NPT-2_NEW_20-11-2010 by nehalwan

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									                                                                                                                                              CODE          GREEN




                                                       NARAYANA
                                                        GROUP OF EDUCATIONAL INSTITUTIONS
                                           ALL INDIA TEST SERIES (AIEEE)

                                   NARAYANA PART TEST- 2
                                                                                                          Exam date: 20-11-2010

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

                          INSTRUCTIONS                                                    C.      Question paper format:
A.   General:                                                                                     11.   The question paper consists of 3 parts (Part I: Physics:, Part
     1.     This booklet is your Question Paper containing 90 questions.                                II: Chemistry, Part III: Mathematics). Each part has 3
     2.     The question paper CODE is printed on the right hand top                                    sections.
            corner of this booklet.                                                               12.   Section I contains 12 multiple choice questions. Each question
     3.     Blank papers, clipboards, log tables, slide rules, calculators,                             has 4 choices (A), (B), (C) and (D), out of which only one is
            cellular phones, pagers, and electronic gadgets in any form are                             correct.
            not allowed to be carried inside the examination hall.                                13.   Section II contains 6 multiple choice questions. Each question
     4.     The answer sheet, a machine–readable Objective Response                                     has 4 choices (A), (B), (C) and (D), out of which only one is
            Sheet (ORS), is provided separately.                                                        correct.
     5.     DO NOT TAMPER WITH / MUTILATE THE ORS OR THE                                          14.   Section III contains 12 multiple choice questions. Each
            BOOKLET.                                                                                    question has 4 choices (A), (B), (C) and (D), out of which only
                                                                                                        one is correct.
B.   Filling the ORS
     6.     On the lower part of the ORS, write in ink, your name in box L1,
            your Registration No. in box L2 and Name of the Centre in box                 D.      Marking Scheme
            L3. Do not write these anywhere else.                                                 15.   For each question in Section – I, you will be awarded 3 marks
     7.     Write your Registration No. in ink, in the box L4 provided in the                           if you have darkened only the bubble corresponding to the
            lower part of the ORS and darken the appropriate bubble                                     correct answer and zero mark if no bubble is darkened. In case
            UNDER each digit of your Registration No. with a good quality                               of bubbling of incorrect answer, minus one (–1) mark will be
            HB pencil.                                                                                  awarded.
     8.     The ORS has a CODE printed on its lower and upper parts.                              16.   For each question in Section II, you will be awarded 8 marks if
                                                                                                        you have darkened only the bubble(s) corresponding to the
     9.     Make sure the CODE on the ORS is the same as that on this                                   correct answer and zero mark if no bubble is darkened. In case
            booklet and put your signature in ink in box L5 on the ORS                                  of bubbling of incorrect answer, minus one (–2) mark will be
            affirming that you have verified this.                                                      awarded.
     10.    IF THE CODES DO NOT MATCH, ASK FOR A CHANGE OF                                        17.   For each question in Section III, you will be awarded 4 marks
            THE BOOKLET.                                                                                if you have darkened only the bubble corresponding to the
                                                                                                        correct answer and zero mark if no bubble is darkened. In case
                                                                                                        of bubbling of incorrect answer, minus one (–1) mark will be
                                                                                                        awarded.




                                                              The distribution of marks in each subject is as under
                                                                                                      FOR CORRECT                            FOR WRONG
                         SUBJECT                                  QUESTIONS                              ANSSWER                               ANSWER
                                                                    1 to 12                                   +4                                   -1
                         PHYSICS                                    13 to 18                                  +8                                   -2
                       (144 MARKS)                                  19 to 30                                  +4                                   -1
                                                                    31 to 42                                  +4                                   -1
                       CHEMISTRY                                    43 to 48                                  +8                                   -2
                       (144 MARKS)                                  49 to 60                                  +4                                   -1
                                                                    61 to 72                                  +4                                   -1
                     MATHEMATICS                                    73 to 78                                  +8                                   -2
                       (144 MARKS)                                  79 to 90                                  +4                                   -1


