Find the smallest number which when increased by 19 is exactly divisible by both 266 and 196.

A.	3743
B.	14
C.	3705
D.	3713

If α and β are the zeros of quadratic polynomial x² + px + 3q, find the value of α² + β².

A.	p2 - 12q
B.	p2 + 6q
C.	p2 - 6q
D.	p2 - 3q

A boat running upstream takes $5{\space} hours$ $24{\space} minutes$ to cover a certain distance, while it takes $4{\space} hours$ to cover the same distance in running downstream. What is the ratio between the speed of the boat and the speed of stream?

A.	$47:7$
B.	$57:12$
C.	$62:15$
D.	None of these

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

A.	$19$
B.	$13$
C.	$22$
D.	$14$

The sum of the first 6 terms of an arithmetic progression is 156. The ratio of term 10^th to term 30^th of the AP is 39:119. What is the value of the 78^th term of the AP?

A.	630
B.	622
C.	606
D.	614

In $\Delta ABC$, $AD \perp BC$ and $AD^2 = BD \times CD$. What is the measure of $\angle BAC$ ?

A.	$90^\circ$
B.	$80^\circ$
C.	$180^\circ$
D.	$75^\circ$

Find the coordinates of the points of trisection of the line segment joining the points $A(9, 15)$ and $B(6, 21)$.

A.	$(31 , 67) \text{ and } (17 , 29)$
B.	$(22 , 59) \text{ and } (10 , 24)$
C.	$( 8 , 17) \text{ and } (7 , 19)$
D.	$\text{None of these}$

Which of the following equals $\dfrac { sin \space x } { cos \space x } ?$

A.	$cot \space x$
B.	$tan \space x$
C.	1
D.	None of these

Marcela drew the following figure in her mathematics notebook. In which $AB$ and $BC$ are co-initial tangents drawn from an external point $A$ to the circle $OB$ and $OC$ are the radii of the circle. Then what is always true $?$

A.	$\angle OAB + \angle OBA = 90 ^ \circ$
B.	$\angle OAC + \angle AOC = 90 ^ \circ$
C.	$\angle AOB = \angle AOC = 180 ^ \circ$
D.	$\angle OBA = \angle AOB$

A.
B.
C.
D.

The perimeter of a semi-circular protractor is $133 \space cm$. What is the radius of that protractor?

A.	$38.79 \space cm$
B.	$25.86 \space cm$
C.	$51.72 \space cm$
D.	$12.93 \space cm$

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

The following table shows the number of books read by $80$ children. Find the mode of this distribution.

$\text { Number of books }$	$\text { Number of Children }$
$\text { Less than } 10$	$12$
$\text { Less than } 20$	$15$
$\text { Less than } 30$	$38$
$\text { Less than } 40$	$48$
$\text { Less than } 50$	$53$
$\text { Less than } 60$	$54$
$\text { Less than } 70$	$60$
$\text { Less than } 80$	$73$
$\text { Less than } 90$	$80$

A.	$26.06$
B.	$28.06$
C.	$26.67$
D.	$24.06$

What is the probability that an integer in the set 1, 2, 3, ...160 is divisible by 2 and not divisible by 3?

A.	24 78
B.	25 82
C.	30 81
D.	27 80

If $tan \theta = \dfrac{ a } { b }$ and $90^\circ > \theta > 0^\circ,$ find value of $sec \theta.$

A.	$\sqrt{ \dfrac{ b^2 + a^2 } { b^2 } }$
B.	$\sqrt{ \dfrac{ b^2 + a^2 } { a^2 } }$
C.	$\sqrt{ \dfrac{ b^2 } { b^2 - a^2 } }$
D.	$\sqrt{ \dfrac{ b^2 - a^2 } { b^2 } }$

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 face opposite to face E ?

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

Following chart shows number of students in a school who play one of three sports. Find the number of students who play exactly two sports.

A.	51
B.	50
C.	54
D.	52

Find the missing number.

8	2	10
8	2	10
24	6	?

A.	40
B.	38
C.	30
D.	20

Which of the following choices would replace the blank below
DFH:WUS::HJL:____

A.	TRP
B.	SPP
C.	SQO
D.	RPN

Find the next term of given sequence ..
14, 14, 17, 25, 40, 64, ....

A.	135
B.	93
C.	99
D.	123