KEAM 2019 Question Paper Maths

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THE CANDIDATE.
PAPER - II MATHEMATICS-20I9
Version
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8727980
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BLANK PAGE

Maths-II-B ll20l9 z

PLEASE ENSURE THAT THIS QUESTIOI{ BOOKLET CONTAINS 120
QUESTTONS SERTALLY NUMBERED FROM 1 TO 120. PRII{TED PAGES 32.

1. The aus of the parabola x2 + 6x + 4y + 5 = 0 is
(A) x: o (B) v: 7 (C) x*3:0
(D) v:4 (E) y + 2:0

2. The distance between the foci of the ellipse @#.9+: I is
(A) .6 (B) 2Ji (c) 3Ji
(D) e6 (E) Ji7

3. The value of k, if the circles 2x2 +2y2 -4x+6y =3 and *2 +y2 +kx+ y--0
cut orthogonally is
(A) 2 (B) 3 (c) 4
(D) s (E) I
4. The circle passing through (1,1) and touching the x-axis at (3, 0) also passes
through the point
(A) (2, -s) (B) (-s, -2) (C) (-2, s)
(D) ( 5,2) (E) (s, -2)
5. If o and B are the roots of the equation x2 + ax + F = 0, then
(A) cx,=-1,F=-2 (B) g=0,0=1 (C) a=-2,9=0
(D) a = -2,9 =7 (E) = 1, I = -2
c{,

Space for rough work

Maths-II-B ll20l9 lP.r.o.

6. lf d=(i,1,-i),6=G1,2,1) andd=(_1,2,-1). then t;-f r ,r--t is
(A) 2 (B) 4 (c) 6
(D) 8 (E) 10
7. A particie is displaced from the point (2,l,-l) to the point (J. -1. -- :',, i:l.. lorce
2i + 4 j - 5k. Then the work done by the force is
(A) t6 (B) 27 (c),r6
(D) 48 (E) s2
8. The value of mif the vectors 4i-3j +5k and mi-4j +k are perpendrcL:.-,:. i.
(A)
+ (B)
+ -lq
(c) -.4

(D) 0 (E) +

'9 11 3\
9. If A and B are tu'o matrices such thar *l { - B :
1l .+ D)
t'-te rl
rr '.Th.nthen::.:'.3:
)
and2A-3B: I '" ql
t\ -1" -)) -/
(o -1 o) (s -r o
(A) (B) (C) r80-r\
[, 8 t) [, t t) [3 1 2)
I

(s 3 -r\ (t -3 4\
(D) (E)
[o t 2) [, o ,)
Space for rough work

Maths-II-Bll20l9 4

a3 +7 a2 "l
10. If a, b and c are distinct reals and the determinant b3 +l 62 al = o, then the
c3 +1 c2 ,l

product abcis
(A) -l (B) 0 (c) I
(D) 2 (E) 3
11. lf (x,y,z) is the solution of the equations
x-y-22=3
2x+y+42:5
4x-y-22:ll
then the value ofy equals
(A) 0 (B) -1t2 (C) -t/3
(D) -1/4 (E) -1
(, b\ (1 s\
12. tt inverse of the matrix ,n.n dequals
[" O)rrthe Iz _r,,|,
(A) -t/38 (B) -7/38 (c) 3/38 i.
(D) s/38 (E) et38 l.
I

13. If f :R -+ R is a function defined by f (*)= sinr, then which of the following
is true? I
(A) f is l-1 but not onto
(B) f is onto but not l-1
(C) f is both 1-1 and onto
(D) I is neither l-l nor onto
(E) / has finite number of zeros
Space for rough work

Maths-II-B 112019 5 [P.r.o.