                                     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-II (AIEEE MOD) 20-11-2010




                                          PHYSICS
1.      Two uniform metal rods of lengths                l1 and l2 and   linear coefficients
        of expansion        1 and 2 respectively are connected to form a single
        rod of length l1  l2 . When the temperature of the combined rod is
        raised by tºC, the length of each rod increases by the same
                                  2
        amount. Then                     is
                                1   2
               l1                                             l1  l2
        (1)                                               (2)
            l1  l2                                              l1
               l2                                              l1  l2
        (3)                                               (4)
            l1  l2                                               l2
2.      A pendulum clock runs fast by 5 seconds per day at 20ºC and goes
        slow by 10 seconds per day at 35ºC. It shows correct time at a
        temperature of
        (1) 27.5ºC                          (2) 25ºC
        (3) 30ºC                             (4) 33ºC

3.      A specific gravity bottle contains m grams of liquid of apparent
        expansion  a at 0ºC. When it is heated to tºC the mass of liquid
        expelled is
           1  a t                                           am
        (1)                                               (2)
             a mt                                           1 at
             mt                                               mt
        (3) a                                             (4) a
           1 at                                            1  a t

4.      When a monoatomic gas expands at constant pressure the
        percentage of heat supplied that increases the internal energy of
        the gas and that which is involved in expansion respectively is
        (1) 75%, 25%                               (2) 25%, 75 %
        (3) 60%, 40%                               (4) 40%, 60%
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                                                                  NPT-II (AIEEE MOD) 20-11-2010




5.      Match the following
         Column-I (Process)                     Column II( Workdone )
     (a )     Isothermal process         ( p ) W=0
     (b )     Adiabatic process          (q)                   1
                                                 W                P V  P V 
                                                              1 1 1 2 2
     (c )     Isobaric process           (r)     W  P  V2  V1 
     (d )     Isochoric process          (s)
                                                               V 
                                                 W  nRT log e  2 
                                                                V1 
        (1) a  p;b  q;c  r;d  s                 (2) a  q;b  s;c  r;d  p
        (3) a  r;b  p;c  r;d  q                 (4) a  s;b  q;c  r;d  p


                                                                          7
6.      The pressure and density of a given mass of a diatomic gas   
                                                                          5
                                                                            
                                                                      1
                                                        d1           P
                                             1 1
        change adiabatically from (p,d) to (p ,d ) . If     32 then    is
                                                        d            P
        (  = ratio of specific heats)
               1                                           1
        (1)                                         (2)
              128                                          64
        (3) 64                                      (4) 128


7.      30g of ice at 0ºC and 20g of steam at 100ºC are mixed. The
        composition of the resultant mixture is
        (1) 40g of water and 10g steam at 100ºC
        (2) 10g of ice and 40g of water at 0ºC
        (3) 50g of water at 100ºC
        (4) 35g of water and 15g of steam at 100ºC

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NPT-II (AIEEE MOD) 20-11-2010




8.      A Carnots engine whose sink is at a temperature of 300K has an
        efficiency of 40%. The increase in temperature of the source, so
        that the efficiency of that engine increases to 60% is
        (1) 250 K                              (2) 275 K
        (3) 300 K                              (4) 325 K


9.      During an experiment an ideal gas is found to obey an additional
        law V P  constant. The gas is initially at a temperature T and
              2

        volume V. When it expand to a volume 2V, the temperature
        becomes
        (1) T                               (2) 2T
                                                       T
        (3) T 2                                 (4)
                                                       2


10.     An open pipe is suddenly closed at one end, as a result of which
        the frequency of the third harmonic of the closed pipe is found to
        be higher by 100 Hz than the fundamental frequency of the open
        pipe. The fundamental frequency of the open pipe is
        (1) 200 Hz                          (2) 300 Hz
        (3) 240 Hz                          (4) 480 Hz


11. The vibrations of a string of length 600 cm fixed at both ends are
                                                    x 
      represented by the equation         y  4sin   cos  90t  cm . The
                                                    15 
      maximum displacement of a point at x = 5 cm is
      (1) 3cm                                    (2) 2 3cm
           3
      (3)    cm                                  (4) 3 3cm
          2


                                Space for rough work                           4
                                                             NPT-II (AIEEE MOD) 20-11-2010




