JEE Mains Question Paper II 2013

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Text of JEE Mains Question Paper II 2013

  • Part I I~ I Mathematics I 'l'1'fUrn

    1. If a variable plane passes through a fixed (i) ~ ~ "11: W!CR'f ~ fBn: ~ (1, - 2, 3) "#

    2.

    3.

    point (1, -2, 3) and meets the coordinate ~ ~ t ~ B4Mi'i "'liT 9f ~a:r ~ awR il> qfl:q

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    4. Consider

    5.

    Lt: 3x+y+a-2=0; 1.:1: 3x+y-a+3=0, where a is a positive real number, and

    Statement 1 : If line L1 is a chord of the circle C, then the line 1.:1 is not always a diameter of the circle C.

    Statement 2 : If line Lt is a diameter of the circle C, then the line L2 is not a chord of

    the circle C.

    Then,

    (1) both the statements are true.

    (2) both the statements are false.

    (3) Statement - 1 is true and statement- 2 is false.

    (4) Statement - 2 is true and Statement- 1 is false.

    If the system of linear equations, r.'~ x+2ay+az=O, x+3by+bz=O and G

    x+4cy+cz=O has a non- zero solution, then a, b, c satisfy :

    (1) 2b=a+c (2) b2 =ac

    (3) 2ac=ab+bc

    (4) 2ab=ac+bc

    Lt: 3x+y+a-2=0; L2 :3x+y-a+3=0~~a~ ~ qlfdfqq> ~t ([~

    C: x2 +y2 -2x+4y-4=0.

    l~~t m1.:1 ~ 'fl c 'liT "O!!R'I m ~ 1

    ' cn?.R 2 : ~ Lt

  • 6. Let S be the set of all real matrices, 6. >!RT S P:!R ~:

    (1) -5

    (2) 3

    (3) 6

    (4) -9

    'l~ 'll:'F

  • ' ' l t J 7x13 + 5x15 () J 7x13 + 5x15 9. 3 dx equals: 1 dx 'ffliR 't : I (./ + x2+ 1) ( x7 + x2+ lt i I

    l

    I (1)

    x14 +C (1)

    xl4 +C

    2 2

    (x7 + x2+ 1) (x7 + x2+ 1) i

    ) j (2) x14 +C (2)

    x14 +C

    ! 2 2

    2(x7 + x2+ 1) 2(x7 + x2+ 1) I l ! l (3) x7 +C (3)

    x7 +C

    (x7 + x2+ 1)2 2

    ! (x7 + x2+ 1)

    j

    (4) (4)

    10. If for some real number a, f'l'

  • 11. Let A and B be two events such that 11. liRTA(1) "'~ - 1 m~ - 2 m~ 1\1\1\ --4/\1\ 12. l1RT v = 2 i + j - k
  • \ \

    ) 13. Statement 1 : The line 2x + y + 6 = 0 is 13

    . 211- 2, >211- 1 "'fiif% I

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  • 16. The coefficient of t24 in (1 + t2)12 (1 + t12) (1 + t24) is.: (1) Izc +13 6 (2) Jzc +2 6 (3) Jzc + 1 6 (4) Jzc 6

    17. The general solution of the differential equation

    : + sin ( x : Y J = sin ( x ; y J is:

    (1) log (tan~)+ 2sinx = C (2) log (tan~) +2sin~ = C (3) log (cot~)+ 2sinx = C (4) log (cot~)+ 2sin~ = C

    18. If the quadratic equation 3x2 + 2(a2 + l)x + (a2- 3a + 2) = 0 possesses roots of opposite signs, then a lies in the interval : (1) (-oo,-1) (2) (-1, 1) (3) (1, 2) (4) (2, 3)

    16. (1+ t2)12 (1+ tl2) (1 + t24) if; "\ltlR if t24 'fiT TTf'n~: (1) 12c + 13 6 . (2) Jzc +2 6 (3) Izc +1 6 (4) 12c 6

    17. ~ +14l'fi{Oi dy . (X + y ) . (X - y ) -+sm -- =sm -

    -

    "'liT dx 2 2 mtlR!m'l ~:

    (1) log (tan~)+2sinx= C (2) log (tan~)+ 2sin~ = C (3) log (cot~)+ 2sinx = C (4) log (cot~)+ 2sin~ = C

    18.

