CUSAT CAT 2019 Question Paper Maths
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Page 1
CAT - 2019 MATHEMATICS PG
019
2
S T
E
1. Let T
be a matrix of order m × n, where for all i, j. Then rank(A) is
N
O
(A) m SI
(B) m–n IS
M
M
(C) 1
(D) 0 D
A
N
2. TheM
O
vectors , and are linearly independent in if
SA
O
T (B)
M
C (A) and
and
O
CU (C)
S IO
(D)
2 0
3.
U
C IS S E ST
The number of non-trivial subspaces of
(A) 0 T
over is
(B) infinite N
O
M I
(C) 3
S
IS
(D) 6
A D
4. If and , then
A
(A)
N
O
(B) x < 4
M
(C) 3 < x < 4 M
C O
(D)
A T
S
5.
C U
The area enclosed within the curve |x| + |y| = 1 is
019
2
S T
E
1. Let T
be a matrix of order m × n, where for all i, j. Then rank(A) is
N
O
(A) m SI
(B) m–n IS
M
M
(C) 1
(D) 0 D
A
N
2. TheM
O
vectors , and are linearly independent in if
SA
O
T (B)
M
C (A) and
and
O
CU (C)
S IO
(D)
2 0
3.
U
C IS S E ST
The number of non-trivial subspaces of
(A) 0 T
over is
(B) infinite N
O
M I
(C) 3
S
IS
(D) 6
A D
4. If and , then
A
(A)
N
O
(B) x < 4
M
(C) 3 < x < 4 M
C O
(D)
A T
S
5.
C U
The area enclosed within the curve |x| + |y| = 1 is
Page 2
(A) 2 sq units
19
(B) 4 sq units
(C)
(D)
6 sq units
8 sq units 20
S T
E
T
6.
N
If the point P(4, 3) is shifted by a distance unit parallel to the line then the
O
I
coordinates of P in the new position is
S
(A) (–5, –4) IS
M
D
(B) (5 + A 4 +
M )
N
(C) O
M
A T
S 7.
CO
If
M
(D) (5, 4)
O
C T E and are two tangents to a circle, then the radius of
CU
(A) 1
AT
the circle is
N 19
S IO 0
(B) 2
2
U
(C)
S T
4
(D) 6
S
8. C IS N
T E
The locus of the centers of the circles which touch both the axes is given by
O
(A)
S I
(B)
A
(C)
(D)
O
N
A
D
M
M
9. If , then x is
C O
(A) 3
AT
(B) 2
S
(C)
(D)
log3 2
log2 3
CU
19
(B) 4 sq units
(C)
(D)
6 sq units
8 sq units 20
S T
E
T
6.
N
If the point P(4, 3) is shifted by a distance unit parallel to the line then the
O
I
coordinates of P in the new position is
S
(A) (–5, –4) IS
M
D
(B) (5 + A 4 +
M )
N
(C) O
M
A T
S 7.
CO
If
M
(D) (5, 4)
O
C T E and are two tangents to a circle, then the radius of
CU
(A) 1
AT
the circle is
N 19
S IO 0
(B) 2
2
U
(C)
S T
4
(D) 6
S
8. C IS N
T E
The locus of the centers of the circles which touch both the axes is given by
O
(A)
S I
(B)
A
(C)
(D)
O
N
A
D
M
M
9. If , then x is
C O
(A) 3
AT
(B) 2
S
(C)
(D)
log3 2
log2 3
CU
Page 3
019then
10. If the fourth roots of unity are 2 is equal to
(A) 1 S T
E
(B) 0 T
N
O
(C) i
SI
IS
M
M
(D) i
D
A
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
10. If the fourth roots of unity are 2 is equal to
(A) 1 S T
E
(B) 0 T
N
O
(C) i
SI
IS
M
M
(D) i
D
A
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 4
11. The equation represents a
019
(A) pair of straight lines 2
(B)
(C)
circle
parabola S T
E
(D) hyperbola T
N
O
S I
IS
M
M
12. The radius of the circle is equal to
D
A
(A) N
O
M
M
O
(B)
SA
T
O
C (C) 5
(D) 625
CU
13.
The sum of the series (1 + 2) + (1 + 2 + 22) + (1 + 2 + 22 + 23) + … up to n terms is
(A)
S IO 2 0
(B)
U
C IS
(C) S T E ST
N
(D)
O
S I
14.
A
(A)
O
N
A
D
is equal to
M
(B)
M
(C) C O
AT
(D) S
CU
019
(A) pair of straight lines 2
(B)
(C)
circle
parabola S T
E
(D) hyperbola T
N
O
S I
IS
M
M
12. The radius of the circle is equal to
D
A
(A) N
O
M
M
O
(B)
SA
T
O
C (C) 5
(D) 625
CU
13.
The sum of the series (1 + 2) + (1 + 2 + 22) + (1 + 2 + 22 + 23) + … up to n terms is
(A)
S IO 2 0
(B)
U
C IS
(C) S T E ST
N
(D)
O
S I
14.
A
(A)
O
N
A
D
is equal to
M
(B)
M
(C) C O
AT
(D) S
CU
Page 5
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 6
15. The solution of the differential equation
019 is
(A)
2
S T
E
(B) y
T
N
(C) O
SI
(D) IS
M
A
D
M
N
16. O
The integrating factor of the differential equation is
M
SAT
CO
M
(A)
(B)
O
CU (C)
S IO
(D) log y
2 0
17.
U S ST
The number of distinct real values of , for which the vectors
and
C IS T E
are coplanar, is
N
(A) 0
O
M I
(B) 1
S
IS
(C) 2
D
(D) 3
M
18. If A
(A) 2
N
A
D
are three non-coplanar mutually perpendicular unit vectors, then
O
is
(B) 0 M
(C) 1 M
(D) 3
C O
AT
S
CU
019 is
(A)
2
S T
E
(B) y
T
N
(C) O
SI
(D) IS
M
A
D
M
N
16. O
The integrating factor of the differential equation is
M
SAT
CO
M
(A)
(B)
O
CU (C)
S IO
(D) log y
2 0
17.
U S ST
The number of distinct real values of , for which the vectors
and
C IS T E
are coplanar, is
N
(A) 0
O
M I
(B) 1
S
IS
(C) 2
D
(D) 3
M
18. If A
(A) 2
N
A
D
are three non-coplanar mutually perpendicular unit vectors, then
O
is
(B) 0 M
(C) 1 M
(D) 3
C O
AT
S
CU
Page 7
19. If then is equal to
019
2
(A)
S T
E
T
N
(B) O
SI
IS
M
M
(C)
D
A
N
(D) O
M
A T
S 20.
CO
M
O
T
If then is
CU
(A)
A N 19
S IO 2 0
U S
(B)
ST
C IS
(C)
O
N
T E
(D)
S I
21. If A O
N
A
then
D
is equal to
(A) M
M
(B) C O
AT
S
CU
019
2
(A)
S T
E
T
N
(B) O
SI
IS
M
M
(C)
D
A
N
(D) O
M
A T
S 20.
CO
M
O
T
If then is
CU
(A)
A N 19
S IO 2 0
U S
(B)
ST
C IS
(C)
O
N
T E
(D)
S I
21. If A O
N
A
then
D
is equal to
(A) M
M
(B) C O
AT
S
CU
Page 8
(C)
019
2
(D)
S T
E
T
N
O
SI
22. If
IS by
is defined for where [x] is the greatest integer
M
D
M
A x, then the set
not exceeding is equal to
N
O
M the set of all integers
(A)
SA
O
M
O E
C (B) the set of all natural numbers
C T
T (C) , the empty set
CU (D)
S IO 2 0
U S T
23. The value of is
S
C IS E
(A) 1
T
(B)
N
O
(C) 0
(D)
S I
24.
