Simplify ^@ \sqrt{ 18 \left( 1 + \sqrt{ 1 + \left( \dfrac{ x^{ 8 } - 1 }{ 2 x^{ 4 } } \right)^2 } \right) }, ^@ where ^@ x ^@ is any positive real number.

A.	^@ \dfrac{ 3 ( x^{ 4 } + 1 ) } { x^{ 2 } } ^@
B.	^@ \sqrt{ \dfrac{ 3 ( x^{ 4 } + 1 ) } { \sqrt{ x^{ 2 } } } } ^@
C.	^@ \dfrac{ 3 ( x^{ 4 } - 1 ) } { x^{ 4 } } ^@
D.	^@ \dfrac{ 3 ( x^{ 4 } + 1 ) } { \sqrt{ x^{ 2 } } } ^@

If two zeros of polynomial x³ + bx² + cx + d are 5+√3 and 5-√3, find its third zero.

A.	b - 10
B.	-b - 10
C.	10 - b
D.	c - 10

The pair of equations y = -6 and y = -5 has

A.	two solutions
B.	infinitely many solutions
C.	a unique solution
D.	no solution

A piece of copper wire costs ^@108^@. If it was ^@3 \space meters^@ longer and the price of each meter of copper wire costs ^@3^@ less, the total cost of the piece would remain unchanged. Find the length of the copper wire.

A.	^@10 \text{ meter }^@
B.	^@11 \text{ meter }^@
C.	^@9 \text{ meter }^@
D.	^@8 \text{ meter }^@

Find the arithmetic mean between ^@(f + e)^@ and ^@(f - e)^@.

A.	^@ f ^@
B.	^@ fe ^@
C.	^@ \dfrac { f } { e } ^@
D.	^@ e ^@

Two poles of heights ^@ 24 \space metres^@ and ^@48 \space metres^@ stand vertically on a plane ground. If the distance between their feet is ^@32 \space metres^@, find the distance between their tops.

A.	^@46 \space m^@
B.	^@45 \space m^@
C.	^@40 \space m^@
D.	^@39 \space m^@

Find those points on the ^@y^@-axis, which are at a distance of 20 units from the point ^@A(12,-2)^@.

A.	^@ (0,18) \text{ and } (0,-18) ^@
B.	^@ (0,14) \text{ and } (0,-18) ^@
C.	^@ (0,14) \text{ and } (0,-14) ^@
D.	^@ (0,10) \text{ and } (0,-18) ^@

Without using trignometric tables, evaluate the value of ^@ sin^2 {\space} 36^\circ + sin^2 {\space} 54^\circ ^@.

A.	1
B.	2
C.	90
D.	None of these

Tangents ^@ PA ^@ and ^@ PB ^@ are drawn from an external point ^@ P ^@ to two concentric circles with center ^@ O ^@ and radii ^@ 13 \space cm ^@ and ^@ 10 \space cm ^@ respectively. If ^@ AP = 8 \space cm ^@, what the length of ^@ BP ^@ ?

A.	^@ 21.53 \space cm ^@
B.	^@ 15.26 \space cm ^@
C.	^@ 11.53 \space cm ^@
D.	^@ \text{ None of these } ^@

A.
B.
C.
D.

The radii of two circles are ^@ 5 \space cm ^@ and ^@ 16 \space cm ^@ respectively. Find the radius of the circle which has its circumference equal to the sum of the circumference of the two circles.

A.	^@ 42 \space cm ^@
B.	^@ 10 \space cm ^@
C.	^@ 21 \space cm ^@
D.	^@ \text{ None of these } ^@

The perimeters of the ends of the frustum of a cone are ^@7.92 \space cm^@ and ^@11 \space cm^@. If the height of the frustum is ^@24 \space cm^@, find its curved surface area. (Take ^@\pi = \dfrac { 22 } { 7 }^@).

A.	^@ 72.24 \space cm^2 ^@
B.	^@ 227.04 \space cm^2 ^@
C.	^@ 9.46 \space cm^2 ^@
D.	^@ \text { None of these } ^@

Find the mode of the following data:

^@ \begin{align} \text { Salary (in thousands) } \end{align}^@ ^@ 10 - 15^@ ^@ 15 - 20^@ ^@ 20 - 25^@ ^@ 25 - 30^@ ^@ 30 - 35^@ ^@ \begin{align} \text { Number of employees } \end{align}^@ ^@13^@ ^@10^@ ^@7^@ ^@14^@ ^@5^@

A.	^@25.19^@
B.	^@ 27.19 ^@
C.	^@27.25^@
D.	^@30.19^@

4 coins are tossed in parallel. What is the probability of getting at least one head?

A.	1 16
B.	15 16
C.	4 16
D.	20 16

A building of height 24.6 m is in the form of a right circular cylinder of diameter 17 m and height 20.1 m, surmounted by a right circular cone of the same diameter, then the cost of the canvas of the building at the rate of Rs.444 per m² is Rs.

A.	590919.6
B.	256.99
C.	591019.6
D.	None of these

Faces of a cube are marked with 1,2,3,4,5 and 6. If two views of a cube are as shown below, what will be there on the face opposite to face 4?

A.	3
B.	6
C.	1
D.	Cannot be determined

Which of following shows relation between eagle, Crow and Bird.

A.
B.
C.
D.

Find the next term of given sequence ..
23, 24, 28, 37, 53, ....

A.	83
B.	74
C.	78
D.

Which of the following is the next terms in the series given below?
EW, HU, KS, NQ, ___

A.	PN
B.	RN
C.	QO
D.	PO

Which of following shows relation between Fruits, Pomegranate and Orange.

A.
B.
C.
D.