14. consider the set M: {r,2,3} along with the relation R: {(l ,2), (1, I), (3, l),
(3,4), (3, 3), (4, 3)). Which of the following statements is true?
(A) The relation is symmetric but not transitive
(B) The relation is transitive but not symmetric
(C) The relation is both symmetric and transitive
(D) The relation is neither symmetric nor transitive
(E) The relation is reflexive

15. Let zr= 1 + i..6 and, zr= 1+ i, thenarg(+) -

(A) i5n (B) Jn (cr ;lt-r
i
(D) 3n (E) Not defined
i

76. rhe comptex numbe. 0[r,r;*,.orf,]u represents

(A) -i (B) l (c) l_i
(D) l+i (E) t+2i
17. rf z2 + z +l = 0, where z is acomplex number, then the varue of

(' z, *(t','*l]'
[,*1)' ' ,21*((','*l)'+ + ( ,u *l)' ,,
-; ) -'"''(- '7 ) 'Ii

(A) 18 (B) s4 (c) 6
(D) 1e (E) t2
Space for rough work

Maths-II-B ll20l9 6

18. The value of tan lrir_r*l ,,
I ^lz)
(A) -1 (B) 0 (c) 1

(D) Infinity (E) 2

19. If sin-l , + cos-1 ,* =t, then the value of x is
(A) u2 (B) Ji rz (c) .6
(D) 1 (E) J'

20. If x= 2cosr-cos 2t and !=Zsin/-sin 2t, thenff t =$ i,
^t
(A) -l (B) 0 (c) u2
(D) I (E) 3
21. The equation of the tangent to the curve given by *2+2x-3y+3=0 at the
point (1, 2) is
(A) 4x-3y-2=0 (B) 3y-4x-2-0 (C) 4x+3y+2=0
(D) 4x+ 3y-2--0 (E) 4y-3x+2=0

,r.in[1)
I x -2xz
22. The value of lim,-*-ffi-is )

(A) o (B)
+ (q -1
(D) -) (E) -l
; T
Space for rough work

Maths-II-Bll20l9 7 [P.r.o.

/r)' , x>0 is
23. The maximum value of y = t-l
(*/
(A) (B) ee (c) I
"t/e
(D) Infinity (E) 0

24. The value of the integral to'I a, l,
ll l+sin2x
'o
(A) 0 (B) I (c) ;
(D) n (E) 2n

25. The area enclosed between the curves ! = 2x2+ 1 and
I = x2+ 5 is
(A) 4/3 (B) 8/3 (c) t6/3
(D) 32/3 (E) 1t3
26' The solution of the differential equation 5y dx:2x
&passing through the point
(1, 1) is
(A) 2lnx:5 hy l5
n
n'
(C) ln (y+ x):2
(D) ln (1 + ry):O rEr -1 ln.r:i lnl
27. The area of the region bo-unded by the curves y =l x
-21, *= 1, x = 3 and y: 0 is
(A) 4 (B) t2 (c) 3
(D) t4 (E) I
Space for rough work

Maths-II-B l/2019

28. If in a frequency distribution, the mean and median are 2l and 22 respectively,
then its mode is
(A) 22.0 (B) 20.s (c) zs.s
(D) 23.2 (E) 24.0
29. For two data sets, each of size 5, the variances are given to be 4 and 5 and the
corresponding means are given to be 2 and 4, respectively. The variance of the
combined data set is

(A) 15
2 (B)6
- ,A\ Ii
(c)+
(D) ;
s _. l1
(E)
i
30. If the mean of the first n odd numbers is {, tfr"n r equals

(A) e (B) 18 (c) 27
(D) 81 (E) s2
31. A bag contains 5 red balls and some blue balls. If the probability of drawing a
blue ball is double that of red ball, the number of blue balls must be
(A) 10 (B) 15 (c) 20
(D) 2s (E) 30
32. A pair of fair dice are rolled together. The probability of getting a total of 8 is
(A) Us (B) st36 (C) 7 t36
(p) 11/36 (E) 1/36
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Maths-II-B 112019 9 [P.r.o.