(A)
A
The value of
log 5 O
N
A
D
is
(B) 0 M
(C) 1
M
(D) 2log 5
C O
A Tis decreasing function of x in the largest possible interval
25. If
Sof is equal to
U
, then the value
C
019
2
(D)
S T
E
T
N
O
SI
22. If
IS by
is defined for where [x] is the greatest integer
M
D
M
A x, then the set
not exceeding is equal to
N
O
M the set of all integers
(A)
SA
O
M
O E
C (B) the set of all natural numbers
C T
T (C) , the empty set
CU (D)
S IO 2 0
U S T
23. The value of is
S
C IS E
(A) 1
T
(B)
N
O
(C) 0
(D)
S I
24.
(A)
A
The value of
log 5 O
N
A
D
is
(B) 0 M
(C) 1
M
(D) 2log 5
C O
A Tis decreasing function of x in the largest possible interval
25. If
Sof is equal to
U
, then the value
C
Page 9
(A) 12
(B) 12
019
2
(C) 6
S T
E
(D) 6 T
N
O
SI
IS
M
26. D
M
The maximum sum of the series 20 + 19
A
is
(A) 310N
O
(B)M 290
SAT
M
CO (C) 320
(D) 360
O
CU
27.
AT N
The product (32)
9
is equal to
1
(A)
(B)
16
64
S IO 2 0
(C)
(D)
U
32
C IS
0
S T E ST
N
28.
O
The sum of 20 terms of the series is equal to
S I
D
(A) 210
M
A D
(B) 220
A
(C) 300
N
O
(D)
320 M
M
C O
29. If
T
is one of the factors of the expression
A
then
(A) 4, 5 S
CU
(B) 12
019
2
(C) 6
S T
E
(D) 6 T
N
O
SI
IS
M
26. D
M
The maximum sum of the series 20 + 19
A
is
(A) 310N
O
(B)M 290
SAT
M
CO (C) 320
(D) 360
O
CU
27.
AT N
The product (32)
9
is equal to
1
(A)
(B)
16
64
S IO 2 0
(C)
(D)
U
32
C IS
0
S T E ST
N
28.
O
The sum of 20 terms of the series is equal to
S I
D
(A) 210
M
A D
(B) 220
A
(C) 300
N
O
(D)
320 M
M
C O
29. If
T
is one of the factors of the expression
A
then
(A) 4, 5 S
CU
Page 10
(B) 5, 4
(C) 5, 4 019
2
(D) 5, 4
S T
E
T
N
O
S Ithe value of
IS
30. If , then is
M
M
(A) 3
D
(B) 2 A
(C) 1N
(D) O
4
M
SA T
31.
CO
If
M
O
C T E , then
CU (A)
S IO
(B) abc = 1
2 0
(C)
U
C IS
(D) S .
T
.
E ST
N
O
32.
S I
The number of numbers greater than 1000 but not greater than 4000 that can be formed
D
with the digits
M
repetition of digits being allowed, is
A
(A)
(B)
(C)
(D)
374
375
376
377 O
N
A
D
M
M
33. O
The number of divisors of the form
C
of the integer 240 is
(A) 4
(B) 8 A T
(C) 10 S
(D) 3
C U
(C) 5, 4 019
2
(D) 5, 4
S T
E
T
N
O
S Ithe value of
IS
30. If , then is
M
M
(A) 3
D
(B) 2 A
(C) 1N
(D) O
4
M
SA T
31.
CO
If
M
O
C T E , then
CU (A)
S IO
(B) abc = 1
2 0
(C)
U
C IS
(D) S .
T
.
E ST
N
O
32.
S I
The number of numbers greater than 1000 but not greater than 4000 that can be formed
D
with the digits
M
repetition of digits being allowed, is
A
(A)
(B)
(C)
(D)
374
375
376
377 O
N
A
D
M
M
33. O
The number of divisors of the form
C
of the integer 240 is
(A) 4
(B) 8 A T
(C) 10 S
(D) 3
C U
Page 11
019
34. The coefficient of in 2 is
S T
E
(A)
T
(B) N
O
SI
(C) IS
M
(D)
A
D
M
N
O
M
SA T
35.
CO
M
O
The solution set of the equation determinant of the matrix = 0 is
CU (A)
(B)
AT
{0, 1}
N 19
S IO
(C) {1, –1}
(D) {1, –3}
2 0
36.
U
C IS S
The system of linear equations
has T E ST and
N
O
M
(A) infinite number of solutions
(B)
S I
exactly 3 solutions
IS
D
(C) a unique solution
(D) no solution
M
37.
A
If the matrix
O
N
A
D
is commutative with the matrix , then
(A) M
M
(B)
C O
(C)
AT
S
(D)
CU
34. The coefficient of in 2 is
S T
E
(A)
T
(B) N
O
SI
(C) IS
M
(D)
A
D
M
N
O
M
SA T
35.
CO
M
O
The solution set of the equation determinant of the matrix = 0 is
CU (A)
(B)
AT
{0, 1}
N 19
S IO
(C) {1, –1}
(D) {1, –3}
2 0
36.
U
C IS S
The system of linear equations
has T E ST and
N
O
M
(A) infinite number of solutions
(B)
S I
exactly 3 solutions
IS
D
(C) a unique solution
(D) no solution
M
37.
A
If the matrix
O
N
A
D
is commutative with the matrix , then
(A) M
M
(B)
C O
(C)
AT
S
(D)
CU
Page 12
019
2
38. If and
S T are two matrices such
E
that AB is a null matrix, then
T is
N
(A) 0 O
S I
IS of
(B) an odd multiple
M
(C)
A
D
M
anNeven multiple of
(D) O
=
M
SA T
39.
CO
M
O
C T
The value of the sum E is equal to
CU (A)
(B)
(C)
e
AT
e2 + e
e2
N 19
S IO 0
(D) e2 – e
2
40. U
C IS S
The sum of the series
T E ST
is
N
O
M I
(A)
S
IS
(B)
A
(C)
O
N
A
D
M
(D) M
C O
A T
41. Let Sand Then the set is equal to
CU
2
38. If and
S T are two matrices such
E
that AB is a null matrix, then
T is
N
(A) 0 O
S I
IS of
(B) an odd multiple
M
(C)
A
D
M
anNeven multiple of
(D) O
=
M
SA T
39.
CO
M
O
C T
The value of the sum E is equal to
CU (A)
(B)
(C)
e
AT
e2 + e
e2
N 19
S IO 0
(D) e2 – e
2
40. U
C IS S
The sum of the series
T E ST
is
N
O
M I
(A)
S
IS
(B)
A
(C)
O
N
A
D
M
(D) M
C O
A T
41. Let Sand Then the set is equal to
CU
Page 13
(A)
(B) 019
2
(C)
S T
E
(D) T
N
O
S I
42. IS set all real numbers and it is defined by
If R is a relation over the then R is
M
(A) reflexive
M
D and transitive
A and symmetric
(B) reflexive
N
(C) symmetric and transitive
(D) O
M an equivalence relation
SA
T
O
M
43. C Let O
be the mapping defined by Then f is
T
(A) bijective
CU
N
(B) surjective
A
(C) injective
19
S IO
(D) automorphism
2 0
44. Let
(A) U
C IS S and
T E ST
be coprime. If and then
(B) N
O
(C)
S I
(D)
45.
