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    IIT-JEE CLASSROOM CENTRE

    WEEKLY NORTH INDIA COMPETITIVE EXAMINATION-2(WNICE)ALL RESHUFFLED BATCHES

    Time: 3 Hours Maximum Marks: 264

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

    INSTRUCTIONS:

    A. GENERAL

    1. This booklet is your Question Paper containing 72 questions. The booklet has 24 pages.

    2. No additional sheets will be provided for rough work.

    3. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers &

    electronic gadgets in any form are not allowed to be carried inside the examination hall.4. Write your Name and Enrollment No.in the space provided below.5. The answer sheet, a machine-readable Objective Response Sheet (ORS), is provided separately.

    B. Filling the ORS

    6. On the upper part of the ORS, write in ink, your name, enrollment number and batch numberin the space provided. Do not write these anywhere else.

    C. Question paper format:

    7. This question paper has 3 sections: Section-A, B & C. Section-A has 60 questionsof physics, chemistry & mathematics (20 per subject), Section-B has 6 questions of

    matrix match type (2 per subject) & Section-C has 6 questions of single integer type(2 per subject).

    8. Each subject of Section-A contains 8 questions of single correct choice type,2 reasoning type, 2 set of paragraph type questions. The paragraph is followed by3questions. Each of these questions has 4 choices: (a), (b), (c) & (d), out of which only onechoice is correct. Each subject also contains 4questions of multiple correct choice type.Each of these questions has 4 choices: (a), (b), (c) & (d), out of which one or more than onechoice is correct.

    9. Each subject of Section-B contains 2 questions of matrix match type. Each question hasfour statements (A, B, C and D) given in Column I and five statements (1, 2, 3, 4 and 5) inColumn II. Any given statement in Column I can have correct matching with one or morestatement(s) given in Column II.

    10. Each subject of Section-C contains 2 questions of integer answer type ranging from0 to 9. The answer will have to be appropriately bubbled in the ORS as per the instructionsgiven at the beginning of the section.

    D. Marking Scheme:

    11. In Section-A, for single correct choice typequestions, you will be awarded 3 marks if youhave darkened only the bubble corresponding to the correct answer and zero mark if no

    bubble is darkened. In all other cases, minus one (1) mark will be awarded.12. In Section-A, for multiple correct choice type questions, you will be awarded

    4 marks if you darken only the bubble(s) corresponding to the correct answer and zero mark

    if no bubbles are darkened. No negative marks will be awarded.13. In Section-A, for reasoning type and paragraph type questions,you will be awarded

    3 marks if you darken only the bubble corresponding to the correct answer and zero mark ifno bubbles are darkened. In all other cases, minus one (1) mark will be awarded.

    14. For each question in Section-B, you will be awarded 8 marks if you have darkened ALL thebubbles corresponding ONLY to the correct answer or awarded 2 marks each for correctbubbling of answer in any row. No negative mark will be awarded foran incorrectly bubbled answer.

    15. For each question in Section-C, you will be awarded 4 marks if you darken the bubblecorresponding to the correct answer and zero mark if no bubble is darkened.No negative marks will be awarded in this Section.

    Name: Enrollment No.:

    Batch number:

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 2

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

    Space for rough work

    PHYSICSSECTIONA

    Single Correct Choice Type

    This section contains 8 multiple choice questions.Each question has 4 choices (a), (b), (c)and (d), out of which ONLY ONEis correct.

    1. Four charges +2q, 2q, 3qand +3qare kept on the cornersof a square of side a. The net electric field at the centre Ois,

    (a) zero (b)2

    04

    22

    a

    q

    (c)2

    04

    2

    a

    q

    (d)2

    04

    210

    a

    q

    O

    +2q 2q

    +3q 3qa

    2. Position of a particle moving on a straight line is given as 2123 ++= ttx . Here x is inmeter and tis in second. Distance travelled by particle in starting 3 seconds is

    (a) 9 m (b) 11 m (c) 23 m (d) 18 m

    3. Seven point charges each of charge qis placed at the seven corners of a cube of side a(onecorner is empty). Find the magnitude of electric field at centre of cube.

    (a) zero (b)2

    04

    1

    a

    q

    (c)

    2

    03

    1

    a

    q

    (d)

    2

    0

    7

    4

    1

    a

    q

    4. A positive charge particle q is placed at rest at the origin on smooth surface. The electric

    field on the surface at a point is given as ixE =r

    , herexisx-coordinate of the point andEisin N/C. Then

    (a) particle will move along positivex-axis with increasing speed.