33' In a chess tournament, assume that your probability of u,inning a game is 0.3
against level 1 players, 0.4 against level 2 players and 0.5 against level
3 players.
It is further assumed that among the players 50 Yo are at level 1.25 % are at level
2 and the remaining are at level 3. Suppose thar 1'ou u.in the game. Then the
probability that you had played with level I player is
(A) 0.3 (B) 0.4 (c) 0.5
(D) 0.6 (E) 0.2
34. A sum of Rs. 280 is to be used to award four prizes. Ii each prize after the first
prize is Rs. 20 less than its preceding prize, then the r:lue ot rhe tbunh
prize is
(A) 20 (B) 40 rC r 60
(D) 80 (E) 10
35. The coefficient of x3 in the expansion of (l +.r - l"-.I , - - l.r )j is
(A) -20 (B) 40 Cr -60
(D) -80 (E) -100

36. The constant term in the expansion of
(r, -i)tO
(A) 60 (B) 180 (c) 24A
(D) 360 (E) 420
Space for rough u'ork

Maths-II-B Il20l9 10

31. If the equation of the sphere through the circle
*2 + y2 + 22 =9; 2x+3y + 4z =5 and through the point(1,2,3)
is 3(x2 + y2 + z\ -2x -3y - 4z = C, then the value of C is
(A) 11 (B) 22 (C) 36
(D) 4t (E) s4
* :':T
38. The equation of the plane containingalmn
the line ,o :'=9 is

a(x-o-)+b(y -0)+ c(z-Y) = 0, where al* bm* cnis equal to
(A) 1 (B) -1 (c) 2
(D) 8 (E) 0
39. Let f (*) and g(x) be two differentiable functions for 0 < x < i such that
_f(0):2,g(0)=0,f(l)=6. If there exists a real number c in (0,1) such that
-f '(c) ='2g'(c), then g(1) is equal to
(A) 0 (B) -1 (c) 4
(D) -2 (E) 2

40. The equation of the tangent to the curve y = x + \ thatis parallel to the x-axis is
x-
(A) y: 1 (B) y:2 (C) y:8
(D) y: 0 (E) y:3
Space for rough rvork

Maths-II-B ll2019 11 [P.r.o.

41. The number 81 is the coefficient of xk in the binomial expansion of
( " 3\4
I ,' +;x/I , x * 0. Then the value of fr equals
\
(A) -2 (B) 2 (c) 4
(D) 4 (E) 5
42. The possible number of arrangements starting rvith K of the word KALINGA is
(A) 300 (B) 330 (c) 360
(D) 3e0 (E) 37A
43. A bag contains 3 black and 2 white balls. A ball is drawn ar random and is put
back in the bag along with one ball of the same colour. A ball is asain drawn at
random. What is the probability that it is white?
(A) Us (B) 2ts (c) u6
(D) Ut2 (E) 2n3
44. If A and B are two events associated with an experiment such that
P(A u B) = P(A n B), and P(A) = I /3, then p(B) equals
(A) 0 (B) U3 (c) 2t3
(D) U2 (E) 2t5
45. Three identical fair dice are rolled. The probabilitl,that the same number appears
on each of them is
(A) 1t3 (B) U6 (c) 1t36
(D) U2t6 (E) Ue
Space for rou_sh rvork

Maths-II-B 112019 t2

6- Let co + 1 be a cube root of unity and (1+ o)7 = a*ctl'Then the value of a is
(A) ,,t' (B) o (C) ll2
(D) (E) 0
- . If w 1, which of the following must be true?
. Let w =tz-l
47 ", I l=

(A) z lies inside the unit circle
(B) zlies on real axis
(C) z lies on imaginary axis
(D) z lies outside the unit circle
(E) Re z <0

48. F or I z l> 2, if . k,theminimum possible value of ft is
l, +l>
(A) v2 (B) 3t2 (c) 2
(D) s/2 (E) 3
n ag< n. Thenthevalue of sin 0 is
49. Letcot0:-5112 where
2

(A) -;
12 G -; '
(B) (c)12
\-/ 13

(D)
5
(E) 1
r3 13

i ,, I-he value of tan I is
8

(A) J' (B) _J' (c) Jl-t
(D) rJ' (E) -r-J'
Space for rough work

Maths-II-B ll20l9 13 [P.T.O.

