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

If α and β are the zeros of quadratic polynomial x² + 5x - 4, find the value of α³ + β³.

A.	-181
B.	-190
C.	-180
D.	-185

Solve the following system of linear equations by using the method of elimination by equating the coefficients. @^\begin{aligned} & \dfrac { x } { 3 } + \dfrac { y } { 5 } = 50 \\ & \dfrac { x } { 9 } + \dfrac { y } { 2 } = 47 \end{aligned}@^

A.	^@x^@ = ^@107^@ and ^@y^@ = ^@69^@
B.	^@x^@ = ^@73^@ and ^@y^@ = ^@108^@
C.	^@x^@ = ^@108^@ and ^@y^@ = ^@70^@
D.	^@x^@ = ^@71^@ and ^@y^@ = ^@108^@

Find the roots of the quadratic equation ^@ z^2-4z + 2 = 0 ^@.

A.	^@ \dfrac{ -4 + \sqrt{ 3 } } { 2 } \text{ or } \dfrac{ -4 - \sqrt{ 3 } } { 2 } ^@
B.	^@ \dfrac{ 4 + \sqrt{ 3 } } { 2 } \text{ or } \dfrac{ 4 - \sqrt{ 3 } } { 2 } ^@
C.	^@ \dfrac{ 2 + \sqrt{ 2 } } { 1 } \text{ or } \dfrac{ 2 - \sqrt{ 2 } } { 1 } ^@
D.	^@ \dfrac{ -4 + \sqrt{ 2 } } { 2 } \text{ or } \dfrac{ -4 - \sqrt{ 2 } } { 2 } ^@

21^st term of the arithmetic progression 8, -2, -12, -22 is:

A.	-202
B.	-182
C.	-172
D.	-192

The areas of two similar triangles are ^@ 144\space cm^2^@ and ^@16\space cm^2^@ respectively. If the altitude of the bigger triangle is ^@10.8 \space cm^@, find the corresponding altitude of the smaller triangle.

A.	^@ 5.6 \space cm ^@
B.	^@ 3.6 \space cm ^@
C.	^@ 4.6 \space cm ^@
D.	^@ 2.6 \space cm ^@

The points ^@(-5, 6)^@, ^@(3, 0)^@, and ^@(9, 8)^@ form the vertices of

A.	Isosceles triangle
B.	Equilateral triangle
C.	Right-angled triangle
D.	Isosceles right-angled triangle

If ^@sin A = \dfrac{1}{ 2 }^@ and ^@cos B = \dfrac{1}{ 2 }^@, then ^@ (A + B)^@ is

A.	^@90^\circ^@
B.	^@105^\circ^@
C.	^@60^\circ^@
D.	^@75^\circ^@

In the given figure, three circles with centers ^@ A, B, ^@ and ^@ C ^@ touch each other externally. If ^@ AB = 9 \space cm, BC = 11 \space cm,^@ and ^@ AC = 8 \space cm^@. What is the radius of the circle with center ^@B^@ ?

A.	^@6 \space cm^@
B.	^@2 \space cm^@
C.	^@5 \space cm^@
D.	^@3 \space cm^@

A.
B.
C.
D.

A chord of a circle of radius ^@ 28 \space cm ^@ subtends a right angle at the center. Find the area of the corresponding major segment.^@ \bigg[\pi = \dfrac { 22 } { 7 }\bigg] ^@

A.	^@ 224 \space cm^2 ^@
B.	^@ 2240 \space cm^2 ^@
C.	^@ 474 \space cm^2 ^@
D.	^@ \text { None of these } ^@

A object is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 3 cm and the total height of the object is 84 cm, then choose the correct inner surface area of the object.

A.	806.14 cm2
B.	45144 cm2
C.	537.43 cm2
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	8	5	14	10	29

A.	158
B.	168
C.	163
D.	178

What is the probability that a leap year will contain 53 Thursdays and 52 Fridays?

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

A flag pole ^@12 \space m^@ high casts a shadow ^@6.4 \space m^@ long. Then, the distance of the top of the pole from the far end of the shadow is

A.	^@17.6 \space m^@
B.	^@13.6 \space m^@
C.	^@23.6 \space m^@
D.	^@10.6 \space m^@

Faces of a cube are marked with A, B, C, D, E and F. If two views of cube are as shown below, what will be there on the face opposite to face B ?

A.	D
B.	C
C.	E
D.	Cannot be determined

Following chart shows number of students in a school who play one of three sports. Find the number of students who play exactly two sports.

A.	50
B.	47
C.	48
D.	44

Find the next term of given sequence ..
13, 65, 91, 143, 169, 221, ....

A.	234
B.	247
C.	260
D.	252

Which of the following can take the place of the blank in the series below?
B2Z, F3V, J5R, _____, R11J

A.	N7N
B.	O8O
C.	N8O
D.	M7N

Select the figure from the options which satisfies the same conditions of placement of the dots as in the figure.

A.
B.
C.
D.