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Online Tests

ECAT Computer Science Entry Test MCQs With Answers

Question # 1

How many signals can be given by 5 flags of different colours, using 3 flags at a time

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120

60

24

15

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Question # 2

The distance of the point (a, b) from x-axis is

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a

b

a + b

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Question # 3

The expansion (1 + x)^-3holds when

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|x| > 1

|x| < 1

x < 1

x > 1

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Question # 4

Cos 60° = ______

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1

2

1/2

3

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Question # 5

Which of the following is not a unit vector

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[1, 1, 1]

[0, 1, 0]

[0, 0, 1]

[1, 0, 0]

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Question # 6

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 # 7

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Question # 8

2/9,5/7∈ R,(2│9)(5│7)=10/63∈R this property is called

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Associative property

Identity property

Commutative property

Closure property w.r.t multiplication

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Question # 9

The sum of the squares of three distinct real numbers, which are in G.P., is S². if their sum isαS then

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Question # 10

If #n = (n-5)2 + 5, then find #3 x #4.

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54

12

4

9

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Question # 11

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(x, y)

(kx, y)

(x, ky)

(kx, ky)

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Question # 12

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0

U

u/2

log u

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Question # 13

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Question # 14

Let S_ndenote the sum of the first n terms of an A.P. If S_2n= 3 S_n: S_nis equal to

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4

6

8

10

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Question # 15

For all points (x,y) on x-axis

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x is positive

x is negative

y = 0

y is negative

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Question # 16

Derivative of a w.r.t x is

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0

1

x

x

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Question # 17

The solution of the equation 3 tan²x = 1 is ____________

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none of these

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Question # 18

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π

π / 2

π / 3

π / 4

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Question # 19

QUQ'

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Question # 20

Cofactor of an element aij denoted by Aij is

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(-2)i+j

Mij

(-1)i+j Mij

None of above

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Question # 21

The positive real number which is the measure of the length of a vector is called the

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Unit vector

Modulus

Inverse

None of these

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Question # 22

Sine rule for a triangle states that

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a/sin A = b/sin B = c/sin C

sin A/a = sin B/b = sin C/c

a/sin A + b/sin B + c/sin C

2a/sin A = 2b/sin B = 2c/sin C

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Question # 23

Power set of X i.e P(X) _______ under the binary operation of union U

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Forms a group

Does not form a group

Has no identity element

Infinite set although X is infinite

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Question # 24

An equation in which at least one term contains dy/dx, d² y /dx²etc, is called.

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Differential equation

Initial condition

General solution

Singular equation

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Question # 25

To each element of a group there corresponds ______ inverse element

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Two

One

No

Three

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Question # 26

The point ________ is in the solution of the inequality 2x - 3y < 4

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(0, -2)

(1, -3)

(2, 2)

(3, 0)

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Question # 27

If the intersection of two sets is non-empty, but either is a subset of other are called

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Disjoint sets

Over lapping

Equal sets

None of these

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Question # 28

The roots of the equation ax²+ bx + c = 0 are real and equal if

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b²- 4ac < 0

b²- 4ac = 0

b²- 4ac > 0

None of these

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Question # 29

The sum of the focal distance from any point on the ellipse 9x2 +16y2 =144 is

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32

16

18

8

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Question # 30

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Question # 31

If f(x) = cos x then f(0) is

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0

1

1/2

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Question # 32

Given two independent event A and B such that P(A) = 0.30 and P(B) = 0.60. Probability of getting neither A nor B is

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0.28

0.13

0.12

0.42

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Question # 33

Two matrices A and B are conformable for the product AB if

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Both A and B are square

Both A and B are symmetric

Number of rows of A = number of columns of B

Number of columns of A = number of rows of B

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Question # 34

Number of terms in the expansion of (a+x)ⁿis

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n - 1

n + 1

n + 2

n + 3

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Question # 35

The set of integer is

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Finite group

A group w.r.t addition

A group w.r.t multiplication

Not a group

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Question # 36

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2

-3/2

1

0

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Question # 37

The period of|sin⁡2x| is

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π/2

-π/2

π

π/3

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Question # 38

The 5th term of (3a-2b)^-1is

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77b²/a⁵

16b²/243 a⁵

17b⁴/43a⁵

25b³/43a⁵

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Question # 39

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Question # 40

The locus of the centre of a circle which touches two given circles externally is:

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a hyperbola

an ellipse

a circle

a parabola

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Question # 41

Period of tan 4x is ______

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Question # 42

Range of y = sec x is

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-1≤ y≤ 1

y≥ 1 or y≤ -1

y≤ 1or y≥ -1

-∞ < y < +∞

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Question # 43

If A(x₁, y₁) , B(x₂, y₂) and C(x₃, y₃) are the vertices of a triangle then its centroid is

