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Online Tests

ECAT Computer Science Entry Test MCQs With Answers

Question # 1

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Question # 2

The roots of the equations will be equal if b²- 4ac is

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Positive

Negative

1

Zero

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Question # 3

The parabola y²= x is symmetric about

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x-axis

y-axis

Both x and y-axis

The line y = x

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Question # 4

The maximum value of Z = 3x+ 4y subjected to the constrains x+ y≤ 40,x+ 2y≤ 60, x≥ 0 and y≥ 0 is

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120

100

140

160

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Question # 5

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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 # 6

If z=(x,y) then z has no multiplicative inverse when

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x ≠ 0, y = 0

x = 0, y = 0

x = 0, y ≠ 0

None of these

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Question # 7

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12

6

8

none of these

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Question # 8

n² - 1 divisible by 8 when n is

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an odd integer

an even integer

Irrational

Prime Number

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Question # 9

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Improper rational fraction

Proper rational fraction

Polynomial

Equation

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Question # 10

If the lines 2x-3y-1=0,3x-y-5=0 and 3x+py+8=0 meet at a unique point then

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p = -14

p = -1

p =0

p=12

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Question # 11

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Question # 12

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2

4

3

16

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Question # 13

The graph of y < 2 is the

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Left half plane

upper half plane

Right half plane

Lower half plane

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Question # 14

Let A and B be two sets. If every element of A is also an element of B then

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Question # 15

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Question # 16

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Question # 17

The intercepts of the plane 2x - 3y + 4z = 12 on the co-ordinate axes are given by

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2, -3, 4

6, -4, -3

6, -4, 3

3, -2, 1.5

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Question # 18

If 2x +y + λ =0 is normal to parabola y2 =-8x,λ= _____

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12

8

24

-24

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Question # 19

nCn-r is equal to

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n!

n-1Cr

nCr

None of these

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Question # 20

For any positive integer n

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ABn = Bn A ⇔ AB = BA

ABn = Bn A⇔ A,B are square matrices and AB = BA

ABn = BnA⇔ A + B

ABn = BnA ⇔ A and B are square matries

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Question # 21

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The law of sines

The law of tangents

The pythagorus theorem

None of these

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Question # 22

If (0, 0) and (-1, 0) are end points of a diameter, then the equation of the circle is

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Question # 23

If n is odd then the middle terms in the expansion of (a + x)ⁿare

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Question # 24

The period of tan [x/3] is ______

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2π

4π

3π

5π

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Question # 25

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 # 26

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 # 27

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A rational number

A irrational number

An even integer

A factor of 36

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Question # 28

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Question # 29

If the roots of ax²+ bx + c = 0 (a > 0) be greater than unity, then

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a + b + c = 0

a + b + c > 0

a + b + c < 0

None of these

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Question # 30

If Sin A = sin B, cos A = cos B, then the value of A in terms of B is

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Question # 31

The number of permutation that can be formed from the letters of the word OBJECT is

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700

600

720

620

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Question # 32

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A natural number

A rational number

An irrational number

A whole number

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Question # 33

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 # 34

Group of none-singular matrices under multiplication is

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None-Abelian group

Semi group

Abelian group

None of these

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Question # 35

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n!

0!

1

None of these

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Question # 36

If sin 6θ+ sin 4θ+ sin 2θ, thenθ=

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Question # 37

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Question # 38

If the sum of co-efficient in the expansion of (a+b)ⁿis 4096, then the greatest co-efficient in the expansion is

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1594

792

924

2924

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Question # 39

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Question # 40

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

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|x| > 1

|x| < 1

x < 1

x > 1

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Question # 41

Empty set is

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Not the member of real numbers

Infinite set

Finite set

Not subset of every set

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Question # 42

√23 is

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A rational number

A irrational number

An even integer

A factor of 36

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Question # 43

sin (α +β)=

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sinαcosβ- cosαsinβ

sinαcosβ- cosαsinβ

sinαcosα- cosβsinβ

sinαcosα+ cosβsinβ

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Question # 44

In a country, 55% of the male population has houses in cities while 30% have houses both in cities and in village. Find the percentage of the population that has house only in villages.

