KCET Sample Paper Maths

Sample Paper

Maths

Q.No. 1 If Aisa square matrix of order 3 × 3, then |KA| is equal to

(A) K|A|

(B) K |A| 2

(C) K |A| 3

(D) 3K|A|

Q.No. 2 If n
C 12 = nC 8 then n is equal to

(A) 26

(B) 12

(C) 6

(D) 20
1/2
Q.No. 3 ∫ 0 2
dx

2
is equals to
(1+x )√ 1−x

(A) √2
1
tan
−1
√
2

3

(B) √2
2
tan
−1
(
√2
3
)

(C) √2

2
tan
−1
(
3
2
)

(D)
√2 −1 √3
tan ( )
2 2

−1 18
7 −10 17 ⎡ ⎤
Q.No. 4 If 3A + 4B’ =[ ] and 2B − 3A ∗
4 0 then B =
0 6 31
⎣ ⎦
−5 −7

−1 −18
⎡ ⎤
(A) 4 −16

⎣ ⎦
−5 −7

1 3
⎡ ⎤
(B)

−1 1

⎣ ⎦
2 4

1 3
⎡ ⎤
(C) −1 1

⎣ ⎦
2 −4

(D)

(A) e

(B) 1

(C) -1

(D) 0

(D)

(B) 2

(C) 4

⎢⎥
⎡

⎣

Q.No. 6 ∫

(A) tan

(C) 2 tan
1

2

(D) 7/2

Q.No. 8 ∫

(A) 6 π

(B) 3 π

(C) 3

(D) 0
1

−1

2

Q.No. 5 If f (x) = {

−1

tan
−1

3

−3
−3

1

4

√x+x√x

√x + C

(B) 2 log(√x + 1) + C
−1
⎤

⎦

1

√x + C

√x + c
log

x−1

dx =
k
e
x
;

;
x ≠ 1

x = 1
is continuous at x = 1, then the value of k is

Q.No. 7 The value of C in Mean value theorem for the function f (x) = x in [2, 4] is

(A) 3

cot
−1
xdx =

Q.No. 9 If sin-1x + cos-1y = 2π/5 then cos-1x + sin-1y is

(A) 2π/5

(B) 3π/5

(C) 4π/5

(D) 3π/10

Q.No. 10 If y = tan −1
(
sin x+cos x

cos x−sin x
); then :
dy

dx
is equal to
2

(A) 1/2

(B) π /4

(C) 0

(D) 1

Q.No. 11 The negation of the statement “72 is (divisible by 2 and 3”

(A) 72 is not divisible by 2 or 72 is not divisible by 3

(B) 72 is is divisible by 2 or 72 is divisible by 3

(C) 72 is divisible by 2 and 72 is divisible by 3

(D) 72 is not divisible by 2 and 3

Q.No. 12 The order of the differential equation y = C e 1
C 2 +x
+ C3 e
C 4 +x
is

(A) 3

(B) 1

(C) 4

(D) 2

Q.No. 13 A bag contains 17 tickets, numbered from 1 to 17. A ticket is drawn and then another ticket is
drawn without replacing the first one. Find the probability that both the tickets may show even numbers.

(A) 7/34

(B) 8/17

(C) 7/16

(D) 7/17
x+1

Q.No. 14 If f (x) = sin −1
[
2

1+4
x ] then f’(0) =

(A) 2 log 2

5

(B) 2 log 2

(C) 2 log 2

7

(D) log 2

Q.No. 15 √y√x 3
6
√ (x + y) 5 then dy/dx

(A) x – y

(B) x/y

(C) y/x

(D) x + y

(A) 0°

(D) 3

(B)

(C)

(D)

(B)

(C)

