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Online Tests

ECAT Computer Science Entry Test MCQs With Answers

Question # 1

∫Sec² (ax + b) dx is equal to:

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tan² (ax + b)

1/a tan² (ax + b)

1/atan (ax +b)

tan (ax + b)

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Question # 2

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Question # 3

if A = (x/x€ Q˄ 0 < x < 1}, the A is

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Infinite set

Finite set

Set of rational numbers

Set of real numbers

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Question # 4

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 # 5

If Cosθ=0, thenθ= ______

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nπ/2

(2n + 1)π/2

(2n - 1)π/2

(4n + 1)π/2

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Question # 6

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Question # 7

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4x + 1

4x

2x³

none of these

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Question # 8

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Question # 9

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Question # 10

i =

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√1

√2

√-2

√-1

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Question # 11

2x = 3 is a conditional equation it is true for

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2

3

3/2

2/3

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Question # 12

A ________ divides the plane into left and right half planes.

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Vertical line

Horizontal line

Non vertical line

Inequality

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Question # 13

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I quadrant

II quadrant

III quadrant

IV quadrant

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Question # 14

Which is an explicit function

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y = x²+ 2x - 1

x²+ xy + y²= 2

x²+ y²= xy + 2

All are

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Question # 15

The straight lines represented by the equation ax2+ 2hxy +by2 =0 intersects at

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(1,1)

(0,1)

(1,0)

(0,0)

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Question # 16

Sec 30° = ______

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Question # 17

The point where the axis meets the parabola is called

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Directrix

Foucu

Chord

Vertix

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Question # 18

cos (α+β) + cos (α-β) =

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4 cosαcosβ

2 cosαcosβ

2 sinαsinβ

2 sinαcosβ

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Question # 19

Cot 45° = ______

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Question # 20

The mid point of the line segment joining the points (4,0) and (0,4) is

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(4,4)

(2,2)

(-4,-4)

(-2,-2)

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Question # 21

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Question # 22

The differential equations of all conis whose axes coincide with the co-ordinate axis is

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Question # 23

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a^xIn a + c

a^x+ c

x a^x+ c

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Question # 24

A square is inscribed in the circle x²+ y²- 2x + 4y + 3 =0. Its sides are parallel to the co-ordinate axes. Then one vertex of the square is

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Question # 25

The eccentricity of the parabola y²= -8x is

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-2

2

-1

1

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Question # 26

If n is any positive integer then n! > 2^n-1for

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Question # 27

The span of a standard parabola depends upon

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x

a

y

y2

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Question # 28

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0

1

undefined

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Question # 29

To express a single rational fraction as a sum of two or more single rational fractions which are called

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improper fractions

Partial fractions

mixed form

Polynomials

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Question # 30

The mid point of the line segment joining the points (3,-1) and (-3,1) is

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(3,-1)

(0,0)

(2,2)

(4,4)

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Question # 31

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Question # 32

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Question # 33

The set of complex numbers forms a group under the binary operation of

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Addition

none of these

Division

Subtraction

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Question # 34

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Question # 35

The negation of a number

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a relation

a function

unary operation

binary operation

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Question # 36

The magnitude of vector a 2i-7j is

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√23

√43

3

√53

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Question # 37

The central angle of an arc of a circle whose length is equal to the radius of the circle is called one

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Degree

Second

Minute

Radian

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Question # 38

The points (5, 2, 4)(6, -1, 2) and (8, -7, k) are collinear if k is equal to

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-2

2

3

-1

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Question # 39

(1 + 2x)⁴= ______

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1 + 4x + 6x²+ 4x³+ x⁴

1 - 4x + 6x²- 4x³+ x⁴

1 - 8x + 24x²- 32x³+ 16x⁴

1 + 8x+ 24x²+ 32x³+ 16x⁴

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Question # 40

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0

1

-1

none of these

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Question # 41

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Question # 42

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Orthogonal

Involutary

Idempotent

Nilpotent

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Question # 43

A function f is said to be an even if f(-x) =

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0

1

f(x)

-f(x)

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Question # 44

In R the right cancellation property w.r.t. addition is

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Question # 45

The sum of the roots of the equation x2 -6x +2 = 0 is

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-6

2

-2

6

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Question # 46

Some of two real numbers is also a real number , this property is called:

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Commutative property w.r.t addition