    (b) particle will move along negativex-axis with decreasing speed.

    (c) particle will oscillate about origin.

    (d) particle will not move.

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 4

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

    Space for rough work

    Multiple Correct Choice Type

    This section contains 4 multiple correct questions. Each question has 4 choices: (a), (b), (c)

    and (d) for its answer, out of which ONE OR MOREmay be correct.

    9. A point charge qis placed at origin. Let AEr

    , BEr

    and CEr

    be the electric field at three points

    A(1,2,3),B(1, 1, -1) and C(2, 2, 2) due to charge q. Then

    (a) BA EErr

    (b) BA EErr

    || (c) ||4|| CB EErr

    = (d) ||16|| CB EErr

    =

    10. A positively charged thin metal ring of radiusRis fixed in thexyplane, with its centre at theorigin O. A negatively charged particle P is released from rest at the pint (0, 0, z), wherez>0. Then the motion ofPis

    (a) periodic, for all values ofzsatisfying

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 5

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

    Space for rough work

    12. A non conducting wheel having mass mhas charges+q and q on diametrically opposite points asshown in figure. It remains in equilibrium on a

    rough non conducting incline plane in the presenceof uniform electric field of intensity Ein verticallyupward direction. Neglecting the mass of charges incomparison to mass of wheel. Which of thefollowing statements is/are true?

    q

    +q

    E

    (a) The value ofEisq

    mg

    2

    (b) The value ofEisq

    mg

    (c) The friction force on the wheel is mgsin

    (d) The direction of friction force on the wheel is up the plane.

    Reasoning Type

    This section contains 2 reasoning type questions.Each question contains Statement-1 andStatement-2. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE iscorrect.

    Directions: Read the following questions and choose

    (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation forStatement-1.

    (B) Statement-1is True, Statement-2is True; Statement-2is not a correct explanation forStatement-1.

    (C) Statement-1is True, Statement-2is False.(D) Statement-1is False, Statement-2is True.

    13. Statement-1:When charges are shared between two bodies, there occurs no loss of charge,but there does occur a loss of energy.

    Statement-2:In case of sharing of charges, conservation of total energy fails.

    (a) A (b) B (c) C (d) D

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 6

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

    Space for rough work

    14. Statement-1:Horizontal range is same for angle of projection and (90 )Statement-2:Horizontal range is independent of angle of projection.(a) A (b) B (c) C (d) D

    Paragraph Type

    This section contains 2 paragraphs. Based upon the paragraph 3 multiple choice questionshave to be answered. Each question has 4 choices (a), (b), (c) and (d), out of which ONLYONEis correct.

    Paragraph 1

    A uniformly charged ring carrying charge +Qand of radiusRisplaced in y - zplane with its centre at origin. A long wire with

    uniform linear charge density () is placed along y-axis, suchthat wire and ring does not touch each other. A particle withcharge +qand mass m is placed on x-axis, at a distance x fromthe origin as shown in figure. For x = 2R the net force on theparticle is zero. (Neglect gravity)

    x x+q,mR

    y

    +Q

    15. The value ofR

    Q

    5

    2is

    (a) 3 (b) 5 (c) 4 (d) 18

    16. For ,22 Rx= the acceleration of the particle is

    =

    04

    1k .

    (a)mR

    qk (b)

    23

    12

    m

    qk (c)

    23

    82

    mR

    qk (d) none of these

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 7

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

    Space for rough work

    17. If another long wire with linear charge density + is also placed along z-axis withouttouching ring and the other infinite wire. The variation of net electric field intensity (due totwo long wires and ring) withx-coordinate on the points onx-axis (for 0 x) is (takingfield intensity to be positive if it is along positivex-axis and vice-versa).

    y

    x

    (a)E

    x

    E

    x(b)

    y

    x

    E

    x(c)

    x

    y

    (d) none of these

    Paragraph 2

    Due to charge on a large plate, a constant electric field of intensity Eexist everywhere. Anobject of mass mand charge qis projected from the plate with velocity uat an angle withthe plate. It follows the path as shown with maximum height h above plate and range R(Neglect gravity).

    + + + + + + +

    u

    R

    h

    E

    E

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 9

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

    Space for rough work

    SECTIONBMatrix Type

    This section contains 2 questions. Each question has four statements(A, B, C and D) givenin Column I and five statements (1, 2, 3, 4 and 5) in Column II. Any given statement inColumn I can have correct matching with one or more statement(s) given in Column II.For example, if for a given question, statement B matches with the statements given in 2 and3, then for that particular question, against statement B, darken the bubbles corresponding to2 and 3 in the ORS.

