Find the smallest number which when increased by 13 is exactly divisible by both 252 and 154.

A.	2772
B.	2804
C.	2759
D.	14

If two zeros of polynomial $x^3 + bx^2 + cx + d$ are $2 + \sqrt{ 2 }$ and $2 - \sqrt{ 2 }$, find its third zero.

A.	$- c - 4$
B.	$-b - 4$
C.	$c - 4$
D.	$4 - b$

A sailer can row $30{\space} km$ downstream in $4{\space} hours$ and $8{\space} km$ upstream in $6 {\space}hours$. Find the speed of the sailer in still water.

A.	$9.42{\space} km/h$
B.	$14.42{\space} km/h$
C.	$4.42{\space} km/hr$
D.	None of these

Shreya buys a number of toys for $$24$. If she had bought $2$ more toys for the same amount, each toy would have cost $$1$ less. How many toys did she buy?

A.	$7$
B.	$9$
C.	$8$
D.	$6$

If the sum of the first $n$ terms of an arithmetic progression is given by the equation $21 n + 3n^2 ,$ then what is the $21^{ st }$ element of this $AP?$

A.	$156$
B.	$150$
C.	$138$
D.	$144$

A right-angle triangle has a hypotenuse of length $p \space cm$ and one side of length $q \space cm$. If $p - q = 1 \space cm$, then the length of the third side of the triangle is

A.	$\sqrt{ p - q } \space cm$
B.	$\sqrt{p} + \sqrt{q} \space cm$
C.	$\sqrt{ 1 + 2q } \space cm$
D.	$\sqrt{p} - \sqrt{q} \space cm$

Find the area of a parallelogram $ABCD$ with vertices $A(10,-4)$, $B(22 + \sqrt { 3 }, -4)$, and $C(12,-16)$.

A.	$92.39 {\space} \text{sq.unit}$
B.	$264.78 {\space} \text{sq.unit}$
C.	$164.78 {\space} \text{sq.unit}$
D.	None of these

If $m \space tan 30^\circ cot 60^\circ = tan 45^\circ cos 45^\circ$ , then the value of $m$ is

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

In the given figure, $ABCD$ is a quadrilateral such that $\angle D = 90^\circ$. A circle with center $O$ and radius $r$, touches the sides $AB, BC, CD,$ and $DA$ at $P, Q, R,$ and $S$ respectively. If $BC = 59 \space cm, CD = 44 \space cm$, and $BP = 49 \space cm.$ What is the radius of the circle?

A.	$34 \space cm$
B.	$39 \space cm$
C.	$41 \space cm$
D.	$36 \space cm$

A.
B.
C.
D.

A sector is cut from a circle of diameter $42 \space cm$. If the angle of the sector is $90^\circ$, find its area.

A.	$326.5 \space cm^2$
B.	$346.5 \space cm^2$
C.	$1384.74 \space cm^2$
D.	$\text { None of these }$

A drinking glass is in the shape of a frustum of a cone of height $15 \space cm$. The diameters of its two circular ends are $14 \space cm$ and $10 \space cm$. Find the capacity of the drinking glass.(Use $\pi = \dfrac { 22 } { 7 }$)

A.	$109\space cm^3$
B.	$1812.86 \space cm^3$
C.	$1712.86 \space cm^3$
D.	$\text { None of these }$

The salary of the employees was noted and the data was recorded in the table given below.

$\begin{align} \text { Salary (in thousands) } \end{align}$ $4 - 13$ $14 - 23$ $24 - 33$ $34 - 43$ $44 - 53$ $\begin{align} \text { Number of employees } \end{align}$ $16$ $7$ $11$ $19$ $4$

Which of the following option is correct.

A.	$\text { mode } > \text { mean }$
B.	$\text { mode } < \text { mean }$
C.	$\text { mode } = \text { mean }$
D.	$\text{None of these}$

Katie and Chloe each have a bag that contains one ball each of the colors black, pink, orange, blue and red. Katie randomly selects a ball from her bag and puts it in Chloe's bag. Then Chloe randomly selects a ball from her bag and puts it in Katie's bag. What is the probability that after this the contents of the bag are the same as before?

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

An equilateral triangle has side length 9 cm. What is the area of a region of all the points outside the equilateral triangle that are within 3 cm of the triangle?

A.	81 + 9π cm2
B.	54 - 3π cm2
C.	27 + 3π cm2
D.	68 - 9π cm2

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 top when D is at the bottom?

A.	A
B.	E
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.	44
B.	45
C.	41
D.	43

Find the next term of given sequence.
20, 22, 25, 30, 37, 48, 61, ....

A.	86
B.	70
C.	78
D.	81

Which is the odd one out in this set
bino, ekqw, hntz, ciou

A.	ciou
B.	bino
C.	ekqw
D.	hntz

Find the next term of given sequence.
21, 41, 61, 81, 101, 121, 141, ....

A.	153
B.	161
C.	168
D.	181