Question # 1

If a rectangle has an area 81x² and length of 27x. then what is its width?

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3x

9x

3x²

9x²

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 point (-5,3) is the center of a circle and P(7,-2) lies on the circle the radius of the circle is

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2

13

7

8

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

∫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)|

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

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1

0.5

2

0

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

Let A, B, and C be any sets such that A∪B=A∪C and A∩B=A∩C then

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A ≠ C

B = C

A = B

A ≠ B

In 30,60,90 triangle if the smallest side is 6 than the side opposite to the angle of 60^o is

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12

3

6√3

6

x² +2x -25 = 0 is

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1

2

3

4

What is the period of Cot x?

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2π

π

π/2

4π

Domain of Y = csc x is

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R - nπ, n ε I

R

R -nπ/2,nεI

All negative Integers

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

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True

False

Fallacious

Some times true

Which of the following is the subset of all sets ?

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A ≠ C

B = C

A = B

A ≠ B

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

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X

φ

Universal set

The radius of the circle (x- 1)² + (y + 3)² =64 is

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8

2√2

4

64

The set (Z, +) forms a group

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Function on B

Range

Domain

A into B

In the figure angle A is =

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15

60

90

20

6 is

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A prime integer

An irrational number

A rational number

A odd integer

Sec^-1 x=

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Cos^-1 1/x

Cosec^-1 1/x

Cos-1 (-x)

Tan^-1 x

Cos 315° =

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0.707

0.5

1

0

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

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√3 I

√7

-2-1

√5

If in isosceles right angled triangle one side is a then hypotenuse is

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a√2

a/2

a

Cannot be determined by given

Unit vector in the positive direction of x-axis is

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î

ĵ

k̂

All

What is the conjugate of -7 -2i ?

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-7 + 2i

7 + 2i

7-2i

√53

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

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1-i √-3 / 2

-1+i √-3 / 2i

-1+i √3 / 2

1+i √3 / 2

The end points of the major axis of the ellipse are called its

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foci

Vertices

Co-vertices

eccentricity

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

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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

Sin-1 (√2/2)=?

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π/2

π/3

3π/4

2π

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

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1

2

3

4

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

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b

-b

-a

(a - b)²

Cos^-1 x =

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∏ = sin^-1 x

∏ + sin^-1 x

∏/2 - sin^-1 x

∏/2 +sin^-1 x

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

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0

±1

1

{0,1}

The multiplicative inverse of x such that x = 0 is

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-x

does not exist

1/x

0

Cos^-1 (-x) =_______.

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π +cos^-1 x

π -sin^-1 x

π +sin^-1 x

π -cos^-1 x

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

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(3,0)

(4,1)

(1,3)

None

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

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n(n +1)/2

n +1/2

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

n³

If the diagonal of a square has coordinates (1,2) and(5,6) the length of a side is

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3

4

1

5

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

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

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25, 20

20, 10

20, 5

15, 10

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

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

Sin^-1 √3/2 =?

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2π/3

π/2

π/3

v/5

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

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

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

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

The magnitude of a vector can never be

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Zero

Negative

Positive

Absolute

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

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10

20

12

1

The direction cosines of y-axis are

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1,0,0

0,1,0

0,0,1

1,1,1

For any set X, X∪X is

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15

15i

-15i

-15

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

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

d/dx [cos x²] =________

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-2x cos x²

-2x² sin x²

x² sin x

-2x² sin x²

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

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

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40

30

50

20

Multiplicative inverse of "1" is

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4

3

2

1

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

In which quadrant is the solution of the equation sin x - 1 = 0

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II quadrants

II and III quadrants

III and Iv quadrants

I quadrant

r + 3 > 5 then which is true

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r + 2 > 4

r + 2 < 4

r + 2 + 4

None

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

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π/3

-π/3

2π/3

5π/3

3/2 is

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An irrational number

Whole number

A positive integer

A rational number

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

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Circle

Ellipse

Parabola

Hexagon

ωⁿ = ?, when n = 3k

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0

ω

1

1 / ω

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

In general matrices do not satisfy

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Not a group

A group w.r.t. subtraction

A group w.r.t. division

A group w.r.t. multiplication

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

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

Period is Tan x/5 is

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5π

4π

2π

π/5

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