A number, when divided by 30 gives 55 as the quotient and 18 as the remainder. Find the number.

A.	1678
B.	1650
C.	1668
D.	None of these

If two zeros of polynomial x³ + bx² + cx + d are 1+√2 and 1-√2, find its third zero.

A.	c - 2
B.	-b - 2
C.	b - 2
D.	- c - 2

Find the values of $p$ and $q$ for which the following pair of linear equations have an infinite number of solutions: $$6x + y = 3, (p + q)x + (p - q)y = (2p - 24)$$

A.	$\begin{aligned}p = 21 \text{ and } & q = 16\end{aligned}$
B.	$\begin{aligned}p = 21 \text{ and } & q = 15\end{aligned}$
C.	$\begin{aligned}p = 26 \text{ and } & q = 15\end{aligned}$
D.	$\begin{aligned}p = 20 \text{ and } & q = 13\end{aligned}$

The sum of the n consecutive natural numbers starting from 5 is 68. Find the value of n.

A.	8
B.	10
C.	7
D.	9

Which term in the arithmetic progression 8, 17, 26, 35 will be 261 more than the 30^th term?

A.	59
B.	56
C.	58
D.	62

Two poles of heights $20 \space metres$ and $40 \space metres$ stand vertically on a plane ground. If the distance between their feet is $21 \space metres$, find the distance between their tops.

A.	$29 \space m$
B.	$36 \space m$
C.	$31 \space m$
D.	$28 \space m$

If $A(2,8)$, $B(6 , y)$, $C(x, 4)$ and $D(0, 4)$ are the vertices of a parallelogram $ABCD$, find the values of $x$ and $y$.

A.	$x = 4, y = 8$
B.	$x = 8 , y = 12$
C.	$x = 6 , y = 10$
D.	$x = 7 , y = 11$

An equilateral triangle with a side of length 14√3 cm is inscribed in a circle. Find the radius of the circle.

A.	14√2 cm
B.	11.2 cm
C.	7 cm
D.	14 cm

If the lengths of tangents drawn from an external point $A$ to a point $P$ and $Q$ on the circle are equal then $AP$ is equal to:

A.	$OP$
B.	$AQ$
C.	$OQ$
D.	$OA$

A.
B.
C.
D.

A chord of a circle of radius $28 \space cm$ subtends a right angle at the center. Find the area of the corresponding major segment.$\bigg[\pi = \dfrac { 22 } { 7 }\bigg]$

A.	$224 \space cm^2$
B.	$2240 \space cm^2$
C.	$474 \space cm^2$
D.	$\text { None of these }$

There is a cylindrical scale holder of height $12 \space cm$ and diameter $14 \space cm$. Now the scale holder is cut into two pieces such that the height of the new scale holder is reduced to $\left(\dfrac{ 5 }{ 6 } \right)^{th}$ of the height. The diameter of the new scale holder remains the same. If the new scale holder is filled with water up to the brim, then find the amount of water held in liters. (Where $\pi = 3.14$)

A.	$1846.32 \space l$
B.	$184.632 \space l$
C.	$1.84632 \space l$
D.	$18.4632 \space l$

Calculate the median for the following data:

$\text{ Marks obtained }$	$\text{ Number of students }$
$\text{ Less than } 10$	$16$
$\text{ Less than } 20$	$44$
$\text{ Less than } 30$	$58$
$\text{ Less than } 40$	$80$
$\text{ Less than } 50$	$101$
$\text{ Less than } 60$	$126$
$\text{ Less than } 70$	$153$
$\text{ Less than } 80$	$174$

A.	$45.333$
B.	$44.333$
C.	$41.333$
D.	$43.333$

Two dice are rolled. What is the probability that the two numbers add up to a prime number?

A.	12 36
B.	19 36
C.	17 36
D.	15 36

If the zeros of the polynomial $x^3 - 10 x^2 + 27 x - 18$ are $(a - b), a, (a + b)$, find $a$ and $b$.

A.	$a = \dfrac { 10 } { 3 } \space \text{and} \space b = \pm \sqrt{\dfrac { 19 } { 2 }}$
B.	$a = \dfrac { 10 } { 3 } \space \text{and} \space b = \pm \sqrt{\dfrac { 19 } { 3 }}$
C.	$a = \dfrac { 3 } { 10 } \space \text{and} \space b = \pm \sqrt{\dfrac { 19 } { 3 }}$
D.	$\text{ None of these }$

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

A.	F
B.	B
C.	D
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.	45
B.	38
C.	42
D.	44

Find the missing number

8	4	11
52	32	?

A.	55
B.	67
C.	79
D.	71

Which is the odd one out in this set:
XCI, HMT, GLR, JOU

A.	HMT
B.	GLR
C.	XCI
D.	JOU

Which is the odd one out in this set:
     nails, lanis, slain, snail

A.	nails
B.	lanis
C.	snail
D.	slain