KCET 2024 Question Paper Maths

Entrance Exam
2024

QUESTION
PAPER

IM0418K24 (DAY-1, SECOND SESSION)

a. 2.30 dod
M 3.50 dJon
A-2 2159826

80 Daar 70 0ban 60 60 2

1.

3

2. hedse zso a. 2.40 erbs, egodorno;

1. 38neO weAdba SIGNS AND SYMBOLS rieao,, esed deSbo dedd odb, aNds dobx8dQ sdr dorisðedet.

Ba Barto WRONG METHODS
CORRECT METHOD

D D A

M A-2 (1)

1. If 2 sinx-3cos- x=4 xe -l, 1] then 2 sin- x +3 cos x is equal to
4 -67 6-4 37
(A) (C) (D) 0
5 5 2

2, IfAis a square matrix such that A = A, then (I + A)° is equal to
(A) 7A-I (B) ZA 7¢ +I (D) I-7A

3. IfA= then A" is equal to

A (D) 21A

x -3 2x-18 2x - 81
4. If f(x) =x 5 2x-50 4x-500 then f(1).f(3) + f(3).f5) + f(5). (1) is
2 3

(A) -1 (C) 1 (D) 2

5. Let (gof) (x) = sin x and (fog) (x) = (sin yx y. Then
(A) f(x) = sinx, g(x)=x (B) f(x) = sin x, g(x) Vx
f(x) = sinx, g(x)= Vx (D) f(x) =sin x, g(x) = x²

6. Let A = {2, 3, 4, 5, 16, 17, 18}. Let Rbe the relation on the set Aof ordered pairs of
positive integers defined by (a, b) R(C, d) if and only if ad = befor all (a, b), (c, d) in A x A.
Then the number of ordered pairs of the equivalence class of (3, 2) is
(A) 4 (B) 5 (C) 6 (D) 7

7. If cos x+ cos y+ cos z=31, then x (y + z) + y (z + x) + z (x + y) equals to
(A) 0 (B) 1 Aes 6 (D) 12

Space for Rough Work / de Os

M A-2 2

8.) The function fx) =cos x is
(A) everywhere continuous and differentiable
everywhere continuous but not differentiable at odd multiples of 2

(C) neither continuous nor differentiableat (2n + 1)*,ne Z
(D) not differentiable everywhere

If y=2x3x then dy at x= 1 is
dx

(A) 2 (C) 3 (D) 1

10. Let the function satisfy the equation f(x + y) = f(x) fly) for all x, ye R, where f(0) ÷ 0.
If f(5) = 3 and f'(0) = 2, then f'(5) is
(A) 6 (C) 5 (D) -6

The value of Cin (0, 2) satisfying thefmean value theoremj for the function fx) =x (x-1;
xe [0, 2) is equal to
4 2
(A) (B) (C) (D)
4 3 3 3

d cotl Z+x
12 dx cos2/
V2- x
is

3 1 1 1
(A)
4
(B)
2
(C)
2
H

H|
4

13. For the function fx) =x-6x + 12x 3; x=2 is
(A) a point of minimum (B) a point of inflexion
not a critical point (D) apoint of maximum

(C)
Space for Rough Work / deo Beod de

M A-2
(4)

14. The function x*; x>0 is strictly increasing at
(A) xe R E) x< 1 e
(C) x>= (D) x<0

l5. The maximum volume of the right circular cone with slant height 6 units is
(A) 4V3 cubic units B16 V3 cubic units
(C) 3N3 cubic units (D) 6/3 n cubic units

|16.) If f(x) =xel -x) then fx) is
(A) increasing in R (B) decreasing in R

deereasing in-1 (D) increasing in

sin x
17. dx =
3+ 4 cos x
2 cos x COS X
tan-l (B) tan-l +C
2/3 v3 3

tan-l
COS X 2 cos x
+C (D) tan-l +
243 3 3

18. (1-x) sin x.cos x dx =

(A) T co (B) 2n-18
3

(C)
2

Space for Rough Work / d s $Oz

-(6)
M A-2

1
19. dx =
x6 (log x)+7 log x +2
1
(A)
2
log 2logx +1 +C (B)
2log x + 1
log 3 logx + 2 +C
3log x + 2

es log 3 logx + 2 +C (D) log
3 log x + 2 +C
2log x + 1 2log x + 1
5x
sin
2 dx =
X
sin
2

(A) 2x + sin x + 2 sin 2x + C (B) X+2 sin x +2 sin 2x +C
(C) x+2 sin x+ sin 2x + C (D) 2x + sin x + sin 2x + C
5

21) x-3|+1-x) dx =
1

5
(A) 12 (C) 21 (D) 10
6

n
22. lim +
n ’0 n+12 n²+92 n²+32 5n

T
(B) tan3 (C) tan-l2 (D)
4

23. The area of the region bounded by the line y= 3x and the
curve y = x in sg. units is
9
(A) 10 (Br (C) 9 (D) 5
2

24. The area of the region bounded by the line y=x and the curve y= x3 is
(A) 0-2 sq. units R 03 sq. units
(C) O:4 sq. units (D) 0·5 sq. units