12. A motor boat with a sound source is moving across the river at 90ºC
                                            1
    to the flow of water with a velocity12ms . Width of river is 169m
                                                        1
      and the velocity of stream in the river is 5ms . Stationary observer
      is on one bank of the river. At t = 0, the motor boat starts from the
      other bank. The observer will hear actual frequency released by the
      source after a time of




       (1) 10 S                                  (2) 12 S
       (3) 8 S                                   (4) 6 S

13.    On a smooth inclined plane a body of M is attached between two
       springs. The other ends of the springs are fixed to firm supports. If
       each spring has a force constant K, the period of oscillation of the
       body is(Assume the springs as massless)




              M                                                2M
       (1) 2                                           (2) 2
              2K                                                K
              Msin                                            2Msin 
       (3) 2                                           (4) 2
               2K                                                 K
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NPT-II (AIEEE MOD) 20-11-2010




14.     The relation between internal energy U, pressure P and volume V
        of a gas in an adiabatic process is:
        U=a + bPV where a and b are constants. The value of the ratio of
        the specific heats is
            a                                         b 1
        (1)                                       (2)
            b                                           b
            a 1                                      b
        (3)                                       (4)
              a                                       a

15.     The apparent coefficient of expansion of liquid, when heated in a
        copper vessel is C and when heated in a silver vessel is S. If A is
        the linear coefficient of expansion of copper, linear expansion
        coefficient of silver is
            C  S  3A                                C  3A  S
        (1)                                       (2)
                 3                                         3
            S  3A  C                                C  S  3A
        (3)                                       (4)
                 3                                         3


16.     The length of a potentiometer wire is l. A cell of EMF E is balanced
                   ' l'
        at a length     from the positive end of the wire. If the length of the
                    5
                               l
        wire is increased by     , the new balancing length with the same
                               2
        cell is
             2                                         3
        (1)    l                                  (2)    l
            15                                        15
             3                                         4
        (3)    l                                  (4)    l
            10                                        10



                                  Space for rough work                            6
                                                             NPT-II (AIEEE MOD) 20-11-2010




17.   A rectangular coil of single turn, having area A, rotates in a
      uniform magnetic field B with an angular velocity  about an axis
      perpendicular to the field. If initially the plane of wire is
      perpendicular to the field, then the average induced emf when
      rotated through 900 is
          2BA                                      BA
      (1)                                       (2)
                                                    4
          BA                                       BA
      (3)                                       (4)
           2                                         
18.   A rod of length L has a total charge Q distributed along its length,
      it is bent in the shape of a semicircle. The magnitude of the electric
      field at the centre of curvature of the semi circle is
            Q2                                         Q
      (1)                                       (2)
          2 0 L2                                   2 0 L
             Q                                        Q
      (3)                                       (4)
          2 0 L2                                   0 L2

19.   Three charges Q, + q and + q are placed at the vertices of a right
      angle triangle (isosceles triangle) as shown. The net electrostatic
      energy of the configuration is zero, if Q is equal to :




           q                                         2q
      (1)                                       (2)
          1 2                                      2 2
      (3) 2q                                   (4)  q

                                Space for rough work                                         7
NPT-II (AIEEE MOD) 20-11-2010




20.     A parallel plate capacitor filled with a dielectric of relative
        permittivity 5 between its plates is charged to acquire an energy E
        and isolated. If the dielectric is replaced by another of relative
        permittivity 2, its energy becomes
        (1) E                                 (2) 0.4 E
        (3) 2.5 E                             (4) 6.25 E
21.     In the part of the circuit given below, potential difference between
        the points M and N is




        (1) 8V                                             (2) 7V
        (3) 6V                                             (4) 9V

22.     Six spokes of resistance r each are connected between the axle and
        the rim of a wheel. If r  2 and a 2V battery is connected
        between the rim and the axle. The power consumed is (neglect
        resistance of the rim)
        (1) 24W                              (2) 12W
        (3) 6W                               (4) 3W

23.     In wheat stones bridge in the four arms, four conductors of lengths
        l1 ,l2 ,l3 ,l4 and areas of cross-section a1 ,a2 ,a3 ,a4 are connected to
        balance. If their resistivities are          1 ,  2 ,  3 and  4 respectively, then
        (1) 1  4 1  4   2  3l2 l3              (2) 1  4l1 l4 a1 a4   2  3l2 l3 a1 a4
        (3) 1  4l1 l4 a1 a2   2  3l2 l3 a3 a4     (4) 1 4 l1 l4 a 2 a 3  2 3l2 l3a 1 a 4