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Question # 44

In set builder notation the set {0,1,2,........100} can be written as

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{x / xε B ∧ x ≤ 100}

{x / x ∈ W ∧ x < 101}

{x / x ∈ Z ∧ x < 101}

The set of first 100 whole numbers

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Question # 45

The lines l1and l2intersect. The shortest distance between them is

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Positive

Negative

Zero

Infinity

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Question # 46

√11 is

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an irrational number

Rational number

odd number

Negative number

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Question # 47

The n numbers A₁,A₂,A₃,.....A_nare called an arithmetic means between a and b if a.A₁,A₂,A₃.....A_n, b is ______

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An arithmetic series

An arithmetic sequence

A geometric sequence

A harmonic sequence

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Question # 48

In one hour the minute hand of a clock turns through

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Question # 49

an - an-1 will be common difference in an A.P if

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n = 1∀n∈ N

n>1∧n∈N

n∈Z

None of the above

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Question # 50

The vertex of the graph of the quadratic function f(x) = x2 -10, is

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(0 , -10)

(-10,0)

(10,0)

(0,10)

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Question # 51

Tan 2θ=

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Question # 52

The roots of (x - a)(x - b) = ab x2 are always

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Real

Depends upon a

Depends upon b

Depends upon a and b

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Question # 53

If P, Q, R be the A.M., G.M., H.M. respectively between any two rational numbers a and b, then P - Q is

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Question # 54

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Question # 55

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Question # 56

∫f(x) is known as:

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Definite itegral

Indefinite integral

Fixed integral

Multiple integral

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Question # 57

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 # 58

The 31 term of the A.P 5,2,-1.....is

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-82

82

85

-85

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Question # 59

Name the property used in 100 + 0 = 100

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Additive inverse

Multiplicative inverse

Additive identity

Multiplicative identity

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Question # 60

The geometrical representation of a linear function is

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Circle

Parabola

Straight lie

None of these

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Question # 61

If A and B are two sets then any subset R of A x B 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 # 62

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c = 0

c = -1

c = -2

c = 1

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Question # 63

The domain of the principle sine function is

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Question # 64

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Question # 65

The set of positive integers, 0 and negative integers is known as the set of

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Natural numbers

Rational numbers

All integers

Irrational numbers

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Question # 66

For all points (x,y) in second quadrant

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x > 0 , y < 0

x > 0 , y > 0

x < 0 , y < 0

x < 0 , y > 0

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Question # 67

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Question # 68

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Question # 69

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Question # 70

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Question # 71

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Question # 72

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36

360

24

6

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Question # 73

If ax + bx + c =0 is satisfied by every value of x,then

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b = 0,c = 0

c = 0

b = 0

a = b = c = 0

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Question # 74

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1

2

3

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Question # 75

If a > 0, b > 0, c > 0, then the roots of the equation ax²+ bx + c = 0 are

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Real and negative

Non-real with negative real parts

Real and positive

Nothing can be said

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Question # 76

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 # 77

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images

pre-images

constants

none of these

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Question # 78

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1

3

2-i

-1

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Question # 79

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Question # 80

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Parallel to the plane

At right angles to the plane

Lies in the plane

Meet the plane obliquely

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Question # 81

The standard parabolic form of the equation f(x) = x² +4 x +1 is

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x(x+4)+1

(x+2)²-3

(x+4)³ + 9

x(x-2)²+1

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Question # 82

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 # 83

If a polynomial P(x) is divided by x - a, then the remainder is

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P(o)

P(-a)

P(a)

None of these

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Question # 84

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y + 1 = Ae^x

y + 1 = Axe^x

xe^x= C

y + xe^x= C

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Question # 85

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Singular

Non-singular

Adjoint

None of above

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Question # 86

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 # 87

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Question # 88

The distance between the points (0,0) and (x,y) is

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x²+ y²

x

y

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Question # 89

Which of the vectors have opposite direction?

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Question # 90

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Question # 91

(1, 1) is the in the solution of the inequality

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3x + 4y > 3

2x + 3y < 2

4x = 3y > 5

2c - 3y > 2

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Question # 92

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Question # 93

If the angle of a triangle are in the ratio 2 : 3 : 7, the triangle is

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Obtuse

Acute

Right angle

Isosceles

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Question # 94

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Question # 95

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4

6

8

10

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Question # 96

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cot x + c

tan x + c

-cot x + c

-tan x + c

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Question # 97

An integer is chosen at random from the number ranging from 1 to 50. the probability that the integer chosen is a multiple of 2 or 3 or 10 is

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3 / 10

5 / 10

7 / 10

9 / 10

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Question # 98

The feasible region which can be enclosed within a circle is called

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Bounded region

Convex region

Unbounded region

None

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Question # 99

If 3x⁴+ 4x³+ x - 5 is divided by x + 1, then the reminder is

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0

7

-7

5

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Question # 100

The term independent of x is the expansion (x³+1/x)¹²

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295

495

395

722

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Question # 101

Only one of the root of ax2 + bx + c =0, a≠ 0 is zero if

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c = 0

c = 0,b≠ 0

b = 0,c = 0

b = 0,c≠ 0

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