A positive number $n$ when divided by $12$ leaves a remainder $5$. What is the remainder when $3 n + 8$ is divided by $12$?

A.	$5$
B.	$2$
C.	$11$
D.	$1$

If the zeros of the polynomial $x^3 - 27 x^2 + 200 x - 300$ are $(a - b), a, (a + b)$, find $a$ and $b$.

A.	$a = 1 \space \text{and} \space b = \pm \sqrt{43}$
B.	$a = 9 \space \text{and} \space b = \pm \sqrt{43}$
C.	$a = 9 \space \text{and} \space b = \pm \sqrt{443}$
D.	$\text{ None of these }$

The pair of equations y = -6 and y = -1 has

A.	two solutions
B.	a unique solution
C.	no solution
D.	infinitely many solutions

A family has 180 kg of wheat for x number of weeks. If they need to use same amount of wheat for 3 more weeks, they need to cut down their weekly consumption of wheat by 5 kgs. Find value of x.

A.	9 weeks
B.	10 weeks
C.	11 weeks
D.	7 weeks

There are $39$ trees at equal distances of $9$ meters in a line with a well, the distance of the well from the nearest tree being $12$ meters. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.

A.	$14274 \space m$
B.	$14273 \space m$
C.	$14270 \space m$
D.	$14278 \space m$

In the figure below, $ADE$ is a triangle with $\angle AED = 120^{ \circ }$, and $B$ and $C$ are points on side $AD$ such that $BCE$ is an equilateral triangle. If $AB = 2 \space cm$, $CD = 8 \space cm$ and $BC = x \space cm$, find the value of $x$.

A.	$4 \space cm$
B.	$12 \space cm$
C.	$14 \space cm$
D.	$6 \space cm$

Find the centroid of $\Delta {ABC}$ whose vertices are $A(9,12)$, $B(6,18)$ and $C(12,21)$.

A.	$(11,19)$
B.	$(12,20)$
C.	$(9,17)$
D.	$(13,21)$

If $cosec \space \theta + cot \space \theta = m,$ then $\dfrac { m^2 + 1 } { m^2 - 1 }$ is equal to:

A.	$cos \space \theta$
B.	$sin \space \theta$
C.	$sec \space \theta$
D.	$cosec \space \theta$

In the given figure, $XP$ and $XQ$ are the two tangents to a circle with center $O$ drawn from an external point $X$. $AB$ is another tangent touching the circle at $R$, then $XA + AR$ is equal to:

A.	$BQ + BR$
B.	$BQ + AP$
C.	$AR + RB$
D.	$XB + BR$

A.
B.
C.
D.

A chord of a circle of radius $42 \space cm$ subtends a right angle at the center. Find the area of the corresponding major segment.$\bigg[\pi = \dfrac { 22 } { 7 }\bigg]$

A.	$504 \space cm^2$
B.	$5040 \space cm^2$
C.	$754 \space cm^2$
D.	$\text { None of these }$

A decorative block shown in the figure is made of two solids_a cube and a hemisphere. The base of the block is the cube with edge of 5.9 cm and the hemisphere attached on the top has a diameter of 5 cm. If the block to be painted, then the total area to be painted is:

A.	228.51 cm2
B.	39.29 cm2
C.	189.22 cm2
D.	None of these

Use the method of Step-Deviation to find the mean of the data given in the table.

$\text{ Height (in cm) }$ $240-250$ $250-260$ $260-270$ $270-280$ $280-290$ $\text{ Number of plants }$ $14$ $14$ $16$ $22$ $34$

A.	279.8
B.	269.8
C.	264.8
D.	259.8

In 2008, the meteorological office predicted the weathers completely right for the months of february and april, and completely wrong for all the other months. What is the probability that the forecast was wrong for a given day that year?

A.	307 366
B.	308 366
C.	307 365
D.	59 365

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 $9$ 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.	$V_3 > V_1 > V_2$
B.	$V_1 < V_2 < V_3$
C.	$V_1 > V_2 > V_3$
D.	$V_3 < V_1 < V_2$

A dice has numbers $1$ to $6,$ such that sum of opposite faces are always $7.$ Which is the correct view of dice$?$

A.
B.
C.
D.

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.	49
B.	50
C.	47
D.	43

Find the missing number.

9	4	12
6	2	12
42	18	?

A.	60
B.	72
C.	68
D.	48

Which of the following choices would replace the blanks below
_tfx_f_tfxt_

A.	xfff
B.	txtt
C.	xtxf
D.	tfft

Find the next term of given sequence ..
11, 36, 114, 351, 1065, 3210, ....

A.	9640
B.	9648
C.	9651
D.	28944