24.     An ideal inductor draws a current of 12.5A when connected to an
        alternating source 250V, 50Hz. A pure resistance across the same
        source draws a current of 25A. If the resistor and inductor are
        connected in series with same source, then the current in circuit is
        (1) 8.3A                             (2) 12.5A
        (3) 5 5 A                                          (4) 10 5 A
                                           Space for rough work                                      8
                                                               NPT-II (AIEEE MOD) 20-11-2010




25.   A metal conductor of length 1m rotates vertically about one of its
      ends at angular velocity 5 rad/sec. If the horizontal component of
                                         4
      earth’s magnetic field is 0.2  10 T , then the emf developed
      between the two ends of the conductor is
      (1) 5V                              (2) 50 V
      (3) 5mV                                   (4) 50mV

26.   A transformer has primary, secondary turns ratio 1:2. Its efficiency
      is 80%. When 50V battery is connected in the primary, then
      voltage across the secondary is
      (1) 92V                            (2) 40V
      ((3) 80V                           (4) 0V

27.   When a conductor in the form of wire is connected in the left gap
      and known resistance in the right gap of a metre bridge. The
      balancing length is 50cm. If the wire is stretched so that its length
      is increased by 100% then the new balancing length is (in cm)

      (1) 70                                    (2) 20
      (3) 80                                    (4) 60

28.   An inductor of 1H is connected across a 220 V, 50 Hz supply. The
      peak value of current is approximately

      (1) 0.5 A                                 (2) 1 A
      (3) 4 A                                   (4) 6 A

29.   An alternating emf E = 100 sin (100  t) is connected to a choke of
      negligible resistance and current oscillations with a amplitude 1A
      are to be produced. The inductance of the choke should be
                                                       1
      (1) 100 H                                 (2)        H
                                                   
      (3) 1 H                                   (4)  H

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NPT-II (AIEEE MOD) 20-11-2010




30.     When a 30 V dc source is connected to L-R series with ammeter,
        2A current is recorded. When 30 V ac source of frequency 100 Hz
        is connected a current 1.2A is recorded. The inductance reactance
        is
        (1)100                             (2) 20 
        (3) 5 34                                  (4) 40 


                                   CHEMISTRY

31.     The boiling point of C6 H 6 ,CH 3OH ,C6 H 5 NH 2 and C6 H 5 NO2 are
        80 ºC, 65ºC, 184ºC and 212ºC respectively. Which will show
        highest vapour pressure at room temperature?
        (1) C6 H 6                              (2) CH 3OH
        (3) C6 H 5 NH 2                            (4) C6 H 5 NO2

32.     In the electrolysis of Na2 SO4 solution using inert electrodes
        a) the anodic reaction is
                 2H 2O  O2 g   4e  4H 
        b) H 2 g  and O2 g  is produced in a molar ratio of 2:1
        c) 23 grams of sodium is produced at the cathode
                                                
        d) the cathode reaction is Na  e  Na
        (1) a and b are correct                    (2) c, d are correct
        (3) Only c is correct                      (4) All are correct

33.     d-block elements form complexes because they have:
        (1) Vacant orbitals                (2) Small sizes
        (3) Higher nuclear charge          (4) All of the above

34.     If 20ml of 0.4M – NaOH solution completely neutralized
        by 40ml of a dibasic acid, the molarity of the acid
        solution is
        (1) 0.1 M                                     (2) 0.2 M
        (3) 0.3 M                                     (4)
                                     Space for rough work 0.4 M               10
                                                            NPT-II (AIEEE MOD) 20-11-2010




35.   Which of the following type of forces are present in natural rubber?
      (1) Weakest intermolecular forces           (2) Hydrogen bonding
      (3) Three dimensional network of bonds      (4) Metallic bonding

36.   A metal in its highest oxidation state can acts as
      (1) A reducing agent
      (2) An oxidising agent
      (3) An oxidizing agent and reducing agent
      (4) Neither oxidising agent nor reducing agent

