If ^@n^@ is an even natural number, then which of the following is the largest natural number by which ^@n (n + 1) (n + 2)^@ is definitely divisible?

A.	^@12^@
B.	^@24^@
C.	^@8^@
D.	^@2^@

Find the sum of the roots of the quadratic equation x² + 2x - 24 = 0

A.	-2
B.	-3
C.	0
D.	-1

Solve the following system of linear equations by equating the coefficients. @^\begin{aligned} & 9 x - 6 y = -72 \\ & 5 x + 4 y = -128 \end{aligned}@^

A.	^@x^@ = ^@-17^@ and ^@y^@ = ^@-13^@
B.	^@x^@ = ^@-12^@ and ^@y^@ = ^@-16^@
C.	^@x^@ = ^@-15^@ and ^@y^@ = ^@-11^@
D.	^@x^@ = ^@-16^@ and ^@y^@ = ^@-12^@

Solve the quadratic equation ^@ z^2-4z + 3 = 0 ^@ to find its roots.

A.	^@ 3 \text{ or } 1 ^@
B.	^@ \dfrac{ 5 } { 2 } \text{ or } 1 ^@
C.	^@ 3 \text{ or } \dfrac{ 5 } { 2 } ^@
D.	^@ \dfrac{ 5 } { 2 } \text{ or } \dfrac{ 5 } { 2 } ^@

The sum of all terms of the arithmetic progression having ten terms except for the first term, is ^@93^@, and except for the sixth term, is ^@78^@. The ^@9^{ th }^@ term of the progression if the sum of the first and the fifth term is equal to ^@14^@ is

A.	^@31^@
B.	^@22^@
C.	^@25^@
D.	^@28^@

In a rhombus of side ^@ 45 \space cm^@, one of the diagonals is ^@54 \space cm^@ long. Find the length of the second diagonal.

A.	^@ 74 \space cm^@
B.	^@ 72 \space cm^@
C.	^@ 76 \space cm^@
D.	^@ 77 \space cm^@

How many points on the line segments joining ^@ (20,5) ^@ and ^@(25,7)^@ have integer coordinates including the endpoints?

A.	^@ 9 ^@
B.	^@ 3 ^@
C.	^@ 2 ^@
D.	^@ 1 ^@

If ^@7 sin^2 \theta + 3 cos^2 \theta = 4^@, then which of the following is equal to ^@cot \theta^@?

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

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 = 7 \space cm ^@, what the length of ^@ BP ^@ ?

A.	^@ 10.86 \space cm ^@
B.	^@ 14.76 \space cm ^@
C.	^@ 20.86 \space cm ^@
D.	^@ \text{ None of these } ^@

A.
B.
C.
D.

A chord of a circle of radius ^@ 70 \space cm ^@ subtends a right angle at the center. Find the area of the corresponding major segment.^@ \bigg[\pi = \dfrac { 22 } { 7 }\bigg] ^@

A.	^@ 1650 \space cm^2 ^@
B.	^@ 14000 \space cm^2 ^@
C.	^@ 1400 \space cm^2 ^@
D.	^@ \text { None of these } ^@

Choose the correct ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

A.	6 : π
B.	7 : π
C.	π : 6
D.	None of these

Find the median height from the following data

Class interval	150-155 cm	155-160 cm	160-165 cm	165-170 cm	170-175 cm
Frequency	6	10	13	10	23

A.	171
B.	166
C.	176
D.	161

Seoyoon draws one card from a shuffled deck of 52 cards. What is the probability that she drew a diamond or a 2?

A.	2 13
B.	1 13
C.	1
D.	4 13

A building is in form of a right circular cylinder and cone as shown in the picture. The radius of cone and cylinder is 4 meters. The height of cylinder and cone are 4.5 meters and 3 meters respectively. Find the outer surface area of the building. (Assume π =  

22

7

 )

A.	88 m2
B.	528 m2
C.	176 m2
D.	352 m2

A dice has numbers ^@1^@ to ^@6,^@ such that sum of opposite faces are always ^@7.^@ Which is the correct view of dice^@?^@

A.
B.
C.
D.

Which of following shows relation between Stationary, Eraser and Ruler.

A.
B.
C.
D.

Find the next term of given sequence ..
12, 12, 15, 23, 38, 62, ....

A.	121
B.	93
C.	133
D.	97

Which of the following is the next term in the series:
Y, V, T, Q, O, L, J, ___

A.	E
B.	I
C.	F
D.	G

Find the next term of given sequence ..
11, 11, 14, 22, 37, 61, ....

A.	96
B.	132
C.	92
D.	120