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ECAT Computer Science Entry Test MCQs With Answers
Question # 1
Choose an answer
0
-1
1/2
1
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Question # 2
If f(x) = -x
2
then f(-2) is
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-2
2
-4
4
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Question # 3
If y=f(x) is a function then x is called
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dependent variable
independent variable
constant
none of these
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Question # 4
An equation which holds good for all values of variables is called
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Equation
Conditional equation
Constant
None
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Question # 5
The sum of the cubes of three consecutive natural number is divisible by
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9
6
5
10
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Question # 6
The equation of the circle with centre (-h, -k) and radius r is
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(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 # 7
The centroid of a triangle divides each median in the ratio
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2 : 1
3 : 1
3 : 2
1 : 1
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Question # 8
sin 3a = ______;
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3sin a - 4sin3a
4sin a -3 sin3 a
3 cos3 a -cosa
4cos3 a - 3cos a
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Question # 9
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Question # 10
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Question # 11
For the parabola the line through focus and perpendicular to the directrix is called
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Tangent
Vertex
Axis
None
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Question # 12
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Question # 13
e-radii are denoted by
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η
r2
r3
All of these
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Question # 14
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3K
K2
K3
K
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Question # 15
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square root function
identity function
linear function
quadratic function
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Question # 16
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At
-A
A
A-1
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Question # 17
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2
-3/2
1
0
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Question # 18
If three unequal numbers p, q, r are in H.P. and their squares are in A.P., then the ration p : q : r is
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Question # 19
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Question # 20
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Question # 21
The second degree equation of the form Ax2 +By2 +Gx +Fy +C =0 represent hyperbola if
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A = B≠ 0
A≠ B and both are of same sign
A≠ B both are of opposite sign
Either A = 0 or B =0
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Question # 22
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0
1
2
none of these
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Question # 23
The slope of y-axis is
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0
undefined
1
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Question # 24
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0
20
90
80
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Question # 25
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1 / 2
1 / 3
1 / 4
None of these
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Question # 26
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-a -b -c
1
0
-1
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Question # 27
If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then the probability that the drawn balls are of different colours is
Choose an answer
1 / 66
3 / 66
19 / 66
47 / 66
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Question # 28
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(g,f)
(-g,f)
(g,-f)
(-g,-f)
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Question # 29
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cos 2x + c
- cos 2x + c
tan 2x + c
cot 2x + c
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Question # 30
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none of these
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Question # 31
For a square matrix A, if A = A
t
, then A is called
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matrix
Transpose
Symmetric
Non-symmetric
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Question # 32
Equation of the chord of contact to the tangents drawn from (-3,4) to the circle x2 + y2 = 21
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-3x + 4y =21
4x - 3x = 0
-3x + 4y = 25
None of these
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Question # 33
What is the number of elements of the power set of {0, 1}
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1
2
3
4
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Question # 34
Roots of the equation x
2
+ 5x - 1 = 0 are
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Rational
Irrational
Complex
None of these
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Question # 35
In R the number of identity elements w.r.t.'.' is
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One
Two
Three
Four
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Question # 36
Which of the following is factor of x11+a11, where n is an odd integer
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x-a
x+a
2x-a
2x+a
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Question # 37
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Question # 38
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Question # 39
Any recurring decimal represents a
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Irrational no
Integer
Rational no
None of these
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Question # 40
An ellipse slides between two lines at right angles to one another. The locus of its centre is :
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a parabola
an ellipse
a circle
a hyperbola
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Question # 41
A triangle which is not right angle is called ______ triangle
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acute
Obtuse
Right
Oblique
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Question # 42
The equation x2+ y2- 8x+ 6y+ 25= 0 represents
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A circle
A pair of straight lines
A point
None of these
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Question # 43
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xy
y
0
x
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Question # 44
Two coins are tossed twice each. The probability that the head appears on the first toss and the same forces appear in the two tosses is
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1/4
1/2
1/3
1/7
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Question # 45
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Question # 46
If (x
1
, y
1
) and (x
2
,
y
2
) are the end points of a diameter then the centre of the circle is
Choose an answer
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Question # 47
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12
13
14
15
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Question # 48
f(x) = 2
x
+ 3 . 2
2x
+ 5 is
Choose an answer
trigonometric function
algebraic function
exponential function
logarithmic function
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Question # 49