Space for Rough Work /d35 BOzE

M A-2

dy
25. The solution of edx =x+ 1, y(0) = 3 is

(A) y-2 = x log xX

yx-3=xlog x
(C) y-x-3= (x+ 1) log (x+ 1)
(D) y + X-3= (x+ 1)log (x +1)

26. The family of curves whose x and y intercepts of a tangent at any point are respectively
double the x and y coordinates of that point is
(A) Xy = (
B +y=C
(C) x-y'=C (D)

27. The vectors AB +3i + 4k'and AC =5i - 2j +4k are the sides of a A ABC. The length
of the median through A is
(A) V18 B) V72 (C) V33 (D) 288

28. The volume of the parallelopiped whose co-terminous edges are j + k,i+ k and i +j is
(A) 6 cu.units (B) 2 cu.units
(C) 4 cu.units 3cu,units

29. Let a and b be two unit vectors and 0 is the angle between them. Then a + b is a
unit
vector if
271
=
(B) =
(C) = (D) =
4 3
2

Space for Rough Work / d5 BORE T

10
M A-2

30. If : D C are three non-coplanar vectors and p. a, r are vectors defined by

bxc cxa axb
p= q = r = then

(a + b).p +(6+.+ + a). r is
(B) 1 (C) 2 (D) 3

31. If lines X -1 = y - 2 Z-3 X-1 y 5 z 6
3
and are mutually perpendicular.
2k 2 3k 1 -5
then k is equal to
10 7
(B) (C) -10 (D) 7
7 10

32. The distance between the two planes 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is
(A) 2 units 2
(B) 8units units (D) 4 units
V29
33. The sine of the angle between the straight line X - 2 y-3 4- z
3 4
and the plane
-5
2x2y +z=5 is
1 2
(A) (B) (C) 3
542 5/2 50 V50
34. The equation xy = 0 in three-dimensional space represents
(A) a pair of straight lines
(B) a plane
(C) a pair of planes at right angles
a pair of parallel planes
X 3
35. The plane containing the point (3, 2, 0) and the line -y-6 z- 4
is
1 5 4
(A) X-y+z=1 kB) x +y+z=5
(C) x+ 2y--Z=1 (D) 2x-y+ z=5

Space for Rough Work /ts0 BOx T

M A-2 (12 )

36. Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let
z= 4x + 6y be the objective function. The minimum value ofz'bccurs at
(A) Only (0, 2)
(B) Only (3, 0)
e ) The mid-point of the line segment joining the points (0, 2) and (3, 0)
(D) Any point on the line segment joining the points (0, 2) and (3, 0)

37. A die is thrown 10 times. The probability that an odd number will come up at least once 1s
11 1013
(A) (B)
1024 1024

1023 1-
(C) DY
1024 1024

38. A random variable X has the following probability distribution :
X 1 2

25 1
P(X) k
36 36

If the mean of the random variable X is then the variance is

1 5 7 11
(A) (B) (C)
18 18 18 18

R9. Tf a random variable X follows the binomial distribution with parameters n = 5. p
and
P(X=2) = 9P(X = 3), then p is equal to
1
(A) 10 (B) (D)
10

Space for Rough Work / de0 BO X

14
M A-2

40. The real value of 'g' for whichl
Sna is purely real is
1+2i sin a

(A) (n+ 1) ,n e N
(BY (2n + 1) 2
(C) n+, n e N
(D) (2n -1),neN
41. The length of a rectangle is five times the breadth. If the
minimum perimeter of the
rectangle is 180 cm, then
(A Breadth < 15 cm (B) Breadth > 15 cm
(C) Length s 15 cm (D) Length = 15 cm
42. The value of
49C3 +"Cg + 45Ca +0C4 is
(B)
(C) (D)
43. Two finite sets have m and n elements respectively. The total
number of subsets of the first
set is 56 more than the total number of subsets of the
second set. The values of mand n
respectively are
(A) 7, 6 (B 5, 1 (C) 6,3 (D) 8, 7
44. If [x]-5[x] +6 = 0, where x] denotes the greatest
integer function, then
(A) x e [3, 4] (B) xe [2, 4) e xe (2, 3] (D) XE (2, 3]

45. If in twocircles, arcs of the same length subtend angles 30° and 78°
at the centre, then the
ratio of their radii is
5 13 13
(A) (C) (D)
4
13 4 13

46. If AABC is right angled at C, then the value of tan A + tan B is

(AY a +b (B) (C) (D)
bc ab

Space for Rough Work / d3 #Ox 3e

16

47. In the expansion of (1+ x)"

+2 n
is equal to
n-1

n(n +1) n n +1
(A) (B) (C) (D) 3n (n + 1)
2 2

48. lf S,, stands for sum to n-terms of a G.P. with 'a' as the first term and T as the common
ratio then S, :S, is
(A) 1
(B) (C) r-1
r - 1

49. If A.M. and G.M. of roots of a quadratic equation are 5 and 4
respectively, then the
quadratic equation is
(A) -10x- 16 =0
B) x + 10x + 16 = 0
(C) x + 10x 16 = 0
(D) x- 10x +16 = 0

