If $a$ and $b$ are rational numbers such that $a\sqrt5 = b\sqrt{ 15 }$, then the possible values of $a$ and $b$ are$:$

A.	$a = 0, b = 0$
B.	$a = 0, b = \dfrac{ 1 } { \sqrt{ 5 } }$
C.	$a = \dfrac{ 1 } { \sqrt{ 15 } }, b = 0$
D.	$a = \dfrac{ 1 } { \sqrt{ 5 } }, b = \dfrac{ 1 } { \sqrt{ 15 } }$

Factorize: $$\begin{aligned} a^2 - 3a - a + 3 \end{aligned}$$

A.	$(a - 1)^2$
B.	$(a - 3) (a - 1)$
C.	$(3 - a) (1 - a)$
D.	$(a - 3)^2$

What is the abscissa of the point $R(-4,5)$ ?

A.	$5$
B.	1
C.	$4$
D.	$-4$

Find the linear equation represented in the graph below.

A.	y = -x + 2
B.	y = 0
C.	y = 2
D.	y = - 2

If AB and CD are parallel, find the value of ∠x.

A.	50°
B.	140°
C.	120°
D.	130°

In a right-angled triangle $ABC$, if $\angle ACB = 2 \angle CAB$, then:

A.	$2AC = BC$
B.	$AC = 2BC$
C.	$AC = 3BC$
D.	$3AC = BC$

In a quadrilateral ABCD, O is a point inside the quadrilateral such that AO and BO are the bisectors of ∠A and ∠B respectively. The value of ∠AOB is:

A.	180° - (∠A + ∠B)
B.	1 2  (∠A + ∠B)
C.	1 2   (∠C + ∠D)
D.	∠C + ∠D

In the rhombus, ∠PRS = 6X - 526° and ∠QSP = 2X - 16°. Find the value of X.

A.	95°
B.	79°
C.	63°
D.	158°

In a circle with center O, if OA = 25 cm, CD = 18 cm and OD is perpendicular to AB, then AB is:

A.	50 cm
B.	48 cm
C.	47cm
D.	49 cm

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.	Center of the circle
B.	Anywhere in the circle
C.	On chord $AB$
D.	None of the above

The perimeter of a rhombus is 164 cm and one of its diagonals is 80 cm. What is the length of other diagonal?

A.	18 cm
B.	9 cm
C.	81 cm
D.	720 cm

A sphere is just enclosed inside a right circular cylinder. If the surface area of the sphere is 140 cm², find the total surface area of the cylinder.

A.	280 cm2
B.	105 cm2
C.	420 cm2
D.	210 cm2

The given table shows the marks of 10 students in Science exam.

Name	Marks (Out of 50)
Ramakrishnan	24
Harsh	11
Joel	32
Iqbal	44
Sunil	28
Shyam	50
Sneha	22
Pranav	14
Neha	41
Madhav	31

What is the mean value of the marks.

A.	30.1
B.	28.6
C.	29.3
D.	29.7

What is the probability that a leap year will contain 53 Mondays?

A.	1 52
B.	2 366
C.	1 366
D.	2 7

Pradip is on the left of the person sitting in center but is on the right of Ismail. Iqbal is on the right of Meenakshi and Gauri is on the right of Iqbal. Gauri is the second person from the person sitting in the center. Who is sitting in center.

A.	Ismail
B.	Iqbal
C.	Pradip
D.	Meenakshi

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

A.	70°
B.	100°
C.	90°
D.	80°