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ECAT Computer Science Entry Test MCQs With Answers
Question # 1
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sin h x
cos h x
sec h x
cosec h x
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Question # 2
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Question # 3
If 0 = R, thenthe additive inverse of a is
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1/9
1/-9
a
-a
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Question # 4
If the distance of any point on the curve from any of the two lines approaches zero then it is called
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Axis
Directrices
Asymptotes
None
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Question # 5
The set { {a, b} } is
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Infinite set
Singleton set
Two points set
Empty set
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Question # 6
If a = 2i +2j, b= 3i -j and c=4i +5j, the 3b -a-2c =
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-i -15j
i-15j
i-3j
None of these
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Question # 7
If x
2
- 7x + a has remainder 1 when divided by x + 1, then a = ______
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-7
7
0
None of these
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Question # 8
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Question # 9
If a
1
, r and a
n
are the first term, common ratio and the nth term respectively of a G. P. then a
n
=
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a
1
r
n
a
1
r
n-1
a
1
r
n+1
a
1
r
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Question # 10
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Question # 11
In R the left cancellation property w.r.t addition is
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Question # 12
If A = {2m/m
3
= 8 , m€ Z} then A =
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{1,8,27}
{4}
(2,4,6}
{2,16,54}
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Question # 13
The approximate percentage increase in the volume of a cube if the length of its each edge changes from 5 to 5.02 is
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1.2%
1.5%
0.16%
100.16%
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Question # 14
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Question # 15
The standard parabolic form of the equation f(x) = x
2
+4 x +1 is
Choose an answer
x(x+4)+1
(x+2)
2
-3
(x+4)
3
+ 9
x(x-2)
2
+1
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Question # 16
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Question # 17
A conditional is regarded as false only when the antecedent is true and consequent is
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True
False
Known
Unknown
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Question # 18
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0
1
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Question # 19
Period of cos 2x is ______
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Question # 20
1 + 2 + 3 + ...... + n = ______
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Question # 21
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quadratic function
constant function
linear function
exponential function
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Question # 22
Derivative of x
3
w.r.t x is
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0
1
3x
2
x
3
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Question # 23
The expansion of (1 + 2x)
-2
is valed if
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| x | < 1/2
| x | < 1
| x | < 2
| x | < 3
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Question # 24
The magnitude of vector a=i-3j+5k is:
Choose an answer
3
√35
√17
√35
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Question # 25
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Question # 26
The number of subsets of B = {1,2,3,4,5}
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10
32
16
5
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Question # 27
The range of the tangent function is
Choose an answer
all real numbers
-1 ≤ x ≥ 1
natural number
z
+
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Question # 28
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 # 29
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Question # 30
The no of term is the expansion of (a+x)n-1 is
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n+1
n-1
n
n-2
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Question # 31
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Question # 32
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 # 33
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Question # 34
G = {e, a, b, c} is an Abelian group with e as identity element The order of the other elements are
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2,2,2
3,3,3
2,2,4
2,3,4
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Question # 35
s > t then
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(s - t)
2
> (t - s)
2
(s - t)
2
< (t - s)
2
(s - t)
2
= (t - s)
2
None
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Question # 36
sin (
α +
β)=
Choose an answer
sin
α
cos
β
- cos
α
sin
β
sin
α
cos
β
- cos
α
sin
β
sin
α
cos
α
- cos
β
sin
β
sin
α
cos
α
+ cos
β
sin
β
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Question # 37
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5
-5
none
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Question # 38
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Question # 39
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Question # 40
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a = -1/2, b = -1
a = 1, b = 2
a = 2, b = 3
None of above
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Question # 41
What is the period of 6 sin x=?
