Question # 1

If the order of A is n x m. Then order of kA is

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Forms a group

Does not form a group

Contains no additive identity

Contains no additive inverse

The set of the first elements of the ordered pairs forming a relation is called its

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-x

does not exist

1/x

0

If -1 < x < 0, which of the following statement must be true?

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x < x² < x²

x < x³ < x²

x² < x³ < x

x²< x < x³

The two consecutive positive integers whose product is 56 are

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7, 8

14, 4

28, 2

56, 1

The general solution of the differential equation dy/dx = log x is

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Y = -x log x- x +c

Y = x log x + x²

Y = x log x -x +c

Y= 2x log x + 2x +c

If Cⁿ_r, Pⁿ_r = 24:1 then r = ?

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1

2

3

4

Which is in the solution set of 4x - 3y <2

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(3,0)

(4,1)

(1,3)

None

2/(x+1)(x-1) = A/x+1 + B/x-1 corresponds to

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α = b/a and β = ca

α = a/b and β = -c/a

α² + β² = 1

α = -b/a and β= c/a

If Cosα = 3/5, Cosβ = 5/13, then

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Cos(α +β) =33/65

Sin(α +β) =56/65

sin²(α +β/2) =1/65

Cos(α +β) =63/65

The number of diagonals of a six sided figure are

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9

6

12

3

If the 9^th tern of A.P is 8 and the 4^th term is 20. then the first term is

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1

2

-2

-1

If A and B are two events then P(A∪B) =? (when A and B are disjoint)

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P(A) - P(B)

P(A) x P(B)

P(A) + P(B)

P(A) + P(B) -P(A∩B)

If the sum of the roots of (a + 1)x² + (2a + 3)x + (3a + 4) = 0 is -1, then product of the roots is

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Commutative law w.r.t multiplication

Associative law w.r.t addition

Distributive law w.r.t addition

Multiplication of a scalar with the matrix

1+2+3+......+n=?

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n(n +1)/2

n +1/2

n(n +1)(2n +1)/6

n³

If 1 + Cos x = 0 then x =

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π +2n π

π + nπ

π - nπ

π/2

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

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X

φ

Universal set

d/dx ∫x¹ dx =________.

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1/4 x⁴

X³

3x³

x⁴/4

1/x² -1 = ? (in case of making partial fraction)

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Ax +B/x² -1

A/x + B/ x- 1

A/ x+1 + B/x-1

None

Sin^-1 x =?

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π/2- Sin^-1 x

π/2 -Cos^-1 x

-Sin^-1 x

-Cos^-1 x

Period of Sin 2x =

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π

4π

2nπ

2π

The Domain of f(x) = log x is

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[0,∞]

(0, ∞)

[0,∞[

[∞ ,∞]

120° degrees are equal to how many radians?

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π/3 radians

2π/3 radians

π/4 radians

π/2 radians

A standard deck of 52 cards shuffled what is the probability of choosing the queen of the diamonds

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1/5

1/13

5/52

1/52

The nth term of A,P:1,5,9,15...........is given by

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4n - 3

4n + 1

3n -4

4n +3

The vertices of the ellipse x² + 4y² = 16 are

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(±,4,0)

(0,±,4)

(± 2,0)

(0,± 2)

Cos^-1 x =

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∏ = sin^-1 x

∏ + sin^-1 x

∏/2 - sin^-1 x

∏/2 +sin^-1 x

If ab > 0 and a < 0, which of the following is negative?

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b

-b

-a

(a - b)²

If x lies in {0, 2π} and Cosec x = 2 then x =

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π/ 6 and 5π/6

π +2nπ

nπ

2π/3 and π/3

Cos^-1 (-x) =_______.

