Question # 1

What is the conjugate of -7 -2i ?

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-7 + 2i

7 + 2i

7-2i

√53

x-1/(x+2)(x-2) =

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4/3(x-4) -1/3(x-1)

3/4(x+2) + 1/4(x-2)

2/3(x-2) - 4/3(x+2)

3/x - 2/x+1

Sin(a + b) + Sin(a- b) =

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Sin a Cos b

Sin a Sin b

Sin a + Cos b

Sin a - 2Cos b

The axis of the parabola y² = 4ax is

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x =0

Y =0

X = y

X = -y

The sum of the series 1+5+9+13+17+21+25+29 is:

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10 cm

20 cm

30 cm

40 cm

If a and b are any two distinct negative real numbers and G-ab where A.G.H represent arithmetic geometric and harmonic means then

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1

ω²

ω

0

8 > t then

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(s -t) ²>(t -8)²

(s -t) ²<(t -8)²

(s -t) ²=(t -8)²

None

The difference of two consecutive terms of an A.P is called

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Zero

One

Four

Infinite

Sum of integers starting from to n is

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n(n+1)/4

n(n+1)/6

n(n+1)/2

n(n-1)/2

3/2 is

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An irrational number

Whole number

A positive integer

A rational number

The mid point of the line joining (=1,-3) to(3,-5) is

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(1, 1)

(1,-1)

(2, -8)

(1, -4)

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

The number of ways in which we can courier 5 packets to 10 cities is

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2 x 5^o

5¹⁰

10⁵

2¹⁰

Complex roots of real quadratic equation occur in

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Nilpotent matrix

Singular matrix

Non singular matrix

Diagonal matrix

If θ= 60° then

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sin θ = 1/2

tan θ = cot 30°

θ = π/4

Sec θ =4

What is the period of Cot x?

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2π

π

π/2

4π

π/3 is

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A positive integer

A negative integer

A natural number

An irrational number

The average of first 100 integers is=

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50 1/2

25 1/4

100

5050

The number of diagonals of a six sided figure are

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9

6

12

3

The Domain of f(x) = log x is

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[0,∞]

(0, ∞)

[0,∞[

[∞ ,∞]

The angle a (0° < a< 180°) measured counterclockwise from positive x-axis to a non-horizontal straight line / is called the

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Rotation

Inclination

Radian

None

ωⁿ = ?, when n = 3k

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0

ω

1

1 / ω

A relation in which the equality is true only for some values of the unknown variable is called

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An identity

An equation

A polynomial

Inverse function

In a school, there are 150 students. Out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for Physics class. The student enrolled for English cannot attend any other class, but the students of mathematics and Physics can take two courses at a time. Find the number of students who have taken both physics and mathematics.

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40

30

50

20

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

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

What is the domain of y = Cot^-1 x?

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Set of irrational numbers only

Set of all real numbers

Set of integers only

Set of complex numbers only

If sin θ= 3/5 Cos θ=

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1/2

3/5

4/5

1

If sinθ = 1 then θ =

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2nπ +π/2

2nπ

2π +n

Nπ +π/2

The set (Q, .)

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Infinite set

Singleton set

Two points set

None

If P(E) is the probability that can event will occur then P(E)=

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1

0.5

2

0

Domain of Cosecθ is

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is R but θ= nπ

is R but θ ≠ nπ

is R but θ ≠ 2nπ

is R but θ ≠ nπ/2

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

If x² +y² = 4, Then dy/dx =

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2x +2y

4 -x²

-x/y

y/x

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

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

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addition

multiplication

subtraction

None

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

Any point where f is neither increasing nor decreasing and f(x) =0 at that point is called a

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Minimum

Maximum

Stationary point

Constant

The area of circle of unit radius=

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0

1

4

π

If y = (ax)^m + b^m, then dy/dx equals

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m (ax)^m x^m-1

ma^m x^m-1

m a^m x^m-1

m a^m x^m-2

Every prime number is also

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Rational number

even number

Irrational number

multiple of two numbers

6 is

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A prime integer

An irrational number

A rational number

A odd integer

The range of inequality x + 2 > 4 is

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(-1,2)

(-2,2)

(1,∞)

None

Sin (2π -θ) =______.

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Cosθ

-Sinθ

-cosθ

Sin x + Cos x=1 x=

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π

π/2

π/3

π/4

In the figure PS is perpendicular to QR, if PQ = PR 26 and P8 = 24,then QR=

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10

20

40

26

In the triangle Δ ABC, where C is the right angle Tan A + Tan B=

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A +B

C² /AB

A²/BC

B²/AC

The value of x, and y, when (x+iy)²=5+4i

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X=2, y=-1

X=-2, y=1

X=2, y=-i

X=2, y=2

∫cot (ax + b) dx =

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1/a log |sin (ax + b)| +c

1/a log |cos ax + b)

1/b |sin (ax + b)|

1/a log |sin (bx + a)|

Cot 360° =______.

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Undefined

0.707

-0.5

0

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

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A =B

A < B

A< X

B < y

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

The fifth term of the sequence a_n = 3n - 2 is

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3

-3

13

-13

The two different parts of the hyperbola are called is

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Vertices

Directrices

Nappes

Branches

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 graph of a quadratic function is

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Circle

Ellipse

Parabola

Hexagon

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

If 0 is not an integral multiple of π/2 then Cot⁴ θ+ Cot² θ=?

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Cosec⁴ θ -Cosec²θ

Tan θ - Tan² θ

Cosec² θ + Cosec θ

Sinθ Cosθ

If 2 Sin x Cos 2 x = Sin x then?

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X = nπ+ π/6

X = nπ +π/3

X = nπ +1

X = nπ + π/2

Write the first four term of the arithmetic sequence if a₁ = 5 and other three consecutive terms are 23,26,29

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18 years

36 years

8 years

16 years

Which of the following is the subset of all sets ?

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A ≠ C

B = C

A = B

A ≠ B

√23 is

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A rational number

A irrational number

An even integer

A factor of 36

The principal value of sin^-1 [√3/2] is

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π/3

-π/3

2π/3

5π/3

The common difference of the sequence 7,4,1......is

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1

-3

5

0

AreCot √3 =?

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π/2

π

2π

π/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

If y = sin(ax + b) then fourth derivative of y with respect to x=

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a⁴ cos (ax + b)

a⁴ sin (ax + b)

-a⁴ sin(ax +b)

a4 tan (ax + b)

An m x n matrix is said to be rectangular if

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Forms a group w.r.t. addition

Non commutative group w.r.t. multiplication

Forms a group w.r.t. multiplication

Doesn't form a group

If the vector 2i+4j-2k and 2i +6j+xk are perpendicular then x-7

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4

8

14

7

The sum of the ages of Nazish and his son is 56 years. Eight years ago. Nazish was 3 time as old as his son. How old is the son now?

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m = n

m ≠ n

mn = 1

mn = 0

The number of ways in which 5 distinct toys can be distributed among 3 children is

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3⁵

5³

C⁵₃

P⁵₃