37.   The standard reduction potential of three metals X, Y, Z are 0.52,
      -3.03 and -1.18V respectively. The order of reducing power of the
      corresponding metals is
      (1) Y > Z > X                       (2) X > Y > Z
      (3) Z > Y > X                       (4) Z > X > Y

38.   Which of the following monomer in excess makes PHBV more
      flexible
      (1)  - hydroxy butanoic acid      (2)  - hydroxy butanoic acid
      (3)  -hydroxy pentanoic acid      (4)  - hydroxy pentanoic acid

39.   Chlorine gas can be dried by passing over
      (1) Quick lime                     (2) Soda lime
      (3) Caustic potash sticks          (4) Concentrated sulphuric acid

40.   Oxides of sulphur present in the atmosphere are washed down by
      rain and will result in
      (1) Lowering of pH of the soil      (2) Increase in pH of the soil
      (3) Increase in O3 quantities       (4) Increase in population

41.   The important features of genetic code are
      a) It is universal                b) It is comma less
      c) It is degenerate
      d) The third base in the codon is not always specific
      Find the correct one
      (1) a only                                 (2)
                                Space for rough work b, c only                              11
      (3) b, c and d only                        (4) all a, b, c and d
NPT-II (AIEEE MOD) 20-11-2010




42.     What structural feature distinguishes proline from other natural
         - amino acids
        (1) It is optically inactive
        (2) It contains aromatic group
        (3) It is a di carboxylic acid
        (4) It has a secondary amine group

43.     Following solutions at the same temperature will be isotonic
        (1) 3.42 g of cane sugar in one litre water and 0.18 g of glucose in
            one litre water
        (2) 3.42 g of cane sugar in one litre water and 0.18 g of glucose in
            0.1 litre water
        (3) 3.42 g of cane sugar in one litre water and 0.585 g of NaCl in
            one litre water
        (4) 3.42 g of cane sugar in one litre water and 1.17 g of NaCl in one
            litre water
        Equivalent conductance at infinite dilution,  of NH4Cl, NaOH
                                                           0
44.
                                                        1   2   1
        and NaCl are 128.0,217.8 and 109.9 ohm cm eq      respectively.
        The equivalent conductance of 0.01 N NH4OH is 9.30
        ohm1cm2eq1 , then the degree of ionization of NH4OH at this
        temperature would be (approximately)
        (1) 0.04                                (2) 0.1
        (3) 0.4                                 (4) 0.62

45.     Which of the following is not a draw back of Werners theory
        (1)Does not explain the valency of metal ions in the complex
        (2)Does not give any explanation for the colour of complex
           compounds
        (3)Does not explain the magnetic behaviour of complex compounds
        (4)Does not correlate electronic configuration of the metal with the
           formation of complex.

46.     Hypo solution reacts with chlorine gas the products formed are
        (1) Na2 S4O6  NaCl                  (2) Na2 SO4  S  HCl
        (3) Na2 SO4  NaCl                       (4) Na2 SO4  SO2  HCl
                                 Space for rough work                           12
                                                             NPT-II (AIEEE MOD) 20-11-2010




47.   The correct statements from the given statements are
      i) Nalgonda technique is a cheap defluoridation method
      ii) Dental flourisis and skeletal flourisis results if the fluoride ion
          concentration in water is less than 3 ppm.
      iii) Defluoron -1, Defluoron-2, coconut charcoal are used as
      adsorbent for fluoride ions
      The correct answer is
      (1) i, ii                                (2) ii, iii
      (3) i, iii                               (4) All are correct

48.   Cimetidine acts as
      (1) Antibiotic                             (2) Antifertility
      (3) Antihistamine                          (4) Antipyretic

49.   Which of the following statement is not correct?
      (1)   La(OH)3, is less basic than Lu(OH)3
                                                      
      (2)   In Lanthanoid series ionic radius of Ln 3 ions decreases
      (3)   La is actually an element of transition series
      (4)   Atomic radii of Zr and Hf are same because of Lanthanoid
            contraction

50.   sp3d 2 hybridization is present in
      (1)  CoF6                                (2)  Ni  CO 4 
                  3
                                                                 
