The following are the first and last steps in finding the $H.C.F.$ of $15760$ and $642$ using Euclid's algorithm.

Step $1: 15760 = 642 \times 24 + 352$

Step $2:$ _______________

Step $3:$ _______________

Step $4: 290 = 62 \times 4 + 0$

Choose the steps $2$ and $3$.

1. $642 = 352 \times 1 + 290$
2. $352 = 290 \times 1 + 62$
3. $641 = 351 \times 1 + 290$
4. $351 = 289 \times 1 + 62$

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

If the zeros of the polynomial $x^3 - 12 x^2 + 41 x - 30$ are $(a - b), a, (a + b)$, find $a$ and $b$.

A.	$a = 1 \space \text{and} \space b = \pm \sqrt{7}$
B.	$a = 4 \space \text{and} \space b = \pm \sqrt{89}$
C.	$a = 4 \space \text{and} \space b = \pm \sqrt{7}$
D.	$\text{ None of these }$

Find value of k for which equations $-2p - 2q - 7 = 0$ and $kp - 2q - 3 = 0$, will have no solution.

A.	$-4$
B.	$-2$
C.	$0$
D.	$-1$

Solve the quadratic equation $a^2 - 2 \sqrt{ 7}a - 105 = 0$ to find its roots.

A.	$-5 \sqrt{ 7} \space and \space -4 \sqrt{ 7}$
B.	$5 \sqrt{ 7} \space and \space -3 \sqrt{ 7}$
C.	$-6 \sqrt{ 7} \space and \space 3 \sqrt{ 7}$
D.	$-6 \sqrt{ 7} \space and \space 4 \sqrt{ 7}$

What is the difference between the 29^th term and 16^th term of the arithmetic progression 6, -8, -22, -36?

A.	-182
B.	-168
C.	-210
D.	-196

A man goes $24 \space m$ due west and then $10 \space m$ due north. How far is he from the starting point?

A.	$23.98 \space m$
B.	$32.36 \space m$
C.	$29.18 \space m$
D.	$26 \space m$

Find the length of the median $BE$ of the $\Delta ABC$ whose vertices are $A(8,13), B(10,15)$ and $C(6,11)$.

A.	$6.24$ units
B.	$4.24$ units
C.	$5.24$ units
D.	$7.24$ units

If $tan \theta + sec \theta = l$, then the value of $sec \theta$ is

A.	$\dfrac{ l^2 + 1 }{ 2l }$
B.	$\dfrac{ l^2 - 1 }{ l }$
C.	$\dfrac{ l^2 + 1 }{ l }$
D.	$\dfrac{ l^2 - 1 }{ 2l }$

In the given figure, $XY$ and $X'Y'$ are two parallel tangents to a circle with center $O$ and another tangent $AB$ with the point of contact $C$ intersects $XY$ at $A$ and $X'Y'$ at $B$. Find the measure of $\angle AOB$.

A.	$90^\circ$
B.	$75^\circ$
C.	$180^\circ$
D.	$120^\circ$

A.
B.
C.
D.

A sector is cut from a circle of diameter $28 \space cm$. If the angle of the sector is $30^\circ$, find its area.

A.	$51.33 \space cm^2$
B.	$31.33 \space cm^2$
C.	$615.44 \space cm^2$
D.	$\text { None of these }$

Sanjeewa filled a glass with water. The lower base radius and the upper base radius of the glass is $7 \space cm$ and $10 \space cm$ respectively. The height of the glass is $12 \space cm$. At first, the glass is filled full with water and the water is poured into another container which is cylindrical in shape with the diameter and the height as $30 \space cm$ and $17 \space cm$ respectively. Again the glass is filled one-fifth with water and then this water is poured into the same cylindrical container. How much more water is to be put into the cylindrical container so as to fill the container up to the brim? (Where $\pi = 3.14$)

A.	$8837.73 \space cm^3$
B.	$8787.73 \space cm^3$
C.	$8789.73 \space cm^3$
D.	$8709.73 \space cm^3$

A survey regarding the age of $81$ people was conducted and the following data was obtained:

$\begin{align} \text { Age (in years) } \end{align}$	$40 - 42$	$42 - 44$	$44 - 46$	$46 - 48$	$48 - 50$
$\begin{align} \text { Number of people } \end{align}$	$17$	$12$	$15$	$18$	$19$

Determine the modal age of people.

A.	$46.105 \space years$
B.	$46.255 \space years$
C.	$45.247 \space years$
D.	$45.533 \space years$

Three coins are tossed simultaneously $500$ times and it is found that three heads appeared $250$ times, two heads appeared $175$ times, one head appeared $50$ times and no head appeared $25$ times.
If three coins are tossed simultaneously at random, what is the probability of getting $1 \text { head }$?

A.	$0.5$
B.	$0.35$
C.	$0.1$
D.	$1$

Find the middle term of the sequence formed by all three-digit numbers which leave a remainder $3$ when divided by $5$.

A.	$538 \text { and } 558$
B.	$548 \text { and } 553$
C.	$553 \text { and } 563$
D.	$\text{ None of these}$

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

A.	6
B.	3
C.	5
D.	4

Which of following shows relation between Burger, Pizza and Food.

A.
B.
C.
D.

Find the missing number.

9	3	11
7	3	11
25	9	?

A.	44
B.	33
C.	22
D.	38

Which of the following is the next term in the series:
D, G, F, I, H, K, J, ___

A.	L
B.	S
C.	J
D.	M

Find the missing term.

A.	44
B.	40
C.	43
D.	42