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ECAT Computer Science Entry Test MCQs With Answers
Question # 1
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Question # 2
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Question # 3
The distance of the points (3, 4, 5) from y-axis is
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Question # 4
In a triangle if a > 45°,β > 30° then y cannot be
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90°
100°
10°
120°
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Question # 5
i
2
=
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1
2
-1
0
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Question # 6
The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is
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x + y + z - 15 = 0
x - y + z - 15 = 0
x - y - z - 15 = 0
x + y + z + 15 = 0
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Question # 7
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Question # 8
In R, the multiplicative inverse of a is
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0
1
-a
1/a
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Question # 9
If a
1
= 3, r = 2, then the nth term of the G.P. is
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2.3
n-1
3.2
n
3.2
n+1
3.2
n-1
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Question # 10
If cos 20°=K and cos x=2 k
2
-1, then the possible values of x between 0° and 360° are
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140°
50° and 140°
50° and 130°
40° and 320°
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Question # 11
x = r2, y = 1 are the parametric equation of
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Circle
Hyperbola
Ellipse
Parabola
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Question # 12
The trigonometric function are continuous whenever
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They are defined
their limit exist
Their period is given
All are incorrect
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Question # 13
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Question # 14
Range if y = cos x is
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-1≤ y≤ 1
-1 < y < 1
-∞ < x < +∞
None of these
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Question # 15
Distance between A(3, 8), B(5, 6) is
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Question # 16
P∉ A means
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P
is subset of A
P
is an element of A
P does not belongs to A
A does not element of
P
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Question # 17
Which of the following is the subset of all sets?
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Question # 18
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Question # 19
Which of the following is a scalar
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weight
force
speed
momentum
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Question # 20
The tangents drawn from the point P to a circle are real and distinct if
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P is on the circle
P is inside the circle
P is outside the circle
none of these
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Question # 21
ab > 0 and a > 0 then
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a > b
a < b
a = b
None
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Question # 22
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Question # 23
An infinite arithmetic series is always
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Convergent
Oscillatory
Divergent
None of these
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Question # 24
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Question # 25
the curve of the parabola y
2
= -4ax is symmetric with respect to
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x -axis
y - axis
Botha x and y- axis
None of thes
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Question # 26
The point which is closet to the focus of a parabola is:
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vertex
Chord
Focus
Directix
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Question # 27
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0
1
-1
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Question # 28
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8
9
10
11
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Question # 29
The length of the tangent from (2, 1) to the circle x
2
+ y
2
+ 4y + 3 = 0 is
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Question # 30
30° = ______
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Question # 31
The solution set of x
2
- 5x + 6 = 0 is
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{1, 3}
{2, 3}
{1, 2}
None of these
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Question # 32
The process of finding the unknown elements in triangle is called the
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solution of the triangle
Mean differnece
Engineering distance
angle of depressin
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Question # 33
If 5,7 and 9 are A.Ms between a and b, then a and b is equal to
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2 and 12
1 and 10
3 and 11
-7 and 2
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Question # 34
For each even natural number n (n
2
-1) is divisible by
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6
3
4
8
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Question # 35
What is the period of tan 4/3 x =?
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π/4
4π/3
7π/4
3π/4
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Question # 36
∀a,b,c∈R and c>0,then
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a>b ⇒ ac < bc
a>b ⇒ ac > bc
a<b ⇒ ac > bc
None of these
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Question # 37
Multiplicative inverse of 0 is
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0
1
±1
Does not exist
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Question # 38
In a class of 100 students, 60 drink tea, 50 drink coffee and 30 drink both. A student from his class is selected at takes at last one of 2 drinks is
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2 / 5
3 / 5
4 / 5
None of these
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Question # 39
The graph of the linear equation of the form ax =by = c is a line which divided the plane into:
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Two similar regions
Two disjoint regions
Four equal parts
One region
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Question # 40
(a,b) +(-a,-b) =
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(0,0)
(a,b)
(-a,-b)
(1,1)
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Question # 41
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Rational fraction
Proper fraction
Improper rational fraction
None of these
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Question # 42
(A ∩ B)c =
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A∩ B
(A ∪ B)c
Ac∪Bc
Φ
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Question # 43
A circle is a limiting case of an ellipse whose eccentricity
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Tends to a
Tends to b
Tends to 0
Tends to a + b
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Question # 44
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Question # 45
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Question # 46
Apollonius was a:
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Rocket
Muslims scientist
Greek mathematicians
Method of finding conics
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Question # 47
The condition for polynomial equation ax2 + bx + c = 0 to be quadratic is
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a > 0
a < 0
a≠ 0
a≠ 0,b ≠ 0