A O
N
A
D
The number of onto mappings from the set in to the set is
(A) 2m – 2 M
(B) 2m M
(C)
(D)
2m – 1 – 2
2m C O
AT
S
CU
(B) 019
2
(C)
S T
E
(D) T
N
O
S I
42. IS set all real numbers and it is defined by
If R is a relation over the then R is
M
(A) reflexive
M
D and transitive
A and symmetric
(B) reflexive
N
(C) symmetric and transitive
(D) O
M an equivalence relation
SA
T
O
M
43. C Let O
be the mapping defined by Then f is
T
(A) bijective
CU
N
(B) surjective
A
(C) injective
19
S IO
(D) automorphism
2 0
44. Let
(A) U
C IS S and
T E ST
be coprime. If and then
(B) N
O
(C)
S I
(D)
45.
A O
N
A
D
The number of onto mappings from the set in to the set is
(A) 2m – 2 M
(B) 2m M
(C)
(D)
2m – 1 – 2
2m C O
AT
S
CU
Page 14
46. If the probability of a defective bolt is 0.1, then the mean and the standard deviation of
distribution of bolts in a total of 400 are
019
(A) 30, 3 2
(B) 40, 5
S T
E
(C) 30, 4
(D) 40, 6 T
N
O
47.
certain married M
I
SIto be chosen from a group of 9 people. The probability that a
A committee of fiveSis
M
couple will either serve together or not at all is
D
A
(A) N
O
M
SA
T
CO
M
(B)
O
T
(C)
CU
(D)
A N 19
S IO 2 0
48.
U S ST
Seven balls are drawn simultaneously from a bag containing 5 white and 6 green balls.
C IS E
The probability of drawing 3 white and 4 green balls is
T
(A) N
O
S I
(B)
(C)A O
N
A
D
(D) M
M
C O
AT
S
CU
distribution of bolts in a total of 400 are
019
(A) 30, 3 2
(B) 40, 5
S T
E
(C) 30, 4
(D) 40, 6 T
N
O
47.
certain married M
I
SIto be chosen from a group of 9 people. The probability that a
A committee of fiveSis
M
couple will either serve together or not at all is
D
A
(A) N
O
M
SA
T
CO
M
(B)
O
T
(C)
CU
(D)
A N 19
S IO 2 0
48.
U S ST
Seven balls are drawn simultaneously from a bag containing 5 white and 6 green balls.
C IS E
The probability of drawing 3 white and 4 green balls is
T
(A) N
O
S I
(B)
(C)A O
N
A
D
(D) M
M
C O
AT
S
CU
Page 15
49. A biased coin with probability p, of heads is tossed until a head appears for
019
2 number of tosses required is even is
the first time. If the probability that the , then p is
equal to S T
TE
(A)
O
N
S I
IS
(B)
M
A
D
M
(C) N
O
M
A T
S 50.
CO
M
(D)
O
CU
(A)
AT
Which of the following numbers is rational?
N 19
S IO
(B) cos 15
2 0
U
(C) sin 15 cos 15
51.
S
(D) sin 15 cos 75
C IS
The equation
N
T E ST
has
O
(A)
M S
only one solution
IS
I
D
(B) two solutions
(C) infinitely many solutions
M
A
(D) no solutions
D
A
N
52. The equation
O represents
(A) circle M
(B) M
a pair of two distinct straight line
(C)
(D)
a point
C O
a pair of coincident straight line
AT
S
CU
019
2 number of tosses required is even is
the first time. If the probability that the , then p is
equal to S T
TE
(A)
O
N
S I
IS
(B)
M
A
D
M
(C) N
O
M
A T
S 50.
CO
M
(D)
O
CU
(A)
AT
Which of the following numbers is rational?
N 19
S IO
(B) cos 15
2 0
U
(C) sin 15 cos 15
51.
S
(D) sin 15 cos 75
C IS
The equation
N
T E ST
has
O
(A)
M S
only one solution
IS
I
D
(B) two solutions
(C) infinitely many solutions
M
A
(D) no solutions
D
A
N
52. The equation
O represents
(A) circle M
(B) M
a pair of two distinct straight line
(C)
(D)
a point
C O
a pair of coincident straight line
AT
S
CU
Page 16
53. In the interval , the function
019 is
(A) increasing
2
(B) decreasing S T
E
(C)
T
neither increasing nor decreasing
(D)
N
partly increasing and partly decreasing
O
SI
54. Let G be a group ofISeven order with identity element e. Then
M
(A)
A
M
Dfor some
(B) O
N for some
M
SA T
O
M
(C)
C (D) O
for some
for no
CU
55.
AT N 9
If every element of a group G is its own inverse, then G is
1
(A)
S IO
abelian
2 0
U
(B) infinite
S T
(C) cyclic
S
C IS E
(D) finite
T
N
O
M I
56. The set of congruent 8 classes under multiplication modulo 8 forms
S
IS
D
(A) a cyclic group
(B) a monoid
M
A
(C) an abelian group
(D) D
the Klein four group
A
N
57. O
Consider the group where is the set of all positive relational numbers and
M
M
* is defined by a * b =
C O. Then the inverse of 3 is
(A)
AT
S
(B)
CU
019 is
(A) increasing
2
(B) decreasing S T
E
(C)
T
neither increasing nor decreasing
(D)
N
partly increasing and partly decreasing
O
SI
54. Let G be a group ofISeven order with identity element e. Then
M
(A)
A
M
Dfor some
(B) O
N for some
M
SA T
O
M
(C)
C (D) O
for some
for no
CU
55.
AT N 9
If every element of a group G is its own inverse, then G is
1
(A)
S IO
abelian
2 0
U
(B) infinite
S T
(C) cyclic
S
C IS E
(D) finite
T
N
O
M I
56. The set of congruent 8 classes under multiplication modulo 8 forms
S
IS
D
(A) a cyclic group
(B) a monoid
M
A
(C) an abelian group
(D) D
the Klein four group
A
N
57. O
Consider the group where is the set of all positive relational numbers and
M
M
* is defined by a * b =
C O. Then the inverse of 3 is
(A)
AT
S
(B)
CU
Page 17
(C)
(D) 019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
(D) 019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 18
19
58. The generators of the cyclic group are
20
(A)
2 and
S T
E
T
(B) N
O
4 and
SI
IS
M
M
(C)
6 andD
A
(D) N
O8 and
M
T
59.
CO
M
O
The number of points on the circle
SA point (–2, 1) is
which are at distance 2 from the
CU (A)
(B)
2
0
S IO
(C) 1
(D) 3
2 0
60. Let
U
C IS S Then T E ST
is equal to
N
O
(A)
S I
A D
(B)
A
(C) N
O
(D) 1 M
M
C O
61. If and
AT are in geometrical progression, then are in
(A) AP S
CU
58. The generators of the cyclic group are
20
(A)
2 and
S T
E
T
(B) N
O
4 and
SI
IS
M
M
(C)
6 andD
A
(D) N
O8 and
M
T
59.
CO
M
O
The number of points on the circle
SA point (–2, 1) is
which are at distance 2 from the
CU (A)
(B)
2
0
S IO
(C) 1
(D) 3
2 0
60. Let
U
C IS S Then T E ST
is equal to
N
O
(A)
S I
A D
(B)
A
(C) N
O
(D) 1 M
M
C O
61. If and
AT are in geometrical progression, then are in
(A) AP S
CU
Page 19
(B) GP
(C) HP
019
2
(D)
S T
E
T
N
O
62.
I
The interior angles of a polygon are in AP. The smallest angle is 120 and the common
S
IS
difference is 5. The number of sides of the polygon is
M
M
(A) 9
D
(B) 10 A
(C) N
16
(D) O
5
M
SA T
63.
CO
If
M
O
C T
then E is equal to
CU (A) 0
(B) 5
(C)
S IO 2 0
U
(D) 10
C IS S T E ST
64. If roots of the equation N are , then the value of
O
S I is
(A)
(B)
D n
n2 M
A
(C)
(D)
nn
0
O
N
A
D
65. If M
does not have two distinct real roots, then the least value of is
M
(A)
C O
(B)
AT
(C) 3 S
(D) 2
CU
(C) HP
019
2
(D)
S T
E
T
N
O
62.