If 2x +y + λ =0 is normal to parabola y2 =-8x,λ= _____
Choose an answer
12
8
24
-24
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Question # 50
If line through (4,3) and (2,k) is perpendicular to y =2x +3, then k =_______
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-1
1
-4
4
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Question # 51
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Question # 52
A right angle is the angle of measure
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90'
60°
60"
90°
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Question # 53
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Question # 54
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1
-1
0
None of these
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Question # 55
The transport of a null matrix is
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Row matrix
Column matrix
Square matrix
Null matrix
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Question # 56
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Question # 57
1
0
= ______
Choose an answer
1.5 rad
0.5 rad
0.175 rad
None of these
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Question # 58
If sin x + sin
2
x = 1, then the value of Cos
12
x + 3cos
10
x + 3cos
8
x + cos
6
x + 2 cos
4
x + cos
2
x-2 is equal to
Choose an answer
0
1
2
sin
2
x
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Question # 59
tan(cot
-1
x) is equal to
Choose an answer
cot(tan
-1
x)
tan x
secon x
None of these
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Question # 60
Z is the set of integers, (z, *) is a group with a * b = a + b + 1, a, b
∈
G. then inverse of a is
Choose an answer
-a
a + 1
-2 -a
None of these
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Question # 61
System of linear equation is inconsistent if
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System has no solution
System has one solution
System has two solution
None of above
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Question # 62
Each point of the feasible region is called
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Solution
feasible solution
Both a & b
None
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Question # 63
The multiplicative inverse of (a,b) is
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Question # 64
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Question # 65
Associative law of multiplication
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ab = ba
a(bc) = (ab) c
a(b+c) = ab + ac
(a + b)c = ac + bc
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Question # 66
If y = 2x , then
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y1 -ln2y = 0
y2-(ln2)2 y = 0
y2-(ln2)y1 = 0
All are correct
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Question # 67
Range of 2 tan x is ______
Choose an answer
[-2, 2]
-1 < x < 1
R
None of these
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Question # 68
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Question # 69
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Question # 70
If
∀a,b ε R,then a +b ε R is a property
Choose an answer
Closure law of addition
Associative law of addition
Additive inverse
Additive identity
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Question # 71
An A.P., a G.P. and a H.P. have the same first and last terms and the same odd numbers of terms, the middle terms of the three series are in
Choose an answer
A.P.
G.P.
H.P.
None of these
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Question # 72
If A and B are two disjoint events then
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P(A∪B)=P(A)+P(B)
P(A∪B)=P(A)-P(A∪B)
P(A∪B)=P(A)or P(B)
None
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Question # 73
The lotus of intersection of perpendicular tangents to the parabola y
2
= 4ax is:
Choose an answer
Axis of the parabola
Focal chord of the parabos
The tangent at vertex of the parabola
a directrix of the parabola
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Question # 74
Choose an answer
0
2
4/3
5/3
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Question # 75
A vector with magnitude one is called
Choose an answer
constant vector
unit vector
zero vector
null vector
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Question # 76
If the exponent in the binomial expansion is 6, then the middle term is
Choose an answer
2nd
3rd
4th
5th
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Question # 77
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none of these
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Question # 78
A diagonal matrix in which the diagonal elements are equal is called a
Choose an answer
Null matrix
Identity matrix
Scalar matrix
Row matrix
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Question # 79
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Question # 80
Choose an answer
4
6
8
10
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Question # 81
Choose an answer
Commutative law of multiplication
Closure law of multiplication
Associative law of multiplication
Multiplication identity
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Question # 82
For a square matrix A, if A = At, then A is called
Choose an answer
Matrix
Transpose
Symmetric
Non-symmetric
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Question # 83
n! > 2
n
-1 is true when
Choose an answer
n≤ 3
n≤ 6
n≥ 4
n≤ 6
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Question # 84
Choose an answer
all
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Question # 85
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Question # 86
The expression x2 - x + 1 has
Choose an answer
One proper linear factor
No proper linear factor
Two proper linear factors
None of these
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Question # 87
Choose an answer
6x + 2 + c
6x + x
2
+ c
6x
3
+ x
2
+ x
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Question # 88
Choose an answer
a constant function
linear function
quadratic funtion
none of these
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Question # 89
If you are looking a high point from the ground, then the angle formed is
Choose an answer
Angle of elevation
Angle of depression
Right angle
Horizon
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Question # 90
The greatest integer which divides the number 101
100
- 1 is
Choose an answer
100
1000
10000
100000
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Question # 91
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Question # 92
The parametric equations of a circle are
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Question # 93
f(x) = 3x
4
-2x
2
+ 7 is:
Choose an answer
an even function
an odd function
an even and implicit function
neither even nor a odd
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Question # 94
If for the matrix A,A5 = 1,then A-1=
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A2
A3
A
None of above
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Question # 95
tan (
π
-
θ
) = ______
Choose an answer
- sin
θ
- tan
θ
- cos
θ
- cot
θ
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Question # 96
Which is an explicit function
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y = x
2
+ 2x - 1
x
2
+ xy + y
2
= 2
x
2
+ y
2
= xy + 2
All are
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Question # 97
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 # 98
The area of the circle centred at (1,2) and passing through (4,6) is
Choose an answer
30 πsq.units
5π sq.units
15π sq.units
25π sq.units
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Question # 99
If the graph of f is entirely below the x-axis, then the value of definite integral is
Choose an answer
= 0
< 0
> 0
None
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Question # 100
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Question # 101
sin(3π/2 -θ)=_______;
Choose an answer
sinθ
cosθ
-sinθ
-cosθ
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