51. In an A.P., if 5th term is 1 and Jth ter
m is
I

7 ;, then the sum of first 35 terms is
(A) e (B) 18 (c) 36
(D) 72 (E) 83

In a G.P., ,,:,+,..., when the first n number of terms are added, the sum

Then the value of n is
#
(A) l0 (B) t2 (c) 1.+
(D) t6 (E) 18
53' If A.M. and G'M. of the roots of a quadratic equation are 8 and 5 respectir eiy,
then the quadratic equation is
(A) x2+8x+5=0 (B) x2-r6x+10=0 (c) *2-r6x+25=o
(D) x2+8x+25=0 (E) x2 +10x + 15 = 0

54. Given that rhe equation x2 - 72a + b)x *( ,o, + bz
\ -,.1)2) : 0 has rwo real roots.
The value of D is
(A) I (B) 2 (c) -1
(D) -2 (E) 0
Space lor rough u'ork

Maths-II-B 112019 t4

r 55. If sP,": 6P.-1, then the value of r is
(A) r: I (B) r:5 (c) r:3
(D) r:2 (E) r: 4
56. If nc2'fi ='C2Ot6, then "CoOr, equals
(A) 1 (B) 20t6 (c) 2017
(D) 2033 (E) 2019
57. The image of the point P(2,1) on the straight line 2x-3y + I = 0 is
(A) (*,f) c")
[ij,f) (c) (f,#)

(D)
[ii,#) (D (i+,H)
58. If the centre of the circle inscribed in a square formed by the lines
x2-8x+12=0 and y2 _14y+45=0is(a,D), then a+bis
(A) 11 (B) e (c) 7
(D) s (E) 4
Space for rough w'ork

Maths-II-Bll20l9 15 [P.T.O.

59. The equation of the directrix of the parabola ,r,l - 4r, + 4x +2 = 0 is
(A) x: -l (B) x: 1 (C) x:312
(D) x: -312 (E) x:2

60. The foci of the hyperbola +-+i= I are
COS- CX, SIN- C[
(A) (*1, 0) (B) (*o,0) (C) (0, *1)
(D) (0, *o,) (E) (1, *u)

61. The domain of definition of the luncrio n -f (x)- logr(I* 7i i,
x- -5x+6
(A) (-7, *) \ {3,2} (B) (-3, *) \ {3,2} (C) (-7, co) \ {3 }
(D) (-3, m) \ {3} (E) (-5, m) \ {3}
62. Let f (x) = 3x - 5. The inverse of / is given by
(A) 1

3x-5
(D) I*1
(B)
+ (c)
irl
35
(E) 3
3s x-5
Space for roush ri'ork

Maths-II-B Il20l9 t6

63" Let R = {(r,b): a < b2y be a relation on the set of all real numbers. Then R is
(A) symmetric but not transitive
(B) transitive but not symmetric
(C) both symmetric and transitive
(D ) neither s;zmmetric nor transitive
(E) having finite range
Aunitvector 6 is coplanaru,ith i+ j+2k and i+2j+k andisperpendicularto
i + j +k. 'fhen 5. i equals
(A) 0 (B) I (c) 3t2
(D) 2 (E) 4
65. Suppose o'i+aj+"1k, i+k and yi+y j+Bk are coplanarwhereo, Bandyare
positive constants. Then the product u B is
(A) y (B) v' (c) 2v
(D) z^f (E) 3v
66. The area of the triangie whose vertices areA(1, -1,2), B(2,1, -1) and
c(3, - 1, 2) is
(A) J1 (B) Jil (c) Ji5
(D) JB (E) fi
Space for rough u.ork

Maths-II-B ll2019 17 [P.r.o.