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Question # 48
Which of the following is a vector
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length
momentum
volume
speed
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Question # 49
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Question # 50
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quadratic function
constant function
linear function
exponential function
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Question # 51
If|a| =|b|=|a + b|=1, then|a+ b| = 5, then|a-b| =
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4
6
5
3
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Question # 52
The line joining the center of a circle to the midpoint of the chord is
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Perpendicular to the tnagent
Perpendicular to the normal
Perpendicular to the chord
Perpendicular to the chord
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Question # 53
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Question # 54
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A variable
A constant
0
None of these
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Question # 55
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Question # 56
If
θ
= 60° then
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sin
θ
= 1/2
tan
θ
= cot 30°
θ
=
π
/4
sec
θ
= 4
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Question # 57
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sec 3x + c
- cosec 3x + c
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Question # 58
The sum of first n even number is
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n2
n(n+1)
n+1
n+2
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Question # 59
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Question # 60
Cos
-1
12/13 =
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tan
-1
3/5
cot
-1
13/12
Sec
-1
13/12
sin
-1
5/13
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Question # 61
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Question # 62
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-1
0
1
undefined
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Question # 63
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Question # 64
The period of the trigonometric function y = sin x cos x is
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2π
π
4π
π / 2
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Question # 65
The period of cosec 10x is _______
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Question # 66
Tan
-1
1/x = ______
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sin x
sec
-1
X
cot
-1
X
None of these
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Question # 67
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(g,f)
(-g,f)
(g,-f)
(-g,-f)
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Question # 68
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Question # 69
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0
-1
1
1/2
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Question # 70
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Question # 71
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y/x
x/y
y/z
None
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Question # 72
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(a + b)c = a . c + bc
a + b = b + a
(a + b) + c = a + (b + c)
a(b+ c) = ab + ac
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Question # 73
Choose an answer
2x cos x2
-2xcosxsinx
2x Sin x2
-Sin x2
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Question # 74
A polynomial P(x)has a factor (x-a)if P(a) =
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a
x
1
0
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Question # 75
The total number of subsets that can be formed out of the set {a, b, c} is
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1
4
8
12
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Question # 76
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 # 77
Ifᵨ> 1 , then the conic, is:
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Ellipse
Parabola
Hyperbola
None of these
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Question # 78
x
4
- 3x
3
+ 3x + 1 = 0 is called ______
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Reciprocal equation
Exponential equation
Radical equation
None of these
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Question # 79
Range of sin x is ______
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[-1, 1]
R
Negative real numbers
None of these
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Question # 80
Each point of the feasible region is called
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Solution
feasible solution
Both a & b
None
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Question # 81
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Question # 82
There are ______ types of rational fraction
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Three
Four
Five
Two
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Question # 83
If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a
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parabola
circle
hyperbola
ellipse
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Question # 84
The set of real roots of the equation log
(5x + 4)
(2x +3)
3
- log
(2x + 3)
(10x
2
+ 23x + 12) = 1 is
Choose an answer
{-1}
{-3/5}
Empty set
{-1/3}
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Question # 85
Root of the equation 3
x-1
+ 3
1-x
= is
Choose an answer
2
1
0
-1
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Question # 86
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Question # 87
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Question # 88
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Question # 89
There are n seats round a table numbered 1, 2, 3 .... n. The number of ways in which m person can take seats is
Choose an answer
n
P
m
n
C
m
x (m - 1) !
n-1
P
m
None of these
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Question # 90
An event having more than one sample point is called
Choose an answer
Certain event
Compound event
Simple event
None
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Question # 91
Product of any n consecutive positive integers is divisible by
Choose an answer
n
√n
n!
None
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Question # 92
If the domain of the function f: x⟶ 2x
3
+ 1 is {-1,2,3}, the range of the function is
Choose an answer
{3,2,5}
{1,3,9}
{-1,-2,-3}
{3,9,19}
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Question # 93
The domain of y = cos-1 x is
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-∞ < x < ∞
-1≤ x≤ 1
x≤ -1 or x ≥ 1
None of these
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Question # 94
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3 x 2
2 x 3
3 x 3
2 x 2
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Question # 95
A and B be two square matrices and if their inverse exist, the (AB)
-1
=
Choose an answer
A
-1
B
-1
AB
-1
A
-1
B
B
-1
A
-1
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Question # 96
The order axioms are satisfied by set of
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C
C and R
R
None of these
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Question # 97
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Question # 98
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none of these
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Question # 99
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(-1, 2)
(-1, 1)
(1, 2)
{-1}
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Question # 100
If A is any matrix then its additive inverse is
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A
A
-1
A
t
-A
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Question # 101
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