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KCET 2016 Maths Question Paper with Answers COMMON ENTRANCE TEST-2016
DAlE
SUBJECT
TIME
DAY-l
MATHEMATICS
02.30 P.M. TO 03.50 P.M.
MAXIMUM MARKS
TOTAL DURATION
MAXIMUM TIME FOR ANSWERING
80 MINUTES
70 MINUTES
60 MENTION YOUR CETNUMBER
QUESTION BOOKLET DETAILS VERSION CODE SERIAL NUMBER
A-I
381617
DOs: 1. Check whether the CET No. has been entered and shaded in the respective circles on the OMR answer sheet. 2. TIlis Question Booklet is issued to you by the invigilator after the 2nd Bell i.e., after 2.30 p.m. 3. The Serial Number of this question booklet should be entered on the OMR answer sheet. 4. The Version Code of this question booklet should be entered on the OMR answer sheet and the respective circles should also be shaded completely. 5. Compulsorily sign at the bottom portion of the OMR answer sheet in the space provided. DON'Ts: 1. THE TIMING AND MARKS PRINTED ON THE OMR ANSWER SHEET SHOULD NOT BE DAMAGED I MUTILATED I SPOILED. 2. The 3 n1 Bell rings at 2.40 p.m., till then; Do not remove the paper seal present on the right hand side of this question booklet. Do not look inside this question booklet. Do not start answering on the OMR answer sheet.
I IMPORTANT INSTRUCTIONS TO CANDIDATES I
1. 2.
3.
This question booklet contains 60 questions and each question will have one statement and four distracters. (Four different options I choices.) After the 3rd Bell is rung at 2.40 p.m., remove the paper seal on the right hand side of this question booklet and check that this booklet does not have any unprinted or torn or missing pages or items etc., if so, get it replaced by a complete test booklet. Read each item and start answering on the OMR answer sheet. During the subsequent 70 minutes: Read each question carefully. Choose the correct answer from out of the four available distracters (options I choices) given under each question I statement. Completely darken I shade the relevant circle with a BLUE OR BLACK INK BALL POINT PEN against the question number on the OMR answer sheet. Correct Method of shading the circle on the OMR answer sheet is a~ shown below:
0_00 4.
9.
Please note that even a minute unintended ink dot on the OMR answer sheet will also be recognized and recorded by the scanner. Therefore, avoid multiple markings of any kind on the OMR answer sheet. Use the space provided on each page of the question booklet for Rough Work. Do not use the OMR answer sheet for the same. . After the last beU is rung at 3.S0 p.m., stop writing on the OMR answer sheet and affix your LEFT HAND THUMB IMPRESSION on the OMR answer sheet as per the instructions. Hand over the OMRANSW ER SHEET to the room invigilator as it is. After separating the top sheet (Our Copy), the invigilator will return the bottom sheet replica (Candidate's copy) to you to carry home for seU:'evaluation. Preserve the replica of the OMR answer sheet for a minimum period of ONE year.
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5. 6. 7. 8.
III
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2.
3.
4.
KCET 2016 Maths Question Paper with Answers
The Set A has 4 elements and the Set B has 5 elements then the number of injective mappings that can be defined from A to B is (1)
144
(2)
72
(3)
60
(4)
120
Let f: R -+ R be defined by f(x) by
= 2x + 6 which is a bijective mapping then r-l(x)
(1)
~-3
(2)
2x+ 6
(3)
x- 3
(4)
6x+2
2
Let * be a binary operation defined on R by a
* b = a + b 'if a, b e 4
(1)
Commutative and Associative
(2)
Commutative but not Associative
(3)
Associative but not Commutative
(4)
Neither Associative nor Commutative
is given
R then the operation * is
531t). · ~1( cosThevaIue 0 f sm - IS S
(1)
(3)
31t
5 1t
10
(2) (4)
-31t 5 -1t
10
Space For Rougb Work
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6.
