Simplify $\sqrt{ 18 \left( 1 + \sqrt{ 1 + \left( \dfrac{ x^{ 12 } - 1 }{ 2 x^{ 6 } } \right)^2 } \right) },$ where $x$ is any positive real number.

A.	$\dfrac{ 3 ( x^{ 6 } + 1 ) } { x^{ 3 } }$
B.	$\sqrt{ \dfrac{ 3 ( x^{ 6 } + 1 ) } { \sqrt{ x^{ 3 } } } }$
C.	$\dfrac{ 3 ( x^{ 6 } + 1 ) } { \sqrt{ x^{ 3 } } }$
D.	$\dfrac{ 3 ( x^{ 6 } - 1 ) } { \sqrt{ x^{ 6 } } }$

If $\alpha$ and $\beta$ are the zeros of quadratic polynomial $x^2 + x + 2$, find the value of $\dfrac{1}{ \alpha^3 } + \dfrac{1} { \beta^3 }$.

A.	$\dfrac { 7 } { 8 }$
B.	$\dfrac { 5 } { 8 }$
C.	$\dfrac { 3 } { 8 }$
D.	$\dfrac { 3 } { 4 }$

If thrice the daughter's age in years is added to mother's age, the sum is 84. If thrice the mother's age is added to the daughter's age, the sum is 132. Find the age of mother and daughter.

A.	39 and 16 years
B.	39 and 14 years
C.	38 and 15 years
D.	39 and 15 years

Choose the correct roots of the equation $6 c^2 - 2 c - 20 = 0$ by completing the square method.

A.	$2$ and $\dfrac { -5 } { 3 }$
B.	$\dfrac { 2 } { 3 }$ and $\dfrac { -5 } { 3 }$
C.	$\dfrac { -5 } { 1 }$ and $\dfrac { -5 } { 3 }$
D.	$2$ and $\dfrac { 2 } { 3 }$

The production of television sets in a factory increases uniformly by a fixed number every year. The factory produced $2262$ television sets in the $3^{ rd }$ year and $4902$ television sets in the $8^{ th }$ year. Find the production of television sets in the $5^{ th }$ year.

A.	$11810$
B.	$12310$
C.	$13310$
D.	$3318$

A lamp is $15.4 \space m$ above the ground. A boy $55 \space cm$ tall walks away from the base of this post at a speed of $1.7 \space m/s$. Find the length of the shadow of the boy after $8 \space seconds$.

A.	$2\space m$
B.	$0.5\space m$
C.	$2.5\space m$
D.	$1.5\space m$

Let $D(11,10), E(9,12),$ and $F(8,7)$ be the mid points of the sides $BC, CA,$ and $AB$ respectively of a $\Delta{ABC}$. Then, find the coordinates of the vertex $A$.

A.	$(12,15)$
B.	$(6,9)$
C.	$(6,9)$
D.	None of these

If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.

A.	True
B.	False
C.	Depends on the height of tower
D.	Depends on value of angle

Two tangents $PA$ and $PB$ are drawn to a circle with center $O$ from an external point $P$, then $\angle APB$ is equal to:

A.	$\angle OAB$
B.	$3 \angle OAB$
C.	$\angle PAB$
D.	$2 \angle OAB$

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.	$474 \space cm^2$
C.	$2240 \space cm^2$
D.	$\text { None of these }$

A wooden toy rocket is in the shape of a cone mounted on a cylinder as shown in the figure.The height of the entire rocket is 35 cm, while the height of the conical part is 25 cm. The base of the conical portion has a diameter of 13 cm,which the base diameter of the cylinderical portion is 10 cm. If the conical portion is painted yellow , choose the area of the rocket painted with yellow colours.

A.	185.15 cm2
B.	581.88 cm2
C.	74.64 cm2
D.	None of these

The table below shows the number of books read by five children in a year.

Name	Number of books
Lou	22
Marie	44
Tristan	x
Aurore	30
Antoine	42

If the average number of books read by the children was 34, then how many books did Tristan read over the year?

A.	36
B.	28
C.	34
D.	32

Olivier and Vincent sit on the 6-member board of directors for company X. If the board is to be split up into two 3-person subcommittees, what is the percentage that Vincent and Olivier are included in the same sub-committee?

A.	52%
B.	40%
C.	45%
D.	35%

Find $\angle P$ in the given figure

A.	$100^o$
B.	$50^o$
C.	$90^o$
D.	$95^o$

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

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

In this diagram, the triangle represents men, the square represents doctors and the circle represents employed. Find the number of men who are employed but not doctors.

A.	7
B.	8
C.	3
D.	6

Find the next term of given sequence ..
8, 38, 110, 242, 452, , ....

A.	758
B.	764
C.	753
D.	1516

Which of the following choices would replace the blanks below
babb_abbbabb_a_b

A.	bbbb
B.	bbab
C.	babb
D.	abbb

Find the next term of given sequence.
16, 18, 21, 26, 33, 44, 57, ....

A.	82
B.	66
C.	77
D.	74