The value of ^@ \dfrac{ 1 } { 1 + \sqrt{ 2 } } + \dfrac{ 1 } { \sqrt{2} + \sqrt{3} } + \dfrac{ 1 } { \sqrt{3} + \sqrt{4} } + \dfrac{ 1 } { \sqrt{4} + \sqrt{5} } + \ldots + \dfrac{ 1 } { \sqrt{n-1} + \sqrt{n} } ^@ is:

A.	^@ \dfrac{ n -1 }{ n } ^@
B.	^@ \sqrt{n-1} ^@
C.	^@ \sqrt{n} - 1 ^@
D.	^@ \sqrt{n+1} ^@

If ^@ x = 1 + \sqrt{ 2 } + \sqrt{ 3 }, ^@ then ^@ x^4 - 4x^3 -4x^2 + 16x = ? ^@

A.	^@7^@
B.	^@10^@
C.	^@ 8 ^@
D.	^@12^@

If coordinates of the point shown in the picture are (p+30, p+20), find the value of p.

A.	-65
B.	-50
C.	-55
D.	-60

If point (3, 2) lies on the graph of linear equation 5x + py = 25, find the value of p.

A.	5
B.	4
C.	7
D.	3

Find the number of angles formed in the given figure.

A.	4
B.	10
C.	6
D.	8

If the altitude from vertex ^@A^@ of ^@ \triangle ABC ^@ bisects the opposite side, then:

A.	^@AC = CD^@
B.	^@AC = AD^@
C.	^@AB = AD^@
D.	^@AB = AC^@

The three angles of a quadrilateral are 51°, 77° and 113° respectively. Find the fourth angle.

A.	61°
B.	119°
C.	241°
D.	29°

In the rhombus, ∠PRS = 3X - 225° and ∠QSP = 2X - 10°. Find the value of X.

A.	65°
B.	130°
C.	75°
D.	55°

Two chords ^@AB^@ and ^@CD^@ of length ^@ 4 \space cm ^@, and ^@ 5 \space cm ^@ respectively of a circle are parallel to each other and are on the opposite sides of its center. If the distance between ^@AB^@ and ^@CD^@ is ^@ 3 \space cm,^@ find the approximate radius of the circle.

A.	^@ 3 \space cm ^@
B.	^@4 \space cm^@
C.	^@6 \space cm^@
D.	^@2 \space 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.	Anywhere but the center
B.	Center of the circle
C.	On chord ^@AB^@
D.	None of the above

Find the area of an isosceles triangle ^@ X Y Z ^@ in which ^@ Y Z = 6 \space cm ^@ and ^@ X Y = X Z = 5 \space cm ^@. If ^@ Z W \perp X Y ^@, find ^@ Z W ^@.

A.	^@ 2 \space cm ^@
B.	^@ 4.8 \space cm ^@
C.	^@ 10 \space cm ^@
D.	^@ 14 \space cm ^@

Find the surface area of the biggest sphere, which can fit in a cube of side 8x.

A.	4πx2
B.	64πx2
C.	36πx2
D.	16πx2

The mean of the following data is ^@11.75.^@ The value of ^@t^@ is:

^@ x_i ^@	^@7^@	^@12^@	^@17^@	^@22^@
^@f_i^@	^@7^@	^@t^@	^@4^@	^@1^@

A.	^@ 8^@
B.	^@6^@
C.	^@10^@
D.	^@15^@

Lien and Lian each have a bag that contains one ball each of the colors blue, white, yellow, grey and pink. Lien randomly selects a ball from her bag and puts it in Lian's bag. Then Lian randomly selects a ball from her bag and puts it in Lien's bag. What is the probability that after this the contents of the bag are the same as before?

A.	^@\dfrac{1}{3}^@
B.	^@\dfrac{2}{3}^@
C.	^@\dfrac{1}{2}^@
D.	^@\dfrac{1}{4}^@

There is a rectangle ABCD, with sides AB = CD = 27, and sides and BC = DA = 36. The rectangle is rotated 90° clockwise about C, then rotated 90°clockwise about the new location of the point that D after the first rotation. What is the length of the path traveled by point A?

A.	^@40.5 \pi^@
B.	^@42.5\pi^@
C.	^@39.5\pi^@
D.	^@45.5\pi^@

AD is a diameter of a circle and AB is a chord. If AD = 10 cm, AB = 8 cm, find the perpendicular distance of AB from the centre of the circle.

A.	2 cm
B.	3 cm
C.	5 cm
D.	4 cm