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KEAM 2018 Question Paper Maths

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Page 1

WARNING:
Any malpractice or anv attempt to commit rrv fii@
the Examination w,!l DIIQUALIFY Tfm CANDIDAT'E.
PAPER-II MATHEMATICS-20IS
Version Question Booklet
Code B1 Scrial \umber : 4131000
-l-inre:
150 Minutes \umber of Questions: 120 Maximum Marks: 480
\ame of thc Candidate
Iloll Number
Signature of the Candidate
INSTITUCTIO\ S TO CAN I)IDA'I'ES
Please ensure tlrat the version code shorvn at the top of this
Qucstion Booklet
is same as that shown in the O\IR .\nslycr Sheet issued to vou. If yor.r havc
rc-Ccii.-d a Question llooklet w'ith a diitercnt Version Codc, plcase gct i1 rcplacccl
n ith a Qucstron Booklct rvith thr-- sarne Vcrsion Code as that of O\41{ Answcr
Shect fior:r tir". Inr isilator. TIIIS IS \-ER\-llIpOIfTAN.I..
I)lcas.-:-.- ,-.'.- t:--ltts such as \ame. Roll Nurnber and Signaturc in thc columns
':r'. ::. -:::''. :. P.:asc e1so .,r'rire Question Booklet Serial Number siven at the top of
-
:,.-. ':,=:.- asainst ii.-m ,l in the O\IR,,\ns,uver Sheet.
. 1,1s Question Booklet contains 120 questions. For each question fir,e ansrvers
:uegestcd and grven against (A), (B), (c), (D) and (ri) of uhich onl.v onc rvill bc
a1e
H
the ')lost Appropriate Answer.' Mark the bubblc containir g the letter
corr"esponding to the 'Most Appropriate Answer' in the O\,fR Ansu,cr Sheer, by
using eithcr Blue or Black Ball point pen only.
I
\egative Marl<ing: In order to discouragc u,ilc1 gucssing the score q,ill bc
subjected to pcnalization formula based on the nurnber of riglit answors act"ually
rnarked and thc number of wrong answcr urarkcd. Each correct answcr will bc
:'," artied I;OUI{ marks. ONE mark will be deducted for eaoh incorrect answcr.
\i-re lhan one answer n-rarked against a question wiil be deernccl as incorrect
an-i',,. Jr ,tnti ri ill bc negatively marked.
5. Plcase rr'ad the rnstructions in the OMR Answcr Shcet ior rnarking thc
answers.
CandidateS ar.' adr ised to strictly follow the instruction containe<i in thc OMR
Answer Shctr.
TMMIIDIATI,ILY rF I'r-R OPENING THI! euEs't'roN IlooKL[]T, l.rIE cANfiD,\Tp
sIrouLD VEIIIFY \\'IrEI-IIER THE QUESTTON BOOKLET COI{TAI|{S ALL l.IrE I20
QUES'I'IONS IN SERIAL ORDER. rr- NO]" nEQULS',t'l'OR RBpLACTil\{l1N.r.
:

DO NOT OPEN THE SEAL T]NTIL THE INVIGILATOR ASKS YOU TO DO SO.

Page 2

G

I

BLANK PAGE
E

Maths-II-B I /2018 2

Page 3

PLEASB ENSURE'TIIAT THIS QUESTION BOOKLET CONTAINS 120
QUBSTTONS SBRIALLY I\UMBERED FROM I TO 120.
PRINTED PAGES 32.

l. I'hevatue"rffi is

(A);(1 +i) 1e)#(1 +;) (q#(1 -,) (D)*(1 -,) (E)*(r+i)

2. If the conjugate of a complex number z is A, then z is

(A)* rg)# (c)* (D)* (E)i

3. 'fhe value or
(i'o * (+)") is eclual to

(A)T (B)2+2i (c)? @),12-lZt @)z-zi

l. Ihernoduluso[H-H,t
\, 2 (B) /z (c) 4 (D) B (L) 10

Maths-II-B ll2018
lP. t'.o.

