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ECAT Computer Science Entry Test MCQs With Answers
Question # 1
In R the number of identity element w.r.t '+' is
Choose an answer
One
Two
Three
Four
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Question # 2
The roots of the equation 4x - 3.2x+2 + 32 = 0 would include
Choose an answer
1 and 3
1 and 4
1 and 2
2 and 3
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Question # 3
Choose an answer
-1
0
1
None of these
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Question # 4
The term involving x4 the expansion (3-2x)7 is
Choose an answer
217 x4
15120x4
313x4
-25x4
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Question # 5
Tan
-1
1/x = ______
Choose an answer
sin x
sec
-1
X
cot
-1
X
None of these
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Question # 6
The set of ordered pairs (x,y) such that ax+ by < c, and (x,y) such that ax + by>0, are called
Choose an answer
Linear Inequalities
Feasible regions
Half planes
Boundary
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Question # 7
Period of cos 2x is ______
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Question # 8
Choose an answer
1
-1
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Question # 9
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Question # 10
Choose an answer
Orthogonal
Involutary
Idempotent
Nilpotent
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Question # 11
Ifπ≤x≤2π, then cos-1 (cos x)=
Choose an answer
cos x
-x
1/x
-x
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Question # 12
The roots of the equations will be equal if b
2
- 4ac is
Choose an answer
Positive
Negative
1
Zero
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Question # 13
(A ∩ B)c =
Choose an answer
A∩ B
(A ∪ B)c
Ac∪Bc
Φ
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Question # 14
6! = ______
Choose an answer
360
720
6.5.4
None of these
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Question # 15
Coordinates of the focus of the parabola x
2
- 4x -8y-4=0 are:
Choose an answer
(0,2)
(,0,1)
(2,0)
(1,2)
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Question # 16
Every natural number is
Choose an answer
A prime number
An irrational number
An integer
An even number
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Question # 17
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Question # 18
If a +b +c =0 then which of the following is true
Choose an answer
a =b =c =0
a,b =b,c =c,a
a xb=b xc =c xa
None
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Question # 19
A circle is a limiting case of an ellipse whose eccentricity
Choose an answer
Tends to a
Tends to b
Tends to 0
Tends to a + b
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Question # 20
If z
1
= (a,b), z
2
=(c,d), then z
1
z
2
= -------------------
Choose an answer
(ac,bd)
(ac+bd, ad-bc)
(ac-bd , ad+bc)
(ac-bd , ad-bc)
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Question # 21
The third term of the sequence a
n
= (-1)
n-1
(n-7) is ______
Choose an answer
8
4
-4
8
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Question # 22
If n∈Z+ then(a+x)n is a/an
Choose an answer
Finite series
Convergent series
Infinite series
Divergent series
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Question # 23
Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =
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Question # 24
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Question # 25
Choose an answer
1
7
4
None of these
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Question # 26
The multiplicative inverse of -1 in the set {1-,1} is
Choose an answer
1
-1
±1
0
Does not exist
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Question # 27
A square matrix A = [aij] is upper triangular when
Choose an answer
cij = 0
bij = 0
aij = 0 for all i > j
dij = 0
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Question # 28
The roots of ax2 + bx + c = 0 are always unequal if
Choose an answer
b2 - 4ac = 0
b2- 4ac ≠ 0
b2- 4ac > 0
b2- 4ac ≥ 0
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Question # 29
When a selection of object is made without paying regard to the order of selection, it is called
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Sequence
Series
Combination
Permutation
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Question # 30
The set {1,-1, i, -i} form a group under
Choose an answer
Addition
Multiplication
Subtraction
None
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Question # 31
The sum of the roots of the equation x2 -6x +2 = 0 is
Choose an answer
-6
2
-2
6
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Question # 32
Which of the following is not a quadrantal angle
Choose an answer
90°
100°
180°
270°
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Question # 33
A line joining two distinct points on a parabola is called a ______ of the parabola.