If3 ,tan-Ix + ~Clx = 11: then x equal to (1)
0
(2)
(3)
-I
(4) . 112
1
tan~l(
The simplified fonn of tan-I(x.) _ x- Y)iS equal to , y . . x+y . (1)
0
(2)
(3)
11:
(4)
2
7.
KCET 2016 Maths Question Paper with Answers
11:
4
11:
l+x 1 Ifx y z are all different and not equal to zero and 1 1+ y 1
1
1 1 = 0 I+z
then the value of x-I + y-I + z-I "is equal to '
8.
(1)
xyz
(2)
x-I y-I z-I
(3)
-x-y-z
(4)
-1
If A is any square matrix of order 3 x 3 then I 3A I is equal to (1)
31AI
(2) .!.IAI
(3)
271AI
(4)
3
91AI
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9.
.
- -I 2_
If y =esm (1)
(3)
10.
1 If A=1t
(t
I)
& x =e
KCET 2016 Maths Question Paper with Answers d _ ( I) ~I then Ix equal to
- I2sec. t
IS
x
-
(2)
y
Y
(4)
x
[Sin -I (It!;) --I (x) sm -
tan - IC') ] 1t
coCI(ru:)
-y x -x
y
1 [ - cos-I (It!;)
1t
1t
sin-I (x)
1t
11.
12.
tan-I(x) ]
, B--
then A - B is equal to
- tan-I(n:x)
1t
(1)
I
(2)
0
(3)
21
(4)
1.1 2
If xY = ef-Y then dy is equal to dx
eX .
(1)
log x log(x-y)
(2)
(3)
log x (l +logx)2
(4) - - - -
xX-y.
1.
1
Y
x-y
If A is a matrix of order m x n and B is a matrix such that AB' and B'A are both defined, the order of the matrix B is (1)
mxm
(2)
nxn
(3)
nxm·
(4)
mXn
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The value of .
KCET 2016 Maths Question Paper with Answers e x (1 + x)dx .. 2 is equal to cos (e.... x)
J
(1)
- cot(er) +
(3)
tan(~
c
+c
(2)
tan( tf. x) + c
(4)
cot(tf) + c
log x
14.
log3y
(1)
log(x y z)
(2)
log(6 x y z)
(3)
0
(4)
log(x+ y+ z)
log3z
The function f(x) = [xl where [xl the greatest integer function is continuous at
. (1) (3)
16•
logz
If x y z are not equal and :F- 0, :F- 1 the value of log2x log2y log2z is equal to log3x
15.
logy
1.5
(2)
4
1
(4)
-2
. The vaIue·0 f ..
JeX( x
2
-I
tan .2x + tan x +1
(1)
eftan-1x+c
(3)
tan-:-I(x,) + c
-I
x+
I)
dx'IS equa1 to
(4)
etan
-I
x+ c
Space For Rougb Work
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18.
If 28.b =I 81.1
30°
(2)
0°
(3)
90°
(4)
60°
(2)
xy
(4)
y x
d
.
If my" = (x + y)m+n then -1 is equal to . .. dx
(3)
x+y xy
0
The general solution of cot 8 + tan 8 = 2 is
(I)
8= nx +(--ltx/8 2
. (3)
8= nx + (_I)n x/6
2
.
10.
hi then the angle between ; & bis
(1)
(I)
19.
KCET 2016 Maths Question Paper with Answers
.
K/4
The value of Isin 103x .coslO 1x dx
(4)
8=nx+(-I)n X/ 8
(2)
(:)'"'
(4)
0
is
-K/4
(3)
2
Space For Rougb Work
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The length oflatus rectUm ofqte parabola 4y + 3x + 3y + 1 = 0 is (1)
413
(2)
7
(3)
12
(4)
3/4
. 22.
23.
24.
KCET 2016 Maths Question Paper with Answers
Ie
61og ,f
_
e51ol! x
.
