Question # 1

∀x∈(a,b),f(x) is increasing if

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f′(x) >0

f′(x) <0

f′′(x) >0

f′′(x) =0

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none of these

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Composition of functions is

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Non-commutative (fg ≠ gf)

non-associative [8(fh) ≠(8f)h]

Commutative (fg = gf)

f of-1≠ 1

For trival solution |A| is

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A

|A| is non zero

A = 0

None of these

If (2, 3) is the mid point of (a, 3) and (5, b) then

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a = 1 , b = -3

a = -1 , b = 3

a = 1 , b =3

a = -1 , b = -3

Sand falls from a tube in such a way that it forms a cone whose height is always 4/3 times the radius of its base and radius of the base increases at the rate of 1/8 cm/sec. When this radius is 1 meter, the rate at which the amount of sand increases is

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none of these

Area ofΔABC=

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ab sinα

1/2 ab sinα

1/2 ac sinγ

1/2 ac sinβ

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additive property

multiplicative property

additive inverse

additive identity

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In a class of 100 students, 60 drink tea, 50 drink coffee and 30 drink both. A student from his class is selected at takes at last one of 2 drinks is

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2 / 5

3 / 5

4 / 5

None of these

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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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11

61

1

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The area between the x-axis the curve y =4x-x2 is :

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32/2

15

18

21

If z₁ = 1 + 2i, z₂ = 3 + 4i then

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z₁ > z₂

z₁ = z₂

z₁ < z₂

None of these

If sin 6θ+ sin 4θ+ sin 2θ, thenθ=

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A rule that assigns to each elements x in X a unique element y in Y is called a ____________

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domain

range

function

none of these

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

Domain of 2 cos x is ______

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[-2, 2]

R

Negative real numbers

None of these

The set of rationals numbers between 0 and I is

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Finite

Null set

Infinite

None of these

In R, the multiplicative identity is

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0

1

-1

None

Range of cosθis

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The angle of depression of a point A on the ground from the top of the tower is 30𝜊,then the angle of elevation of the top of the tower at the point A is

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60𝜊

40𝜊

41𝜊

30𝜊

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The set {0,-1} hold closure property under

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Addition

Both a & c

Multiplication

None of these

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The law of of sines

The law of tangents

The law of consines

None of these

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ⁿC_r

ⁿ⁺¹C_r+1

ⁿC_r+1

None

If B-A≠φ , then n(B-A) is equal to

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n(a)+n(c)

n(c)-n(a)

n(a)-n(c)

None of these

A point where two of its boundary lines intersect is called

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Corner point

Feasible point

Vertex

Feasible solution

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8

4

64

The multiplicative inverse of x such that x = 0 is

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-x

Does not exist

1/x

±1

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The middle term of (x-y)⁸is

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25 x⁴y⁴

70 x⁴y⁴

120 x⁴y⁴

97x⁴y⁴

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Additive property in R

Multiplication property in R

Cancellation property in R

Distribution property in R

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0

Independent of a

Independent of b

Independent of c

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QUQ'

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

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2

3

3/2

2/3

Which is a proper rational fraction

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The range of the principle cot function is

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A function F(x) is called even if

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F(x) = F (-x)

F(x) = F(-x)

F(x) = -F(x)

2F(x) = 0

∫sin(ax+b) dx is equal to:

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1/2a cos (ax + b)

-1/a cos (ax +b)

1/a cos (ax +b)

1/a ln (ax + b)

Which shape of the following objects are approximately parabolic ares?

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Light reflectors

Force

Weight of the pendul

None of these

There are 25 tickets bearing number from 1 to 25. One ticket is drawn at random. The probability that the number on it is a multiple of 5 or 6 is

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7 / 25

9 / 25

11 / 25

None of these

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

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For three consecutive terms in A.P middle term is called

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A.M

nth term

Central term

None of these

If t is the parameter for one end of a focal chord of the parabola y²= 4ax, then its length is

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Less then 1

Equal to 1

Greater than 1 but less then 2

Greater then or equal to 2

Total number of subsets that can be formed out of the set {a,b,c} is

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1

4

8

12

Which of the following is skew symmetric matrix

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If you are looking someone on the ground from the top of a hill the angle formed is called angle of _______;

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Elevation

Depression

Right angle

None off these

Ifπ≤x≤2π, then cos-1 (cos x)=

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cos x

-x

1/x

-x

(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

The matrix A = [aij]1xn is a

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Vector

Rectangular matrix

Column vector

Square matrix

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Two real roots

Two positive roots

Two negative roots

One positive and one negative root

3.5+5.4=5.4+3.5 =8.9 this property of addition is called

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additive identity

assoclative property

commulative property

closure property

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cos 2x + c

- cos 2x + c

tan 2x + c

cot 2x + c

A point of a solution region where two of its boundary lines intersect, is called

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Boundary

Inequality

Half plane

Vertex

The sum of an indicated number of terms in a sequence is called

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sequence

progression

Series

Mean

if Z1 = 1+i, Z2= 2+3i, then |Z2 -Z1| =

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√3 i

√7

-2-i

√5

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none of these

The tangents drawn from the point P to a circle are real and distinct if

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P is on the circle

P is inside the circle

P is outside the circle

none of these

The equation of the line perpendicular to x- axis and passing through (-5,3) is

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y -3 =0

x+ 3 =0

y- 3 =∞

x +5 =0

The slope of the tangent of the circle x³ + y³ =25 at (4,3) is:

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-4/5

4/3

-25/4

25/3

[i,j,k]

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0

2

1

-2

The sum of infinite numbers of terms of an arithmetic series is

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Finite

Infinite

May or may not finite

None of these

The set of rational numbers is subset of

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The set of natural numbers

The set of real numbers

The set of integers

The set of whole numbers

The standard form of the quadratic function f(x) = -x² +4x+2, is

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(x-2)²+6

-(x-2)² + 6

(x-3)²+5

(x+4)²-7

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Associate law of addition

Commutative law of addition

Additive identity

Closure law of addition

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If p and q are two statements then their conjunction is denoted by

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a >b, b >c ⇒a >c is a

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Multiplicative property

Additive property

Trichotomy property

Transitive property of inequality

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

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0

1

1/2

The position vector of the point P(a, b, c) is

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none of these

A key ring is an example of

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Permutation

Circular permutation

Combination

None

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Reciprocal equation

Exponential equation

Radical equation

None of these

In common logarithm the base is

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1

0

10

e

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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Principle of equality of fractions

Rule for product of fraction

Rule for quotient of fraction

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1, 1/2, 0

1, 2, 1

1, 2, 3

1, 2, 0

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1

2

0

4

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A non-homogeneous linear system AX = B has no solution if

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|A| = 0

|A|≠ 0

Rank (a) = no of variables

Rank > no of variables

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none of these

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Addition

Subtraction

Multiplication

None of these

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)