The rational number that does not have a reciprocal is

A.	1
B.	2
C.	3
D.	0

If the number in the center is the sum of all other numbers, find the value of b.
(Clarification: In the figure, the terms containing b are products of b with single digit numbers.)

A.	0
B.	1
C.	3
D.	2

Each side of an equilateral triangle is increased by $2\%$. The percentage increase in its area is

A.	$14.04\%$
B.	$6.04\%$
C.	$2.04\%$
D.	$4.04\%$

Which is the smallest number that can be used to divide 29040 to give a perfect square?

A.	12
B.	5
C.	15
D.	18

Find the value of $A$ if
$\sqrt[3] { 392 \times A } = 14$

A.	7
B.	$11$
C.	$2$
D.	$8$

Find the compound interest on $2000$ at the rate of $10\%$ p.a. for $18$ months when interest is compounded half-yearly.

A.	$¥335.25$
B.	$¥315.25$
C.	$¥311.25$
D.	$¥355.25$

What is the value of $\left(-3a^{ 2 } + 3\right)\left(5a^{ 4 } - 5\right)$ at $a = -2$?

A.	$275$
B.	$-275$
C.	$675$
D.	$-675$

$ABCD$ is a parallelogram as shown below. If $AB=2AD$ and $P$ is the midpoint of $AB,$ then find $\angle CPD.$

A.	$135^\circ$
B.	$60^\circ$
C.	$90^\circ$
D.	$45^\circ$

The area of a rhombus is 68 cm² and one of it's diagonal is 17 cm. Find the length of the other diagonal.

A.	8 cm
B.	6 cm
C.	11 cm
D.	4 cm

If the mean of three numbers $x, \space y$ and $z$ is $6$, then find the value of
$\sqrt[3]{ (3^{ x + y - z }) (3^{ y + z - x}) (3^{ z + x - y}) }$.

A.	$3^{ 9 }$
B.	$3^{ 3 }$
C.	$3^ {\dfrac{1}{ 6 }}$
D.	$3^ { 6 }$

Katashi alone can do a piece of work in $20$ days and Chou alone can do the same work in $14$ days. If Chou works for $7$ days and then leaves, then in how many days can Katashi alone finish the remaining work$?$

A.	$10$ days
B.	$9$ days
C.	$15$ days
D.	$16$ days

Factorize:
$p^2 - p(x + 5y) + 5xy$

A.	$(p - 5x)(p - y)$
B.	$(p - x)(p - 5y)$
C.	$(p + x)(p + 5y)$
D.	$(p + 5x)(p + y)$

A point whose y-coordinate is zero and x-coordinate is non-zero will lie on which axis?

A.	x axis
B.	y axis
C.	Depends on value of x-coordinate
D.	Cannot be determined

If a number is divided by 5, remainder is 3. If same number is divided by 2, remainder is 1. What should be the last digit of the number?

A.	3
B.	8
C.	5
D.	4

Find the median of the following set:

$10, 20, 13, 14, 14, 15, 22, 21, 15, 11, 20$

A.	$15$
B.	$13$
C.	$16$
D.	$17$

Keiji makes a profit of $¥ 35$ if he sells a certain number of pencils he has at the price of $¥ 2.05$ per pencil and incurs a loss of $¥ 40$ if he sells the same number of pencils of $¥ 1.55$ per pencil. What should be the selling price of all the pencils in order to make a profit of $15\%$?

A.	$¥323.375$
B.	$¥311$
C.	$¥313.375$
D.	$¥613.375$

How long will it take for an amount to become double of itself at 4% per annum simple interest?

A.	23 years
B.	27 years
C.	25 years
D.	24 years

The value of a property increases every year at the rate of $20\%$. If its value at the end of $3\%$ years is $¥224640$, what was its original value at the beginning of these years?

A.	$¥250000$
B.	$¥130000$
C.	$¥400000$
D.	$¥300000$

Find product of following polynomials:
(3p² - 3p + 3) and (2p² + 4p + 2)

A.	6p4 - 6p3 + 6p + 6
B.	6p4 + 6p3 - 6p + 6
C.	6p4 + 6p3 + 6p - 6
D.	6p4 + 6p3 + 6p + 6

(5q² + 4pq - 35q - 28p) ÷ (q - 7) = ?

A.	-4p + 5q
B.	5q + 4p
C.	-4p - 5q
D.	-5p + 4q

From a deck of cards, Daisuke took out one card at random. What is the probability that he got a prime number?

A.	4 13
B.	2 13
C.	6 13
D.	7 13

Four friends Hiroyuki, Juro, Kazou, and Aimi are standing in a row. Hiroyuki is not standing at the first position. Juro is not standing at the last position. Kazou is standing behind Juro. Aimi is standing between Kazou and Hiroyuki.
Who is standing at first position?

A.	Aimi
B.	Kazou
C.	Hiroyuki
D.	Juro