(D) ∣
Q.No. 16 The angle between the lines 2x = 3y = -z and 6x = -y = -4z is

(B) 45°

(C) 90°

(D) 30°

Q.No. 17 √3 cosec 20° - sec 20° =

(A) 4

(B) 2

(C) 1

Q.No. 18 ∫ √x + 2x + 5dx is equal to

(A)
1

2

π

4

π

4

3

2
(x + 1)√ x

(x + 1)√ x

x + 1 + √x

x + 1 + √x

(x + 1)√ x

x + 1 + √x

Q.No. 19 ∫

−

−

−
4

3

2

2

3

π

4
2

2

2
2

x + 1 + √ x 2 + 2x + 5

2

2

2

(B) 2(sin x − x cos θ) + c

(C) 2(sin x + 2x cos θ) + C

(D) 2(sin x − 2x cos θ) + C
+ 2x + 5 + 2 log

+ 2x + 5

(x + 1)√ x 2 + 2x + 5 − 2 log

+ 2x + 5

+ 2x + 5 +

+ 2x + 5

cos 2x−cos 2θ

cos x−cos θ

(A) 2(sin x + x cos θ) + c
+ C

+ 2x + 5 + 2 log

+ C

+ C

1

2

+ C
log

dx is equal to

Q.No. 20 The area of the region above X-axis included between the parabola y2 = x and the circle x2 + y2 =
2x in square units is

(A) 2

3
−
π

Q.No. 21 3 + 5 + 7 + … . to n term is

(A) n(n + 2)

(B) n(n − 2)

(C) n 2

(D) (n + 1) 2

Q.No. 22 Everybody in a room shakes hands everybody else. The total number of handshakes is 45. The total
number of handshakes is 45. The total number of persons in the room is

(A) 9

(B) 10

(C) 5

(D) 15

Q.No. 23 The area of the region bounded by the a curve y = cos x between x = 0 and x = π is

(A) 1 sq. unit

(B) 4 sq. units

(C) 2 sq. units

(D) 3 sq. units
2
Ax x 1 A B C

Q.No. 24 Let Δ = By y
2
1 and Δ 1 = x y z then
2
Cz z 1 zy zx xy

(A) Δ 1 = −Δ

(B) Δ 1 = Δ

(C) Δ 1 ≠ Δ

(D) Δ 1 = 2Δ

Q.No. 25 The value of lim θ→0
1−cos 4θ

1−cos 6θ
is

(A) 4/9

(B) 9/4

(C) 9/3

(D) 3/4

Q.No. 26 If [x] represents the greatest integer function and f (x) = x – [x] – cos x then f’(π/2) =

(A) 2

(B) 0

(C) does not exist

(D) 1
m
Q.No. 27 If ( 1+i

1−i
) = 1 , then the least positive integral value of m is (

(A) 2

(B) 3

(C) 4

(D) 1

Q.No. 28 If a + π/2 < 2 tan-1 x + 3 cot-1 x < b then ‘a’ and ‘b’ are respectively.

(A) 0 and 2π

(B) 0 and π

(C) -π/2 and π/2

(D) π/2 and 2π
x

Q.No. 29 ∫ is equal to
(x+3)e
2
dx
(x+4)

(A) (x+4)
1
2
+ C

(B)
x
e
2
+ C
(x+4)

(C)
x
e
+ C
(x+4)

(D)
x
e
+ C
(x+3)

Q.No. 30 Acute angel between the line x−5

2
=
y+1

−1
=
z+4

1
and the plane 3x – 4y – z + 5 = 0 is

(A) cos −1
(
5
)
2√ 3

(B) cos −1
(
√ 364
9
)

(C) sin −1
(
5
)
2√ 13

(D) sin −1
(
9

√ 364
)

Q.No. 31 If (x1, y1), (x2,y2)and (x3,y3) are the vertices of a triangle whose area is ‘k’ square units, then
2
x1 y1 4

x2 y2 4 is

x3 y3 4

(A) 32 k2

(B) 16 k2

(C) 64 k2

(D) 48 k2

Q.No. 32 For the probability distribution given by the standard
deviation (σ) is

(A) √ 1

3

(B) ⅓ √ 5
2

(C) √ 5

36

(D) None of the above
16
Q.No. 33 The constant term in the expansion of a (x − 2 1

x
2
) is

(A) 16
C8

(B) 16
C7

(C) 16
C9

(D) 16
C 10

Q.No. 34 The third term of a G.P. is 9. The product of its first five terms is

(A) 310

(B) 35

(C) 312

(D) 39

Q.No. 35 If a, b, c are three consecutive terms of an AP and x, y, z are three terms of a GP, then the value of
xb-c .yc-a .Za-b is