Page 4

5. If z : ui+n/s , then (ytvz + z1e4)3 is equal to
(A) -2 (B) -1 (c)-l (D) -2i -.

6. If cr and b at"e real nurnbers and (a + ib)l1 : 1 + 31, then (b * ia)11 is o.
-. ,
to

(A)r+3 (B)1+31 (c)1-31 (D)0 (i:) -i - s

7. If a* {J, o'--5q-3, p, - 5p - 3, then the equation
, havins I and - as its
.B
"B CI

roots is

(A)3x2-19x-3=0 (B) 3x2 * 19x - 3 = 0
(C)x'*i,9x*3:0 1D.1 3x2 - 19x - 19 : 0
(E)3x2-19x*3:0

'l'he focus oftheparabola yz
- 4y - x *3 _ 0 is
(A) (;,2) re) (; ,-2) rq (z,i) rnr (f ,z) rsl (2,=)

Maths-II-B 112018 4

I

Page 5

9. If f :R -+ (0, co) is an increasing function and if limx_zors ,# :
,,
then limr- ,oruffi is equal to
(A); re); e) 2 e) 3 (E) 1

10. Ifl is differentiable at x : 7,then lim,
-rff is

{A) -f '(r) (s) f (1) - f ,(r) rc) zf (r) _ f ,(t)
(D) zf(t) + f, (7) (E)/(1) + f, (t)

11. Eccentricity of the eflipse 4xz + yz
- Bx * 4y -B = 0 is
(A)
f, (B)
f (c)
f (D)
f, (E)
f
12. 'fhe focus ofthe parabola (y + I), _ _B(x + 2) is
(A) (-4, *1) (B) (_ 7,_4) (C) (1,4)
(4,1) 0)) (E) (_1,4)

"..:."

Maths-II-B t/2}fi
lP.t'.o.

Page 6

r----

13. Which of thc following is the equation of a hyperbola?

*2y' * 4x +2y -27 * 0 (D) x' * y2 + 3x - 21, - -: : 0
(C) x'
(E)x2*4x+6y-2=o

14. Let f (x) : px2 * qx * r, wherep,Q,r are constants and p + 0
lf /(5) = -3f (2) and f (*4) = 0, then the other root of / is
(A) 3 (B) -7 (cr) -2 (D) 2 (r:) 6

15. Let /:lR.--+llR satisfy f (x)f (y): f (xy) for all real numbets .).' ,r .
tf f (2) = 4., thoi f (;) :

(A) 0 (B)
i (c)
'2
1 (D) 1

L6. Sum clf last 30 coefficients in thc binornial expansion of (1 + r):

(A) 2" (B) 2u' (c) ztu (D) 2s, - 22e G) Zm

Maths-II-I] 1/2018 6

I

Page 7

17. (/s + ,/z)n - (VT - ,12)n :
11^7 zo,la 61 So\6 (C) s\mo (D) 40/6 (t,) 10V6
a

'l'hrce players
18. A, B and C play a garne..Ihe probability tbat A,B
and C will
rlnish the garne are respectively 'l'he probability that
),! ^"a | . the garne is
flnished is

.B I
(A) (B) 1 (C); (D); (E) 1

19. lf z, = 2 - i and zr- 1 * i, then
lffil 1S

(A) z (B) \U (C) 3 (D) V5 (E) 1

20. tf f(x) - then lim, -* f (x) is eclual to

(A) 1 (B) 2 (c); (D) 0 (lj) oo

1r::'.- li-B 1 20 I 8 7
" IP.]"O.

Page 8

21. 'l'he valuc of sinan is
3

(A)
,6
,2 T (B)
# (c):f (,)# (E) 1
2
'2
r
)') Thc sum of odd intcgers from 1to 2001 is

(A) (1 1-21)2 (B) (1101)'z (C) (1001)'z (D) (1021)2 (r1) (10- -

23. ll y::++
.l coLx
'9:1" , rhc. y'(x) is equal to
1-{-tan-n

(A) 2 cosz x 0f) 2 cos3 x (C) -cos 2x (D) cos 2x (E) 3 cos x

24. The foci of the hyperbola 76x2 - 9y' - 64x * 1By - 90 :0are
z++sr/r+s\
(A)(ruF,1) rn)(8F,1) (c) ( ,l
(D)(1,*y) (E)(ruF,-1)

