Question # 1

d/dx (√x) =

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2√x

1/√x

1/2√x

None of these

In the figure angle A is =

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15

60

90

20

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)

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

Every prime number is also

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Rational number

even number

Irrational number

multiple of two numbers

If k₁ : k₂ = 1:1 then the point P dividing the line is

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Mid point

Extreme left point

Extreme Right point

Plies out side k₁ and k₂

The set of all positive even integers is

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Φ

{1,2,3}

{Φ}

{0}

If p and r are integers P = 0, and p ≠ -r, which of the following must be true?

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p < r

p > r

p + r < 0

p - r < -0

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

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1

2

3

4

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

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π/3

-π/3

2π/3

5π/3

6 is

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A prime integer

An irrational number

A rational number

A odd integer

If sinθ = 1 then θ =

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2nπ +π/2

2nπ

2π +n

Nπ +π/2

Period is Tan x/5 is

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5π

4π

2π

π/5

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

The curves y =x², y= x interest at

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(0,0) ,(1,1)

(2,4)

(0,),(2,4)

(0,3),(-1,1)

The cube roots of unity ω = -------------------------

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1-i √-3 / 2

-1+i √-3 / 2i

-1+i √3 / 2

1+i √3 / 2

If a line passes through origin then the equation of the line is

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y = m/x

y = mx

x = my

None

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

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b

-b

-a

(a - b)²

Partial fraction of 1/x³-1 will be of the form

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Conjugate pair

ordered pair

reciprocal pair

quadratic function

Sin^-1 x =?

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π/2- Sin^-1 x

π/2 -Cos^-1 x

-Sin^-1 x

-Cos^-1 x

Sin x + Cos x=1 x=

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π

π/2

π/3

π/4

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

If Sin θ =Cosθ then θ=

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30°

45°

60°

90°

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

π/3 is

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A positive integer

A negative integer

A natural number

An irrational number

The range of inequality x + 2 > 4 is

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(-1,2)

(-2,2)

(1,∞)

None

The direction cosines of y-axis are

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1,0,0

0,1,0

0,0,1

1,1,1

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

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A =B

A < B

A< X

B < y

The equation of two polynomials P(x)/Q(x) where Q(x) ≠ 0 with no common factor is called

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12

1

10

-10

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

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120

20

40

90

Complex roots of real quadratic equation occur in

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Nilpotent matrix

Singular matrix

Non singular matrix

Diagonal matrix

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

Derivative of strictly increasing function is always

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Zero

Positive

Negative

Both A and B

Cos^-1 x =

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∏ = sin^-1 x

∏ + sin^-1 x

∏/2 - sin^-1 x

∏/2 +sin^-1 x

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

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

The parametric equation of a curve are x = t², y = t²then

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dy/dx =3t/2

dy/dx =t⁵

dy/dx =5t⁴

None

If θ= 60° then

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sin θ = 1/2

tan θ = cot 30°

θ = π/4

Sec θ =4

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

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True

False

Fallacious

Some times true

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

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(3,2)

(2,3)

(1,8)

(0,3)

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

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Boundary

Inequality

Half plane

Vertex

There are 30 Red balls and 25 Green balls in a bag of a ball is drawn from the bag randomly what is the probability that a Blue ball comes out?

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1

0.5

0

None

0 (zero) is

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A irrational number

A rational number

A negative integer

A positive number

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)

Sec^-1 x=

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Cos^-1 1/x

Cosec^-1 1/x

Cos-1 (-x)

Tan^-1 x

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)

If sin θ= 3/5 Cos θ=

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1/2

3/5

4/5

1

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

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 number of real roots in cube roots of 8 is ?

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n x m

m x n

km x n

m x kn

d/dx a^x is

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xa^x-1

a^x

x in a

a^x in a

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

How many different arrangements of the letters in the word QABABA are Possible?

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720

40

60

30

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

A function F(x) is called even if

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F(x) = F(-x)

F(x) = -F(x)

2F(x) = 0

Period of Sin 2x =

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π

4π

2nπ

2π

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

Which is not a half plane

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ax + by < c

ax + by > c

Both A and B

None

The length of rectangle is twice as much as its breadth. If the perimeter is 120 cm, the length of the rectangle is

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Same as the original determinant

Additive inverse of the original determinant

Both A and B

Adj of the original matrix

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

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

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3⁵

5³

C⁵₃

P⁵₃

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

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Zero

One

Four

Infinite

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

The multiplicative inverse of -1 in the set {1-,1} is

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40

30

50

20

(x+2)² = x² +4x +4 is

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1

2

3

4

The magnitude of a vector can never be

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Zero

Negative

Positive

Absolute

The two different parts of the hyperbola are called is

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Vertices

Directrices

Nappes

Branches

d/dx (3y⁴) =

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12y³ dy/dx

8y³

8y³ dy/dx

12y³

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

Sin^-1 (-x) =?

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Sin^-1 x

-Sin^-1 x

Cos^-1 x

-Cos^-1 x

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