The value of e410[l .~ -e 310g.\. dxis equal to (1)
0
(3)
3 x3
(4)
1
x
The differential coefficierit oflog1cr with respect to logxlO is
(1)
1
(3)
(lo~1 0)2
(4)
x2 100
The slope of the tangent to the curve x = t2 + 3t - 8, Y= 2~ - 2t - 5 at the point (2, ....:.1) is (1)
(3)
22 7
-' 67
(2)
(4)
6 7
-6 7
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(1)
1 2
(3)
tan·2
28..
(2)
a
x dx I sin sin x + cos
0
27.
a + i sin arl is
The real part of (1- cos
Jt/2
26.
KCET 2016 Maths Question Paper with Answers
1000
lOOO x
1000
(1 )
1000
(3)
-
. IS
1
I +cosO
a
(4)
cot2
(2)
1
(4)
-
equal to
1t
2
If 1 + sin a + sin2a + .... upto
00
1t
4
= 2.J3 + 4, then a = _ _ (2)
1t/4
(4)
31t/ 4
r1m
xex -sinx. IS equal to x~o x (1)
.3
(2)
1
(3)
0
'(4)
2
Space For Rough Work
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Iftan-I(~ + (1)
(3)
30.
31.
32.
r)
=
a then
KCET 2016 Maths Question Paper with Answers dy is equal to
dx
-x y
x y
(2)
xy
(4)
-xy
The simplified fonn ofi" + i"+1 + i"+2 + i"+3 is
(1)
0 .
(3)
-I
The two curves~ -
- (2) (4)
1
i
3xY + 2 = 0 and 3~y- ~ == 2
(1)
Touch each other
(2)
Cut each other at right angle
(3)
Cut at an arigle 1tI3
(4)
Cut at an angle 1tI4
'.
The equation of the nonnal to the ,curve y( 1 +~) = 2 -
x where the tangent crosses x-axis is
(1)
5x-:- y-1O = 0
(2)
x- 5y-IO =·0
(3)
5x + Y + 10 = 0
(4)
x + 5y + 10 = 0
Space For Rough Work
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34.
35.
The maximum value of (:
r
rn=
is
~
(1)
e
(2)
ee
(3)
eYe
(4)
(~r
The solution for the differential equation dy + dx == 0 is x . y
1
1
(1)
-+-=c y x
(2) . log x . log y = c
(3)
xy=c
(4)
x+y=c
[, (d)2 d2 Ix + sin(dZx )]~ =dx~
,
The order and degree of the differential equation 1 +
(1)
(3)
36.
KCET 2016 Maths Question Paper with Answers
If ; and vector?
order= 2 degree = 3 order = 2 , ,3 degree=4
(2)
(4).
order= 2 degree =4 order = 2 degree = not defined
bare unit vectors then what is the angle between ;
(1)
30°
(3)
60°
and
b for
/37,. ~ bto be unit
Space F~r Rough Work
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The sum of 1It n terms of the series 12
12 +22
1
1+2
-+
38.
KCET 2016 Maths Question Paper with Answers
+
12 +22 +3 2 1+2+3
+ ...
"(I)
n+2 -3
(2) . n(o + 2) 3
(3)
n(n-2)· 3
(4)
The \I,h term i" the expansion of ( x + (1)
999
(3)
39.
1001
x x
1001
Suppose ;+b+~=O, ,;,=3; Ibl=S, 1~1=7, then the angle between ;&bis (1)
7t
(2)
(3) K/3
7th
(4) 7t/4 . ....
~
40.
i.
(4)
I
6
Er (2)
x
n(o - 2)
~
If a = 3, b = 4, c = 5 each one of a, b 8i c is perpendicular to the sum of the remaining then
I; +b+ 4is equal to (1) (3)
5
12
(2)
2 Ts
sJ2
(4)
~ "
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KCET 2016 Maths Question Paper with Answers
If the straight lines 2x + 3y - 3 ::;:: 0 and x + ky + 7 = 0 are perpendicular, then the value ofk is ~
(1)
2/3
(3)
-2/
3
(2)
3/2
(4)
'-3/ 2
.
