Question # 1

∫sec (ax + b) tan(ax + b) dx=_______

Choose an answer

sec(ax + b)/a

sec² (ax + b)/2

sec(ax + b)/x

1/2

Sin^-1 x =?

Choose an answer

π/2- Sin^-1 x

π/2 -Cos^-1 x

-Sin^-1 x

-Cos^-1 x

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

Choose an answer

18 years

36 years

8 years

16 years

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

Choose an answer

1

-3

5

0

The perpendicular bisector of any chord of a circle

Choose an answer

Passes through the center of the circle

Does not pass through the center of the circle

May or may not pass through the center of the circle

None of these

Sin 720° = ________

Choose an answer

1

0

2

1/2

The set of all positive even integers is

Choose an answer

Φ

{1,2,3}

{Φ}

{0}

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

Choose an answer

(3,0)

(4,1)

(1,3)

None

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

Choose an answer

Ax +B/x² -1

A/x + B/ x- 1

A/ x+1 + B/x-1

None

A fraction in which the degree of the numerator is less than the degree of the denominator is called

Choose an answer

1-i √-3 / 2

-1+i √-3 / 2i

-1+i √3 / 2

1+i √3 / 2

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

Choose an answer

Set of irrational numbers only

Set of all real numbers

Set of integers only

Set of complex numbers only

A die is thrown what is the probability that there is a prime number on the top?

Choose an answer

1/2

1/3

1/6

2/3

Cot 360° =______.

Choose an answer

Undefined

0.707

-0.5

0

The associative angle of 280^o is

Choose an answer

100^o

10^o

80^o

-80^o

The direction cosines of y-axis are

Choose an answer

1,0,0

0,1,0

0,0,1

1,1,1

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

Choose an answer

b

-b

-a

(a - b)²

The magnitude of a vector can never be

Choose an answer

Zero

Negative

Positive

Absolute

Tan (π + Tan^-1 x) =?

Choose an answer

Tan x

X

-x

Cot^-1 x

The equation of the normal to the circle x² + 2² = 25 at (4,3) is

Choose an answer

3x -4y =0

3x -4y= 5

4x + 3y=5

4x - 3y =25

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

Choose an answer

4n - 3

4n + 1

3n -4

4n +3

If Cosα = 3/5, Cosβ = 5/13, then

Choose an answer

Cos(α +β) =33/65

Sin(α +β) =56/65

sin²(α +β/2) =1/65

Cos(α +β) =63/65

In the figure angle A is =

Choose an answer

15

60

90

20

If |A| ≠ 0 then A is called

Choose an answer

1

-1

±1

0

The nth term in G.P 3,-6,12,............ is

Choose an answer

25, 20

20, 10

20, 5

15, 10

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

Choose an answer

3⁵

5³

C⁵₃

P⁵₃

Which of the following is not defined?

Choose an answer

Arcsin 1/9

ArcCos (-4/3)

Arctan 11/12

Arccot (-4)

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

Choose an answer

1

2

3

4

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

Choose an answer

1/5

1/13

5/52

1/52

Which is a proper rational fraction

Choose an answer

3x - 7/x² +4

2x² - 5/x² + 4

3x⁴/2x² - 15

All are proper rational fraction

The gradient of the line joining (1,4) and (-2,5) is

Choose an answer

3/8

-2 2/3

-1/3

2

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

Choose an answer

True

False

Fallacious

Some times true

Sin (2π -θ) =______.

Choose an answer

Cosθ

-Sinθ

-cosθ

There are 30 Red, 20 Green and some Blue bells in a bag if the probability of finding a Red ball is 1/3,how many are red balls in the bag

Choose an answer

120

20

40

90

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

Choose an answer

1

2

-2

-1

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

Choose an answer

A =B

A < B

A< X

B < y

For which of the following ordered pairs (s,t) is s + t> and s- t < -3?

Choose an answer

(3,2)

(2,3)

(1,8)

(0,3)

An m x n matrix is said to be rectangular if

Choose an answer

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

Period is Tan x/5 is

Choose an answer

5π

4π

2π

π/5

Which of the following is solution of Tan² x = 1/3

Choose an answer

7π/6

5π/6

π/6

All

Cos 315° =

Choose an answer

0.707

0.5

1

0

6 is

Choose an answer

A prime integer

An irrational number

A rational number

A odd integer

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

Choose an answer

An identity

An equation

A polynomial

Inverse function

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

Choose an answer

16

64

28

36

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?

Choose an answer

m = n

m ≠ n

mn = 1

mn = 0

The center of a circle of radius 10 is on the origin which of the following points lies with in the circle

Choose an answer

(10,0)

(8,8)

(8,4)

(0,10)

Sum of integers starting from to n is

Choose an answer

n(n+1)/4

n(n+1)/6

n(n+1)/2

n(n-1)/2

The area of circle of unit radius=

Choose an answer

0

1

4

π

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

Choose an answer

x² + y² = 2√2

x² + y² = 8

x² - y² = 2√2

x² - y² = 8

Sin-1 (√2/2)=?

Choose an answer

π/2

π/3

3π/4

2π

Which of the following is the solution of Cot²x = 1/√3

Choose an answer

π/5

π/3

π/7

π/9

If A = [a_ij] and b = [b_ij] are the matrices of the order 3x3 then A-B=

Choose an answer

Circle

Ellipse

Parabola

Hexagon

One of the roots of the equation 2x² + 3x + n = 0 is the reciprocal of the other, then n = --------------------

Choose an answer

Both A,B have the same number of columns

Both A,B do not have the same order

Number of col A is same as number of rows of B

Number of rows of A is same as number of col of B

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

Choose an answer

(±,4,0)

(0,±,4)

(± 2,0)

(0,± 2)

An angle of one radian is equivalent to

Choose an answer

90^o

60^o

67^o

57^o, 18^o

If A and B are matrices of same order than (A + B)(A + B)=

Choose an answer

addition

multiplication

subtraction

None

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

Choose an answer

A variable

A constant

Undefined

Infinity

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

Choose an answer

√3/2

-3/4

1/16

1/4

The set (Q, .)

Choose an answer

Infinite set

Singleton set

Two points set

None

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

Choose an answer

(1, 1)

(1,-1)

(2, -8)

(1, -4)

If 4 - x > 5, then

Choose an answer

x > 1

x > -1

x < 1

x < -1

If sinθ = 1 then θ =

Choose an answer

2nπ +π/2

2nπ

2π +n

Nπ +π/2

Derivative of strictly increasing function is always

Choose an answer

Zero

Positive

Negative

Both A and B

An angle 0 is such that tan θ = 1 and cos θ is negative then

Choose an answer

Sin θ is positive

Cos θ = √2/4

cosθ = -1

sec θ is negative

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

Choose an answer

0

-2

1

4

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

Choose an answer

Minimum

Maximum

Stationary point

Constant

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

Choose an answer

√3 I

√7

-2-1

√5

Corola available in 5 models 8 colours and 3 sizes how many Corola must a local dealer have no hand in order to have one of each kind avialable?

Choose an answer

24

120

16

39

If Z= (1,2). tjem Z^-1 = ?

Choose an answer

(0.2, 0.4)

(-0.2, 0.4)

(0.2, -0.4)

(-0.2, -0.4)

If any two rows (or any two columns) of a square matrix are inter changed, the determinant of the resultant matrix is

Choose an answer

True

False

Fallacious

Some times true

If A and B are matrices such that AB=BA=I then

Choose an answer

A and B are multiplicative inverse of each other

A and B are additive inverses of each other

A and B are singular matrices

A and B are equal