If $a$ and $b$ are rational numbers such that $a\sqrt7 = b\sqrt{ 17 }$, then the possible values of $a$ and $b$ are$:$

A.	$a = 0, b = 0$
B.	$a = \dfrac{ 1 } { \sqrt{ 17 } }, b = 0$
C.	$a = \dfrac{ 1 } { \sqrt{ 7 } }, b = \dfrac{ 1 } { \sqrt{ 17 } }$
D.	$a = \dfrac{ 1 } { \sqrt{ 17 } }, b = \dfrac{ 1 } { \sqrt{ 7 } }$

Factorize: $$\begin{aligned} x^2 + \dfrac { 1 } { x^2 } + 2 - 9 x - \dfrac { 9 } { x } \end{aligned}$$

A.	$\bigg(x - \dfrac { 1 } { x }\bigg) \bigg( x + 9 \bigg)$
B.	$\bigg(x - \dfrac { 1 } { x }\bigg)^2 \bigg( x + \dfrac { 1 } { x } - 9 \bigg)$
C.	$\bigg(x + \dfrac { 1 } { x }\bigg) \bigg( x + \dfrac { 1 } { x } - 9 \bigg)$
D.	$\bigg(x + \dfrac { 1 } { x }\bigg) \bigg( x - \dfrac { 1 } { x^2 } - 9 \bigg)$

The point in which the abscissa and the ordinate have different signs will lie in:

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

The equation of a straight line which is parallel to x-axis, and is at a distance of b from x-axis is

A.	x + y = b
B.	y = b
C.	x - y = b
D.	x = b

If AB and DE are parallel, find the value of ∠ACB.

A.	91°
B.	96°
C.	92°
D.	86°

$D$ is the midpoint of the hypotenuse $AC$ of a right $\triangle ABC.$ If $AC = 22 \space cm,$ then the length of $BD$ is:

A.	$11 \space cm$
B.	$22 \space cm$
C.	$12 \space cm$
D.	$6 \space cm$

In a quadrilateral PQRS, the diagonals PR and QS are equal and are perpendicular to each other. The quadrilateral PQRS is a:

A.	Rhombus
B.	Rectangle
C.	Square
D.	All of above

In the rhombus, ∠PRS = 7X - 522° and ∠QSP = 2X - 18°. Find the value of X.

A.	140°
B.	70°
C.	52°
D.	88°

The bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle circumscribing it at the points P and Q. If radius of the circle is 11 cm, find the distance between points P and Q.

A.	22√2 cm
B.	11 cm
C.	22 cm
D.	11√2 cm

The contruction of a triangle $ABC$ in which $AB = 11 \space cm$, $\angle A = 30^\circ$ is possible when $BC - AC$ is equal to:

A.	$12 \space cm$
B.	$11.5 \space cm$
C.	$12.5 \space cm$
D.	$10 \space cm$

The area of the parallelogram ABCD and the length of the altitude DE respectively in the figure below are,

A.	42 cm2, 21 cm
B.	84 cm2, 12 cm
C.	42 cm2, 12 cm
D.	126 cm2, 15.6 cm

Find the volume of the biggest cone that can fit inside a cube of side 6 cm.

A.	72π cm3
B.	3π cm3
C.	18π cm3
D.	36π cm3

If there are $n$ numbers of which one is $\left( 1 - \dfrac{ 1 } { n } \right)$ and all the others are $1's,$ then by how much is the arithmetic mean of these numbers less than $1.$

A.	$n$
B.	$n^{ 2 }$
C.	$\dfrac{ 1 } { n }$
D.	$\dfrac{ 1 } { n^2 }$

Fia and Alex sit on the 8-member board of directors for company P. If the board is to be split up into two 4-person subcommittees, what is the percentage that Alex and Fia are included in the same sub-committee?

A.	45.86%
B.	60.86%
C.	42.86%
D.	38.86%

In a basketball game, Kaymar made 11 baskets. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points that Kaymar could have made?

A.	15
B.	11
C.	12
D.	9

We use n! to mean the following expression
n × n-1 × n-2 × n-3 × ... × 2 × 1 (the product of all numbers from 1 to n)

In the range of numbers 16 <= x <= 60, how many numbers are there such that (x - 1)! is not divisible by x?

A.	12
B.	13
C.	11
D.	9