                           4
      (3)  Fe  CN 6 
                                               (4) All



51.   The effective atomic number of central metal ion is wrongly
      calculated in the following complexe?
      (1) In [Ni(CO)4] the EAN of Ni is 36
      (2) In [K2 Ni(CN)4] the EAN of Ni is 36
      (3) In [K3 Fe(CN)6] the EAN of Fe 35
      (4) In[Co(NH3)6] Cl3 the EAN of Cr is 36


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NPT-II (AIEEE MOD) 20-11-2010




52.     The IUPAC name of the coordination compound K3 {Fe(CN)6] is
        (1) Potassium hexacyanoferrate (II)
        (2) Potassium hexacyanoferrate (III)
        (3) Potassium hexacyanoiron (II)
        (4) Tripotassium Hexacyanoiron (II)

53.     The substances which affect the central nervous system and
        induce sleep are called.
        (1) Antipyretics                    (2) Tranquilizers
        (3) Analgesics                      (4) Antibiotics

54.     In which of the following statements about halogens is correct?
        (1) They are all diatomic and form univalent ions
        (2) They are all capable of exhibiting several oxidation states
        (3) They are all diatomic and form divalent ions
        (4) They can mutually displace each other from the solution of
            their compounds with metals.

55.     The TLV values of four pollutants A, B, C and D are 9 ppm,
        10ppm, 100 ppm and 500 ppm respectively. The most toxic is
        (1) A                                (2) B
        (3) C                                (4) D

56.     Which of the following statements regarding ozone is not true
        (1) Ozone is an allotrope of oxygen
        (2) The ozone layer protects the earths surface from an excessive
        concentration of harmful ultraviolet radiation
        (3) The conversion of oxygen in to ozone is an exothermic process
        (4) Ozone is much more powerful oxidizing agent than molecular
        oxygen

                    23
57.     3.01× 10 NaCl ion pairs are dissolved in water and diluted to a
        volume of 10 liters. The molar concentration of the solution is
        (1) 0.5M                            (2) 0.25M
        (3) 1M                              (4) 0.05M


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                                                                   NPT-II (AIEEE MOD) 20-11-2010




58.   The    observed     magnetic      moment          value  abs  is    higher      than
      calculated magnetic moment value  cal  for
            3                                               2
      (1) Ti                              (2) V
             2                                  2
      (3) Co                              (4) Cr
59.   The number of electrons required for deposition of one mole of
      copper on the cathode during the electrolysis of CuSO4 solution is
                     23                                             24
      (1) 6.0 × 10                                    (2) 1.2 × 10
                   24                                            23
      (3) 4.8 × 10                                    (4) 3 × 10

60.   Chemically inert halide of sulphur is
      (1) S 2Cl2                            (2) SF4
      (3) SCl2                                        (4) SF6


                               MATHEMATICS

61. In,  ABC if A:B:C = 3:5:4 then a + b + 2 C =
    (1) 2b                                 (2) 2c
    (3) 3b                                 (4) 3a
                                             1       R 
62.   In  ABC, right angled at A, cos                      is
                                                   r2  r3 
      (1) 30º                                         (2) 60º
      (3) 90º                                         (4) 45º

63.   If in  ABC,
      sin4 A  sin4 B  sin4 C  sin 2 B  sin 2 C  2 sin 2 C sin 2 A  2 sin 2 Asin 2 B
      then A =
          5                                             5
      (1) ,                                           (2) ,
         6 6                                             3 6
                                                        3
      (3) ,                                           (4) ,
         3 2                                             4 4
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                                                                 a b c
64.     In a triangle ABC, if r1 = 2r2 = 3r3 then                    =
                                                                 b c a
            75                                                     155
        (1)                                                    (2)
            60                                                      60
            176                                                    191
        (3)                                                    (4)
             60                                                     60
              1                    3
65. If sin         x  sin 1 y  sin 1 z 
                                         then
                                     2
                                   9
         x100  y100  z 100  101             
                              x  y101  z 101
        (1) 3                                                  (2) 2
        (3) 1                                                  (4) 0
66.      sin1  sin3  cos 1  cos7   ta n1 ta n5  
        (1)  + 1                                              (2)    
        (3) 3  - 1                                            (4)    -1
67.     A person standing on the bank of a river observes that the angle
        subtends by a tree on the opposite bank is 60º, when he retires 40
        mts from the bank perpendicular to it, he finds the angle to be 30º.
        The height of the tree and breadth of the river are
        (1) 20,20 3                                            (2) 10,20 3
        (3) 20 3 ,20                                           (4) 10,30 3