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45

30

25

50

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Question # 45

x = ________ is in the solution of 2x - 5 > 0

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0

2

-2

3

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Question # 46

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 # 47

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A

A'

U

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Question # 48

The principal value of sin^-1(-1/2)

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π/3

π/4

π/6

-π/6

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Question # 49

A monoid (G, *) is said to be group if

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have identity element

is commutative

have inverse of each element

None of these

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Question # 50

If order of A is m x n, then order of A^tis

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m x m

n x n

m x n

n x m

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Question # 51

The slope of y-axis is

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0

undefined

1

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Question # 52

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Question # 53

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Question # 54

If a2 = b2 then

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a = b

a+b= 1

|a+b| =0

None

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Question # 55

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A variable

A constant

0

None of these

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Question # 56

If w+w2 is a root of (x+1)(x+2)(x+3)(x+4) = k, then

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k=0

k=1

k=w

k=w2

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Question # 57

Cos (α+β) - cos (α-β) =

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-2 sinα sinβ

2 sinαcosβ

-2 sinαcosα

4 sinα cosβ

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Question # 58

∀a,b ε R, ab = be is a

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Commutative law of multiplication

Closure law of multiplication

Associative law of multiplication

Multiplicative identity

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Question # 59

The period of|sin⁡2x| is

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π/2

-π/2

π

π/3

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Question # 60

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Question # 61

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Addition

Subtraction

Multiplication

None of these

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Question # 62

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15

15 i

-15 i

-15

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Question # 63

x = -1 is in the solution of the inequality

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x + 5 < 0

2x + 3 < 0

x > 0

2x + 3 > 0

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Question # 64

Every recurring decimal represents

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A natural number

A rational number

An irrational number

A whole number

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Question # 65

sin (α+β) + sin (α-β)

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2 sinαcosβ

sin (2αβ)

sinαcosα

None of these

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Question # 66

csc(-π/2) = __________;

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0

1

-1

Undefined

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Question # 67

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K/6

2K

3K

6K

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Question # 68

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none of these

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Question # 69

The domain of the function x/x² -4 is given by

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R

R + 2

[R - (+2)

R-4

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Question # 70

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Question # 71

The complement of set A relative to universal set U is the set

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{x / x∈ A∧ x∈ U}

{x / x∉ A∧ x ∈ U}

{x / x∈ A and x ∉ U}

A-U

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Question # 72

If one end of the diameter of the circle x² + y²- 5x = 3y -22 = 0 is (3,4) the other end is:

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(2,7)

(-2,-7)

(-2,7)

(2,-7)

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Question # 73

For graphing a linear inequality, solid line is drawn if the inequality involves the symbols:

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> or <

> or <

= or≠

= or >

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Question # 74

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Question # 75

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Question # 76

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Question # 77

tan^-1(1/4) + tan^-1(2/9) is equal to

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1/2 cos^-1(3/5)

1/2 sin^-1(3/5)

1/2 tan^-1(3/5)

tan^-11/2

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Question # 78

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Question # 79

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Question # 80

1⁰= ______

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1.5 rad

0.5 rad

0.175 rad

None of these

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Question # 81

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0

1

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Question # 82

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Question # 83

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

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1 degree

1 second

1 minute

1 radian

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Question # 84

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 # 85

The angle between the vectors 3i + j - k and 2i - j + k is

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Question # 86

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Question # 87

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None of these

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Question # 88

If 4 sin²θ=1, then values ofθare

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Question # 89

The Domain of y = sin x is ______

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Set of real numbers

Rational

Irrational no.

None of above

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Question # 90

The transport of a rectangular matrix is a

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Square matrix

Rectangular matrix

Row matrix

Column matrix

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Question # 91

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π / 4

π / 6

π / 3

0

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Question # 92

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Question # 93

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 # 94

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2

1

5

0

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Question # 95

Tan^-11/x = ______

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sin x

sec^-1X

cot^-1X

None of these

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Question # 96

cot(3π/2 -θ)=______;

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tanθ

cotθ

-tanθ

-cotθ

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Question # 97

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0

Independent of a

Independent of b

Independent of c

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Question # 98

(0.90)^1/2is equal to

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0.99

0.90

0.80

0.88

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Question # 99

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Question # 100

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none of these

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Question # 101

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