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    j J 1 l i

    1 l I }

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    19. Ifj(x)=x I xI, then for any real numbers a and b with a

  • 22. From a window x meter high above the 22. 1l:'fi 1R'ft if, ~ it x 1ft. '1ft~ 1R ~ 1l:'fi

    23.

    24.

    ground, in a street, the angles of elevation ~ it ~ 1R'ft ~ ~ '1ft am ~ 'l1cf'1 and depression of the top and the foot of another house exactly opposite to the window in the same street are a and 13 respectively. Then the height (in meters) of the house on the opposite side is : (1) x(1 + tana cotl3) (2) x(1 + tana cosl3) (3) x(1 + cota tanl3) (4) x(1 +cotoc cosl3)

    Let fbe a differentiable function such that

    8f(x)+6f(~ )-x=5, (wO) and y = x2 f(x), then :~ at x = -1 is :

    15 (1) -14 15 (2) 14 1 (3) --14

    1 (4) -14

    A tree, in each year, grows 5 ern less than it grew in the previous year. If it grew half a metre in the first year, then the height of the tree (in metres), when it ceases to grow, is: (1) 3.00 (2) 2.75 (3) 2.50 (4) 2.00

    23.

    24

    iii fum (f?.Jl '1Ti; iii "3WR (f?.Jl ~ ~ ~: a Tl!R~: 15 (1) 14

    15 (2) 14 1 (3) -14

    1 (4) 14

    1l:'fi its~. ~ crf '1ft aWIW 5 it.lfi. 'l>l! ~~I ~~~crfif1/2"ifi. ~%,

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    25. Statement 1 : If three positive numbers in G.P. represent the sides of a triangle, then

    the common ratio of the G.P. must lie

    be ../5-1 d ../5+1 tween 2

    an 2

    .

    Statement 2 : Three positive numbers can form sides of a triangle if sum of any two numbers is greater than the third number.

    (1) Statement - 1 is true ; Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1.

    (2) Statement - 1 is true ; Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1.

    (3) Statement - 1 is true ; Statement - 2 is false.

    (4) Statement- 1 is false; Statement- 2 is true.

    26. The integral

    is equal to:

    (1)

    (2)

    (3)

    (4)

    1 5 -In-4 7

    .!.In~ 2 7

    1 7 -In-4 5

    .!.ln2'. 2 5

    .Jln7 2 J xcosx dx ,Jln5 cos(ln35 - x2 ) + cosx2

    25. -.n?.Rz: m

  • 27. The least positive integral value of x which satisfies the inequality 1C,_ 1 > 2 x 10Cr is: (1) 5 (2) 8 (3) 9 (4) 6

    28. The angle between the lines 2r = 3y = - z and -6x=y=4z is: (1) 30" (2) 45" (3) 90 (4) 0"

    29. If a variable line, passing through the point of intersection of the lines x + 2y -1 = 0 and 2x- y-1 =0, meets the coordinate axes in A and B, then the locus of the mid-point of AB is : (1) x+3y=O (2) x+3y=10 (3) x+3y=10 xy (4) x+3y+10xy=O

    30. Let y2=16x be a given parabola and L be an extremity of its latus rectum in the first quadrant. If a chord is drawn through L with slope - 1, then the length of this chord is: (1) 32 (2) I6J2 (3) I6J3 (4) 32J2

    27.

    28.

    29.

    30.

