kcet grand text

11 Apr 2025

7) How many arrangements can be made out of the letters of the word
1) If U is the universal set with 100 elements, A and B are two sets such "DRAUGHT", such that the vowels are never separated?
that n (A) = 50, n (B) = 60, n (A ∩ B) = 20 then n (A ′
∩ B ) =
′
(1) 1140
(1) 10 (2) 1420
(2) 90 (3) 1440
(3) 20 (4) 1380
(4) 40
8) Out of 10 white, 9 green and 7 black balls, one can select one or more
2) If tan 3 3π x balls in
x = , π < x < , then the value of cos is
4 2 2
(1) 880 ways
(1) −
1

√10 (2) 630 ways

(2) 3
(3) 879 ways
√10
(4) 550 ways
(3) 1

√10

(4) 3 9) If the coefficients of 2

nd
, 3
rd
and 4
th
terms in the expansion of
−
are in A.P then the value of n is
n
√10 (1 + x)

(1) 2
3) The value of cos 2
45
0
− sin 15
2 0
is
(2) 7
(1) √3
(3) 11
2

(2) √3 (4) 14
4

(3) √3 + 1
10) Let a be a G.P. If
a3
, then
a9
1, a2 , . . . . . . a10 = 25 =
a1 a5
2 √2

(1) 2 (5 )
2

(4) √3 − 1

2 √2 (2) 4 (5 )
2

(3) 5
4

4) 1 + i
2
+ i
4 6
+ i +. . . . . . . . +i
2n
is
(4) 5
3

(1) Positive
(2) Negative 11) Equation of line passing through the point (1, 2) and perpendicular to
(3) 0 the line y = 3x - 1 is
(4) Cannot be evaluated (1) x + 3y - 7 = 0
(2) x + 3y + 7 = 0
5) If x 2
− 3x + 2 > 0 and x 2
− 3x − 4 ≤ 0 then (3) x + 3y = 0
(1) |x| ≤ −2 (4) x - 3y = 0
(2) x ∈ [−1, 1) ∪ (2, 4]

(3) x ∈ [−1, 1) 12) Equation of circle with centre (−a, −b) and radius √a 2
− b
2
is
(4) x ∈ (2, 4] (1) x
2
+ y
2
+ 2ax + 2by + 2b
2
= 0

(2) x
2
+ y
2
− 2ax − 2by − 2b
2
= 0

6) If α and β are the roots of x

2
− ax + b
2
= 0, then α
2
+ β
2
is (3) x
2
+ y
2
− 2ax − 2by + 2b
2
= 0

equal to
(4) x
2
+ y
2
− 2ax + 2by + 2a
2
= 0

(1) a
2
− 2b
2

(2) 2a
2
− b
2
13) lim
1 − cos 4θ
is
1 − cos 6θ
θ → 0

(3) a
2
− b
2

(1)
4

(4) a
2
+ b
2

(2) 1

(3)
1
−
2

(4) 1
14) The value of lim |x|
is 22) cos[2sin
−1
3
+ cos
−1
3
] =
x→0 x 4 4

(1) 1 (1) Does not exist

(2) -1 (2) 3

5
(3) 0
(3) 3

(4) Does not exist 4

(4) −3

4
15) The mean deviation from the data 3, 10, 10, 4, 7, 10, 5 :
(1) 3 23) −1 63
sin(2sin √ ) =
65
(2) 2
(3) 3.75 (1) 4√65

65

(4) 2.57 (2) 2√126

65

(3)
√63

65

16) The eccentricity of the ellipse 9x 2

+ 25y
2
= 225 is
(4) 8√63

65

(1) 1

(2)
5

4 24) 1 0 1 0
If A = [ ];I = [
0 1 ] then which one of the following holds
(3) 4

5
1 1

(4)
9 for all n ⩾ 1, by the principle of mathematical induction
25

(1) A
n
= nA − (n − 1) I

17) The value of θ satisfying sin 7θ = sin 4θ − sin θ and 0 < θ < π
are (2) A
n
= 2
n−1
A − (n − 1) I
2

(1) π

9
,
π
(3) A
n
= nA + (n − 1) I
4

(2) π
,
π
(4) A
n
= 2
n−1
A + (n − 1) I
3 9

(3)
π π
,
6 9

25) 1 0 0 1 cos θ sin θ

(4) π

3
,
π

If I=[ 0 ] and J = [ ] and B=[ ] then B=

4
1 −1 0 − sin θ cos θ

(1) I cos θ − J sin θ

18) R be the relation on the set N of natural numbers, defined by xRy if
and only if x + 2y = 8. The domain of R is (2) I cos θ + J sin θ