67. Let f(x).rt(+)=+-5. rhen
ltirrodxleouars
(A) 2 + ln2 (B) 2 -ln2 (c) 2
(D) 3ln2 (E) tn2

68. rhe value or limn--
[*
.
#+...+ *] t'
(A) ln 3 (B) ln 6 (c) d
(D) uu (E) tn 2

69. Let f(x) be differentiable una Jj' x .f (x) d* =!to fo, all r."Then the value of
f (t7) is
(A) t7 (B) 1 (c) vr7
(D) 17t2 (E) te

70. The value of the definite integral Jo2"

(A)
1

4
(B)
+
(c) i
(D) r (p)i
71. Let .f(x)=lx-21and g(x) = f(f(x)). Thenderivative of gatthepointx:5 is
(A) I (B) 2 (c) 4
(D) 5 (E) 0
Space for rough ri'ork

Maths-II-B ll20l9 18

n)
f( x) -f( 1)
72. Let .f (r I = sin .r - cos r. Then the value of log-_*-
x _,
7t

(A r (-) (B) (c) ----
1

+ \IL
rD.) I (E) J'
(o 0) o)
73. Let A=l I and B=('
U t) (s t) be two matrices where o, is a real number.
Then
(A) A2 : B for some q, (B) A' +g for any o (c) A'- - B for some o
(D) lX'l* lBl for any s (E) A: -B for some CI,

74. The values of k for which the system
{k +l)x +8y = g
la+(k+3)y:g
has unique solution, are
(A) 3,1 (B) -3, I (c) 3, -1
(D) -3, -l (E) l, -l
Space lor rough work

Maths-II-B 1t2019 t9 [P.T.O.

75. If M and N are square matrices of order 3 where det(M) : 2 and det(N) : 3,
then det(3MN) is
(A) 27 (B) 8l (c) 162
(D) 324 (E) t2l
r-3 y-\ z-5 .r+l y-2 z-5
76. If the lines , =;: and, t = = 5 are coplanar, then the
value of fr is
(A) i (B) 2 (c)3
(D) 4 (E) 5 .
77. A plane passes through the point P(l. -1. 1) and is perpendiculai to t\\'o planes
2x - 2y t z :0 and x - y + 2z : 4.Then the equation ofthe plane is
(A) x+y * i:0 (B) x-y * l:0 (C) x+2y*1:0
(D) x-2y * l:0 (E) x-y- l:0
78. The differential equation which represents the family of curves .y2 =Zc1x+Ji)
where c > 0, is of
(A) order 2 (B) degree I t- ,:::: l
(D) degree 3 (E) degree ,

79. The number of solutions of the differential equuim
*=y'/3 which are passing
through the origin, is
(A) 0 (B) 1 (c) 2
(D) 3 (E) s
Space f6p p.r*:.1 ',,, ,--,;ii

Maths-II-B ll20l9 20

,-.ir
80. Ii+-
2
dr r+ v and y(1)=0, then x+y+2 equals
(t\ (v\ (r)
(A) 3r(: ) (B) 2n\z ) (c) ,\z )
(r)
(D) o (E) t"\z )
81. The length of the latus rectum of the parabola (x + 2)2 = -14(y - 5) is
(A) 7 (B) 14 (c) 2t
(D) 28 (E) t]

82. One of the foci of the hyperbola
+ *= I is
(A) (3,0) (B) (4,0) (c) (s,0)
tD) (9,0) iE) (2,0)
83. Ifthecircles t'*f -8r-6r,+c=0 and ,2+y2-2y+d=0 cutorthogonally,
thenc+dequals
(A) 6 (c) 2
(D) 0
M. The points with position vector 60i +3j,aOi-Aj and ai -52j are collinear if
(A) a: -10 (B) a -- 40 (C) a:2A
(D) a: l0 (E) a: - 4O
Space for rough w'ork

Maths-II-B 112019 21 [P.r.o.

