The following are the first and last steps in finding the $H.C.F.$ of $22096$ and $774$ using Euclid's algorithm.

Step $1: 22096 = 774 \times 28 + 424$

Step $2:$ _______________

Step $3:$ _______________

Step $4: 350 = 74 \times 5 + 0$

Choose the steps $2$ and $3$.

1. $774 = 424 \times 1 + 350$
2. $424 = 350 \times 1 + 74$
3. $773 = 423 \times 1 + 350$
4. $423 = 349 \times 1 + 74$

A.	$(iii)$ and $(ii)$
B.	$(i)$ and $(ii)$
C.	$(iii)$ and $(iv)$
D.	$(i)$ and $(iv)$

Find a cubic polynomial whose zeros are $5, 6, \space \text{and} \space \dfrac { 8 } { 9 }.$

A.	$9 x^3 - 107 x^2 + 358 x - 240$
B.	$9 x^3 - 107 x^2 - 358 x - 240$
C.	$x^3 - 107 x^2 + 358 x - 240$
D.	$\text{ None of these }$

A pair of linear equations which has a unique solution $x = 4$ and $y = 5$ is

A.	$7 x + 18 y = 123, 13 x -12 y = -4$
B.	$14 x + 10 y = 109, 11 x -6 y = 7$
C.	$2 x + 9 y = 57, 6 x + 11 y = 80$
D.	$6 x + 14 y = 94, 8 x + 19 y = 127$

Which of the following quadratic equations have no real roots?

A.	-4x2 + 7x - 4 = 0
B.	4x2 + 4x + 1 = 0
C.	-x2 + 4x - 2 = 0
D.	-2x2 + 7x - 4 = 0

A piece of wire is used to make circles of the following pattern.

The radius of the first circle is $r \space cm$ and it is increased by $1 \space cm$ successively. Find the length of the wire that is required to make $5$ such circles.

A.	$10\pi(r + 2) cm$
B.	$5\pi(r + 2) cm$
C.	$10\pi(r - 2) cm$
D.	$5\pi(r - 2) cm$

$ABCD$ is a trapezium in which $AB || DC$ and $AB = 2DC$. If the diagonals of trapezium intersect each other at a point $O$, find the ratio of the areas of $\Delta AOB$ and $\Delta COD$

.

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

The distance between the points $(\sqrt{ 5 } + 3, \sqrt{ 2 } - 3)$ and $(\sqrt{ 5 } - 3, \sqrt{ 2 } + 3)$ is

A.	$4\sqrt{ 3 }$ units
B.	$6\sqrt{ 3 }$ units
C.	$4\sqrt{ 2 }$ units
D.	$6\sqrt{ 2 }$ units

Andre and Cristina were studying the ways to shift the arguments in the trigonometric functions. They found the following results and showed it to the teacher. But the teacher pointed out a mistake. Identify the result which has a mistake.

A.	$cos(x \pm y) = cos \space x \space cos \space y \mp sin \space x \space sin \space y$
B.	$cot \left( \dfrac{ \pi }{ 4 } \pm Q \right) = \dfrac{ cot \space Q \mp 1} { cot \space Q \pm 1 }$
C.	$tan \left( \dfrac{ \pi }{ 4 } \pm Q \right) = \dfrac{ 1 \pm tan \space Q }{ 1 \mp tan \space Q }$
D.	$cot \left( \dfrac{ \pi }{ 4 } \pm Q \right) = \dfrac{ cot \space Q \mp 1} { cot \space Q \mp 1 }$

$AP$ and $BP$ are the two tangents at the extremities of chord $AB$ of a circle. $\angle MAP$ is equal to:

A.	$\angle APB$
B.	$\angle MBP$
C.	$\angle APM$
D.	$\angle MPB$

A.
B.
C.
D.

Find the area of the major sector of a circle with radius $10 \space cm$ when the angle subtended by the minor arc is $60^\circ$.(Use $\pi = 3.14$)

A.	$261.67 \space cm^2$
B.	$83.33 \space cm^2$
C.	$300 \space cm^2$
D.	$\text { None of these }$

Rafa loves to play with building blocks. He has building blocks in the shape of a cube. The shape and size of all the blocks are the same. Each edge of the block has a length of $3 \space cm$. This time Rafa tries to form columns by placing the blocks one over the other. He places the blocks in such a way that there is always a block less in the consecutive column. If he starts with $8$ blocks in the first column then what is the volume of the resultant figure?

A.	$36 \space cm^3$
B.	$972 \space cm^3$
C.	$108 \space cm^3$
D.	$324 \space cm^3$

The diameter of $99$ screws was noted and the following data was obtained:

$\begin{align} \text { Diameter (in mm) } \end{align}$	$30 - 32$	$32 - 34$	$34 - 36$	$36 - 38$	$38 - 40$	$40 - 42$	$42 - 44$
$\begin{align} \text { Number of screws } \end{align}$	$12$	$14$	$13$	$18$	$10$	$17$	$15$

Determine the modal diameter of the screws.

A.	$37.242 \space mm$
B.	$37.372 \space mm$
C.	$37.167 \space mm$
D.	$37.017 \space mm$

A die is thrown once. Find the probability of getting a multiple of $3$.

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

Two coins are tossed simultaneously. What is the probability of getting at least one tail?

A.	$\dfrac { 1 } { 2 }$
B.	$\dfrac { 2 } { 9 }$
C.	$\dfrac { 3 } { 4 }$
D.	$\dfrac { 1 } { 9 }$

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

A.	4
B.	2
C.	5
D.	Cannot be determined

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

A.
B.
C.
D.

Find the next term of given sequence ..
14, 31, 68, 145, 302, 619, ....

A.	1248
B.	1259
C.	2512
D.	1256

Which of the following choices would replace the blanks below
_ABAAAABAA_A_AAAA_AAAABA_

A.	AABBA
B.	AAABA
C.	ABBBA
D.	BABBA

Find the next term of given sequence ..
503, 441, 379, 317, 255, 193, 131, ....

A.	69
B.	64
C.	7
D.	77