(1) {2, 4. 7} (3) I sin θ + J cos θ

(2) {1, 2, 4} (4) I sin θ − J cos θ

(3) {2, 4, 6}
26) If A = [a ij
] such that a ij
= (i + j)
2
then trace of A is
(4) {2, 6, 8} n×n

(1) 1
n (n + 1) (2n + 1)
3

19) Which one of the following is not correct for the features of (2) 2
n (n − 1) (2n − 1)
exponential function given by f (x) = b
x
where b > 1 3

(1) For very large negative values of x, the function is very close to 0 (3) 2
n (n + 1) (2n + 1)
3

(2) The domain of the function is R, the set of real numbers (4) 1
n (n − 1) (2n − 1)
3
(3) The point (1, 0) is always on the graph of the function
(4) The range of the function is the set of all positive real numbers
27) If A is singular matrix then adj A is
(1) non-singular
20) The graph of the function y = f (x) is symmetrical about the line
(2) singular
x = 2 , then
(3) symmetric
(1) f (x + 2) = f (x − 2)

(4) not defined

(2) f (2 + x) = f (2 − x)

(3) f (x) = f (−x)

28) The system of linear equations
(4) f (x) = −f (−x)
x + y + z = 6, x + 2y + 3z = 10 and
x + 2y + az = b has no solutions when _______
21) Let f (x) = x
2
and f (x) = 2
x
. Then the solution set of (fog) (x) =
(1) a = 2, b ≠ 3
(gof) (x) is
(2) a = 3, b ≠ 10
(1) R
(3) a = 2, a = 3
(2) {0}
(4) b = 3, a ≠ 10
(3) {0, 2}
(4) none of these
29) a 0 0 36) If y = √ a √x then,
dy
=
⎡ ⎤ dx

If A=⎢ 0 a 0 ⎥ then |adj A| = (1) 1

y
⎣ 0 0 a ⎦ 2

(2)
√x
a log a

(1) a
3
2y√x

√x

(2) a
6 (3) a log a

4y√x

(3) a
9
(4) a
√x
log a

y √x

(4) a
27

37) If y
2
x−√1−x dy
= tan
−1
( ), then =
30) 1 2 x+√1−x
2 dx

If A=[ 5 4 ] then (A+I)(A-6I)= (1) 1

2
1−x

(1) A (2) 1

√1−x2

(2) O (3) 1

2
1+x

(3) 4I (4)
1

√1+x2

(4) I

38) The total revenue in rupees received from the sale of x units of a
31) ∣
1 a b
∣ ∣
a b c
∣ product is given by, R(x) = 3x
2
+ 36x + 5 The marginal revenue,
If D = ∣ ∣ 1 b c ∣ ∣ b c a ∣
∣
, then
∣ ∣
=
when x = 15 is
∣ 1 c a ∣ ∣ 1 1 1 ∣
(1) 116
(1) 0
(2) 96
(2) D
(3) 90
(3) -D
(4) 126
(4) None of these
1

39) The maximum value of [x(x − 1) + 1] , 0 3

⩽ x ⩽ 1 is
32) If f (x) = x ⋅ sin
1

x
, x ≠ 0, then the value of the function at 1

x = 0, so that the function is continuous at x = 0 is (1) 1 3

( )
3

(1) 0 (2) 1

(2) -1 (3) 1
(3) 1 (4) 0
(4) Indeterminate
40) cos 2x − cos 2θ

x − |x|
∫ dx is equal to
33) f (x) =
x
, x ≠ 0, f (0) = 2. f (x) is cos x − cos θ

(1) Continuous nowhere (1) 2 (sin x + x cos θ) + c

(2) Continuous everywhere (2) 2 (sin x − x cos θ) + c

(3) Continuous for all x except x = 1 (3) 2 (sin x + 2x cos θ) + c

(4) Continuous for all x except x = 0 (4) 2 (sin x − 2x cos θ) + c

34) If f (x) = 2x and g (x) = x

2
+ 1, then which of the following 41) ∫ √x
2
+ 2x + 5dx is equal to
can be discontinuous function
(1) 1
(x + 1) √x + 2x + 5 + 2log∣
2 2 ∣
∣(x + 1) + √x + 2x + 5∣+C
(1) f (x) + g (x) 2

