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Online Tests

ECAT Computer Science Entry Test MCQs With Answers

Question # 1

In how many ways can 5 persons be seated at a round table

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5!

4!

3!

120

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Question # 2

If cos (2 sin-1 x) = 1/9 , then what is the value of x?

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1/3

-2/3

2/3

2/3 , -2/3

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Question # 3

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Question # 4

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An empty set

Universal set

A singleton set

None of these

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Question # 5

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4(x³- 3x²)³+ c

3x²- 6x + c

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Question # 6

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Question # 7

If ab > 0 and a < 0, which of the following is negative?

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b

-b

-a

(a - b)²

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Question # 8

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Rational

Irrational

Natural

Odd

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Question # 9

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n < 8/5

n < 5/8

|n| < 8/5

|n|>8/5

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Question # 10

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4

3

2

1

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Question # 11

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Addition

Multiplication

Division

Both addition and multiplication

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Question # 12

The domain of the principal tan function is

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Question # 13

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Question # 14

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0

-1

1

not defined

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Question # 15

If a statement S(n) is true for n = 1 and the truth of S(n) for n = k implies the truth of S(n) for = k + 1, then S(n) is true for all

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Real numbers n

Integers n

Positive integers n

None of these

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Question # 16

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Question # 17

1st four terms of the expansion (1-x)^-2are

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1 + 2x + 3x²+ 4x³

3x²+ 2x + 1

1 + 3x + 4x²+ 5x³

None of these

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Question # 18

Every prime number is also

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Rational number

Even number

Irrational number

Multiple of two numbers

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Question # 19

The solution of the equation cos²θ+ sinθ+ 1 = 0 lies in the interval

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Question # 20

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A finite non-empty set

Null set

Both a and b

None of these

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Question # 21

The point of concurrency of the right bisectors of the sides of a triangle is called

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incentre

circum center

e-center

centroid

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Question # 22

If A and B are two sets then any subset R of B x A is called

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relation on A

relation on B

relation from A to B

relation from B to A

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Question # 23

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A parabola

An ellipse

A hyperbola

A circle

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Question # 24

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Question # 25

If 0 = {1,3,5.......}, then n (0) =

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99

odd integers

Even numbers

Infinite

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Question # 26

The inclination of a line parallel to x-axis is

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Question # 27

Three numbers are chosen random without replacement from {1, 2, 3, ...., 10}. the probability that minimum of the chosen numbering is 3 or their maximum is 7

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7 / 40

5 / 40

11 / 40

None of these

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Question # 28

The maximum value of sinθcosθis

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1

1/2

1/4

1/6

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Question # 29

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Question # 30

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 # 31

If the cone is cut by a plane perpendicular to the axis of the conec, then the section is a:

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Circle

ellipse

hyperbola

parabola

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Question # 32

∛8.6 is approximately equal to

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2.488

2.48

2.0488

2.05

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Question # 33

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Question # 34

If the circumference of a circle is divided into 360 congruent parts, the angle subtended by one part at the centre of the circle is

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1⁰

1'

1"

1 rad

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Question # 35

Arithmetic mean between x - 3 and x + 5 is

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x + 1

x + 2

x + 3

x + 4

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Question # 36

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30°

45°

60°

120°

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Question # 37

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0

-4

none of these

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Question # 38

The graph of linear equation 2x + 3y = 10

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Parabola

Circle

Hyperbola

Straight line

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Question # 39

If the angle between two vectors u and v is 0 orπ, then the vectors u and v are:

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Orthogonal

Collinear

Perpendicular

None of these

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Question # 40

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Question # 41

The two parts into which 57 should be divided so that their product is 782 are

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43,14

34,23

33,24

44,13

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Question # 42

If l, m, n are the d.c.'s of a line, then

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l2+ m2+ n2= 0

l2+ m2+ n2= 1

l + m + n = 1

l = m = n = 1

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Question # 43

If (0,4) and (0,2) are vertex and focus of the parabola respectively, the the equation of the parabola is:

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x² = 4y -32

x² =8y -32

y³ = 16 x

x2 + 8y =32

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Question # 44

Sum of first n terms of an arithmetic series is

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Question # 45

The set of all positive even integers is

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Not a group

A group w.r.t. subtraction

A group w.r.t. division

A group w.r.t. multiplication

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Question # 46

A circle passing through the vertices of any triangle is called

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Circumcirle

Incircle

Escribed circle

Unit circle

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Question # 47

The distance of the point (-2, -3) from the origin is

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2

-5

-3

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Question # 48

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Question # 49

w²⁸+ w³⁸= ______

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0

1

w

-1

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Question # 50

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0

1

-1

None

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Question # 51

In the expansion of (a + x)ⁿthe general term T_{r + 1}is

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Question # 52

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none of these

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Question # 53

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Question # 54

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Does not exist because f is unbounded

Is not attained even though f is bounded

Is equal to 1

Is equal to -1

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Question # 55

For which of the following ordered pairs (s, t) is s + t > 2 and s - t < -3?