68.     From the top of a cliff ‘x’ meters high, the angle of depression of
        the foot of a tower is found to be double the angle of elevation of
        the top of the tower. If the height of the tower is ‘h’ meters, then
        the angle of elevation is

                   1    x                                                1      2h
        (1) sin            h                                  (2) T an        3
                         2                                                         x
                    1    2h                                              1      2h
        (3) Cos                                                (4) T an        3
                           x                                                       x
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                                                                            1
69.   The total number of solutions of cot x  cot x                           , x  0,3 is
                                                                          sin x
      equal to
      (1) 1                                                (2) 2
      (3) 3                                                (4) Zero

70.   The number of solutions of the equation
                                  1     1
      sin 5 x  cos5 x                    sin x  cos x  is
                                cos x sin x
      (1) 0                                                (2) 1
      (3) Infinite                                         (4) 5

71.   The maximum value of  cos 1  cos 2 ...... cos n  , under
                                                         
      the restrictions 0  1 ,  2 ,...... n            and  cot 1  cot 2 
                                                         2
      ...... cot n   1is
             1                                                   1
      (1)                                                  (2)
            n
            2
                                                                 2n
          2
           1
      (3)                                                  (4) 1
          2n
                                                   
72.   If x      sin
                n 0
                        2n
                             , y   cos ,z   sin 2n cos 2n  , then
                                   n 0
                                          2n

                                                    n 0
      (1) XYZ = XY + Z                                     (2) XYZ = XZ + Y
      (3) XYZ = YZ + X                                     (4) XYZ = XY + YZ + ZX

                                                                 cot C
73.   In a triangle if        a 2  b 2  2011c 2 then                     
                                                             cot A  cot B
      (1) 999                                              (2) 1002
      (3) 1000                                             (4) 1005

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NPT-II (AIEEE MOD) 20-11-2010




                                                       sin  sin 3 sin 9
74.     If    K1  Tan27  Tan and K 2                                then
                                                      cos3 cos9 cos 27

        (1)   K1  K 2                                     (2)   K1  2K2
        (3)   K1  K2  2                                  (4)   K2  2K1

                         2       4      6 
75.     If   x  270 cos     cos     cos   3746 , then the value of
                          7        7       7 
        (1) 3880                                           (2) 3881
        (3) 3882                                           (4) 3883


                                                       t
76.     If f(y)=   e , g(y)= Y; y > 0 and F  t    f  t  y  g  y dy, then
                    y

                                                      0
                        t                                                  t
        (1) f(t)= e -(1+ t)                                (2) f(t)= t e
                      t                                                       t
        (3) f(t)= t e                                      (4) f(t)= 1- e -(1+ t)


77.     The slope of the tangent to a curve at any point (x, y) on it in given
            y      y      y
        by     cot cos  x  0, y  0  and the curve passes through the
            x      x      x
               
        point  1,  the equation of the curve is
               4
                y                                    x
        (1) sec  log x  2                  (2) sec    log x  2
                x                                     y
        (3)   sec  yx   log x  2                       (4)   sec  xy   log x  2



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                        dx
78.                    7            9
           x  2   x  3
                        8            8

                                1                                                            1
            8 x  2           8                                             8 x 2       8
      (1)           c                                                (2)           c
            5 x 3                                                          3 x 3 
                                1                                                            1
            8 x  2           8                                             3 x  2      8
      (3)           c                                                (4)            c
            5 x 3                                                          8 x 3

79.   If polynomials P and Q satisfies

         3x  1 cos x  1  2x  sin x dx  P cos x  Qsin x  R
      (ignoring the constant of integration) then
      (1) P = 3x -2 (2) Q = 2 + x     (3) P = 3(x -1)                              (4) Q = 3(x -1)

