Question # 1

The line segments, joining the mid-points of the sides of a quadrilateral, taken in order form a _____________.

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Square

Rectangle

Rhombus

Parallelogram

Two linear-equations are said to be __________ if they have exactly the same solution:

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Equal

True

Equivalent

Open

Conjugate of -3 is:

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3

-3

-3i

3i

a³+b³ is equal to:

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(a-b)(a²+ab+b²)

(a+b)(a²-ab+b²)

(a-b)(a²-ab+b²)

(a-b)(a²+ab-b²)

The point of concurrency of the three altitudes of a triangle is called:

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Centroid

Orthocenter

Circumcentre

Incentre

Every irrational number is _________

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Surd

Not a surd

Rotional

Whole number

If Z₁ = Z₂ then Z₂ = Z₁ this property is known as _______ property:

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Reflexive

Symmetric

Transitive

Closure

Diagonals of a parallelogram do ______ of each other;

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Bisection

Trisection

None of these

(AB)^t=

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A^tB^t

B^tA^t

AB

BA

If a²+b²=c²then triangle is called:

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Acute

Right angled

Obtuse

Scalene

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(x-y)²

x-y

1

The positive square coot of mean of the squared deviations of x₁ (i = 1,2..........n) observation from their arithmetic mean is called.

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Harmonic mean

Range

S.D

Variance

If Y is directly proportional to x it can be written as:

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x = y

y : x

The system of measurement in which angle is measured in radian is called.

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C.G.S System

Sexagesimal system

M.K.S.System

circular system

tan 30^o=...................................

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1/2

√3/2

√3

1/√3

In a proportion a : b :: c : d, b and c are called:

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Means

Extremes

Fourth proportional

None of these

If 1 is the zero of polynomial, then remainder is:

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3

2

0

1

The value obtained by reciprocating the mean of the reciprocal of x₁,x₂,x₃..............x₁₁ observation is called....................

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Geometric mean

Median

Harmonic mean

S.D

The geometric mean of the a observations 2,4,8, is:

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2

8

4

no geometric mean

Power set of an empty set is.

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∅

{a}

{∅,{a}}

{∅}

A'=_____________

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{x|x∈U^x∉A}

{x|x∈U^x∈A}

{x|x∉U^x∈A}

{x|x∉U^x∉A}

A collection of well-defined distinct objects is called.

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subset

Power set

Set

None of these

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9

-9

-6

none

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If a_n-1 = 2n - 3 then a_n+1 =

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2n - 1

2n + 1

2n + 3

none

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diagonal matrix

A circle which touches one side of a triangle externally and the other two produces sides internally is known as:

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The series 2 + 2 + 2 ..... is:

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divergent

convergent

oscillatory

none of these

The real part of the complex number a + bi is:

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b

-b

a

-a

The range of y = sin^-1 x is:

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Sequences are also called:

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Series

Progressions

Means

Convergence

If A = [a_ij], B = [b_ij] and AB = 0 then:

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A = 0

B = 0

either A = 0 or B = 0

A & B not necessarily zero

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Additive property

Multiplicativeproperty

Reflexiveproperty

Transitive property

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e^2x sin x + c

e^2xcosx + c

-e^2xsin x + c

-e^2xcosx + c

The condition for the line y = mx + c to be a tangent to the circle x² + y² = a² is c = _____________:

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4a

2a

4b

2b

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3

4

5

6

x = c is a line:

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Perpendicular to x-axis

Parallel to x-axis

Perpendicular to y-axis

None of these

If r is the radius of any circle and C its center, then any point P(x₁, y₁) lies outside the circle only if:

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|CP| < r

|CP| = r

|CP| > r

None of these

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Derivative

Differential

Integral

None of these

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cosech x coth x

-cosech²x

-cosech x coth x

cosech²x

Area between x-axis and the curve:

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32

16

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0

1

2

4

The graph of the parabola x² = -4ay is symmetric about:

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x-axis

major axis

y-axis

minor axis