Tatiana and George are racing on a circular track. If Tatiana takes 48 minutes and George takes 40 minutes to complete the round. If they both start at the same point at the same time and go in same direction, after how many minutes will they meet again at the start point?

A.	35
B.	240
C.	30
D.	None of above

Find the product of the zeroes of the polynomial m² + 13m + 40.

A.	40
B.	20
C.	-40
D.	80

Find the values of $p$ and $q$ for which the following pair of linear equations have an infinite number of solutions: $$2x + 7y = 4, (p + q)x + (p - q)y = (2p - 20)$$

A.	$\begin{aligned}p = 17 \text{ and } & q = -12\end{aligned}$
B.	$\begin{aligned}p = 20 \text{ and } & q = -10\end{aligned}$
C.	$\begin{aligned}p = 18 \text{ and } & q = -10\end{aligned}$
D.	$\begin{aligned}p = 18 \text{ and } & q = -7\end{aligned}$

Alex buys a number of notebooks for $€60$. If he had bought $2$ more notebooks for the same amount, each notebook would have cost $€1$ less. How many notebooks did he buy?

A.	$12$
B.	$13$
C.	$10$
D.	$11$

In an arithmetic progression, the value of the 20^th element is  

1

21

 , and the value of 21^st element is  

1

20

 . What is the value of 420^th element?

A.	2
B.	1
C.	-1
D.	-3

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

A.	$60^\circ$
B.	$90^\circ$
C.	$180^\circ$
D.	$80^\circ$

Are the points $A(p,q - r), B(q,p - r),$ and $C(r,p - q)$ collinear?

A.	Yes
B.	No
C.
D.

Two poles of equal heights are standing opposite to each other on either side of the road which is $20 \space meters$ wide. From a point between them on the road, the angles of elevation of the top of the poles are $30^\circ$ and $45^\circ$ respectively. Find the height of the poles.

A.	$10 ( \sqrt { 3 } - 1) \space meters$
B.	$\dfrac { 20 } { \sqrt { 3 } } \space meters$
C.	$\dfrac { 22 } {1 + \sqrt { 3 }} \space meters$
D.	$\text{ None of these }$

In the given figure, two circles touch each other at a point $C$. Which of the following is true?

A.	$PR = QR$
B.	$PA = PR$
C.	$BQ = RQ$
D.	$\text { None of these }$

A.
B.
C.
D.

If the perimeter of a semi-circular protractor is $98 \space cm$, find the radius of the protractor.

A.	$19.06 \space cm$
B.	$24.06 \space cm$
C.	$686 \space cm$
D.	$\text { None of these }$

Choose the maximum volume of a cone that can be carved out of a solid hemisphere of radius r.

A.	1 5   πr3
B.	3πr3
C.	1 3   πr3
D.	None of these

Compare the modal salary of two groups of employees in a company.

$\begin{align} \text { Salary (in thousands) } \end{align}$ $110 - 114$ $114 - 118$ $118 - 122$ $122 - 126$ $126 - 130$ $130 - 134$ $\begin{align} \text { Group A } \end{align}$ $102$ $1$ $114$ $65$ $70$ $91$ $\begin{align} \text { Group B } \end{align}$ $75$ $104$ $89$ $138$ $64$ $31$

A.	$($modal salary of group $A)>($modal salary of group $B).$
B.	$($modal salary of group $A)$$<$$($modal salary of group $B).$
C.	$($modal salary of group $A)=($modal salary of group $B).$
D.	None of these

A poll is taken among $10000$ people working in Munich. The aim was to see what their annual salaries were.

Annual Salary	Number of people
Less than $€40000$	$100$
$€40001$ to $€75000$	$760$
$€75001$ to $€150000$	$1060$
$€150001$ to $€250000$	$3232$
More than $€250000$	$4848$

If you choose a person at random from this group, what is the probability that he or she earns more than $€150000$ annually?

A.	$\dfrac { 101 } { 125 }$
B.	$\dfrac { 103 } { 125 }$
C.	$\dfrac { 110 } { 125 }$
D.	$\dfrac { 115 } { 125 }$

In a two digit number,its unit's digit is 6 more than ten's digit. If sum of this number and the number obtained by reversing the order of its digits is 110, find the number.

A.	17
B.	28
C.	39
D.	82

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 A?

A.	A
B.	C
C.	B
D.	F

In this diagram, the triangle represents women, the square represents lawyers and the circle represents tall. Find the number of women who are tall but not lawyers.

A.	8
B.	3
C.	7
D.	9

Find the next term of given sequence ..
-2, 8, 22, 40, 62, , ....

A.	88
B.	92
C.	176
D.	80

Which of the following is the next two terms in the series:
F, C, I, D, L, E, O, F, ___, ____

A.	R, G
B.	S, F
C.	Q, G
D.	Q, F

Find the next term of given sequence ..
$6, 21, 66, 201, 606, 1821, ....$

A.	5472
B.	5466
C.	5469
D.	5460