Choose an answer
Chord
Tangent
Lust rectum
directrix
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Question # 34
The centre of the conic x2 +16x +4y2 -16y +76 =0 is
Choose an answer
(0,10)
(-8,4)
(-8,-2)
(1,1)
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Question # 35
Multiplicative inverse of "1" is
Choose an answer
0
±1
1
{0,1}
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Question # 36
f(x) = ax + b will be an identity function if
Choose an answer
a = 1 , b = 1
a = 1 , b = 0
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Question # 37
Choose an answer
A rational number
A natural number
An irrational number
An integer
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Question # 38
A sequence is a function whose domain is
Choose an answer
N
Subset of N
R
None of these
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Question # 39
The equation of the circle with centre (h, k) and radius r is
Choose an answer
(x+ h)
2
+ (y+ k)
2
= r
2
(x+ h)
2
+ (y - k)
2
= r
2
(x - h)
2
+ (y+ k)
2
= r
2
(x - h)
2
+ (y - k)
2
= r
2
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Question # 40
If A and B are two sets then intersection of A and B is denoted by
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Question # 41
The domain of the principle sine function is
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Question # 42
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Question # 43
(-28,12) divides the join of A(-6,3) and B(5,-2) in ratio
Choose an answer
1:2
3:2
2:3
2:1
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Question # 44
If c is a constant number and if f is the function defined by the equation f(x) =c for all values of x, then f is differentiable at every x and f is defined by the equation f(x)
Choose an answer
f
1
C
0
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Question # 45
The principal value of sin
-1
[-√(√3) /2] is
Choose an answer
5π/3
-2π/3
-
π/3
π/3
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Question # 46
The set of points {(x,y)|y = f(x),∀x∈} is called
Choose an answer
Relation
Graph of f
Function
All are correct
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Question # 47
sin
2
α
cos
2
α
=
Choose an answer
-1
0
1
None of these
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Question # 48
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Question # 49
(x
3
-1/2x)
6
is
Choose an answer
15/16 x
2
2/13 x
2
17/7 x
2
16/15 x
2
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Question # 50
What is the 26th term of the sequence, if its general term is a
n = (-1)
n+1
Choose an answer
2
26
27
1
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Question # 51
In order of A is m x n and order of B is n x p then order of AB is
Choose an answer
m x m
n x n
m x p
p x m
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Question # 52
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Question # 53
The number of triplets (x, y, z) satisfying sin
-1
x +cos
-1
y + sin
-1
z = 2
π
is
Choose an answer
0
2
1
Infinite
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Question # 54
The points of intersection of the line y = 2x -3 and the circle x
2
+ y
2
- 3x =2y -3 = 0 are:
Choose an answer
two
three
less thean two
not intersect
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Question # 55
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Question # 56
For what value of k, 3x -2y+ k= 0 is tangent to the circle x2 +y2 +6x -4y =0
Choose an answer
k=0
k=0 or 26
k = 26
k=-13
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Question # 57
The set {x|x∈N∧x-4=0} in tabular form is
Choose an answer
{-4}
{0}
{}
None of these
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Question # 58
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Question # 59
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Question # 60
Choose an answer
Diagonal matrix
Scalar matrix
Triangular matrix
Identity matrix
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Question # 61
The slope of the normal at (4,3) to the circle x
2
+y
2
=25 is
Choose an answer
3/4
-3/4
4/3
-4/3
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Question # 62
Choose an answer
6
360
120
24
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Question # 63
If e,e′ be the eccentricities of two conics S=0 and S′ =0 and if e2 +e′2 =3 then both S and S′ can be
Choose an answer
Hyperbola
Parabolas
Ellipses
None of these
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Question # 64
The multiplicative inverse of 0 is
Choose an answer
1
-1
0
Does not exist
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Question # 65
G = {e, a, b, c} is an Abelian group with e as identity element. The order of the other elements are
Choose an answer
2, 2, 2
3, 3, 3
2, 2, 4
2, 3, 4
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Question # 66
∀ z ∈ C, multipliucative is
Choose an answer
(1,1)
(1,0)
(0,1)
None of these
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Question # 67
The 6th term of the sequence 7,9,12,16......is
Choose an answer
27
32
20
19
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Question # 68
(1 - x)
3
= ______
Choose an answer
1 + 3x + 3x
2
+ x
3
1 + x + x
2
+ x
3
1 - x + x
2
- x
3
1 - 3x + 3x
2
- x
3
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Question # 69