Maths-Il-B ll20l8 8

I

Page 9

25. If thc sum ol'thc coefficients in thc expansion of (arx,
-Zax + 1)s, is zero,
then rz is equal to

(A) 0 (B) 1 (c) -1 (D) -2 (ri) 2

26. l-he mean derriatio. of tire d,ata 2,9,9,3,6,9,4 frorn the me an is
(A) 2.23 (B) 3.23 (c) 2.s7 (D) 3.s7 (ri) 1.03

27. The mean and variance of a binomial distribution are B and 4 respectively.
What is (X -- r\ o
r) :

(A)+ (B)
# Q* (D); 0j) +

28. The number of diagonars of a polygon with 15 sides is
I
(A) e0 (B) 4s (c) 60 (D) 70 (E) 10

Maths-II-B ll2}rc 9
lP.r.,o.

Page 10

29.lnaolass,4}o/oofstr.rdentsstudymathsandscienceancl60%ofStudcl]ts
stuclymaths.Whatistheprobabilityofastuclentstuclyirrgsciencegir'cntllc
studcnt is alreacly studying maths?

(A): (B): (c): (D)
i (E)
i

30. 'l'heeccentricityoftheconic xz +zyz -2x+3y *2:0
is

(A) 0 Gr) # (c) i (D) vz (t1) 1

20' then the mcan of
3l. If the mcan of a set of observations xl'x'2'""'rro is
x, * 4,x, * 8,x, * 12 "' 'x.o * 40 is
(B) 32 (c) 42 (D) 38 (I1) 40
(A) 34

32.Aletleristakenatranclomfromtheword',STATISTICS,,anclanotlrerlctteris
"ASSISTANT"'The probabitity that thcy arc
taken at ranclom frorn thc word
salre letters is

(A)
* G) H (c); tn) * (E)*

10
Maths-II-B1/2018

Page 11

33. If sin q and cos cr are the roots of the equation axz * bx * c - 0, then
(A)a'-b2 +Zac:0 (B)(a -c)2:bz +cz
(C) a'+b2 -Zac
- 0 (D)az +b2 +Zac - 0
(E)ct+b+c:0

34. Ilthe sidcs of a triangle are 4, 5 ancl 6 cms. Then the area of triangle is
sq.clns.

(A); @;,t7 (q * @ *^t7 @)+^t7
35. In a group of 6 boys and 4 girls, a team consisting of four children is formed
such that the team has atleast one boy. The number of ways of forming a team
iike this is

(A) 1se (B) 20e (c) 200 (D) 240 (E) 21.2

36. A passrvord is set u'ith 3 distinct letters from the word LOGARITHMS. I{ow
many such passwords can be forrred?

(A) e0 (B) 72o (C) Bo (D) 72 (E) 120

Space fol rough work

Maths-II-B 112018 11 fP.T'.O.

Page 12

37. If 5e7 is divided by 52, the remainder obtained is
(A) 3 (B) s (c) 4 (D) 0 (rj) 1

38. A quadratic equation axz * bx * c : 0, with distinct coefficicnts is fonncd. If
a,b,c are chosen from the numbers 2,3,5, then the probabilitl that thc cquation
has real roots is

(u); (Q; ("); (l.ri
(A)
i
-7 x+g
39. limr-* 3x3+x3+ Zxz+gx-2 is equal to

(A); Gl); (Q# (D); (r _

The minimum value of f (x) = max{x,L * x,2 - x} is
(A); (B); (c) 1 (D) 0 (lr :

41. I'he equations of the asymptotes of the hyperbola xy + 3x - 2y - 70 = 0 at'e
(A)x - -2,!:-3 (B)r -2,y--3 (C)x :2,Y --3
(D)x:4,y:3 (E)x:3,y=4

Maths-lI-B ll20l8 t2

Page 13

42. If f (x) : .16 + 6x, then f '(x) is equal to
(A) 12.t (B) x + a (C) 6xs + 6x lo9(6)
(D) 6,t5 - -t6'-1 (E) xu

43. -I'he starrclard deviation of the data 6,5,9,13,12,8,10 is
(A)f (B)z 7
(D)E
7
(E) 6

44. Iimr*s i-c(]s7nx
1-cosnx
:

(N4 (B)
nz
+ (c) - (D) -oo Gr) 0

45. limr-o it+.n-t :

(A) 0 (B) -1 rCi: (D) 1

46. Let f and g be differentiable functions such that f(3) _5, g(3) _7,
f'(3) - 13, g'(3):6, f't7):2 md,-g'(T) = O,Jf h(x) - (fug)(x), then
h'(3) -
(A) 14 (B) 12 (C) 16 (D) 0 (E) 10

Space for rough rvork

Maths-II-Bl'20ri 13 fP.r.o.