Closure property w.r.t. addition

Associative property w.r.t. addition

Distributive property w.r.t addition

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Question # 47

(1 - x)³= ______

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1 + 3x + 3x²+ x³

1 + x + x²+ x³

1 - x + x²- x³

1 - 3x + 3x²- x³

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Question # 48

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 # 49

The square root of every incomplete square is an

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Rational numbers

Even numbers

odd numbers

Irrational numbers

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Question # 50

If distance between (3,b) and (0,0) is 3 then b = _______

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3

9

0

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Question # 51

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 # 52

{x|x∈R∧x≠x} is a

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Infinite set

Null set

Finite set

None of these

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Question # 53

A point (x,y) which satisfy a linear inequality in two variables form its

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Solution

Domain

Range

None

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Question # 54

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Question # 55

If A is an event then which of the following is true

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P(A)<0

0≥P(A)≤1

P(A)>0

None

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Question # 56

The general solution of tan 3x = 1 is

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Question # 57

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Question # 58

for n€ N, 3^{2n + 7 is divisible by}

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7

8

9

10

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Question # 59

The distance between the points (2, 2) and (3, 3) is

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10

5

2

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Question # 60

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12

13

14

15

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Question # 61

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 # 62

cos(3π/2 +θ) = _____;

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sinθ

cosθ

-sinθ

-cosθ

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Question # 63

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Question # 64

The quadratic equation 8 sec²θ- 6 secθ+1 = 0 has

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Infinitely many roots

Exactly two roots

Exactly four roots

No roots

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Question # 65

IfΔABC is right, law of cosine reduce to

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Law of sine

Law of tangent

Phthogorous theorem

Hero's formula

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Question # 66

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Question # 67

The value of n, when ⁿP₂= 20 is

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3

4

6

5

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Question # 68

Which of the following is a quadrantal angle

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100°

200°

170°

270°

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Question # 69

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A finite set

An infinite set

An empty set

None of these

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Question # 70

If a force F = 2i + j +3k acts at point (1,-2,2) of a body then the moment of F about a pint lying on the line of action of the force is

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5

Equal to the moment of the force about origin

0

Cannot be found

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Question # 71

A - B = ______

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Question # 72

sin2 π/6 + sin2 π/3 + tan2 π/4 =______;

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1

2

3

4

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Question # 73

When a selection of object is made without paying regard to the order of selection, it is called

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Sequence

Series

Combination

Permutation

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Question # 74

Range of sinθis

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Question # 75

The distance between the points (1, 2) and (2, 1) is

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3

6

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Question # 76

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Associative law of multiplication

Commutative law of addition

Commutative law of multiplication

Associative law of addition

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Question # 77

A chord passing through the centre of the circle is called

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the secant of the circle

the tangent of the circle

the arc of the circle

the diameter of the circle

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Question # 78

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Question # 79

The proposition S(n) for any n∈ N is only true if k∈ N and

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S(k +1) is true

S(1) is true and S(k+1) is true whenever S (k) is true

S(k+1) is true whenever S (k) is true

S(k) is true

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Question # 80

The set {1, 2, 3, 4, ....} is called

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Set of Natural numbers

Set of whole numbers

Set of rational number

Set of irrational numbers

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Question # 81

A and B throw a dice. The probability that A's throw is not greater then B's is

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5 / 12

7 / 12

1 / 6

1 / 2

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Question # 82

If f(α) = b2 and g (c) =d where c=b2 then (gof)(a) is

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α

c

b

d

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Question # 83

The conic ax2+2hxy+by2+2gx+2fy+c= 0 never represent a circle if

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a≠ b,h≠0

a=b

h≠0

h=0

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Question # 84

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trigonometric equation

conditional equation

identity

None

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Question # 85

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-a -b -c

1

0

-1

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Question # 86

Rank of matrix [1 3 5 0] is

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1

3

2

4

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Question # 87

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Question # 88

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Question # 89

If y=f(x) is a function then y is called

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dependent variable

independent variable

constant

none of these

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Question # 90

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Question # 91

Range of cot x is ______

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[-1, 1]

R

Negative real numbers

R - {x | - 1 < x < 1}

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Question # 92

The multiplicative inverse of 1 is

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1

-1

0

Does not exist

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Question # 93

I f the focus is F ( 0,-a) and directrix is the line v=a, then equation of the parabola is:

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x² = 4ay

y² = 4ax

y² = -4ax

x² = 4ax

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Question # 94

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Question # 95

For any set X, X∪X is

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X

X'

Φ

Universal Set

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Question # 96

Through how many radians does the minute hand of a clock turn in one hour

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Question # 97

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Question # 98

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Question # 99

i is equal

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(1 , 0)

(0 , 1)

(1 , 1)

(0 , 0)

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Question # 100

Which is not included in the domain of cos^-1x

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0

1

-1

2

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Question # 101

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(1,7/3)

(1, 7/5)

(1, 11/7)

(1, 3/5)

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