The $L.C.M.$ and $H.C.F.$ of marks scored by Vincent and Jason in a math test are $5420$ and $15$ respectively. If Jason's score is $100,$ what is Vincent's score?

A.	$813$
B.	$816$
C.	$809$
D.	$819$

If the zeros of the polynomial $x^3 - 4 x^2 - 49 x + 196$ are $(a - b), a, (a + b)$, find $a$ and $b$.

A.	$a = \dfrac { 3 } { 4 } \space \text{and} \space b = \pm \sqrt{\dfrac { 163 } { 3 }}$
B.	$a = \dfrac { 4 } { 3 } \space \text{and} \space b = \pm \sqrt{\dfrac { 163 } { 2 }}$
C.	$a = \dfrac { 4 } { 3 } \space \text{and} \space b = \pm \sqrt{\dfrac { 163 } { 3 }}$
D.	$\text{ None of these }$

Graph of a homogeneous system of equations is

A.	always coincident
B.	always intersecting
C.	parallel
D.	intersecting or coincident

Suppose that the two roots of the equation are $\alpha$ and $\beta$. Find the value of $\alpha + \beta$.

A.	$6$
B.	$14$
C.	$9$
D.	$5$

The angles of a quadrilateral are in AP whose common difference is $10^\circ$. Find the largest angle of the quadrilateral.

A.	$90^\circ$
B.	$115^\circ$
C.	$105^\circ$
D.	$\text{ None of these}$

In a trapezium $ABCD$ , $O$ is the point of intersection of $AC$ and $BD$. $AB || CD$ and $AB = 2 \times CD$. If the area of $\Delta AOB = 72 \space cm^2$, find the area of $\Delta COD$.

A.	$21 \space cm^2$
B.	$19 \space cm^2$
C.	$18 \space cm^2$
D.	$20 \space cm^2$

If $A(5, 3)$, $B(11, -5)$, and $P(12, y)$ are the vertices of a right-angled triangle, right angled at $P$, then $y$ is.

A.	$-2, 4$
B.	$2, 4$
C.	$-2, -4$
D.	$2, -4$

Simplify: $\cot^2 \theta \left( \dfrac{ \sec \theta - 1 } { 1 + \sin \theta } \right) + \sec^2 \theta \left( \dfrac{ \sin\theta - 1 } { 1 + \sec \theta } \right)$

A.	$1 + sin\theta cos\theta$
B.	$1 - sin\theta cos\theta$
C.	$0$
D.	$1$

In the given figure, $PA$ is a tangent from an external point $P$ to a circle with center $O$. If $\angle BOP = 140^\circ$, find $\angle APO$.

A.	$55^\circ$
B.	$50^\circ$
C.	$60^\circ$
D.	$65^\circ$

A.
B.
C.
D.

In a circle of radius $11 \space cm$, an arc subtends an angle of $45^\circ$ at the centre. Find the length of the arc.

A.	$47.54 \space cm$
B.	$8.64 \space cm$
C.	$15.13 \space cm$
D.	$\text { None of these }$

A decorative used by the turks is shaped like the frustum of a cone. If the radius of the open side is $15 \space cm$, the radius of the closed base is $26 \space cm$ and its slant height is $22 \space cm.$ Find the area of the material used for making it.

A.	$210.57 \space cm^2$
B.	$4959.43 \space cm^2$
C.	$928 \space cm^2$
D.	$\text { None of these }$

Find the mode of the following data:

$\begin{align} \text { Age (in years) } \end{align}$ $30 - 38$ $39 - 47$ $48 - 56$ $57 - 65$ $66 - 74$ $\begin{align} \text { Number of people } \end{align}$ $46$ $34$ $37$ $130$ $33$

A.	$55.91\space years$
B.	$62.91 \space years$
C.	$60.91 \space years$
D.	$61.61\space years$

Two coins are tossed simultaneously. What is the probability of getting both tails?

A.	$\dfrac { 1 } { 4 }$
B.	$\dfrac { 3 } { 4 }$
C.	$\dfrac { 1 } { 2 }$
D.	$\dfrac { 3 } { 5 }$

If there are $(2n + 1)$ terms in an $A.P.$, then the ratio of the sum of odd terms and the sum of even terms is

A.	$(n + 1):n$
B.	$n:(n + 1)$
C.	$(n + 2):n$
D.	$n:(n + 2)$

Faces of a cube are marked with A,B,C,D,E and F. If three views of cube are as shown below, what will be there on the face opposite to face D?

A.	B
B.	D
C.	C
D.	A

Which of following shows relation between Aluminum, Silver and Metal.

A.
B.
C.
D.

Find the next term of given sequence ..
6, 10, 18, 34, 66, 130, ....

A.	258
B.	256
C.	266
D.	251

Which of the following choices would replace the blanks below
_abaa_baaab_a_ba

A.	aaba
B.	abaa
C.	baaa
D.	aaaa

Six friends A, B, C, D, E and F are sitting in a circle facing the center. B is not between F and E but some other one. A is next to the left of C. D is 4^th to right of A. Which of the following statements is not true?

A.	C is third to the right of D
B.	A is second to the right of D
C.	C is just next to the right of A
D.	D is third to the left of A