42.
The rate of change of area of a circle with respect to its radius at r: = 2 ems is (1) 4 (2) 27t (3) 2 (4) 47t
43.
The value of tan - is equal to . 8 .
.
7t
(1). (3)
1
2 1
J2+1
(2)
Ji+l
(4)
l-Ji
44.
Area lying between the curves'; = 2x and y = x is 2 . 1 . (1) -sq. Untts (2) -sq. Untts 3 . 3 1 . 3 . (3) -sq. Untts (4) -sq. Untts 4' 4
45.
If P(A (J B) =7/10 and P(B) =17ho ' where P stands', for probability then P(AIB) is equal to (1)
7/8
(3)
14/17
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The coefficient of variation of two distributions are 60 and 70. The standard deviation are 21 and 16 respectively, then their mean is
(1) (3) 47.
(3)
49.
35 28.25
1 26
(2)
1 2
(4)
23 22.85
1 221 1 13
If sin-Ix + sin-Iy = 7t, then ~ is equal to . 2 (1)
l-i
(2)
(3)
0
(4) .Jl-y
f
i
.JIO-x . ~ dx IS x+ 10-x
The value of ~ 2
(1) (3) 50.
(2) (4)
Two cards are drawn at random from a pack of 52 cards. The probability of these two being "Aces" is (1)
48.
KCET 2016 Maths Question Paper with Answers
10 8
(2)
0
(4) 3
The contrapositive of the converse of the statement "If x is a prime number then x is odd" is (1) If x is not a prime number then x is odd. (2) If x is not an odd number then x is not a prime number. (3) If x is a prime number then it is not odd. (4) Ifx is not a prime number then x is not an odd. Space For Rough Work
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Two dice are thrown simultaneously, the probability of obtaining,a ·total score of 5 is
(1)
1 18
If A =
(2)
1 9
(3)
52.
KCET 2016 Maths Question Paper with Answers
(4)
1 12 1
6
29 - sin 29] T and A + A = I, [ sin 29 cos 29 COS
where I is the unit matrix of 2 x 2 & AT is the transpose of A, then the value of 9 is equal to (1) x/6 (2) x/3 (3)
53.
54.
55.
x
If A = [ 3
(4)
3X/2
-I
1] then A2 - 5A IS equal to
-1 2
(1)
I
(2)
(3)
71
(4) -71
J
The value of x if x(i + + k) is a unit vector is
(1)
±
(3)
±3
1
T3
(2)
±.J3
(4)
±.!. 3
If x = 2 + 3 cos 9 and y = 1 - 3 sin 9 represent a circle then the centre and radius is (1) (2, 1),9 (2) (2, i), 3
(3)
(1,2),
3"1
(4)
(-2, -1),3
Spice For Rougb Work
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56.
KCET 2016 Maths Question Paper with Answers
The vector equation of the pl~e which is at a dis~ance of
Y.J14 from the .origin and the
nonnal from the origin is 2i - 3} + k is
57.
(1)
;~(2i-3}+k)=3
(2)
;.(i+}+k)=9
(3)
;.(i + 2}) = 3
(4)
;.(2i+k)=3
Find the co-ordinates of·the foot of the perpendicular drawn from the origin to the plane 5y+ 8 =0: ·(1)
(0, _18·5'·2)
(2)
(O,~,o)
(25,0,°)
(4)
(o,-~,o)
8
(3)
58.
If cos a, cos p, cos "( are the direction cosines of a vector ; , then cos 20. + cos 2P + cos 2"( is equal to (1) 2 (2) 3 (3)
59.
(4)
°
The value of the sin 10 + sin 20 + ..... + sin 3590 is equal to (1) (3)
60.
-1
°- 1
Integratmg factor of (1)
(3)
x 1
x
(2) (4)
x: - = 3x y
X4 -
1.· 180
is (2)
logx
(4)
-x
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