$X _1$, $X _2$, $X _3 .....$, $X _{ 12 }$ 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.	$0$
B.	$1$
C.	$0$ or $2$
D.	$1$ or $2$

Find a quadratic polynomial whose zeros are $- \dfrac { 6 } { 4 } \space \text{and} \space \dfrac { 7 } { 5 }$.

A.	$2 x^2 + 20x - 1$
B.	$20 x^2 + 2 x - 42$
C.	$2 x^2 - 20x - 42$
D.	$x^2 + 20x + 42$

A boat running upstream takes $8{\space} hours$ $11{\space} minutes$ to cover a certain distance, while it takes $2{\space} hours$ to cover the same distance in running downstream. What is the ratio between the speed of the boat and the speed of stream?

A.	$626:379$
B.	$621:376$
C.	$611:371$
D.	None of these

Let $a$ and $b$ be the roots of $x^2 + 2010 x + 1 = 0$ and let $c$ and $d$ be the roots of $x^2 - 2016 x + 1 = 0$. Find the value of $(a + c)(b + c)(a - d)(b - d)$.

A.	$4026$
B.	$24156$
C.	$24158$
D.	$24166$

Find number of terms in the arithmetic progression 8, -5, -18, -31, ... such that sum of the series is -3700?

A.	27
B.	22
C.	26
D.	25

In the given figure, $DE \parallel BC$, $AD = 4 \space cm$, $DB = 12 \space cm$, $AE = 5.5\space cm$ and $DE = 2 \space cm$. What is the $AC$ and $BC$ ?

A.	$22 \space cm \space \text{and} \space 10 \space cm$
B.	$23 \space cm \space \text{and} \space 10 \space cm$
C.	$23 \space cm \space \text{and} \space 8 \space cm$
D.	$22 \space cm \space \text{and} \space 8 \space cm$

In what ratio does the point $P(-23,-8)$ divide the line segment joining $A(-35,7)$ and $B(-7,-28)$?

A.	$3 : 4$
B.	$3 : 1$
C.	$1 : 4$
D.	$4 : 3$

A $2 \space m$ high tower casts $2\sqrt{3} \space m$ long shadow on the ground. Find the angle of Sun's elevation.

A.	$45^\circ$
B.	$30^\circ$
C.	$37.5^\circ$
D.	$60^\circ$

A tangent $PQ$ at a point $P$ of a circle of radius $6 \space cm$ meets a line through the center $O$ at a point $Q$ such that $OQ = 14 \space cm$. What is the length of $PQ$ ?

A.	$12.65 \space cm$
B.	$14.65 \space cm$
C.	$17.65 \space cm$
D.	$\text{ None of these }$

A.
B.
C.
D.

Johan and Yannick made two circles of equal circumference $52.8 \space cm$. Both of them made small circles inside that. Yannick made circles with radii $1.7 \space cm$ an Johan made circles with radii $3.2 \space cm$. Yannick and Johan coloured their circles with purple and blue colours respectively. Both of them coloured the remaining portion inside the circles with violet colour. Find the area of the combined violet portions. (Solve the calculations to 1 decimal place.)

A.	$32.3 \space cm$
B.	$3.43 \space cm$
C.	$343 \space cm$
D.	$34.3 \space cm$

There are a cylinder and a cone with height, $h$ and radius $r$. There is also a sphere of the same radius. The height, $h$ of the cylinder and the cone is $3$ times the radius, $r$. If $V_1$ is the volume of the cylinder, $V_2$ is the volume of the cone and $V_3$ is the volume of the sphere, then which of the following is true?

A.	$V_1 > V_2 > V_3$
B.	$V_1 < V_2 < V_3$
C.	$V_2 < V_3 < V_1$
D.	$V_2 > V_3 > V_1$

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

Name	Number of books
Jennifer	20
Fleur	20
Luna	x
Aaron	21
Marloes	30

If the average number of books read by the children was 23, then how many books did Luna read over the year?

A.	20
B.	30
C.	24
D.	22

Two dice are rolled. What is the probability that the two numbers add up to a prime number?

A.	12 36
B.	7 36
C.	5 36
D.	15 36

In 1996, the meteorological office predicted the weathers completely right for the months of february and april, and completely wrong for all the other months. What is the probability that the forecast was right for a given day that year?

A.	59 365
B.	61 366
C.	59 366
D.	307 365

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 bottom when A is at the top?

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

In this diagram, the triangle represents women, the square represents engineers and the circle represents tall. Find the number of women who are engineers and tall.

A.	3
B.	1
C.	5
D.	4

Find the missing number

$21$	$38$	$124$
$84$	$101$	$?$

A.	$187$
B.	$182$
C.	$191$
D.	$250$

Which of the following can take the place of the blank in the series below?
ew, ht, kq, _____, qk

A.	om
B.	mn
C.	oo
D.	nn

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

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