85. The area enclosed within the curve lxl + lyl : 1 is
(A) I (B) J'
(D) 2J' (E) 2
86. The unit veotor in the direction of the vector AB if \= -l -1,3) and
B=(1, l, 0) is o,i + Bj + yk, then o + B is
a
J
(A)
-
122
(B) -L
"122 1'',
(D) -5
_ (E)
2
--
'lzz 'lZZ
(3x-v x+3y) (t e)
87. If II 1.. / l:l
_ l, then x+y+z equals
\L^_Z 2y+:) [s r)
(A) 3 (B) 6 (c) e
(D) t2 (E) 11
,i-'
88. If the product abc:1, then the value of the determinan: :^-
.,L

)
-c-
(A) I (B) 2
(D) 4 (E) s
Space for rough rvork

Maths-II-Bll20l9 22

89. Ii :,:. ;. .: rs :he solution of the equations
-',,- , =-
: '-_<
-_
--
=/1
...n1tr.*tu.of x+ y+z eqt)als
{) 8 (8)6 (C)3
rD) 0 (E) I
(e f) (a b\
90. If | '_ -
I istheinverseofthematrix l-- -- lwhere ad-bc=l,-'-'thengequals
[s h) [c d)
(A) c (B) -c (C) b
(D) -b (E) d
91. If f :R-+R is a function defined by f(x)=x2, then which of the following is
true?
(A) f is 1- I but not onto
(B) f is onto but not 1- l
(C) f is neither 1-1 nor onto
(D) f is both 1-1 and onto
iE) /-1 : R+R exists
Space lbr rt-,ush u'ork

Maths-II-B 112019 Z) [P.r.o.

92. consider the set A : {1, 2, 3} along with the reration R :
{(1, l), (2, 2), (1, 2),
(2,1), (3, 3)). Which of the following staremenrs is true?
(A) The relation is symmetric but not transitive
(B) The relation is transitive but not symmetric
(C) The relation is neither symmetric nor transitive
(D) The relation is both symmetric and transitive
(E) The relation is a function
93. If (-.5 - i)30 * -4k , then rhe value of k is
(A) 1s (B) 20 (c) 2s
(D) 30 (E) 60
94. If ol is an imaginary cube root of unity, then (1+ rrl - rr), is equal to
(A) i28 or (B) -128 ar (C) 128 a2
(D) -128 co3 (E) -128 a2

95. The value of I Tt Tc
i.
Lcosg+rsrng
(A) -in (Br in (c) i
(D) -i (Er lt

96. If arg(Zr) = arg(zr), then
(A) 22 = kzll,(k > 0) (B) z2 = lep (f > 0) (C) lrzl=lztl
(D) Z1= 22 (E) lrzl=lrtl
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Maths-II-B ll20I9 24

s7. The value of tan .*-'f] i,
[rin-rfr.
(A) 26nt (B) s6t33 (c) 63t4t
(D) 6st43 (E) 32fi3

If tan-i x + 2cot-1 , = *.
J
then the value of x is

(A) -..5 (B) -Ji (c)
(D) .6 (E) .6
99. Which of the follori'ing is not a solution of the equation
3tan20-sin0=o?

(A) nTE (B)
"; nn + (-\'I
(D) 0 (E) N
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)

Maths-lI-B ll20l9 25 [P.r.o.

dy
L00. ,r
\g *E=r, then
dx
equals

(A) (B) (c) ,*
[+ E
(D) x (E) xv
v

3/'., th.n
101. If '*=:!- and 'y=
l+rj l+t5' ff ^rl: equals
1

(A) - 6 (B) -1 (c) 1

(D) 6 (E) 4

102. The equation of the normal to the curve given by *2 +2x -3y +3 = 0 at the point
(1,2) is
(A) 3x+ 4y -11:0 (B) 3x-4y+11=0 (C) -3x+4y-11=0
(D) 3x-4y-11=0 (E) -3x - 4y -ll = 0
103. A point of inflection of the curye given by y = x3 - 6x2 +lzx + 50 occurs rvhen
(A) x:213 (B) x:312 (c) x:2
(D) x:3 (E) x: o
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Maths-II-Bll20l9 26

il
10-1. The value of the integral
io, logtan0 d0 is

(A) 0 (B) I (c) ;
(D) log 2 (E) 2
105. The area enclosed betueen the curve ? = 11x -24-x2and.the line y:x is
(A) u3 (B) 3t4 (c) 1