    1. The position (x) of a particle varies with time asx = t3 3t2, where t is time in second.Match Column I with Column II.

    Column I Column II

    (A) Position of particle is zero at 1. t = 3 s

    (B) Velocity of particle is zero at 2. t = 2 s

    (C) Magnitude of acceleration of particle is non zero at 3. t = 0 s

    (D) Magnitude of displacement is equal to distancetraveled by the particle at

    4. t = 1 s

    5. t= 4 s

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 10

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

    Space for rough work

    2. In the figure shown two identical small charged balls

    having mass m and charge q are suspended with the

    help of two light inextensible silk strings each of lengthl. At equilibrium the angular separation between thestring is .

    T

    m,q

    T

    m,q

    Column I Column II

    (A) If is very small then charge q is proportional to 1.2/3

    (B) If T is tension in the string and is very smallthen (T mg) is proportional to

    2. l

    (C) If the system is taken in satellite then tension T isproportional to

    3.

    (D) Angular separation between the charges (atequilibrium) in the satellite is4.

    2

    l

    5.2/1

    m

    SECTION C

    Integer Type

    This section contains TWO questions. The answer to each question is a single-digit integer,ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.

    1. An infinite number of charges each equal to qare placed along the x-axis at x= 1, x= 2,

    x= 4,x= 8. and so on. The electric field at pointx= 0 is 0nq

    . Find the value of n.

    2. Linear charge density on a rod is varying as

    l

    x0= , here 0is constant, lis length of rod andx

    is distance from pointPas shown in figure. Electric

    field at point P on the axis of rod is ( )nlnl0

    0

    8

    .

    Find the value of n.

    P

    x

    l

    x0=

    ll

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 11

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

    Space for rough work

    CHEMISTRYSECTIONA

    Single Correct Choice TypeThis section contains 8 multiple choice questions.Each question has 4 choices (a), (b), (c)and (d), out of which ONLY ONEis correct.

    1. Which one of the following is most stable free radical?

    (a) (b) (c)

    CH3

    (d)

    2. In benzyne intermediate, the triple bond consists of:

    (a) one spsp sigma bond and two pppi bonds.(b) one sp2sp2sigma bond and two pppi bonds.(c) two spsp sigma bonds and one pppi bond.(d) one sp2sp2sigma bond, one sp2sp2pi bond and one pppi bond.

    3. In which of the following pair of carbocations, the first carbocation is more stable than thesecond?

    (i) 22 HCCHCH

    +

    = and 222 HCCHCHCH+

    =

    (ii) 23 HCNHCH+

    and OHHC 2+

    (iii) 223 HCCHOCH+

    and 23 HCOCH+

    (iv) 3223 CHCHCHHCCH +

    and 3223 CHCHHCCHCH +

    (a) (i), (ii) and (iii) (b) (i), (ii) and (iv)(c) (ii) and (iii) (d) (iii) and (iv)

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 12

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

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    4. In which of the following compounds, allylic hydrogen is most acidic?

    (a) CH3CH=CH2 (b) CH2=CHCH2CH=CH2

    (c)HH

    (d)HH

    5. Thecorrect order of acidic strength is

    (I)

    COOH

    NO2

    (II)

    COOH

    NO2

    CH3H3C(III)

    COOH

    NO2

    CH3H3C

    (a) (III) > (II) > (I)

    (b) (II) > (III) > (I)(c) (I) > (II) > (III) (d) (II) > (I) > (III)

    6. Which of the following intermediate is/are aromatic nature?

    (a)

    (Triplet)

    (b)

    (Singlet)

    (c) (d) both (b) and (c)

    7. A. B. C.

    Compare carbon-carbon bond rotation across A, B, and C

    (a) A > B > C

    (b) A > C > B(c) B > A > C (d) B > C > A

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 13

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

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    8. In which of the following the first compound is more acidic than second?

    (a)

    OH

    CH3

    OH

    CH3 (b)

    OH

    NO2

    OH

    Me

    Me Me

    Me

    NO2

    (c)

    OH

    OH

    OH

    OH

    (d)

    OH

    OH

    OH

    NO2

    Multiple Correct Choice Type

    This section contains 4 multiple correct questions. Each question has 4 choices: (a), (b), (c)and (d) for its answer, out of which ONE OR MOREmay be correct.

    9. Which of the following compound(s) contain same number of linearly arranged carbon atomsin their respective molecules?