80.   Let the equation of a curve passing through the point (0, 1) be
                            y   x 2 ,ex dx .
                                         3
      given by                                   If the equation of the curve is written in
      the form x = f(y) then f(y) is
      (1)       log e  3y  2                                         (2)   3   log e  3y  2 
      (3)   3   log e  2  3y                                         (4)   3   log e  2  y 

81.   Let f(x) be a function satisfying f ' (x) = f(x) with f(0) = 1 and g(x) be
                                                   2
      a function that satisfies f(x) + g(x) = x . Then, the value of the
                    1
      integral       f  x  g  x dx is
                        0
                    2
              e 3                                                               e2 3
      (1) e                                                           (2) e    
              2 2                                                               2 2
              e2 5                                                              e2 5
      (3) e                                                           (4) e    
              2 2                                                               2 2
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                                                  6
                                                          x
82.     The value of the integral                 
                                                  3    9x  x
                                                               dx                is

              3
        (1)                                                       (2) 2
              2
                                                                             1
        (3) 1                                                     (4)
                                                                             2

83.     Let f(x) = Min          x  1;       1 x    then area bounded by y = f(x)          and x-
        axis is
            7                                                         5
        (1)                                                       (2)
            6                                                         6
            1                                                         11
        (3)                                                       (4)
            6                                                          6

        The area bounded by curve y  x  6x  8x and the x-axis is (in
                                                              3          2
84.
        sq.units)
                                                                             8
        (1) 8                                                     (2)
                                                                             3
              3
        (3)                                                       (4) 6
              8


           xdx  ydy xsin  x  y                      has the solution
                                          2       2

85.                  
           ydx  xdy        y3
                                                                                            y2
                       
        (1) log tan x  y              x y          C          (2) log tan  x  y   2  C
                           2      2           2   2                                   2   2

                                                                                            x
                                                                               x 2  y2  x 2
                       
        (3) log tan x  y
                           2      2
                                        xy  C                  (4) log tan           
                                                                                    2  y2
                                                                                               C
                                                                              
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                                                                                                     NPT-II (AIEEE MOD) 20-11-2010




86.   If a, x1 , x 2 are in G.P. with common ratio r and b, y1 , y 2 are in G.P.
      with common ratio s where s - r = 2, , then the area of the triangle
      with vertices is  a,b  ,  x1, y1  and  x 2 , y2 

      (1) ab r  1    2
                                              
                                    (2) ab r  s
                                                   2        2
                                                                      (3) ab s  1        2
                                                                                                               (4) abrs

87.   P and Q are two variable points on the axes of x and y respectively
      such that OP  OQ  a , then the locus of foot of perpendicular
      from (0,0) on PQ is
                    
      (1)  x  y  x  y
                            2
                                      a  x  y
                                    2
                                                                                            
                                                                               (2)  x  y  x  y
                                                                                                          2      2
                                                                                                                    axy
      (3)  x  y   x          y   axy                                    (4)  x  y   x               y   axy
                            2       2                                                                     2      2




88.   If        P1 , P2 , P3 are    lengths            of       perpendiculars                           from        the   points

       m ,2m,  mm ,m  m  and  m                                      
                                                                2
            2                   1          1                1
                                                                    ,2m1                        to              the          line

                         sin 2 
      x cos   ysin            0 respectively then P1 , P2 , P3 are in
                         cos 
      (1) A.P                           (2) G.P                       (3) H.P                                    (4) A.G.P
89.   If the line y = 3 x cuts the curve
      x3  y3  3xy  5x 2  3y2  4x  5y  1  0 at the points A, B, C.
      Then OA.OB.OC =

      (1)
           4
          13
                  
              3 3 1                                                      (2) 3 3  1


      (3)
           2
            3
              7
                                                      1
                                                     13
                                                        3 3 1             (4)                            
      If the pair of lines ax  2  a  b  xy  by  0 lie along diameters of a
                             2                     2
90.
      circle and divide the circle into four sectors such that the area of
      one of the sectors is thrice the area of another sector, then
      (1) 3a  2ab  3b  0                   (2) 3a  10ab  3b  0
             2          2                           2           2


      (3) 3a  2ab  3b  0                                                (4) 3a  10ab  3b  0
                  2                 2                                                   2                        2


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