(D) 4t3 (E) U2
,1
106. The sohitir-,:: :. ::.: dilferential equation
dy y' passing through the point
dxx
-=-
(1"-1 t -:

.
/ _-l
(B) f-togr=o (C) /+logx=0
v
D , -lf='1 -' (E) ,Y logx = o

107. The maxima and minima of the function 2x3 -15x2 +36x+10 occur
respectively at
(A) .r: l..r:3 (B) x--2,x:l (C) -r:3, x:2
(D) r:1,-r:r (E) x:2 , x:3
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Maths-II-B-Ll20l9 21 [P.r.o.

tr08. In a class of 100 students, there are 70 boys lvhose a\,erase marks in a subject are
75.If the average marks of the complete class is 72. then u'hat is the average of
the girls?
(A) 73 (B) 85 iCi 68
(D) 74 (E) 65

109. Let x1,x2,...,x, be r observations such that Z*,'= 400 and v.,: = 80. Then a
possible value of r is
(A) ls (B) 10 (c) e
(D) t2 (E) 18

110. If MandNareeventssuchthat P(MuN:;, F(MnN)=i, p6M)=], rh.o
P(Mng is
1
(A) (ts) (c) ;
E ;
5
(D)
1

4 (E) i
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Maths-tri-Bll20l9 28

111' cards marked with numbers 2 to 105 are placed
in a box and mixed. one card is
chosen at random. The probability that the number
on the card is less than 15 is
(A) tt9 (B) t/s (c) 7/B
(D) 8/e (E) 2/7
112' An urn contains 4 black. 5 rvhite and 6 red balls.
one ball is drawn at random.
The probability that it is not black is
(A) 4t1s (B) efis (c) n/ts
(D) t3ns (E) t4tls
113' In a chess tournanleni. assume that your probability
of winning a game is 0.3
against level 1 plar ers. r-i.-r 3q3in5t level 2 playersand
0.5 against t.rj : ptuy*
It is further assumed th:l amon-q the player s 50% are
atlevel I , 25 ohare at level
2 and the remainine a:e:: 1er.el 3. The probability of winning
a game against a
randomly chosen plar er is
(A) 0.21s (B) 0.37s (c) 0.22s
(D) 0.32s (E) 0.12s
114' A man repays a loan of R.-. 3150 by paying
Rs. 20 in the first month and then
increases the payment b} R-s.l5 every month.
The number of months it takes to
clear the loan is
(A) 20 (B) 2s (c) 35
(D) ,10 (E) 10
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Nlaths-II-B 112019
29
lP.r.o.

( '' 2 \6
I 15. The coefficient of ansion of'
xi in rhe e.rp
[x'-;J 't
(A) -160 (B) -80 (c) 40
(D) 0 (E) -10
116. If the equation of the sphere through the circle
*2 + y2 + 22 = 5; Zx +3y + 4z = 5 and through the origin is
*2 + y2 + z2 *2x-3y - 4z +C = 0 then the value ofC is
(A) i (B) -1
(D) s (E) 2 .(c) 0
117. The equation of the plane containing the lines
x+l y+3 z+5ano-,
, x-2 v-4 z-6
l-= 5 =-- =-3 =-J-,t
(A) x+2y*z=0 (B) x-2y*z=0 (C) x_2y_z=0
(D) x+2y-z=0 (E) 2y-x-z=0
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Maths-II-Bll20I9 30

118. A value of c for which the conclusion of mean value theorem holds
for the
function "f (x) =log, x on the interval [1, 3] is

(A) 8log, e (B) lror"3 (C) togre
(D) log,3 (E) 2togre
119. From 4 men and 6 ladies a committee of five is to be selected. The number
of
ways in which the committee can be formed so that men are in majority is
(A) 68 (B) 1s6 (c) 60
(D) 72 (E) 66
3

r20. rhe degree of the differential equation
= ,# ,,
l,.l*)'7'
(A) 1 (B) 2 (c) 3
(D) 4 (E) s
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Maths-II-B ll20l9 31

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Maths-II-B 112019 3Z