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π
-π
π/2
2π
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Question # 42
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a f(x) + c
f(x) + a
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Question # 43
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Question # 44
for n€ N, 3
2n + 7 is divisible by
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7
8
9
10
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Question # 45
The eccentricity of the conic 9x
2
- 16y
2
= 144 is
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4/5
5/4
4/3
3/4
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Question # 46
The mid point of the line joining the points P(x
1
, y
1
) and Q(x
2
, y
2
) is
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Question # 47
If S is a sample space and event set E =Φ then P(E) is
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>0
1
<1
0
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Question # 48
The maximum value of the quadratic function f(x) = -2x2+20x,is
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4
3
50
7
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Question # 49
The line y =mx +1 is tangent to the parabola y2 =4x if
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m=1
m=2
m=3
m=4
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Question # 50
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Question # 51
The set {1, -1, 1, -1}, form a group under
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Addition
Multiplication
Subtraction
None
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Question # 52
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Additive property in R
Multiplication property in R
Cancellation property in R
Distribution property in R
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Question # 53
To each element of a group there corresponds ______ inverse element
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Two
One
No
Three
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Question # 54
Range of 2 tan x is ______
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[-2, 2]
-1 < x < 1
R
None of these
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Question # 55
The fifth term of the sequence a
n
= 2n + 3 is ______
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13
-13
8
3
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Question # 56
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Question # 57
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15/23
7/15
7/8
15/7
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Question # 58
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Question # 59
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cos 2x + c
- cos 2x + c
tan 2x + c
cot 2x + c
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Question # 60
The expansion (1 + x)
-3
holds when
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|x| > 1
|x| < 1
x < 1
x > 1
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Question # 61
The angle between the vectors 3i + j - k and 2i - j + k is
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Question # 62
The equation of the parabola with directirx x = 2 and the axis y = 0 is
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y
2
= 8x
y
2
= -8x
y
2
= 4x
y
2
= -4x
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Question # 63
A line segment whose end points lie on a circle is called
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the secant of the circle
the arc of the circle
the chord of the circle
the circumference of the circle
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Question # 64
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Question # 65
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A
A'
U
None of these
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Question # 66
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sec 3x + c
- cosec 3x + c
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Question # 67
In any triangle ABC,with usual notationαsinβ =____;
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b sinα
bsinβ
αsinα
None of these
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Question # 68
The root of the quadratic equation are
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3
2
1
4
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Question # 69
F(x) = x
x
decreases in the interval
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(0, e)
(0, 1)
(-
∞
,0)
None
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Question # 70
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At
-A
A
A-1
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Question # 71
If f(x) = tan x then f(0) is
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0
1
1/2
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Question # 72
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Question # 73
If the sum of even coefficients in the expansion of (1+x)n is 128 then
Choose an answer
n=7
n=9
n=8
None
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Question # 74
If a,b c are sides of a triangle taken in order then a x b =
Choose an answer
b x c
b x a
cxa
Both a & b
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Question # 75
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A
A'
U
A A'
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Question # 76
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Question # 77
I f a =5i + 2j, then|a| =
Choose an answer
√13
√7
1/√13
√29
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Question # 78
Domain of 1+cot2θ=csc2θ is
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[0,π]
R-{x/x=nπ,n∈ z}
(-∞,+∞)
[-1,1]
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Question # 79
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A
0
Unit vector
None
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Question # 80
The measure of the acute angle between the lines represented by x2 -xy -6y2 =0 is
Choose an answer
120°
30°
130°
45°
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Question # 81
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 # 82
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Question # 83
A series consisting of an unlimited number of terms is termed as an
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Finite sequence
Infinite sequence
Infinite series
geometric sequence
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Question # 84
The graph of a quadratic function is
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Circle
Straight line
Parabola
Triangle
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Question # 85
The period of the function f(x) = sin
4
x + cos
4
x is
Choose an answer
π
π
/2
2
π
None of these
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Question # 86
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all are correct
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Question # 87
The law of sines can be used to solve oblique triangle when following information is given:
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Two angles and a side
Two sides and an angle opposite one of the given sides
Two sides and the angle between two sided
Option a and b
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Question # 88
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Question # 89
If five triangles are constructed having sides of the lengths indicated below, the triangle that will NOT be a right triangle is
Choose an answer
8, 15, 17
3, 4, 5
12, 15, 18
5, 12, 13
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Question # 90
The second degree equation 2x2 -xy+ 5x -2y +2 =0 represents
Choose an answer
Circle
Hyperbola
Ellipse
Pair of straight lines
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Question # 91
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5x
4 + c
1/6 x
6
+ c
5x
2
+ c
1/5 x
6
+ c
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Question # 92
Matrices A = [aij] 2 x 3 and B = [bij] 3 x 2 are suitable for
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BA
A2
AB
B2
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Question # 93
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Question # 94
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Question # 95
Sin h
-1
x = _________
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Question # 96
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Question # 97
14 is not a
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Prime number
Whole number
Even number
Real number
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Question # 98
A tower subtends an angle
α
at a point on the same level as the root of the tower and at a second point, b meters above the first, the angle of depression of the foot of the tower is
β
. The height of the tower is
Choose an answer
b cot
α
tan
β
b tan
α
tan
β
b tan
α
cot
β
None of these
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Question # 99
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Question # 100
A point of a solution regions where two of its boundary lines intersect, is called:
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Vertex of the solution
Feasible point
Point of inequality
Null point of the solution region
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Question # 101
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(-6,4)
(-3,2)
(6,-4)
(3, -2)
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