I
The interior angles of a polygon are in AP. The smallest angle is 120 and the common
S
IS
difference is 5. The number of sides of the polygon is
M
M
(A) 9
D
(B) 10 A
(C) N
16
(D) O
5
M
SA T
63.
CO
If
M
O
C T
then E is equal to
CU (A) 0
(B) 5
(C)
S IO 2 0
U
(D) 10
C IS S T E ST
64. If roots of the equation N are , then the value of
O
S I is
(A)
(B)
D n
n2 M
A
(C)
(D)
nn
0
O
N
A
D
65. If M
does not have two distinct real roots, then the least value of is
M
(A)
C O
(B)
AT
(C) 3 S
(D) 2
CU
Page 20
0 19
66. The roots of the equation 2
are
(A) 0 and 4 S T
E
T
(B) 0 and 1
N
O
(C) and 4 SI
(D) 1 and 4 M
IS
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
66. The roots of the equation 2
are
(A) 0 and 4 S T
E
T
(B) 0 and 1
N
O
(C) and 4 SI
(D) 1 and 4 M
IS
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 21
67. The total number of 9 digit numbers with different digits is
(A) 10! 019
(B) 9! 2
(C) 9.9!
S T
E
(D) 10.10!
T
N
O
68. If S I numbers which are in AP and
are three natural then the possible
number of values ofISthe ordered triplet is
M
(A) 15 AD
M
(B) 14N
(C) O13
M 12
(D)
SA T
69.
CO
M
O
The digit at the unit place in the number is
CU
T
(A) 2
A N
(B) 1
(C) 0
19
S IO 0
(D) 8
2
70. U
C IS S
In the expansion of
T E ST
, the constant term is
(A) 20 N
O
(B)
S I
D
(C) 30
M
(D)
A O
N
A
D
M
71. For M of
, the constant term in the expansion is
(A) 2 CO
A T
(B) 1
S
(C) 0
C U
(A) 10! 019
(B) 9! 2
(C) 9.9!
S T
E
(D) 10.10!
T
N
O
68. If S I numbers which are in AP and
are three natural then the possible
number of values ofISthe ordered triplet is
M
(A) 15 AD
M
(B) 14N
(C) O13
M 12
(D)
SA T
69.
CO
M
O
The digit at the unit place in the number is
CU
T
(A) 2
A N
(B) 1
(C) 0
19
S IO 0
(D) 8
2
70. U
C IS S
In the expansion of
T E ST
, the constant term is
(A) 20 N
O
(B)
S I
D
(C) 30
M
(D)
A O
N
A
D
M
71. For M of
, the constant term in the expansion is
(A) 2 CO
A T
(B) 1
S
(C) 0
C U
Page 22
(D) 019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 23
72. A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x%
19
of the Americans like both cheese and apples, then
0
(A) x = 39 2
S T
E
(B) x = 63
T
(C) N
O
SI
IS
(D)
M
A
D
M
73. If N then lies in the interval
O
M [0.30, 0.80]
O
(A)
M
E
(B) [0.35, 0.75]
CO (C)
C T
[0.4, 0.70]
AT (D) [0.45, 0.65]
S
CU
S IO
74. If , then is equal to
(A) 0 2 0
(B) ab
U
C IS S T E ST
(C)
N
O
(D)
S I
75. A
The value of
O
N
A
D
is equal to
(A) M
M
(B)
C O
(C) 2
(D) 4
AT
S
CU
19
of the Americans like both cheese and apples, then
0
(A) x = 39 2
S T
E
(B) x = 63
T
(C) N
O
SI
IS
(D)
M
A
D
M
73. If N then lies in the interval
O
M [0.30, 0.80]
O
(A)
M
E
(B) [0.35, 0.75]
CO (C)
C T
[0.4, 0.70]
AT (D) [0.45, 0.65]
S
CU
S IO
74. If , then is equal to
(A) 0 2 0
(B) ab
U
C IS S T E ST
(C)
N
O
(D)
S I
75. A
The value of
O
N
A
D
is equal to
(A) M
M
(B)
C O
(C) 2
(D) 4
AT
S
CU
Page 24
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 25
76. If 19
and
0
then the value of is
2
(A)
S T
E
T
N
(B) O
SI
IS
M
M
(C)
D
A
N
(D) O
M
A T
S 77.
CO
M
O
T
If , then at y = 1 is
CU (A)
A N 19
S IO 0
(B)
2
U S
(C) 3
(D) 1
ST
C IS O
N
T E
M I
78. If , then is equal to
S
IS
(A)
A
(B)
O
N
A
D
(C) M
M
(D) C O
A T
S
79.
C U
The general solution of the differential equation is
and
0
then the value of is
2
(A)
S T
E
T
N
(B) O
SI
IS
M
M
(C)
D
A
N
(D) O
M
A T
S 77.
CO
M
O
T
If , then at y = 1 is
CU (A)
A N 19
S IO 0
(B)
2
U S
(C) 3
(D) 1
ST
C IS O
N
T E
M I
78. If , then is equal to
S
IS
(A)
A
(B)
O
N
A
D
(C) M
M
(D) C O
A T
S
79.
C U
The general solution of the differential equation is
Page 26
(A)
019
(B)
2
(C) S T
E
T
(D) N
O
SI
IS
M
80.
D
For the operation
M
A * defined by the identity element is
(A) O 0
N
M
SA
T
O
M
(B) 1
C (C) 2 O
CU
T
(D)
A N 19
81.
S IO 2 0
If W1 and W2 are finite dimensional subspaces with the same dimension and
U S T
then
S
C IS
(A)
(B)
O
N
T E
(C)
S I
(D)
82.
A
The basis ofO
N
A
D
from the set where
and is M
M
(A)
C O
(B)
AT
S
CU
019
(B)
2
(C) S T
E
T
(D) N
O
SI
IS
M
80.
D
For the operation
M
A * defined by the identity element is
(A) O 0
N
M
SA
T
O
M
(B) 1
C (C) 2 O
CU
T
(D)
A N 19
81.
S IO 2 0
If W1 and W2 are finite dimensional subspaces with the same dimension and
U S T
then
S
C IS
(A)
(B)
O
N
T E
(C)
S I
(D)
82.
A
The basis ofO
N
A
D
from the set where
and is M
M
(A)
C O
(B)
AT
S
CU
Page 27
(C)
(D) 019
2
S T
E
83. Let T
be the vector space of all polynomial functions in x with coefficient as
N
O
elements of the field
I
of real numbers. Let D and T be two linear operators on V
S
IS
M
M
defined by and for every Then
D
(A) TD =AI
N
O
M
(B) DT = I and
SAT
CO
M
(C)
(D)
O
C T
and E
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
(D) 019
2
S T
E
83. Let T
be the vector space of all polynomial functions in x with coefficient as
N
O
elements of the field
I
of real numbers. Let D and T be two linear operators on V
S
IS
M
M
defined by and for every Then
D
(A) TD =AI
N
O
M
(B) DT = I and
SAT
CO
M
(C)
(D)
O
C T
and E
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 28
84. A linear transformation is such that T(1, 0) = (1, 1) and T(0, 1) = (–1, 2).
19
Then T maps the square with vertices (0, 0), (1, 0), (1, 1) and (0, 1) into a
0
(A) rectangle
2
(B) trapezium S T
E
(C) square
T
(D) parallelogram
N
O
SI
85. IS on
Let T be a linear operator defined by for all
M
A
M
D Then
N
(A) O
M
SA T
M
CO (B) O
CU (C)
(D)
S IO 2 0
86.