Page 14

1
47.
arr5
_:
--;---;
sin(z0 ) cos(20')
1
(c) 2 Q)4 (E) 0
(A) 1 (B)
=
\l /

A Poisson variatc X satis{ics P(X -
l) - P(X * 2). P (X : 6) is eclual to

@)f"e-'z (B)
*u-' Q);'-' (il) 1u-' G) *u '
..i1.- first 20 natural
selectecl lrt.:].,
49. I,et a and b be 2 consecutive integers
is an odJ r''-'<itir c rntcgcr is
nutnbers' The probability nattlTTnfTTfr

(A); (il
'19)
19 (q* (D) 1 i.rU

t,ll .i ,. - ^:--^r^ ''r:g-1.) irtsidc
inscribecl in a circle' :\ iltrrii' '> -
An ellipse of ecceutric\ty'z{ is
'''-.' ' 'r':'l i<
at ranclo1r. 'fhe probability that the point lics outsicl'-
the circle

G): (c); ("); tF,*
(A)
i

l4
Maths-II-B 1/20 1 8

I

Page 15

51' Ifthevectors +t+ 71i +mii,7t+2j + 6ii and [+ 5i + 4ii
arecopranar, then
m is equal to
(A) 38 (B) 0 (c) 10 (D) _10 0t) 2s

52. r-etd. - f * i +ii, E -t+3j+5[and d
=Ti*gi+Lt[. Thentheareaof
theparallerogramwithdiagonals d +B
and 6+d is

(^)416 @:,/n s* to) G Gj)*

53. rf ldJ - 3,lit = 1,ldl - 4 and d +i* d _- 0, then the
value of
d.B + E. t + d. d is equal to
(A) 13 @) 26 G) _2s (D) _13 (D _26

54' If d - dl : ldl = lrl : 1, then the angle berween d. arfid
f
is equar to
(A): (r)
+ (c); (D) o (E) rr

Maths-II-B U20tB
15
[P.1'.O.

Page 16

55. lf tlrc veotors d:t.-i+2f{,8:2t.*4i+k and i:7t+9i+pfr
nrutually ortliogonal, then 7 + p is cqual to

(A) s (B) -e (c) -1 (D) 0 (rr) -s

56. 'l'he solutions of *'lu + 3x'lu
- 4 : A are
(A) 1,,1,024 (B) -1,7024 (C) 1,1031 (D) -1.024,1 tL -1,1031

57. If the equations x2+ax*1:0 and x2-x-a- 0 havc a teai ,-r-111111011
root b, then the value of b is equal to

(A) 0 (B) 1 (c) -1 (D) 2 (E) 3

58. 11' sin0 - cos 0 = l,thenthe ,,'alue of sin3 0 - cos3 g is eclual to
(A) 1 (B) -1 (c) 0 (D) 2 (E) -2

59. 'l'wo clice of diflerent coiours are tluown at a tirne. The probability'that the sum
is either 7 or l-l- is

(A)
'7

-Jt)
(B)
t*,
1
g icrz
.-r 3 (D):
. g

Maths-II-II 1/2018 t6

Page 17

7 1
+lisequaito
I
o 1.1.
gl -J-+-1-+
' 3r.7t ' 5l5l 7!3! 9!
.11\ r1o
(A) .29 r1O
(B),l (c) ,{ (D); Gi) *
' -101

61. The order and degree of the differential equation
(y*), +(y"), -(y,)n *ys =0is
(D) 1 and 4 (tl) 3 and 5
(A) 3 and.Z (B) 1 and 2 (C) zand 3

6). I1;*W* is equal to
(D) 4 (li)
,2 1
(A)o G)1 (c) 2

clx
63. "0
T- is equal to
J
-t x2 +'zx+Z
(A) o (B):

