Which of the following is a rational number(s)?

A.	-12 -6
B.	6 -13
C.	4 13
D.	All of these

If $x = 2 + \sqrt{ 3 } + \sqrt{ 5 },$ then $x^4 - 8x^3 + 8x^2 + 32x = ?$

A.	$44$
B.	$41$
C.	$46$
D.	$49$

A point whose abscissa and ordinate are both positive will lie in the:

A.	First quadrant
B.	Second quadrant
C.	Third quadrant
D.	Fourth quadrant

The positive solutions of the equation px + qy + r = 0 always lie in,

A.	Second quadrant
B.	Third quadrant
C.	Fourth quadrant
D.	First quadrant

Which of the following two shapes can be joined together to form a semi-circle?

(a)	(b)	(c)	(d)

A.	d and a
B.	d and b
C.	a and c
D.	b and c

$ABCD$ is a square with each side measuring $100 \space cm$. $M$ is a point on $CB$ such that $CM = 25 \space cm$. If $N$ is a variable point on the diagonal $DB$, find the least value of $CN + MN$.

A.	$125 \space cm$
B.	$225 \space cm$
C.	$134 \space cm$
D.	$123 \space cm$

ABCD is a trapezium with sides AB and CD being parallel to each other. If P and Q are the midpoints of the diagonals of this trapezium, than which of the following statement is true:

A.	PQ =   (AB + BC) 3
B.	PQ || AB, PQ =   |AB - CD| 2
C.	PQ || AB only if AD = BC
D.	PQ || AB, PQ =   (AB + CD) 2

In the rhombus, ∠PRS = 7X - 594° and ∠QSP = 2X - 18°. Find the value of X.

A.	60°
B.	96°
C.	156°
D.	78°

ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Find value of  

AE

AD

 .

A.	√2
B.	1 √3
C.	√3
D.	1

Draw a circle with its two chords $AB$ and $CD$ such that $AB$ is not parallel to $CD$. Draw the perpendicular bisector of $AB$ and $CD$. At what point do they intersect each other.

A.	Anywhere but the center
B.	Anywhere in the circle
C.	Center of the circle
D.	None of the above

Which triangle has the maximum area for a given perimeter :

A.	Obtuse Angle Triangle
B.	Equilateral Triangle
C.	Can not be determined
D.	Isoceles Triangle

If radius of two spheres are in ratio 1:5, find the ratio of their volumes.

A.	1:25
B.	125:1
C.	1:125
D.	1:5

What is the mean of all the internal angles of a hexagon.

A.	130°
B.	120°
C.	110°
D.	140°

$800$ families with $2$ children each, were selected randomly and the following data were recorded.

$\text{Number of boys in a family}$	$2$	$1$	$0$
$\text{ Number of families }$	$200$	$120$	$480$

Out of these families, one family is selected at random. What is the probability that the selected family has $1$ boy?

A.	$0.15$
B.	$0.25$
C.	$0.6$
D.	$1$

If Abrar drives at two third of her usual speed, she covers a certain distance in 2 hours more than the time she takes while driving at her usual speed. Find the time taken by her to cover this distance with her usual speed.

A.	3 hours
B.	4 hours
C.	5 hours
D.	6 hours

If a cone and a hemisphere stand on equal base and have the same height, find the ratio of their volumes.

A.	$1:3$
B.	$2:3$
C.	$3:2$
D.	$1:2$