U
C IS S T E ST
A vector of unit length which is orthogonal to the vector of with
N
O
respect to standard inner product is
M
(A) (2, 2, –1)
IS
S I
A D
(B)
A
N
(C)
O
M
M
(D)
C O
AT
S
CU
19
Then T maps the square with vertices (0, 0), (1, 0), (1, 1) and (0, 1) into a
0
(A) rectangle
2
(B) trapezium S T
E
(C) square
T
(D) parallelogram
N
O
SI
85. IS on
Let T be a linear operator defined by for all
M
A
M
D Then
N
(A) O
M
SA T
M
CO (B) O
CU (C)
(D)
S IO 2 0
86.
U
C IS S T E ST
A vector of unit length which is orthogonal to the vector of with
N
O
respect to standard inner product is
M
(A) (2, 2, –1)
IS
S I
A D
(B)
A
N
(C)
O
M
M
(D)
C O
AT
S
CU
Page 29
87. Let V be the vector space with the standard inner product. Let T be the linear
operator defined by 019 Then its adjoint is
2
(A)
S T
E
(B) T
N
O
(C)
SI
IS
(D)
M
A
D
M
N
88. O
The value of satisfying , where and are constant vectors, given that
M
SAT
M
COwhen
(A)
O
and is
CU
(B)
S IO 2 0
U S T
(C)
S
C IS
(D)
O
N
T E
S I
D
89. The value of is
M
A D
(A)
A
(B)
N
O
(C)
M
M
(D)
C O
AT
S
CU
operator defined by 019 Then its adjoint is
2
(A)
S T
E
(B) T
N
O
(C)
SI
IS
(D)
M
A
D
M
N
88. O
The value of satisfying , where and are constant vectors, given that
M
SAT
M
COwhen
(A)
O
and is
CU
(B)
S IO 2 0
U S T
(C)
S
C IS
(D)
O
N
T E
S I
D
89. The value of is
M
A D
(A)
A
(B)
N
O
(C)
M
M
(D)
C O
AT
S
CU
Page 30
90. Green’s theorem applied to
019 where C is the circle
, yields 2
S T
E
(A) T
N
O
O 20 SI
(B)
IS
M
(C) 0
A
D
M
N
(D) O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
019 where C is the circle
, yields 2
S T
E
(A) T
N
O
O 20 SI
(B)
IS
M
(C) 0
A
D
M
N
(D) O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 31
91. The length of the space curve over the parameter range can be computed
by
0 19
2
(A) integrating the norm of its tangent vector
S T
(B) integrating the square ofEthe norm of its tangent vector
T
N of the norm of
O
(C) integrating the square
S I
IS square root of the norm of
(D) integrating the
M
A
D
M
N
92. O
The sum is equal to
M
SA T
CO
M
(A)
O
T
(B)
CU
A N 19
S IO
(C)
2 0
U S T
(D)
S
93. C IS N
T E
The real and imaginary parts of
O
are respectively
(A)
for S I
A D
(B)
for
A
N
(C)
O for
M
(D)
M
for
C O
AT
S
94. The singularities of
C U are
by
0 19
2
(A) integrating the norm of its tangent vector
S T
(B) integrating the square ofEthe norm of its tangent vector
T
N of the norm of
O
(C) integrating the square
S I
IS square root of the norm of
(D) integrating the
M
A
D
M
N
92. O
The sum is equal to
M
SA T
CO
M
(A)
O
T
(B)
CU
A N 19
S IO
(C)
2 0
U S T
(D)
S
93. C IS N
T E
The real and imaginary parts of
O
are respectively
(A)
for S I
A D
(B)
for
A
N
(C)
O for
M
(D)
M
for
C O
AT
S
94. The singularities of
C U are
Page 32
(A) simple poles at
1 9
(B) simple poles at 0
2and double pole at z = 0
(C) removable singularity at S T
E
and essential singularity at z = 0
T
N
(D) essential singularity at z = 0 and simple poles at
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
1 9
(B) simple poles at 0
2and double pole at z = 0
(C) removable singularity at S T
E
and essential singularity at z = 0
T
N
(D) essential singularity at z = 0 and simple poles at
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 33
19
95. If and , , then is equal to
(A) 2/3 20
S T
E
(B)
T
(C) 1/3 N
O
(D) 1/2
SI
IS
M
96. A
The value of
D
M , where is a circle with center at 0 and radius 2, is
N
(A) O
M
SA T
M
CO (C)
(B)
O
CU
T
(D)
A N 19
S IO 2 0
U S T
97. The set is
S
C IS E
(A) open
(B) closed T
(C) both open and closed
N
O
M I
(D) neither open nor closed
S
IS
A D
98. The value of
A
(A) is 1
N
(B) is
O
(C)
(D)
is 0
does not exist M
M
C O
99. The function
ATis
(A) differentiable U
S
C
95. If and , , then is equal to
(A) 2/3 20
S T
E
(B)
T
(C) 1/3 N
O
(D) 1/2
SI
IS
M
96. A
The value of
D
M , where is a circle with center at 0 and radius 2, is
N
(A) O
M
SA T
M
CO (C)
(B)
O
CU
T
(D)
A N 19
S IO 2 0
U S T
97. The set is
S
C IS E
(A) open
(B) closed T
(C) both open and closed
N
O
M I
(D) neither open nor closed
S
IS
A D
98. The value of
A
(A) is 1
N
(B) is
O
(C)
(D)
is 0
does not exist M
M
C O
99. The function
ATis
(A) differentiable U
S
C
Page 34
(B) continuous everywhere except zero
019
2
(C) continuous for x > 0 alone
S T
E
(D) continuous for T
alone
N
O
SI
IS
M
A
D
M
N
100. The function
O
M is continuous
(A)
SA
T
O
M
(D) O
(B) has a discontinuity of the first kind at x = 1
C (C) has a discontinuity of the first kind from left at x = 1
has a discontinuity of the second kind at x = 1
CU
101.
AT
The integral
N 19
(A)
S IO
converges absolutely
2 0
U S
(B) converges monotonically
(C) converges conditionally
ST
C IS E
(D) diverges
T
N
O
S I
102.
D
The function
M
is
(A)
(B)
(C)
(D)
A D
discontinuous at x = 0
A
not differentiable at x = 0
N
differentiable everywhere but its derivative is not continuous at x = 0
O
not differentiable at x = 0 and its derivative is also not differentiable at x = 0
M
M
C O
103. The Fourier series corresponding to is
AT
S
CU
019
2
(C) continuous for x > 0 alone
S T
E
(D) continuous for T
alone
N
O
SI
IS
M
A
D
M
N
100. The function
O
M is continuous
(A)
SA
T
O
M
(D) O
(B) has a discontinuity of the first kind at x = 1
C (C) has a discontinuity of the first kind from left at x = 1
has a discontinuity of the second kind at x = 1
CU
101.
AT
The integral
N 19
(A)
S IO
converges absolutely
2 0
U S
(B) converges monotonically
(C) converges conditionally
ST
C IS E
(D) diverges
T
N
O
S I
102.
D
The function
M
is
(A)
(B)
(C)
(D)
A D
discontinuous at x = 0
A
not differentiable at x = 0
N
differentiable everywhere but its derivative is not continuous at x = 0
O
not differentiable at x = 0 and its derivative is also not differentiable at x = 0
M
M
C O
103. The Fourier series corresponding to is
AT
S
CU
Page 35
19
(A)
20
(B)
S T
E
T
N
O
(C)
SI
IS
M
M
(D)
D
A
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
(A)
20
(B)
S T
E
T
N
O
(C)
SI
IS
M
M
(D)
D
A
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 36
104. If three coplanar forces keep a rigid body in equilibrium, then
(A) they are all concurrent 019
(B) they are all parallel 2
(C) T
either they are all parallel or concurrent
S
E
(D) they all act along the sides of a triangle in order
T
N
O
105. I
The shape of a uniform string hanging under gravity is given by
S
IS
M
M
(A)
D
A
N
(B) O
M
SAT
M
CO (C)
(D)
O
CU
S IO 0
106. The period of a simple pendulum is
2
(A)
U
C IS S T E ST
(B) N
O
S I
D
(C)
M
A
(D)
O
N
A
D
M
107.