    (a) H2C=CHCCH (b) HCCCCH(c) H2C=CHCH=CH2 (d) CH3CCCH3

    10. Which of the following compound(s) have delocalized electrons?

    (a)

    .H

    (b) CH3CH2NHCH=CHCH3

    (c) CH3CCH2CH=CH2

    CH3

    (d) CH3CH=CHCH2OCH3

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 14

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    11. Which of the following species will be aromatic?

    (a)

    ....

    (b).

    H

    (c)....

    (d)

    12. Which of the following compounds exhibit tautomerism?

    (a) CH=CHOH (b) OO

    (c) O

    O

    (d) O

    O

    Reasoning Type

    This section contains 2 reasoning type questions.Each question contains Statement-1 andStatement-2. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE iscorrect.

    Directions: Read the following questions and choose

    (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation forStatement-1.

    (B) Statement-1is True, Statement-2is True; Statement-2is not a correct explanation forStatement-1.

    (C) Statement-1is True, Statement-2is False.(D) Statement-1is False, Statement-2is True.

    13. Statement 1 : cis-2-butene has higher melting point and trans-2-butene has higher boilingpoint.

    Statement 2 : Geometrical isomers differ in their physical properties.

    (a) A (b) B (c) C (d) D

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 15

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

    Space for rough work

    14. Statement 1 : Extent of enolization depends upon the solvent used.Statement 2 : If the solvent used makes hydrogen bonding with carbonyl group, it decreases

    the enol content.

    (a) A (b) B (c) C (d) D

    Paragraph Type

    This section contains 2 paragraphs. Based upon the paragraph 3 multiple choice questionshave to be answered. Each question has 4 choices (a), (b), (c) and (d), out of which ONLYONEis correct.

    Paragraph 1

    Isomerism is a phenomenon by which two or more compounds have same molecular formulabut different properties. If the difference in properties is due to difference in their structuralformulae, it is called structural isomerism. If the difference in properties is due to difference inarrangement of atoms or groups in space, it is called stereoisomerism. The different compounds arecalled isomers.

    Structural isomers mainly differ in the length of carbon chain (chain isomers) or the positionof substituents/functional groups on same carbon skeleton (position isomers) or functional groups(functional isomers).

    15. The number of structural isomers possible for a compound with molecular formula C4H8O are

    (excluding cyclic isomers)(a) 8 (b) 9(c) 10 (d) 11

    16. How many metamers are possible for given compound? (including the given compound)

    CH3CH2CCH2CH3

    O

    (a) 2 (b) 3(c) 1 (d) 4

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 16

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

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    17. What functional group classes are present in it?

    NC

    CH3

    NHN

    OH5C2

    H5C2

    (a) 3 amide.(b) 2 and 3 amine.(c) aromatic ring and alkene (C=C bonds).(d) all of these.

    Paragraph 2

    The observed wavelengths in the line spectrum of hydrogen atom were first expressed interms of a series by Johan Jakob Balmer, a Swiss teacher.

    Balmer's empirical formula is

    = 22H n

    1

    2

    1R

    1; n = 3, 4, 5, ..........

    RH= 109678 cm1is the Rydberg constant.

    Niel Bohr derived the expression theoretically in 1913. The formula is generalised to anyone electron atom/ion.

    18. Calculate the longest wavelength in (1 = 1010m) in the Balmer series of singly ionizedhelium He+. Select the correct answer. Ignore the nuclear motion in your calculation.

    (a) 2651 (b) 1641.1 (c) 6569 (d) 3249

    19. How many lines in the spectrum will be observed when electron returns from 7th shell to 2ndshell of a Bohr atom?(a) 13 (b) 14(c) 15 (d) 16

    20. In which region of electromagnetic spectrum does the Balmer series of Li2+lie?(a) uv (b) visible(c) infrared (d) far infrared

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 17

    Delhi Office: 50-C, Kalu Sarai (Behind Azad Apartments), New Delhi-110 016, Ph.: 2653 7392/93/94/95, Fax: 2653 7396

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    SECTIONBMatrix Type

    This section contains 2 questions. Each question has four statements(A, B, C and D) givenin Column I and five statements (1, 2, 3, 4 and 5) in Column II. Any given statement inColumn I can have correct matching with one or more statement(s) given in Column II.For example, if for a given question, statement B matches with the statements given in 2 and3, then for that particular question, against statement B, darken the bubbles corresponding to2 and 3 in the ORS.

    1.