50. The angle between the line x+ y=3 and the line joining
the points (1, 1) and (-3, 4) is
(AX tan (7) (B) tan-l

(C)
tan= (D) tan-1

51. The equation of parabola whose focus is (6, 0) and directrix is x=-6 is
(A) y'= 24x B) y =-24x
(C) x²= 24y (D) x²=-24y

Space for Rough Work / lwd $OT0

(18 )

52. lim
J2 cos x-1
cotx - 1
is equal to
X ’
4

1
(A) 2 (B) V2 (C)

53. The negation of the statement
"For every real number x; x + 5 is positive"
is

(A} For every real number x; x+5 is not positive.
(B) For every real number x; x + 5 is negative.
(C) There exists at least one real number x such that x + 5 is not positive.
(D) There exists at least one real number x such that x +5 is positive.

54. Let a, b, C, d and e be the observations with mean m and standard deviation S. The
standard deviation of the observations a+k, b +k, c+ k, d +k and e +k is
(A) kS S
(B) S +k (C)
k

55. Let f: R’ R be given by f(x)= tan x. Then f- (1) is

(A) B nn + 4 :ne Z
4

(C) (D) {na + :ne Z
3

56. Let f: R’ R. be defined by f(x) = x + 1. Then the pre images of 17 and -3
respectively
are

(A) , {4, 4} (B) {3, - 3), ¢
(C) 14, - 4}, ¢ (D) {4, 4),{2, - 2}

Space for Rough Work /d835 tTE t

M A-2 ( 20 )

)-9

|x 1 1
dB
57. If A= and B=1 X 1 then
X dx
|1 1x
-3B

(C) 3B +1 (D) 1-3A

COS X X 1
58. Let flx) = 2 sin x lim f(x)
X 2x Then
X’0 2
sin x X

(A) -1 B)
(C) 3 (D) 2

59. Which one of the following observations is correct for the features of logarithm function to
any base b> 1?
(A) The domain of the logarithm function is R, the set of real numbers.
B) The range of the logarithm function is R*, the set of all positive real numbers.
(C) The point (1, ) isáways on the graph of the logarithm function.
(D) The graph of the logarithm function is decreasing as we move from left to right.

1 3

60. If P=1f3) 3 is the adjoint of a 3 x3 matrix A and |A| =4, then a. is equal to
2 4 4

(A) 4 (B) 5

11 (D) 0

Space for Rough Work / de30 Bot

M A-2 a2)

IM0418K24 (DAY-1, SECOND SESSION)
SUBJECT CODE TIME QUESTION BOOKLET
VERSION CODE SERIAL NUMBER

M 2.30 pm to 3.50 pm
A-2
Total Maximum Time for Maximum Total No. of
Duration Answering Marks Questions Mention your CET Number

80 Minutes 70 Minutes 60 60

DOs:
1. This question booklet is issued to you by the room invigilator after 2.30 pm.
2. Check whether the CET Number has been entered and shaded in the respective circles on the OMR answer sheet.
3. The version code of this question booklet should be entered on the OMR answer sheet and the respective circles should also be
shaded completely.
4. The Version Code and Serial Number of this question booklet should also be entered on theNominal Roll without any mistakes.
5. Compulsorily sign at the bottom portion of the OMR answer sheet in the space provided.
DONT:
1. THE TIMING AND MARKSPRINTED ON THE OMR ANSWER SHEET SHOULD NOT BE DAMAGED /MUTILATED/SPOILED.
2. The 3rd Bell rings at 2.40 pm, till then;
Do not remove the seal present on the right hand side of this question booklet.
Donot look inside this question booklet or start answering on the OMR answer sheet.

IMPORTANT INSTRUCTIONS TOCANDIDATES
1. In case of usage of SIGNS AND SYMB0LS in the questions, the regular textbook connotation should be considered unless stated
otherwise.
2. This question booklet contains 60 questions, each question will have one statement and four different options/responses & out of
which you have to choose one correct answer.
3. After the 3rd Bell rings at 2.40 pm, remove the paper seal of this question booklet and check that this booklet does not have anv
unprinted or torn or missing pages or items etc., if so, get it replacd by a complete test booklet. Read each item and start answering
on the OMR answer sheet.
4. Completely darken / shade the relevant circle with a blue or black ink ballpoint pen against the question number on the OMR
answer sheet,

Ga, 8a0ri WRONG METHoDS
CORRECT METHOD

A
5. Please note that even aminute unintended ink dot on the OMR answer shéet will also be recognized and recorded by the scanner
Therefore, avoid multiple markings of any kind on the OMR answer sheet.
6: Use the space provided on each page of thequestion booklet for Rough Work. Do not use the OMR answer sheet for the same

7. Last Bell will ring at 3.50 pm, stop writing on the OMR answer sheet.
R Hand over the OMR answer sheet to the room invigilator as it is.
9. After separating the top sheet (Ofice copy), the invigilator will return the bottom sheet replica (Candidate's copy) to vou,.
NOTE:In case of any discrepancyinthe English and KannadaVersions, the English version will be taken as final
M A-2 (24 )

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