(c) 3
I
l.* (D) 4 [:t5
I
r.{11 tBt 2
L!
Space for rough rvork

t1 iP.'l-.o.
Maths-Ii-B i/2018

Page 18

65. ii#dx=
1n1fi+, 6)ft+c (c):
-2i

,,\+x * c
-2x
(D)-*c
a-x

''7+x
(l:)-*c
o
.-1+1'

66. I'he remainder when 22000 is divided by 17 is
(A) 1 (B) 2 (C) B (D) 12 (ri) 4

67. 'fhe cocfficient of xs in the expansion of (x * 3)B is

(A) 1,s42 (B) 1s12 (C) 2st2 (D) 2s+2 (L) 24s2

68. The maximum value of 5 cos 0 + 3.ot (A +f) + s is
(A) s (B) 11 (c) 10 (D) -1 (11) 2

69. Ihc area of thc triangle in the complex plane formed by z,iz and z * i"z rs

(A) lzl @) lzl' Q):lrl' (r))
; lz * i.zlz (E) lz + tzl

70. Let f :R -+ IR be a clifferentiable function. If / is evcn, thcn /'(0) is cqual to
(A)1 (B)2 (C)0 G))-1 rEr]

Maths-II-B I /2018 18

I

Page 19

71. The coordinate of the point dividing internally the line joining the points
(4, -Z) and (8,6) in the ratio 7: 5 is

(A) (16,18) (B) (18,16) (c; (?,:) (D) (:,?) 1r) (7,3)

72. The area of the triangle formed by the points (a,b * c),(b,c * a),(c,a* b)
L;

(B)a'+b2+cz G)ab*bc*ca
(E) a(ab * bc * ca)

73- tf (r,y) is equidistant from (a 1- b,b - a) and (a - b, a + b), then
tAlar*by-g (B)ax-by-0 (C)bx*ay*A
lDlbr-a!:0 (E)x-Y

7{ Tb equation of the line passing through (a,b) and parallel to the line
r.y
-+-:
.b I IS

(-{); *';: , 1n) ; +'; (c)
; *'i: o
(D);*";*2:o =z .{
@);+';:n

\ iaths-l1-B 1 201 8 T9 IP.r.O.

Page 20

If thc points (2a, a), (a,Za) and (a, a) enclose a triangle of arca
18 square units, then the centroid of the triangle is equal to

(A) (4,4) (B) (B,B) (c) (-+,-4) (D (+^12,4r2) (ri) (6,6)

76. The area of a triangle is 5 sq.units. Two of its vertices are (2,1) and (3,-2).
The third vertex lies on y = x * 3. The coordinates of the third vener can be
(A) (+,;) ru) (;,f) (c) (;,;) r,) (+,T) Gr) (;,;)

77. If x2+y2*2gx+Zfy *1-0 represenls a pair of straight lines, tircn

f' + g'is equal to
(A) 0 (B) 1 (c) 2 (D) 4 (E) 3

If 0 is the angle between the pair of straight lines x2 -Sxy*4y2 *3x- 4=0,
thcn tan2 g is equal to

(A)
* (u)x (q* @'; (u)
?
Space{or rough wgrk

Maths-II-B ll20l8 20

Page 21

7e. rf 3i +2i - 5[ - x(zt- j +fr) +y(t+3j _ zii) + z(-zt+i _3[),ften
(A)x=1,y=2,2:3 (B)r =2,!=3,2=7
(C)x:3,!=1,2=2 (D)r=1,!=3,2=2
(E)x=2,y=2,2=3

80. sin 15" -
@# G)!# (o)#
81. If d and E:3t+ 6i + 6rt. arccollinearancld. i: zr,then d is eclual to
(A) 3(i +7 + [) (B)r+2j+zfr (c) 2t + 2i + 2i;
(D)i+3i+3[ (E)r-3j+Zii

82. If Af - 13,lBl = 5 and d.i - 30, then la xil is equal to
f

(A)30 (n)#\trB (c)#f,e5 1o)!I,,4q3 lnyfrrnTs
....,.'

83. If s6P.+e saP,+s - 30800:1, then r is equal to
:

(A) 6e (B) 41 (c) s1 (D) 61 (E) 4e

Space tbr rough work

Maths-II-B l,'2018 2t lP.r.o.