1
0
= ______
Choose an answer
360'
60"
60'
3600'
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Question # 70
Choose an answer
quadratic function
constant function
linear function
exponential function
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Question # 71
The distance between the points (0 , 0) and (1, 2) is
Choose an answer
5
0
3
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Question # 72
Choose an answer
sec 3x + c
- cosec 3x + c
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Question # 73
Choose an answer
none of these
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Question # 74
The slope of the normal at the point (at
2
, 2at) of the parabola y
2
= 4ax is
Choose an answer
1/t
t
-t
-1/t
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Question # 75
If f (x) = 2x+1 then fof (x) = _______;
Choose an answer
4x+3
2x +3
4x +1
None of these
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Question # 76
The zero vector is regarded to be parallel to
Choose an answer
Every vector
Is some cases
Both a,b
None
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Question # 77
The coefficient of x
10
in the expansion (x
3
+3/x
2
)
10
is
Choose an answer
1700
17023
17027
17010
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Question # 78
If m and n be two scalars, then (m+n) g =
Choose an answer
0
m+n
m▁a+n▁a
ma - m▁a
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Question # 79
sn (2sin-10.8)
Choose an answer
0.56
0.69
-0.16
0.96
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Question # 80
{0} is a
Choose an answer
Empty set
Singleton set
Zero set
Null Set
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Question # 81
Three dice are thrown together. The probability of getting a total of at least 6 is
Choose an answer
103 / 108
10 / 216
93 / 108
None of these
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Question # 82
In the interval 0≤ x ≤ π, the sine is
Choose an answer
Not a function
Not defined
Infinity
Not one-to-one function
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Question # 83
Choose an answer
2s
2
2s
3
s
3
3s
3
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Question # 84
Tangent is ...............function
Choose an answer
Inverse
one-one
in-to
Periodic
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Question # 85
The equation of the tangent at vertex to the parabola is y2 = -8(x -3)
Choose an answer
y=0
x=3
x=1
x=5
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Question # 86
If the angle between two vectors
u
and
v
is 0 orπ, then the vectors
u
and
v
are:
Choose an answer
Orthogonal
Collinear
Perpendicular
None of these
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Question # 87
If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a
Choose an answer
parabola
circle
hyperbola
ellipse
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Question # 88
The distance between the points A(-8,3) and B(2,-1) is
Choose an answer
116
none of these
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Question # 89
Two tangents drawn from (2,3) to the circle x2+y2 =9 are
Choose an answer
Real and distinct
Imaginary
Real and coincident
None of these
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Question # 90
A square matrix A = [aij] is lower triangular matrix when
Choose an answer
aij = 0 for all i<j
bij = 0
cij = 0
dij = 0
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Question # 91
Choose an answer
real number
complex number
rational number
irrational number
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Question # 92
The value of k (k > 0) for which the equation x
2
+ kx + 64 = 0 and x
2
- 8x + k = 0 both will have real roots is
Choose an answer
8
-16
-64
16
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Question # 93
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Question # 94
Choose an answer
20
10
0
None of these
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Question # 95
Choose an answer
X = 100 sin
θ
X = 10 sin
θ
X = 100 sec
θ
None of these
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Question # 96
If the line 2x -y +k =0 is a diameter of the circle x2 +y2 +6x -6y +5 =0 then k is equal to
Choose an answer
12
9
6
3
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Question # 97
The solution of the equation cos
2
θ
+ sin
θ
+ 1 = 0 lies in the interval
Choose an answer
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Question # 98
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Question # 99
if a
1
=3, d=7 and a
n
=59 , then the number of terms in A.P is
Choose an answer
7
9
11
13
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Question # 100
tan270° =__________;
Choose an answer
0
1
-1
Undefined
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Question # 101
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Question # 102
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Question # 103
Which is not a half plane
Choose an answer
ax + by < c
ax + by > c
Both A and B
None
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Question # 104
Another name of quadratic equation is
Choose an answer
Polynomial
2nd degree polynomial
Linear equation
simaltaneous equations
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