(2) f (x) − g (x)

(2) (x + 1) √x2 + 2x + 5 + 2 log∣ 2 ∣
∣x + 1 + √x + 2x + 5∣ +C

(3) f (x) ⋅ g (x)

(3) (x + 1) √x
2
+ 2x + 5 − 2log∣
2 ∣
∣x + 1 + √x + 2x + 5∣+C

(4)
g (x)
(4) 2
(x + 1) √x + 2x + 5 +
1
log∣
2 ∣
∣x + 1 + √x + 2x + 5∣+C
f (x) 2

35) The function f (x) = 1 + |sin x| is 42) 1

∫ dx =

(1) Continuous nowhere √x + x√x

(2) Continuous everywhere and not differentiable at infinitely many (1) 2tan
−1
√x + C

points (2) tan

−1
√x + C

(3) Differentiable nowhere (3) 1

tan
−1
√x + C
2

(4) Differentiable at x=0

(4) 2 log(√x + 1) + C
 2
43) π/4
50) ∣→ → ∣2
→
→
→ ∣→ ∣
If ∣ a × b ∣ + ( a . b ) = 144 and ∣∣ a ∣∣ = 4 then ∣ b ∣ =
The value of the integral ∫ log(sec θ − tan θ)dθ is ∣ ∣ ∣ ∣

−π/4
(1) 16
(1) 0 (2) 8
π
(2) (3) 3
4

(3) π
(4) 12
π
(4)
2 → →
51) If → →
a and b are unit vectors, then what is the angle between a and b

→
→

44) 8
√10 − x
for √3 a − b to be a unit vector?
The value of ∫ dx is
2 √x + √10 − x (1) 30
0

(1) 8 (2) 45
0

(2) 10 (3) 60
0

(3) 3 (4) 90°

(4) 0
→
52) If the area of the parallelogram with →
a and b as two adjacent sides is

45) 5
→
→

∫ |x + 2| dx is equal to 15 sq. units, then the area of the parallelogram having 3 a + 2 b and
→
→
−5 a + 3 b as two adjacent sides in sq. units is
(1) 29 (1) 45
(2) 28 (2) 75
(3) 27 (3) 105
(4) 30 (4) 120

46) The solution of the differential equation x

dy
− y = 3 represents a 53) The reflection of the point (α, β, γ) in the xy-plane is
dx

family of (1) (α, β, 0)

(1) Straight lines (2) (0, 0, γ)

(2) Circles (3) (−α, −β, γ)

(3) Parabolas (4) (α, β, −γ)

(4) Ellipses
54) The angle between the lines 2x = 3y = −z and 6x = −y = −4z is

47) Integrating factor of dy 1 + y (1) 45°

+ y = is
dx x
(2) 30°
x
(1)
e
x
(3) 0°
x
(2) e
(4) 90°
x

(3) xe
x

55) The co-ordinate of foot of perpendicular drawn from the origin to the
(4) e
x

plane 2x − 3y + 4z = 29 is
(1) (5, -1, 4)
48) Integrating factor of x dy
− y = x
4
− 3x is
dx (2) (2, -3, 4)
(1) 1
(3) (7, -1, 3)
x

(2) x
(4) (5, -2, 3)

(3) −x

56) Two events A and B will be independent, if

(4) log x
(1) A and B are mutually exclusive

49) The order and degree of the differential equation y dy 2 (2) ′ ′

P (A ∩ B ) = (1 − P (A))(1 − P (B))
= x +
dx dy
(3) P(A)=P(B)
dx

is (4) P(A)+P(B)=1

(1) 1, 2
(2) 1, 3
(3) 2, 1
(4) 1, 1
57) Two dice are thrown simultaneously. The probability of obtaining a 59) If A and B are two events of a sample space S such that
total score of 5 is P (A) = 0.2, P (B) = 0.6 and P (A|B) = 0.5 and P (A |B) =
′

(1) 1
(1) 1

9 3

(2) 1
(2) 1

18 2

(3) 1
(3) 2

36 3

(4) 1
(4) 3

12 10

58) Two cards are drawn at random from a pack of 52 cards. The 60) Area of the region bounded by the curve y = cos x between x = 0

probability of these two being "Aces" is and x = π is

(1) 1
(1) 2 Sq. Units
2
(2) 4 Sq. Units
(2) 1

26 (3) 3 Sq. Units

(3) 1
(4) 1 Sq. Unit
13

(4) 1

221