Page 22

84. Distance betwoen trvo parallel lines y : 2x * 4 and! :2x 1is
(A) s (B)s\6 (C)/5 (D) 1
'5 (E) +
\5

85. (7 Co*7 Ct) * ('/ Cz+7 Cz) * ...+ ('Co*7 0) -
(A) 28 -2 (B) 2? - 1 (C) 2, (D) 28 - 1 (1, '_- - z

86. - 3x * 7xz)(1 - r)16 is
The coefficient of x in the expansion of (1

(A) t7 (B) 1e (C) -77 (D) -1e (E) 20

87. The equation of the circle with centre (2,2) which passes through (4,5) is

(A)x' *y' - 4x * 4y -77 - 0 (B)r, *y, -4x - 4y -5 : 0
(C)*'+y'+Zx*Zy - 59:0 (D)x, *y, -Zx-2y -23:a
(E)x'+y'+4x-Zy-26:0

88. T'he point in the xy-planewhich is equidistant frorn (2,,A8),(0,3,2)and (0,0,1)

is
"(C)
(A) (1,2,3) (B) (*3,2,0) (5,-2,s1 (D) (3,2,0) (Et (3,2,1)

Maths-II-B ll2018 22

Page 23

89' r-et f :N ---'; fr;r be such that
f (1)= 2 ancr f (x + y)
numbers.r: and y. If = f (x)71.,1for a, natural
zt=rf (a* /r) = 16(zn* 1), then a is ec1*ar
(A)3 (B)4 (c)s
to
(r))6 (D7
90. If "Gt = 36, oG= 84
and rCr+r
= 1,26,then a =
(A) 3 (B) 4 (C) B (D) e (E) 10
91' l*t f:(-t,t; -+ (-1,1)
be continuous,
/(r) = f @2) for all x e (_1,L) and
.f(o) = J. fn", the value of
4f(_,) ,,
(A) 1 (B) 2 (c) 3 (D) 4 (E) s
92. liftr*,* \nr + l
- \,,?-lJ =
(A) --t (Br 1 (C) 0 (D) 2 (E) +
Space tb..orghioik

Maths-II-B t/2018
23
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Page 24

93. ff / is differentiable at x : 1-
,if O + h) - 5, then f '(1) :
and lim7,-

(A) 0 (B) 1 (c) 3 (D) 4 (E) s

94. The maximum value of the function 2x3 - 1.5x2 + 36x * 4 is attaid at

(A) 0 (B) 3 (c) 4 (D) 2 (E) s

9s. If I f @) cos r d.x : ){f f*>}'* c, then f (;) is
(A) c @)1+c (C)c+1 (D)2r + c tl: - - -

96. Irsn/+ x CLx=
,
/ 4. 1*sin x
J T(

(n) z(VZ - t) @; z(VZ + t) Q) zr(tl1 - r)
(tt) zn(tlT + t) (E) +-
' '12+L

Maths-II-B ll2018 24

Page 25

rfr /, 2 sin -r'
97. l ,.
Jg .1
QX :
2s,n^--.I?

(A) 2 (ts) z (q; (D) 2n (E) 0

98.

(c)
l (D) 0
Gj);
99- The area bounded by y
= sinz x ,* _: and x :TTiS
($: (ry; (c) I il
(D)-16 (L:.) 2r
I 'r' -fhe
criffe.cntiar equation of
the famiry of curves y:ex(Acosn*Bsinx),
,,r-here A
and B arearbitr"ary
constants is
\)y" -2y' +2y* 0 (B) y,,
+2y, *2y _ a (C)y"*y''*y=o
D)Y" *2y'*!
=0 (E)y,,*Zy,*Zy _0
I
Space for rorghm
I

i

Maths-II-B t/2}rc
25
llr.T.O.