M
The moment of inertia of a right circular hollow cylinder of base radius a and mass M
about the axis of the cylinder is
C O
(A)
(B)
Ma3
Ma2 AT
Ma2/3 S
(C)
(D) Ma3/2
CU
(A) they are all concurrent 019
(B) they are all parallel 2
(C) T
either they are all parallel or concurrent
S
E
(D) they all act along the sides of a triangle in order
T
N
O
105. I
The shape of a uniform string hanging under gravity is given by
S
IS
M
M
(A)
D
A
N
(B) O
M
SAT
M
CO (C)
(D)
O
CU
S IO 0
106. The period of a simple pendulum is
2
(A)
U
C IS S T E ST
(B) N
O
S I
D
(C)
M
A
(D)
O
N
A
D
M
107.
M
The moment of inertia of a right circular hollow cylinder of base radius a and mass M
about the axis of the cylinder is
C O
(A)
(B)
Ma3
Ma2 AT
Ma2/3 S
(C)
(D) Ma3/2
CU
Page 37
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 38
108. The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the
19
line whose direction cosines are proportional to 2, 3, – 6 is
0
(A) 2
S T
E
(B)
T
N
(C) 3
O
(D) 1 SI
IS
M
109. The planes
A
D
M and
N at a point
(A) Ointersect
M not intersect at all
(B) intersect along a line
M do
O
(C)
CO
E
(D)
form a triangular prism
A T
S 110. C T
CU
T
The plane and the sphere
(A)
A N
do not meet each other
19
S IO
(B) intersect at only one point
(C)
2 0
intersect along a circle of unit radius
U S
(D) intersect along the great circle
ST
111.
C IS
parallel to the plane
O
N
T E
The equations of two tangent planes to the sphere
are
which are
(A)
S I
A
(B)
D
(C) A
N
(D) O
M
M
112. The equation of a right circular C
O
cone with vertex at origin 0, axis the x-axis and semi-
vertical angle is
A T
S
(A)
C U
19
line whose direction cosines are proportional to 2, 3, – 6 is
0
(A) 2
S T
E
(B)
T
N
(C) 3
O
(D) 1 SI
IS
M
109. The planes
A
D
M and
N at a point
(A) Ointersect
M not intersect at all
(B) intersect along a line
M do
O
(C)
CO
E
(D)
form a triangular prism
A T
S 110. C T
CU
T
The plane and the sphere
(A)
A N
do not meet each other
19
S IO
(B) intersect at only one point
(C)
2 0
intersect along a circle of unit radius
U S
(D) intersect along the great circle
ST
111.
C IS
parallel to the plane
O
N
T E
The equations of two tangent planes to the sphere
are
which are
(A)
S I
A
(B)
D
(C) A
N
(D) O
M
M
112. The equation of a right circular C
O
cone with vertex at origin 0, axis the x-axis and semi-
vertical angle is
A T
S
(A)
C U
Page 39
(B)
019
(C)
2
(D) S T
E
T
N
O
S I which passes through
ISto the x-axis can be obtained by
113. The equation of a cylinder and having
its generator parallel
M
(A) adding
D
A and
M
N
O
(B)M adding with where is a scalar
SA T (D)
M
O
CO (C) eliminating x
C T
multiplying E and
CU
S IO
114. If the equation is exact, then
2 0
U S T
(A)
S
(B)
C IS O
N
T E
(C)
S I
A D
(D)
A
N
O
115. The solution of
M is
M
(A)
C O
AT
(B)
S
CU
019
(C)
2
(D) S T
E
T
N
O
S I which passes through
ISto the x-axis can be obtained by
113. The equation of a cylinder and having
its generator parallel
M
(A) adding
D
A and
M
N
O
(B)M adding with where is a scalar
SA T (D)
M
O
CO (C) eliminating x
C T
multiplying E and
CU
S IO
114. If the equation is exact, then
2 0
U S T
(A)
S
(B)
C IS O
N
T E
(C)
S I
A D
(D)
A
N
O
115. The solution of
M is
M
(A)
C O
AT
(B)
S
CU
Page 40
(C)
019
(D) 2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
019
(D) 2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 41
116. The differential equation obtained by eliminating a, b and c from
is
019
2
(A) S T
E
T
N
O
(B)
SI
IS
M
(C)
A
D
M
N
O
M
O
(D)
M
SAT
CO
CU 117.
AT
An envelope of
N
is
19
S IO
(A)
2 0
U S
(B)
ST
C IS E
(C)
T
(D) y = x
N
O
118.
S I
The Legendre equation is given by
(A)
A
(B)
O
N
A
D
(C)
M
M
(D)
C O
AT
S
CU
is
019
2
(A) S T
E
T
N
O
(B)
SI
IS
M
(C)
A
D
M
N
O
M
O
(D)
M
SAT
CO
CU 117.
AT
An envelope of
N
is
19
S IO
(A)
2 0
U S
(B)
ST
C IS E
(C)
T
(D) y = x
N
O
118.
S I
The Legendre equation is given by
(A)
A
(B)
O
N
A
D
(C)
M
M
(D)
C O
AT
S
CU
Page 42
119. The harmonic function cannot attain either its maximum or minimum inside a
region 019
2
(A) unless is trivial
S T
unless is a constant function
E
(B)
(C) if is unbounded T
(D) N
if and its first partial derivatives are unbounded
O
SI
IS
M
120. Let
A
M
D and let be functions on S defined by ,
N
O . Then these functions under the operation composition of functions form a
M
SAT
M
CO (B) semigroup
(A) group
O
C T
(C) abelian group E
T
(D) monoid
CU
A N 19
S IO
121. The total number of subgroups of contained in 20 is
(A) 6 2 0
U S T
(B) 2
(C) infinite
S
C IS E
(D) zero
T
N
O
M I
122. Let G be the group of all 2 × 2 diagonal matrices under multiplication. Then the centre of
G is
S
IS
A
(A)
D
A
N
(B)
O
M
M
(C)
C O
(D) G itself
AT
S
CU
region 019
2
(A) unless is trivial
S T
unless is a constant function
E
(B)
(C) if is unbounded T
(D) N
if and its first partial derivatives are unbounded
O
SI
IS
M
120. Let
A
M
D and let be functions on S defined by ,
N
O . Then these functions under the operation composition of functions form a
M
SAT
M
CO (B) semigroup
(A) group
O
C T
(C) abelian group E
T
(D) monoid
CU
A N 19
S IO
121. The total number of subgroups of contained in 20 is
(A) 6 2 0
U S T
(B) 2
(C) infinite
S
C IS E
(D) zero
T
N
O
M I
122. Let G be the group of all 2 × 2 diagonal matrices under multiplication. Then the centre of
G is
S
IS
A
(A)
D
A
N
(B)
O
M
M
(C)
C O
(D) G itself
AT
S
CU
Page 43
123. A right inverse of matrix
0
is19
2
S T
E
(A)
T
N
O
SI
IS
M
M
(B)
D
A
N
O
M
M
O
(C)
SAT
CO
CU
T
(D)
A N 19
S IO 2 0
U S T
124. Let R be the ring of all real valued functions defined on under pointwise addition and
S
multiplication. Which of the following subset of R is not a subring?