(A) 0

(B) xyz

(C) -1

(D) 1

Q.No. 36 The shaded region in the figure is the solution set of the inequations

(A) 5x + 4y ≥ 20, x ≤ 6, y ≥ 3, x ≥ 0, y ≥ 0

(B) 5x + 4y ≤ 20, x ≤ 6, y ≤ 3, x ≥ 0, y ≥ 0

(C) 5x + 4y ≥ 20, x ≤ 6, y ≤ 3, x ≥ 0, y ≥ 0

(D) 5x + 4y ≥ 20, x ≥ 6, y ≤ 3, x ≥ 0, y ≥ 0

Q.No. 37 The distance of the point (1, 2, 1) from the line x−1

2
=
y−2

1
=
z−3

2

(A) √5

3

(B) 2 √3

5

(C) 20/3

(D) 2 √5

3

Q.No. 38 Foot of the perpendicular drawn from the point (1, 3, 4) to the plane 2x – y + z + 3 = 0 is

(A) (1, 2, - 3)

(B) (-1, 4, 3)

(C) (-3, 5, 2)

(D) (0, -4, -7)

Q.No. 39 Two events A and B will be independent if

(A) A and B are mutually exclusive

(B) P (A ∩ B ) = (1 − P(A))(1 − P(B))
′ ′

(C) P(A) = P(B)

(D) P(A) + P(B) = 1

Q.No. 40 The feasible region of an LPP is shown in the figure. If z = 3x + 9y, then the minimum value of z

occurs at

(A) (5, 5)

(B) (0, 10)

(C) (0, 20)

(D) (15, 15)

Q.No. 41 Let f (x) = x − 1

x
then f’(-1) is

(A) 0

(B) 2

(C) 1

(D) -2

Q.No. 42 The sides of an equilateral triangle are increasing at the rate of 4 cm/sec. The rate at which its area
is increasing, when the side is 14 cm.

(A) 42 cm2sec

(B) 10√3 cm2/sec

(C) 14 2/sec

(D) 14√3 2/sec

Q.No. 43 If y = √x + √x + √x + … ∞ then dy/dx =

(A) 2
y −1
1

(B) 2y+1
1

(C)
2y
2
y −1

(D) 2y−1
1

cos α sin α
Q.No. 44 If A = [ ] then AA’ = A=
− sin α cos α

(A) A

(B) Zero matrix

(C) A’

(D) I
7

Q.No. 45 ∫ dx is equal to
π/2 tan x
7 7
0 cot x+tan x

(A) π

2

(B) π

4

(C) π

6

(D) π

3

Q.No. 46 If A and B are two events of a sample space S such that P(A) = 2.0, P(B) = 0.6 and P(A|B) = 0.5
then P(A’|B)=

(A) 1/2

(B) 3/10

(C) 1/3

(D) 2/3

Q.No. 47 A random variable ‘X’ has the following probability distribution:

Then the value of k is

(A) 2/7

(B) 1/5

(C) 1/10

(D) -2

Q.No. 48 The range of sec −1
x is

(A) [ −π

2
,
π

2
]

(B) ( −π

2
,
π

4
)

(C) [0, π]

(D) [0, π] − { π

2
}

dy
Q.No. 49 The solution of the differential equation x dx
− y = 3 represents a family of

(A) straight lines

(B) circles

(A)

(B)

(C)

(D)

⎢⎥
(C) parabolas

(D) ellipses

Q.No. 50 The inverse of the matrix

⎡

⎣

⎡

⎣

⎡

⎣

⎡

⎣

Q.No. 51 ∫

(A) 4

(B) 4.5

(C) 3.5

(D) 3

A to B is

(A) 30

(B) 2

(C) 32

(D) 23
3

−1

1

3

−15

3
5

−1

1

3

−1

1
−15

−5

−5

−6

−5
6

−5

−1

−2

−15

6

3.5

0.2
6
−2

5

2

[x]dx
1

−5

2

5

−2

−2

−2
5

2

⎤

⎦
⎤

⎦

⎤

⎦

⎤

⎦

is equal to
⎡

⎣
2

0

−1
5

1

0
0

1

3
⎤

⎦
is

Q.No. 52 If A = {x| x ∈ N, x le 5}, B = { x | x ∈ Z, x2 – 5x + 6 = 0}, then the number of onto functions from