Page 26

101. The real part of (r -./5)" it
(A) z-to (B) 2,, (C) 2-12 (D) -z-t, (E) 2ro

'l-fx-ex
rc2. limr-6 x2

(A); (B)+ (c) 1 (D) -1 (E) 0

103. '1(sinx+co.sx)(2-sin2z)
sin'zx
d.X =

, , sinx+cosx
(A)-+c
^ (B) rirr-.or, + C (L)sln sin r
*c
sin2x sin 2x x+cos x

(D)#+c
' _r-cos.r
sln
(e)+rci+
' 'slnr+cos.r c

104. A plane is at a distance of 5 units from the origin; and perpendicuiar ,- ...-'
vcctor 2t + j + 2f(. 'l'he equation of the plane is

(A)i.(zt+i -zfr):15 (B)i.(zt+ j -fr) = 15
(c)1.(zt+ j +2ft) - 15 (D)i.(i+i +zf<): 15
(E) i. (t, - j + 2f(): L5

Maths-II-B ll20l8 26

Page 27

sin l-sin B
I05 ls equal to
;;"..r,
(.{) sin
ff) (13)2tan(,4+B) (c) cot (T)
(D)tan(T) (E)2cot(A+B)

1 06. Il x *.,{ cos 4.t + B sin 4f, tben t4
=
(A) r (B) *16x (C) 15r (D) 16x ftj) *15x

lA7. -l'he arithnretic mean of nCo, rG, rCz,
..., nC, IS

(A) 4 (B) 1
-TL

n+1 n
(c)'"-'
" n+l (D)tn
(u):-
n
111*7

I 08. 'l'he variance of first 20 natural nurnbers
is
(A)Y G) 12 (C)T (D)T
72
0r) T
Space tor rough work

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Page 28

109. If S is a set with 1"0 elements and A : t(x,!);x,y € S,x + yj, then the
number of elernents in / is

(A) 100 (B) e0 (c) B0 (D) rsO (E) 4s

I10. A coin is tossed and a die is rolled. The probability that the coin shori s iread
and the die shows 3 is

(A): (u); (C); (D)
# (tr)1
' 11

/0 1
11 1. rc t:(1 2 3), ,l., the surn of all the diagonal entries of ,z{-i is
\3 1 1/
(A) 2 (B) 3 (c) -3 (D) -4 (E) 4

3
1,12. Let f (x) -

are
h
x
6 il" x - -9 is a root of f (x): 0, then the othcr roor-<

(A) 2 andT (B) 3 and 6 (C) 7 and 3 (D) 6 and} (E) 6 andl

Maths-II-B 112018 28

Page 29

,13. rrrl x,, 'tlil:o,thenxcanbe
[,i :
(A) -2 (B) 2 (c) 14 (D) _14 (E) 0

rr{. rct:l2* l] ,"0n-,=l!, l),rn"n*-
(^) z 1e); (c) 1 (D) 3 (E) o

lx 2 xl
115. If lxz x 6l= o*n+bx3 *cxz *dx*e,thcn Sa.*4b+3cIZrt*eis
l* x 6l
cqual to

(A) 11 (B) -1L (C) 12 (D) _12 (E) 13

{t

-\.1 :....-ii-IJ. ,L\
29 lP.r.o.

Page 30

11 a b*cl'
116.
ll i ;I,l:
(A) 1 (B) 0 (C) (1 - a)(r - bX1 - c)
(D)a+b+c (F,)2(a+b+c)

r1 1 1l
tt7. If f(x) :l 2x x-t x l, th., f(so) -
l:r(, - r) (x-1)(x-z) x@-Dl
(A) 0 (B) 2 (c) 4 (D) 1 G)r

l- cos x 1-cosx I
' =
ll8. If A(x) - 1-*sinx cosx 1 t sin x - cos xl, tltcrr
sin x sin r rl
.. -7 (B): 1
(A) ,2 (c) 1 (D) -1 (E) 0
-2

I
I

I

Maths-II-B 112018 30

Page 31

It9- '['he cquation of the plane passing through the points (1,2,3),(_\,4,2) and
(3,1,1) is
(A) 5x *y*tZz-23 _0 (B)Sx +6y*22 _23
(C)x+6y*22=!3 (D)x *y*z _73
(E)2x+6y*52=T

120' In an arithrnetic progression, if the kth terrn is 5k * 1, then the sum of first
I 00
temrs is

(A) s0(s07) (B) s1(s06) (c) s0(s06) (D) s1(s07)
(rr) sz(s06)

Maths-ll-B 1l20lg 3l fP.T'.O.

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Maths-II-B 1,2018 32

Document Details

Board / OrgKerala CEE
ExamKerala Engineering Architecture Medical
TypeQuestion Paper
Pages32
Languageenglish
Updated30 Apr 2026