C IS T E
(A) Set of all continuous functions
N
(B) Set of all polynomial functions
O
M I
(C) Set of all functions which are zero at finitely many points together with the zero
function
S
IS
D
(D) Set of all functions which are zero at infinite number of points
M
125.
A
from A to B is
(A) 225 O
N
A
D
If A and B are sets such that and then the number of binary relations
(B) 29 M
(C) 215 M
(D) 224
C O
AT
S
CU
0
is19
2
S T
E
(A)
T
N
O
SI
IS
M
M
(B)
D
A
N
O
M
M
O
(C)
SAT
CO
CU
T
(D)
A N 19
S IO 2 0
U S T
124. Let R be the ring of all real valued functions defined on under pointwise addition and
S
multiplication. Which of the following subset of R is not a subring?
C IS T E
(A) Set of all continuous functions
N
(B) Set of all polynomial functions
O
M I
(C) Set of all functions which are zero at finitely many points together with the zero
function
S
IS
D
(D) Set of all functions which are zero at infinite number of points
M
125.
A
from A to B is
(A) 225 O
N
A
D
If A and B are sets such that and then the number of binary relations
(B) 29 M
(C) 215 M
(D) 224
C O
AT
S
CU
Page 44
126. Let be a relation on the set . The minimum set of
019
elements that should be added to R so that it becomes antisymmetric is
2
(A)
S T
E
T
(B)
N
O
(C) SI
IS
(D) M
A
D
M
N
O
M
O
127. Let the line lie on the plane Then the point
M lie in
SAT
CO
(A)
CU (B)
S IO
(C)
(D) 2 0
U
C IS S T E ST
128. The points on the line N at a distance 5 units from the point (1, 3, 3)
O
M I
are
S
IS
D
(A) (7, 8, 2) and (-3, -4, 2)
(B)
M
(8, 7, 7) and (-2, -3, -3)
A D
(C) (3, 2, 2) and (-2, -1, 3)
(D)
A
(-2, -1, 3) and (4, 3, 7)
N
129. O
Ram and Gopi appear for an interview for two vacancies in a company. The probability
M
of Ram’s selection is
M
and thatOof Gop is . The probability that none of them is
selected is C
AT
(A) S
C U
019
elements that should be added to R so that it becomes antisymmetric is
2
(A)
S T
E
T
(B)
N
O
(C) SI
IS
(D) M
A
D
M
N
O
M
O
127. Let the line lie on the plane Then the point
M lie in
SAT
CO
(A)
CU (B)
S IO
(C)
(D) 2 0
U
C IS S T E ST
128. The points on the line N at a distance 5 units from the point (1, 3, 3)
O
M I
are
S
IS
D
(A) (7, 8, 2) and (-3, -4, 2)
(B)
M
(8, 7, 7) and (-2, -3, -3)
A D
(C) (3, 2, 2) and (-2, -1, 3)
(D)
A
(-2, -1, 3) and (4, 3, 7)
N
129. O
Ram and Gopi appear for an interview for two vacancies in a company. The probability
M
of Ram’s selection is
M
and thatOof Gop is . The probability that none of them is
selected is C
AT
(A) S
C U
Page 45
(B)
019
2
(C)
S T
E
T
(D) N
O
S
130. The number of positive
Idivisors of 50000 is
IS
M
M
(A) 20
D
(B) 30
A
(C) 40
(D) O
N
50
M
SA
CO
M
O
C T
T The slope of the line
131.
E is
CU (A)
(B)
S IO 2 0
U
C IS
(C)
S T E ST
N
O
M
(D)
S I
IS
A D
132. The angle between the lines and is
A
(A)
N
O
(B) 0 M
M
(C)
C O
AT
(D)
S
CU
019
2
(C)
S T
E
T
(D) N
O
S
130. The number of positive
Idivisors of 50000 is
IS
M
M
(A) 20
D
(B) 30
A
(C) 40
(D) O
N
50
M
SA
CO
M
O
C T
T The slope of the line
131.
E is
CU (A)
(B)
S IO 2 0
U
C IS
(C)
S T E ST
N
O
M
(D)
S I
IS
A D
132. The angle between the lines and is
A
(A)
N
O
(B) 0 M
M
(C)
C O
AT
(D)
S
CU
Page 46
133. When a force displaces a particle in the xy plane from
9
, the1work done is
20
(0, 0) to (1, 1) along the curve
(A) S T
E
T
N
O
(B)
SI
IS
M
M
(C) 2
D
(D) A
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
9
, the1work done is
20
(0, 0) to (1, 1) along the curve
(A) S T
E
T
N
O
(B)
SI
IS
M
M
(C) 2
D
(D) A
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 47
134. The unit normal to the surface at the point (1, 1, 1) is
019
(A) 2
S T
E
(B)
T
N
O
(C) SI
IS
M
(D)
A
D
M
N
O
M
M
O
135. The directional derivative of at the point (1, 2, 3) along the x-axis is
SAT
CO (A) 4
(B) 3
T
(C) 7
CU
N
(D) 5
A
S IO 2 0 19
U S
136. The Laplace transform of is
ST
C IS
(A)
O
N
T E
M I
(B)
S
IS
(C)
A
(D)
O
N
A
D
M
137. M
The equation of the sphere which has its centre at (6, -1, 2) and touches the plane
is
C O
(A)
AT
S
CU
019
(A) 2
S T
E
(B)
T
N
O
(C) SI
IS
M
(D)
A
D
M
N
O
M
M
O
135. The directional derivative of at the point (1, 2, 3) along the x-axis is
SAT
CO (A) 4
(B) 3
T
(C) 7
CU
N
(D) 5
A
S IO 2 0 19
U S
136. The Laplace transform of is
ST
C IS
(A)
O
N
T E
M I
(B)
S
IS
(C)
A
(D)
O
N
A
D
M
137. M
The equation of the sphere which has its centre at (6, -1, 2) and touches the plane
is
C O
(A)
AT
S
CU
Page 48
(B)
019
(C)
2
(D) S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
019
(C)
2
(D) S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 49
138. The value of the product
019 is
2
(A) 1
S T
E
(B) T
N
O
(C) 0
SI
(D) IS
M
A
D
M
N
O
M
M
O
139. The value of is
SAT
CO (A)
CU (B)
(C)
S IO 2 0
U
C IS
(D)
S T E ST
N
O
S I
D
140. The matrix is unitary when is
M
A
(A)
(B) O
N
A
D
M
M
(C)
C O
(D) AT
S
CU
019 is
2
(A) 1
S T
E
(B) T
N
O
(C) 0
SI
(D) IS
M
A
D
M
N
O
M
M
O
139. The value of is
SAT
CO (A)
CU (B)
(C)
S IO 2 0
U
C IS
(D)
S T E ST
N
O
S I
D
140. The matrix is unitary when is
M
A
(A)
(B) O
N
A
D
M
M
(C)
C O
(D) AT
S
CU
Page 50
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 51
019
141. The largest eigenvalue of 2 is
S T
E
(A) 16
(B) 21 T
N
(C) 48
O
(D) 64 SI
IS
M
A
D
M
N
142. LetM
O be a matrix with real entries. If the sum and product of the
SA
CO
M
eigenvalues
T (A) 20
(B) 40
O
are 10 and 30 respectively, then equals
CU
(C) 58
(D) 65
143.
S IO 2 0
A group G is generated by the elements x, y with the relations = 1. Then
(A)
(B)
U4
6
S
the order of the group G is
C IS T E ST
(C) 8 N
O
M I
(D) 12
S
IS
144.