Q.No. 53 The maximum area of a rectangle inscribed in the circle (x+ 1)2 + (y-3)2 = 64 is

(A) 64 sq.units

(B) 72 sq. units

(C) 128 sq. units

(D) 8 sq. units

Q.No. 54 Area of the region bounded by the curve y = cos x, x = 0 and x = π is

(A) 2 sq. units

(B) 4 sq. units

(C) 3 sq. units

(D) 1 sq. unit

2 2

Q.No. 55 The degree and the order of the differential equation respectively are
d y 3 dy
2
= √1 + ( )
dx dx

(A) 2 and 3

(B) 3 and 2

(C) 2 and 2

(D) 3 and 3

Q.No. 56 Approximate change in the volume V of a cube of side x metres caused by increasing the side by
3% is

(A) 0.09 x3 m3

(B) 0.03 x3 m3

(C) 0.06 x3 m3

(D) 0.04 x3 m3

Q.No. 57 If P (n) : 2n < n! Then the smallest positive integer for which P (n) is true, is

(A) 4

(B) 2

(C) 5

(D) 3

Q.No. 58 The integrating factor of the differential equation is x ⋅ dy

dx
+ 2y = x
2
is (x ≠ 0)

(A) x 2

(B) log |x|

(C) e log x

(D) x
3 3 3 3

Q.No. 59 ∑ n

r=1
(2r − 1) = x then lim n→∞ [
1

x
2
+
2

x
2
+
3

x
2
+ …….+
n

x
2
]

(A) 1

(B) 1/2

(C) 4

(D) 1/4

Q.No. 60 If f (x) = 8x , g(x) = x
3 1/3
, then f og(x) is

(A) 8x

(B) 8 x
3

(C) (8x) 1/3

(D) 8x 3

Answer Sheet
Q.No Answer
Q.No. 1 (C)
Q.No. 2 (D)
Q.No. 3 (A)
Q.No. 4 (B)
Q.No. 5 (B)
Q.No. 6 (C)
Q.No. 7 (A)
Q.No. 8 (C)
Q.No. 9 (B)
Q.No. 10 (D)
Q.No. 11 (A)
Q.No. 12 (B)
Q.No. 13 (A)
Q.No. 14 (D)
Q.No. 15 (C)
Q.No. 16 (C)
Q.No. 17 (A)
Q.No. 18 (A)
Q.No. 19 (A)
Q.No. 20 (C)
Q.No. 21 (A)
Q.No. 22 (B)
Q.No. 23 (C)

Q.No. 24 (B)
Q.No. 25 (A)
Q.No. 26 (A)
Q.No. 27 (C)

Q.No. 28 (D)
Q.No. 29 (C)
Q.No. 30 (A)
Q.No. 31 (C)
Q.No. 32 (B)
Q.No. 33 (A)
Q.No. 34 (A)
Q.No. 35 (D)
Q.No. 36 (C)
Q.No. 37 (D)
Q.No. 38 (D)
Q.No. 39 (B)
Q.No. 40 (A)
Q.No. 41 (B)
Q.No. 42 (B)
Q.No. 43 (D)
Q.No. 44 (D)
Q.No. 45 (B)
Q.No. 46 (A)
Q.No. 47 (B)
Q.No. 48 (D)
Q.No. 49 (A)
Q.No. 50 (A)
Q.No. 51 (B)
Q.No. 52 (A)
Q.No. 53 (C)
Q.No. 54 (A)
Q.No. 55 (B)
Q.No. 56 (A)
Q.No. 57 (A)
Q.No. 58 (A)
Q.No. 59 (D)
Q.No. 60 (A)