$X _1$, $X _2$, $X _3 .....$, $X _{ 12 }$ are integers none of which are divisible by $3$. The remainder when $X _1^2 + X _2^2 + X _3^2 + ..... + X _{ 12 }^2$ is divided by $3$ is

A.	$0$ or $2$
B.	$1$ or $2$
C.	$1$
D.	$0$

If α and β are the zeros of quadratic polynomial x² + 5x + 1, find the value of α³ + β³.

A.	-105
B.	-110
C.	-111
D.	-109

Solve the following pair of linear equations by using cross multiplication. $$\begin{aligned} &u x - v y = w \\ &v x - u y = 1 - w \end{aligned}$$

A.	$x = \dfrac { v } { (v - u ) ( v + u ) } - \dfrac { w } { (u - v) } \text{ and } y = \dfrac { u } { (v - u ) ( v + u ) } + \dfrac { w } { ( u - v ) }$
B.	$x = \dfrac { - v } { (v - u ) ( v + u ) } - \dfrac { w } { (u + v) } \text{ and } y = \dfrac { u } { (v - u ) ( v + u ) } + \dfrac { w } { ( u + v ) }$
C.	$x = \dfrac { v } { (v - u ) ( v + u ) } - \dfrac { w } { v - u } \text{ and } y = \dfrac { u } { (v - u ) ( v + u ) } - \dfrac { w } { u - v }$
D.	None of these

Age of a mother is equal to the square of her son's age. If one year ago, mother's age was 6 times the son's age. Find their present ages.

A.	16 years and 4 years
B.	25 years and 5 years
C.	49 years and 7 years
D.	9 years and 3 years

If $x \ne y$ and the sequences $x, a _1, a _2, y$ and $x, b _1 , b _2, y$ each are in $A.P.$, then $\left(\dfrac{ a _2 - a _1 } { b _2 - b _1 }\right)$ is

A.	$3$
B.	$1$
C.	$0$
D.	$y - 3$

In the given figure, $AD$ is the bisector of $\angle BAC$. If $AB = 10 \space cm$, $AC = 2 \space cm$ and, $BC = 15 \space cm$, find the length of $BD$ and $DC$.

A.	$13.5 \space cm$ and $3.5\space cm$
B.	$12.5 \space cm$ and $4.5 \space cm$
C.	$12.5 \space cm$ and $2.5 \space cm$
D.	$14.5 \space cm$ and $2.5 \space cm$

If $A(4,2)$, $B(8 , y)$, $C(x, -2)$ and $D(2, -2)$ are the vertices of a parallelogram $ABCD$, find the values of $x$ and $y$.

A.	$x = 10 , y = 6$
B.	$x = 9 , y = 5$
C.	$x = 6, y = 2$
D.	$x = 8 , y = 4$

 

cosθ - 2 cos3θ

2 sin3θ - sinθ

  = ?

A.	tan θ
B.	cot θ
C.	-tan θ
D.	-cot θ

If the lengths of tangents drawn from an external point $A$ to a point $P$ and $Q$ on the circle are equal then $AP$ is equal to:

A.	$OA$
B.	$OQ$
C.	$AQ$
D.	$OP$

A.
B.
C.
D.

The radii of two circles are $5 \space cm$ and $12 \space cm$ respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.

A.	$25 \space cm$
B.	$13 \space cm$
C.	$169 \space cm$
D.	$\text { None of these }$

A hemisphere depression is cut out from one face of a cubical wooden block of length 'l' such that the diameter of the hemisphere is equal to the edge of the cube. Choose the correct surface area of the remaining solid.

A.	l2 4  × (24 + π) sq.units
B.	l2 2  × (24 + π) sq.units
C.	l2 4  × (14 + π) sq.units
D.	none of these

Find the mode of the following data:

$\begin{align} \text { Salary (in thousands) } \end{align}$ $100 - 108$ $109 - 117$ $118 - 126$ $127 - 135$ $136 - 144$ $145 - 153$ $\begin{align} \text { Number of employees } \end{align}$ $125$ $37$ $60$ $148$ $126$ $70$

A.	$133.7 \space thousands$
B.	$135.7 \space thousands$
C.	$134.29\space thousands$
D.	$131.7\space thousands$

A coin is tossed $500$ times and it is found that head comes up $430$ times and tail $70$ times. If such a coin is tossed, then what is the probability of getting a head?

A.	$0.17$
B.	$0.86$
C.	$0.15$
D.	$1$

If $5 x$ = $sec {\space}\theta$ and $\dfrac { 5 } { x }$ = $tan {\space}\theta$. Find the value of $5 (x^2 - \dfrac{1} {x^2})$.

A.	$\dfrac { 6 } { 11 }$
B.	$\dfrac { 11 } { 15 }$
C.	$\dfrac { 1 } { 5 }$
D.	None of these

Faces of a cube are marked with A,B,C,D,E and F. Two views of the cube are as shown below, if face D is opposite to face F, what will be there on the top when C is at the bottom?

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

Which of following shows relation between Dog, Elephant and Animal.

A.
B.
C.
D.

Find the next term of given sequence ..
4, 19, 42, 73, 112, , ....

A.	318
B.	167
C.	159
D.	153

Which is the odd one out in this set:
UZF, CHN, QVC, EJP

A.	CHN
B.	QVC
C.	EJP
D.	UZF

Find the odd one out in the given set:
DGJ, SWY, FIL, EHK

A.	SWY
B.	EHK
C.	DGJ
D.	FIL