Which of the following rational numbers are positive?

A.	$\dfrac{ 140 }{ 141 }$
B.	$\dfrac{ -47 }{ -46 }$
C.	$\dfrac{ 162 }{ 163 }$
D.	$\dfrac{ 164 }{ 165 }$

If the polynomial $p(y) = y^ { 4 }-2y^ { 3 } + 2y^ { 2 } + ky + m$ when divided by $(y - 1)$ and $(y + 1)$ leaves the remainder $7$ and $15$ then what is the remainder when it is divided by $(y - 5)$?

A.	$420$
B.	$426$
C.	$421$
D.	$423$

A point whose abscissa and ordinate are both positive will lie in the:

A.	Third quadrant
B.	Second quadrant
C.	Fourth quadrant
D.	First quadrant

A point of the form (a, a) lies on the line:

A.	x + y = 0
B.	x = 0
C.	x = y
D.	y = 0

If AB and CD are parallel, find the value of x+y.

A.	75°
B.	85°
C.	55°
D.	95°

In $\triangle PQR,$ right-angled at $Q$, we have:

A.	QR is longest
B.	PQ is longest
C.	PR is longest
D.	None of these

In the given figure, $ABCD$ is a square. A line segment $DX$ cuts the side $BC$ at $X$ and the diagonal $AC$ at $O$ such that $\angle COD = 117^\circ$ and $\angle OXC = x^\circ$. Find the value of $x$.

A.	$70^\circ$
B.	$72^\circ$
C.	$67^\circ$
D.	$73^\circ$

The area of a trapezium is 125 cm² and the distance between its parallel sides is 10 cm. If one of the parallel sides is of length 14 cm, find the length of the other side.

A.	11 cm
B.	22 cm
C.	5.5 cm
D.	9 cm

In a circle with center O, if CD = 8 cm, OA = 13 cm and OD is perpendicular to AB, then AB is:

A.	23 cm
B.	25 cm
C.	26 cm
D.	24 cm

To construct an angle of $45^\circ,$ we bisect:

A.	$120^\circ$
B.	$90^\circ$
C.	$105^\circ$
D.	$97.5^\circ$

Find the area of a quadrilateral whose sides are 5 cm, 12 cm, 10 cm and 13 cm and the angle between first two sides is a right angle.

A.	30 cm2
B.	60 cm2
C.	90 cm2
D.	234 cm2

The radius of a cylinder is halved and the height is doubled. What is the area of the curved surface now compared to the previous surface area?

A.	double
B.	four times
C.	half
D.	same

The mean of the following data is $15.24.$ The value of $t$ is:

$x_i$	$3$	$9$	$15$	$21$	$27$	$33$
$f_i$	$13$	$14$	$2$	$t$	$11$	$5$

A.	$13$
B.	$10$
C.	$5$
D.	$3$

A die is thrown $500$ times and the outcomes are noted as given below.

$Outcome$	$1$	$2$	$3$	$4$	$5$	$6$
$Frequency$	$100$	$125$	$25$	$75$	$50$	$125$

From the above table find the probability of getting $6$?

A.	$1$
B.	$0.1$
C.	$0.15$
D.	$0.25$

If xy represents a two-digit number, where x and y are positive single digits, which of the following CANNOT be true?

A.	y - x = 9
B.	8x = y
C.	y + x = 9x
D.	x = y

What is the area of an equilateral triangle with a side of $B \space cm$?

A.	$\dfrac { B \sqrt{ 3 } } {4} \space cm^2$
B.	$\dfrac { B^2 \sqrt{ 3 } } { 4 } \space cm^2$
C.	$\dfrac { B^2 } {4} \space cm^2$
D.	$B^2 \sqrt { 3 } \space cm^2$