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π +cos^-1 x

π -sin^-1 x

π +sin^-1 x

π -cos^-1 x

Given X, Y are any two sets such that number of elements in X=28, number of elements in set Y=28, and number of elements in set X∪Y=54, then number of elements in set X∩Y=

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-7 + 2i

7 + 2i

7-2i

√53

If Sin θ =Cosθ then θ=

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30°

45°

60°

90°

Second derivative of y = x⁹ + 10x² + 2x -1 at x = 0 is

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10

20

12

1

The statement that a group can have more than one identity elements is

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True

False

Fallacious

Some times true

ωⁿ = ?, when n = 3k

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0

ω

1

1 / ω

Unit vector in the positive direction of x-axis is

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î

ĵ

k̂

All

If you looking a high point from the ground then the angle formed is

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Angle of elevation

Angle of depression

Right angle

Horizon

The graph of a quadratic function is

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Circle

Ellipse

Parabola

Hexagon

Two natural numbers whose sum is 25 and difference is 5, are

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25, 20

20, 10

20, 5

15, 10

If A = (3,8) and B = (5,6) then the distance between A and B is

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2√2

2

1

6

Given eight points in a plane no three of which are collinear how many lines do the points determine?

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16

64

28

36

F(x) = xx decreases in the interval

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(0,e)

(0.1)

(-∞.0)

None

3/2 is

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An irrational number

Whole number

A positive integer

A rational number

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

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0

1

-1

2

π/3 is

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A positive integer

A negative integer

A natural number

An irrational number

Two dice are rolled The number of possible out come in which at least one die shows 2 is?

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5

12

11

7

Area of ΔABC=

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ab sin α

1/2 ab sin α

1/2 ac Sin γ

1/2 ac Sin β

Which is not a half plane

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ax + by < c

ax + by > c

Both A and B

None

Which is an explicit function

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y = x² +2x -1

x² +xy +y² =2

xy² -y +9/xy =1

All are

Sin^-1 (-x) =

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Cos^-1 1/x

-Sin^-1 X

1/sin-1x

Sin^-1 1/x

If f (x) = x/x²- 4 then which is not included in the domain of f(x)

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0

-2

1

4

If sinθ = 1 then θ =

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2nπ +π/2

2nπ

2π +n

Nπ +π/2

If f₁ (x) and f₂ (x) are any two anti derivatives of a function F (x) then the value of f₁ (x) = f₂ (x)

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A variable

A constant

Undefined

Infinity

∫1/ax +b dx =

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1/a log |ax + b| +c

Log |ax + b| +c

1/b log |ax +b| +c

1/x log |ax + b| +c

Find the geometric mean between 4 and 16

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7, 8

14, 4

28, 2

56, 1

If x < y, 2x = A and 2y = B then

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A =B

A < B

A< X

B < y

If a cone is cut by a plane perpendicular to the axis of the cone then the section is a

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Parabola

Circle

Hyperbola

Ellipse

6 is

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A prime integer

An irrational number

A rational number

A odd integer

The line joining (1,3) to (a,b) has unit gradient then

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a-b =-2

a+b = 0

A-b =5

2a + 3b =1

x² +2x -25 = 0 is

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1

2

3

4

P(x) = 2x⁴ -3x³ +2x-1 is polynomial of degree

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1

2

3

4

The set {1, -1, i, -i}, form a group under

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addition

multiplication

subtraction

None

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

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0

±1

1

{0,1}

The equation of the circle with center origin and radius 2√2 is

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x² + y² = 2√2

x² + y² = 8

x² - y² = 2√2

x² - y² = 8

The area of circle of unit radius=

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0

1

4

π

If the angle between two vectors with magnitude 8 and 2 is 60° then their scalar product is

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12

8

16

1

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 degree of the polynomial 2x⁴ + 3x² + 16x + 28 = x⁴ + 2x² is

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[a_{ij -}b_ji]

[a_{ij -}b_ij]

[a_{ij] - [}b_ij]

The value of Cos (1/2 Cos^-1 1/2) is equal to

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√3/2

-3/4

1/16

1/4

The total cost of 2 apples and 3 oranges is $1.70,which of the following is true

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The cost of one apple

The cost of one orange

Both have equal cost per item

Cost of each single item can not be determined

The value of the polynomial 3x³ + 4x² - 5x + 4 at x = -1 is

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A² + B²

A² + B²+ 2AB

A + B

A² + B² + AB+BA

Derivative of strictly increasing function is always

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Zero

Positive

Negative

Both A and B