    Column I Column II

    (A) Aromatic 1.CH3

    N+

    CH3

    (B) Non-aromatic 2. BH

    (C) Anti aromatic 3.

    4.N

    (D) Non planar ring

    5.+

    +

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 18

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    2.

    Column I Column II

    (A) O can exhibit1. Position Isomerism

    (B) CH

    CO

    O

    can exhibit

    2. Chain Isomerism

    (C) NO2can exhibit

    3. Metamerism

    (D) CNcan exhibit

    4. Tautomerism

    5. Functional

    SECTION C

    Integer Type

    This section contains TWO questions. The answer to each question is a single-digit integer,ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.

    1. Determine the number of sp hybridized atoms in cyanogen, (CN)2.

    2. Tropylium carbocation is aromatic in nature. How many resonating structures are

    possible for this ion?

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 19

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    MATHEMATICS

    SECTION A

    Single Correct Choice Type

    This Section contains 8 multiple choice questions. Each question has four choices (a), (b),(c) and (d) out of which ONLY ONE is correct.

    1. The number of real roots of the equation 0)3()2()1( 222 =++ xxx is

    (a) 0 (b) 1 (c) 2 (d) 3

    2. If ),,(02 Rcbacbxax =++ has two non-real roots and ,0

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 20

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    7. The equation 022 =+ mmxx has two real roots if

    (a) 10 ++ cb

    12. The points which satisfy 23 +> xy ,y>x,y> 0 is/ are

    (a) (2, 1) (b) (1, 0) (c) (1, 6) (d) (0, 5)

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    Brilliant Tutorials QUESTIONS WNICE-2/RB/020511/PCM 21

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    Reasoning Type

    This section contains 2 reasoning type questions.Each question contains Statement-1andStatement-2.Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONEiscorrect.

    Directions: Read the following questions and choose

    (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation forStatement-1.

    (B) Statement-1is True, Statement-2is True; Statement-2is not a correct explanation forStatement-1.

    (C) Statement-1is True, Statement-2is False.

    (D) Statement-1is False, Statement-2is True.

    13. Statement-1: If the equation 0168 234 =+++ cxbxxx (b, cR) has all positive realroots, then they are equal.

    Statement-2: If 4321 ,,, are positive real numbers, then +++

    44321

    4

    1

    4321 )( and the equality occurs only if 4321 === .

    (a) A (b) B (c) C (d) D

    14. Statement-1: 0)1()1( 22422 =++++ mxmmxmm )( Rm has non-real roots.

    Statement-2: Rmmm >++ 012 .

    (a) A (b) B (c) C (d) D

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    Paragraph Type

    This section contains 2 paragraphs. Based upon the paragraph 3 multiple choice

    questions have to beanswered. Each of these questions has four choices (a), (b), (c) and (d)out of which ONLY ONEis correct.

    Paragraph -1

    Consider the equation .012 22 =+ mmxx

    15. If both the roots of the equation lie between 2 and 4, then

    (a) )4,0(m (b) )3,1(m (c) )0,(m (d) ),2( m

    16. If both the roots are of opposite signs, then

    (a) )1,1(m (b) )2,0(m (c) )0,2(m (d) Rm

    17. If both the roots of the equation are less than 5, then

    (a) )5,0(m (b) )10,5(m (c) )6,1(m (d) )4,(m

    Paragraph 2

    Consider the equation .02 224 =+ aaaxx

    18. The equation has four real distinct roots if(a) 0>a (b) 0a (d) 10 a (b) 0a (d) 10 a (b) 0a (d) 10

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    SECTION B

    Matrix TypeThis section contains 2 questions. Each question has four statements (A, B, C and D)given in Column I and five statements (1, 2, 3, 4 and 5) in Column II. Any givenstatement in Column Ican have correct matching with one or morestatement(s) given inColumn II. For example, if for a given question, statement B matches with the statementsgiven in 2 and 3, then for that particular question, against statement B, darken the bubblescorresponding to 2 and 3 in the ORS.

    1.

    Column I Column II

    (A) Minimum value of )0(11

    )(2

    2 >+++= xxx

    xxxf is 1. 1

    (B) Minimum value of 84)( 2 += xxxf is 2. 2

    (C) Minimum value of 413)( 2 ++= xxxf is 3. 3

    (D) If zyx ,, are real, then the minimum value of

    4222222 ++++++ zyxzyx is

    4. 4

    5. none of these

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    2.

    Column I Column II

    (A) If , are the roots of 0164 2 =+ cxx such that,321