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    Part II I~ II Aptitude Test I ~ ~

    Directions : (For Q. 31 and 32). The problem figure slur.os the top view of an object. Identify the correct front Piew, from amongst the answer figures.

    f.$r : ( JT. 31 3#r 32 ~ fffir) I W'f ~ if fit;ift CRg W a;'lit ~ ~ Tf?.lT t I 3fR" i#l'fitd4T if Problem Figure I W'f ~ Answer Figures I 3fR" 31/'fitd'lt

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

    34 . . /

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

    LIPage 13 SPACE FOR ROUGH WORK I~

  • Directions : (For Q. 35 to 39). Find out the total number of surfaces of the object given below, in the problem figure. ~ : ( 1l. 35 # 39 ~ fffi!:) I W'f awpfrr if /&P.fH=/i&.Tif;=a CRg c1i; ~ F!ft Jiff #1ln ~ ~I Problem Figure I W'f awpfrr

    35. (1) 19 (2} 18 (3) 20 (4) 22

    36. (1) 16 (2} 15 (3) 17 (4) 18

    37. (1) 14 (2} 15 (3} 13 (4) 12

    38. (1) 15 (2} 14 (3} 12 (4) 13

    39. (1) 20 (2} 1!' (3) 16 (4) 17

    LIPage 14 SPACE FOR ROUGH WORK I~ q;11f ~ ~ ~

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    Directions : (For Q. 40 to 42). Find the odd figure out in the problem figures given below : f.$1' : ( 'fT. 40 # 42

  • Directions : (For Q. 45 to 48). Which one of the answer figures is the correct mirror image of the problem figure with respect to X - X ? ~ : ( '11. 45 "# 48 cfi fc;nr) I 6fR: Jll'flfri?jf ff ft Cfil7ift ~
  • Directions : (For Q. 49 to 52).

    f.$T : ('!1. 49 #52 ~ fc;rrr) I

    'vlihich one of the answer figures, will complete the sequence of the three problem figures ?

    ~ wr;R~

  • Directions : (For Q. 53 to 55).

    Problem Figure I w-r~

    vVhich one of the answer figures shows the correct view of the 3 - D problem figure, after the figure is opened up ? 3 - D w-r ~ q;7 ~ w, ~ 3/l'f'Frt

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    Directions : (for Q. 56). How many total number of rectangles are there in the problem figure given below ?

    Problem Figure I Jr.R ~

    (1) 17 (2) 18 (3) 19 (4) 20

    j Directions : (For Q. 57 and 58). Huw many total number of triangles are there, in the problem figures given below ?

    Problem Figure I Jr.R ~

    (1) 20 (2) 18 (3) 17 (4) 19

    (1) 16 (2) 17 (3) 18 (4) 20

    LIPage 19 SPACE FOR ROUGH WORK I 'N ~ ~ ft;ro; ~

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  • Directions : (For Q. 59 to 65).

    f.rrhTr : ( fl. 59 '# 65

  • Problem Figure I "!R"f ~ Answer Figures I ~ 3/Jijitd'li

    112.

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

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

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

    /65.

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

    LIPage 21 SPACE FOR ROUGH WORK I~ cnrd ~ ftolt!: ~

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  • 66. Which one of the following is an 66. f1'"1fAfk.id if"#~ l1:'!i Cll+1ilii{%? Architect ?

    (1) Amrita Sher-Gill (2) M.F. Hussain (3) Christopher Benninger ( 4) Salman Rushdie

    67. Qutab Minar is largely cladded with : (1) Granite (2) Red sand stone (3) Marble (4) Brick

    c1 J 31'p!T m-f1R1 (2) ~.~. ~ (3) fSt>fl2l'h< ~f1 .. 1)il{ (4) "UWIR ~

    67. ~ .ri--m'{{ ~ 3lf!filiiCI~flqifi ffi ~? material ?

    (1) Jute bags (2) Thermocol (3) Glass wool ( 4) Ground glass

    69. Point out the incorrect combination : (1) Pagoda and Burma (2) Vat and Combodia (3) Eiffel Tower and Congo ( 4) Agora and Greece

    70. Natural shadow less light is available from which direction in India ? (1) South (2) North-West (3) East (4) North

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    71 . In which place in India can we find cave y: 'llTl if ~ ~ ~ ~ cfi;l ~ -it 'J!ill'lfu temples of three faiths ? fl:wrH'?

    (1) Madurai (1) ~if (2) Delhi (2) ~if (3) Ellora (3) ~if (4) Agra (4) 3WTU if

    72. Which one of the following is a horizontal :zZ f1"1f('lfl3d if ir '!i