The number of group homomorphisms from to is
(A)
(B)
(C)
A 1
20
29
O
N
A
D
(D) 25
M
M
C O
AT
S
CU
141. The largest eigenvalue of 2 is
S T
E
(A) 16
(B) 21 T
N
(C) 48
O
(D) 64 SI
IS
M
A
D
M
N
142. LetM
O be a matrix with real entries. If the sum and product of the
SA
CO
M
eigenvalues
T (A) 20
(B) 40
O
are 10 and 30 respectively, then equals
CU
(C) 58
(D) 65
143.
S IO 2 0
A group G is generated by the elements x, y with the relations = 1. Then
(A)
(B)
U4
6
S
the order of the group G is
C IS T E ST
(C) 8 N
O
M I
(D) 12
S
IS
144.
The number of group homomorphisms from to is
(A)
(B)
(C)
A 1
20
29
O
N
A
D
(D) 25
M
M
C O
AT
S
CU
Page 52
19
145. Let be continuous function such that is uniformly continuous.
Then
20
(A) f is bounded
S T
E
(B) f may not be uniformly continuous
(C) T
f is uniformly continuous
(D) f is unbounded N
O
S I
146. For each x in [0,M
IS
M
1], let if x is rational and let if x is irrational.
Then D
A
(A) N
O
M
M
O
(B)
SA T
CO (C)
T
(D)
CU
A N 19
S IO 2 0
U S
147. The residue at of is
ST
(A)
C IS
(B) -8
O
N
T E
(C)
S I
D
(D) 0 M
148. A N
A
D
If i and 2i are two roots of a biquadratic equation, then the equation is
O
(A)
M
M
(B)
C O
(C)
AT
(D) S
CU
145. Let be continuous function such that is uniformly continuous.
Then
20
(A) f is bounded
S T
E
(B) f may not be uniformly continuous
(C) T
f is uniformly continuous
(D) f is unbounded N
O
S I
146. For each x in [0,M
IS
M
1], let if x is rational and let if x is irrational.
Then D
A
(A) N
O
M
M
O
(B)
SA T
CO (C)
T
(D)
CU
A N 19
S IO 2 0
U S
147. The residue at of is
ST
(A)
C IS
(B) -8
O
N
T E
(C)
S I
D
(D) 0 M
148. A N
A
D
If i and 2i are two roots of a biquadratic equation, then the equation is
O
(A)
M
M
(B)
C O
(C)
AT
(D) S
CU
Page 53
019
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
2
S T
E
T
N
O
SI
IS
M
A
D
M
N
O
M
SAT
CO
M
O
CU
S IO 2 0
U
C IS S T E ST
N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 54
149. The differential equation of the curve
019 is
2
(A)
S T
E
T
N
(B) O
SI
IS
M
M
(C)
D
A
N
(D)
O
M
SA
C O
M
T The function
150. O
C T E is the general solution of the differential equation
CU (A)
(B)
S IO 2 0
U
C IS
(C)
S T E ST
(D) N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
019 is
2
(A)
S T
E
T
N
(B) O
SI
IS
M
M
(C)
D
A
N
(D)
O
M
SA
C O
M
T The function
150. O
C T E is the general solution of the differential equation
CU (A)
(B)
S IO 2 0
U
C IS
(C)
S T E ST
(D) N
O
S I
A O
N
A
D
M
M
C O
AT
S
CU
Page 55
MATHEMATICS 9 PG - ANSWER KEY
1
20 CODE: 612
TEST
QN. NO. KEY QN. NO. KEY QN. NO. T KEY QN. NO. KEY QN. NO. KEY
E S
1 C 26 A 51 T D 76 A 101 D
2 A 27 B N
O52 C 77 B 102 C
I
3 D 28 A
ISS 53 B 78 D 103 D
4 D 29 C M 54 A 79 B 104 C
5 A 30 B AD
M
55 A 80 C 105 A
6 D 31 N
OCB 56 C 81 D 106 C
7 A 32 M 57 C 82 C 107 B
8
9
10
A
D
B
33
34 T C
SA
35
O
M A
A
D
O
C TE
59
60
58
A
B
D
84
85
83
D
B
B 108
109
110
D
D
C
11
12
A
B
U
C 36
37
D
C
AT N
61
62
A
A
86
87
19
B
C
111
112
B
C
13 A 38 B
S I O 63 A 88
2 0 B 113 C
U S
14 A 39 D 64 A 89 C 114 D
15 C 40 D 65 B ST
90 C 115 B
16
17
D
C
41
42 C IS
A
D
66
67
D
C
O
N
T E 91
92
A
A
116
117
D
D
18 C 43 A
M 68
IS
S I
C 93 D 118 C
D
19 B 44 C 69 B 94 B 119 B
20 A 45 A 70 M A 95 B 120 C
21
22
23
B
C
C
46
47
48
A D
C
C O
71
N
72
73
A
D D
C
D
96
97
98
C
C
D
121
122
123
C
D
A
M
24 D 49 A 74
M D 99 B 124 D
CO
25 A 50 C 75 D 100 B 125 C
AT
S
CU
1
20 CODE: 612
TEST
QN. NO. KEY QN. NO. KEY QN. NO. T KEY QN. NO. KEY QN. NO. KEY
E S
1 C 26 A 51 T D 76 A 101 D
2 A 27 B N
O52 C 77 B 102 C
I
3 D 28 A
ISS 53 B 78 D 103 D
4 D 29 C M 54 A 79 B 104 C
5 A 30 B AD
M
55 A 80 C 105 A
6 D 31 N
OCB 56 C 81 D 106 C
7 A 32 M 57 C 82 C 107 B
8
9
10
A
D
B
33
34 T C
SA
35
O
M A
A
D
O
C TE
59
60
58
A
B
D
84
85
83
D
B
B 108
109
110
D
D
C
11
12
A
B
U
C 36
37
D
C
AT N
61
62
A
A
86
87
19
B
C
111
112
B
C
13 A 38 B
S I O 63 A 88
2 0 B 113 C
U S
14 A 39 D 64 A 89 C 114 D
15 C 40 D 65 B ST
90 C 115 B
16
17
D
C
41
42 C IS
A
D
66
67
D
C
O
N
T E 91
92
A
A
116
117
D
D
18 C 43 A
M 68
IS
S I
C 93 D 118 C
D
19 B 44 C 69 B 94 B 119 B
20 A 45 A 70 M A 95 B 120 C
21
22
23
B
C
C
46
47
48
A D
C
C O
71
N
72
73
A
D D
C
D
96
97
98
C
C
D
121
122
123
C
D
A
M
24 D 49 A 74
M D 99 B 124 D
CO
25 A 50 C 75 D 100 B 125 C
AT
S
CU
Page 56
019
2
QN. NO. KEY
S T
TE
126 D
127 A N
O
128 D SI
129 A IS
M
130 B A
D
M
131 A N
O
132 D M
133
134
135
B
B
D SA
T
CO
M
O
C TE
136
137
B
D
CU
AT N 19
138 A
S I O 2 0
U S
139 B
140 A ST
141
142
B
C C IS O
N
T E
143 B
M IS
S I
D
144 A
145 C M
146
147
148
D
C
A
A O
N
A
D
M
149 D
M
CO
150 C
AT
S
CU
2
QN. NO. KEY
S T
TE
126 D
127 A N
O
128 D SI
129 A IS
M
130 B A
D
M
131 A N
O
132 D M
133
134
135
B
B
D SA
T
CO
M
O
C TE
136
137
B
D
CU
AT N 19
138 A
S I O 2 0
U S
139 B
140 A ST
141
142
B
C C IS O
N
T E
143 B
M IS
S I
D
144 A
145 C M
146
147
148
D
C
A
A O
N
A
D
M
149 D
M
CO
150 C
AT
S
CU
Document Details
| Board / Org | Cochin University |
| Exam | CUSAT Common Admission Test |
| Type | Question Paper |
| Pages | 56 |
| Updated | 30 Apr 2026 |