (a), (b) and (c) are correct           (B) only (a) and (b) are correct
        (C) only (b) and (c) are correct               (D) only (a) and (c) are correct

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                                             SECTION – IV
                                         Matrix Match Type
                                                                                              p   q   r   s   t
 This section contains 2 questions. Each question contains statements given in two
                                                                                          A   p   q   r   s   t
 columns, which have to be matched. The statements in Column I are labeled A, B, C
                                                                                          B   p   q   r   s   t
 and D, while the statements in Column II are labelled p, q, r, s and t. Any given
                                                                                          C   p   q   r   s   t
 statement in Column I can have correct matching with ONE OR MORE
 statement(s) in Column II. The appropriate bubbles corresponding to the answers to       D   p   q   r   s   t

 these questions have to be darkened as illustrated in the following example:
 If the correct matches are A – p, s and t; B – q and r; C – p and q; and D – s and t;
 then the correct darkening of bubbles will look like the following:
59.      Column–I gives certain situations regarding a point object and its image
        formed by an optical instrument. The possible optical instruments are
        concave and convex mirrors or lenses as given in Column–II. Same side of
        principal axis means both image and object should either be above the
        principal axis or both should be below the principal axis as shown in figure.
        Same side of optical instrument means both image and object should be
        either left of the optical instrument or both should be on right of the optical
        instrument as shown in figure. Match the statements in column–I with the
        corresponding statements in column–II and indicate your answer by
        darkening appropriate bubbles in the 4 × 4 matrix given in OMR.




                               Column A                                                  Column B
(A) If point object and its image are on same side of (p) Concave mirror
    principal axis and opposite sides of the optical
    instrument then the optical instrument is
(B) If point object and its image are on opposite side of (q) Convex mirror
    principal axis and same sides of the optical
    instrument then the optical instrument is
(C) If point object and its image are on same side of                           (r)      Concave lens
    principal axis and same sides of the optical
    instrument then the optical instrument is
(D) If point object and its image are on opposite side of                      (s) Convex lens
    principal axis and opposite sides of the optical
    instrument then the optical instrument is
                                                                                (t)      Both convex
                                                                                         lens and
                                                                                         concave mirror
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60.     Four different circuit components are given in each situation of
        column–I and all the components are connected across an ac
        source of same angular frequency = 200rad/sec. The information
        of phase difference between the current and source voltage in
        each situation of column–I is given in column–II. Match the circuit
        components in column–I with corresponding results in column –II.
              Column A                             Column B
(A)                                  (p) the magnitude of required phase
                                                       
                                         difference is
                                                       2
(B)                                  (q) the magnitude of required phase
                                                       
                                         difference is
                                                       4
(C)                                  (r) the current leads in phase to
                                         source voltage
(D)                                  (s) the current lags in phase to
                                         source voltage
                                     (t) Current and source voltage are
                                         in same phase




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