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(3, 2)

(2, 3)

(1, 8)

(0, 3)

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Question # 56

If f(x)= x³ then f(-2) is

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-2

-4

-8

8

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Question # 57

If Z = (1,2), then Z^-1= ?

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(0.2, 0.4)

(-0.2, 0.4)

(0.2, -0.4)

(-0.2, -0.4)

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Question # 58

(ABC)' =

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CBA'

CBA

C'B'A

C'B'A'

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Question # 59

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X = 100 sinθ

X = 10 sinθ

X = 100 secθ

None of these

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Question # 60

If|a| =|b| = |a+b|=1, then|a-b| is equal to:

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1

√3

√2

7

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Question # 61

In R, the additive inverse of a is

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0

1

-a

1/a

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Question # 62

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Question # 63

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cos 2x

2 cos 2x

2 sin2x

-2 cos2x

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Question # 64

What is the value of cos (cos-1 2) ?

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√2

1/2

undefine

0

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Question # 65

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Question # 66

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No solution

One real solution

More than one real solution

None of these

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Question # 67

How many numbers are there between 103 and 750 which are divisible by 6

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125

107

108

113

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Question # 68

Write the first four terms of the arithmetic sequence 5, 2, -1, ... is

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3

-4

7

1

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Question # 69

What is the circular measure of the angles between the hands of which at 4 o clock

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π/6

3π/2

π/4

2π/3

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Question # 70

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 # 71

A triangle has ____ elements

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3

4

5

6

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Question # 72

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2, 3

3, 3

2, 6

2, 4

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Question # 73

(x + 3) (x + 4) = x²+ 7x + 12 is ______

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Quadratic equation

Linear equation

Cubic equation

Identity

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Question # 74

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Question # 75

Two tangents drawn from (2,3) to the circle x2+y2 =9 are

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Real and distinct

Imaginary

Real and coincident

None of these

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Question # 76

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a = 2, b = 3

a = 3, b = 2

a = 2, b = 1, 2

a = 3, b = 3

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Question # 77

Maximum value of z =15x +20y subject to 3x+ 4y≤ 12,x,y≥ 0 is given by

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46

60

50

70

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Question # 78

The set of even prime numbers is

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(2,4,6,8,10}

{2,4,6,8,10,12}

{1,3,5,7,9}

{2}

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Question # 79

The coefficient of x¹⁰in the expansion (x³+3/x²)¹⁰is

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1700

17023

17027

17010

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Question # 80

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Question # 81

f(x) = sin x is:

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an odd function

an even function

an implicit function

an exponential function

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Question # 82

(a,0) x (c, 0) =

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(0,ac)

(ac, 0)

(0,0)

(a, c)

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Question # 83

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Question # 84

The point of concurrency of the angle bisectors of a triangle is called

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incentre

circumcentre

e-centre

centroid

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Question # 85

Projection of vector u along v is

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|v| cosθ

|u| cosθ

|v| sinθ

|u| sinθ

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Question # 86

Which conjunction is not true ?

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Question # 87

14 is not a

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Prime number

Whole number

Even number

Real number

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Question # 88

The sides of a right angled triangle are in A.P The ratio of sides is

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1:2:3

3:4:5

2:3:4

5:8:3

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Question # 89

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Rational

Irrational

Even

Odd

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Question # 90

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Question # 91

If a plane passes through the vertex of a cone then the intersection is

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an ellipse

a hyperbola

a point circle

a parabola

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Question # 92

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none of these

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Question # 93

The roots of the equation 2^2x- 10.2^x+ 16 = 0 are

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2, 8

1, 3

1, 8

2, 3

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Question # 94

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 # 95

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Question # 96

√(-1b) =?

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b i

-i b

b2

i√b

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Question # 97

If Sn is a definite number as n → ∞,then the geometric series is

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Convergent

Divergent

Oscillatroy

None of these

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Question # 98

The period of cosec 10x is _______

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Question # 99

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¹⁰C₆

¹⁰C₅

¹⁰C₄

None

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Question # 100

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Question # 101

(51)⁴is equal to

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7065201

8065201

6765201

6565201

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