What is the standard form of the rational number $\dfrac{ 45 }{ -84 }$?

A.	$\dfrac{ -28 }{ 15 }$
B.	$\dfrac{ -15 }{ 28 }$
C.	$\dfrac{ 15 }{ 28 }$
D.	$\dfrac{ 28 }{ 15 }$

The corners of the square $ABCD$ with side $18 \space cm$ is cut away to form an octagon $PQRSTUVW$ with all sides equal. What is the length of the side of the octagon so formed?

A.	$\dfrac{ 18 \sqrt{3} } { \sqrt{3} + 1 }$
B.	$\dfrac{ 9 \sqrt{2} } { \sqrt{2} - 1 }$
C.	$\dfrac{ 18 }{ \sqrt{2} + 1 } \space cm$
D.	$\dfrac{ 18 \sqrt{2} } { \sqrt{2} - 1 }$

Find the number of sides of a regular polygon whose each exterior angle is $30 ^ \circ.$

A.	$12$
B.	$17$
C.	$11$
D.	$14$

Find the length of each side of square whose area is equal to the area of rectangle with length $54.5 \space m$ and breadth $96.2 \space m$.

A.	$5242.9 \space m$
B.	$125.41 \space m$
C.	$102.4 \space m$
D.	$72.41 \space m$

Simplify:
$\sqrt[ 3 ]{ -1764 } \times \sqrt[ 3 ]{ 1134 }$

A.	$-252$
B.	$126$
C.	$-126$
D.	$-123$

Mathis bought a car at $€50000.$ If its value depreciates at the rate of $20 \%$ per annum, find the value of the car after $3$ years.

A.	$€28160$
B.	$€25230$
C.	$€25600$
D.	$€23040$

Let $n$ be a positive integer such that one of the roots of the quadratic equation $5 x^2 - (5 \sqrt{ 2 } + 5) x + \sqrt{ 2 } n - 280 = 0$ is an integer. Find the value of $n.$

A.	$40$
B.	$48$
C.	$44$
D.	$38$

Identify an closed curve that is made up of curved lines only.

A.
B.
C.
D.

A wireframe is bent into a circle of radius 42 cm is reshaped as a rhombus. What is the length of the side of the resulting rhombus? (assume π =  

22

7

 )

A.	64 cm
B.	62 cm
C.	69 cm
D.	66 cm

What is the value of $(-4.7)^3 + 3 \times (-4.7)^2 \times (7.7) + 3 \times (-4.7) \times (7.7)^2 + (7.7)^3 ?$

A.	$27$
B.	$-3$
C.	$9$
D.	$12.4$

Pump A and B can fill a tank in 16 minutes and 48 minutes respectively. Both the pumps started filling the tank together but Pump B stopped when the tank was half full and the rest of the tank is filled by Pump A alone. How long did it take to fill the tank?

A.	13 minutes
B.	16 minutes
C.	17 minutes
D.	14 minutes

Factorize:
$64p^2 + 2p + \dfrac{1}{ 64 }$

A.	$\left(8p - \dfrac{1}{ 8 }\right)\left(8p - \dfrac{1}{ 8 }\right)$
B.	$\left(8p + \dfrac{1}{ 8 }\right)\left(8p + \dfrac{1}{ 8 }\right)$
C.	$\left(8p + \dfrac{1}{ 8 }\right)\left(8p + 8\right)$
D.	$\left(8p + \dfrac{1}{ 8 }\right)\left(8p - 8 \right)$

The graph below shows the profit (in crores) of two companies (A and B) for ten years. Find the combined profit of two companies in the year when combined profit was maximum.

A.	108 crores
B.	110 crores
C.	109 crores
D.	111 crores

In a $3$-digit number, the hundreds digit is $thrice$ the tens digit while the units digit is $four \space times$ the tens digit. Also, the sum of its digits is $16$. Find the number.

A.	$826$
B.	$268$
C.	$628$
D.	$682$

Coline covers a certain distance in a certain time. If  

2

3

  of the distance is covered in  

1

3

  of the time with speed V₁ and the rest of the  

1

3

  distance in  

2

3

  of the time with speed V₂, then find the ratio V₁:V₂.

A.	4:1
B.	1:2
C.	2:1
D.	1:4

A man sells an article at a profit of $25\%$. If he had bought it at $20\%$ less and sold for $€44$ less, he would have gained $25\%$. Find the cost price of the article.

A.	$€166$
B.	$€186$
C.	$€276$
D.	$€176$

Clement borrowed a certain amount of money from Alice at $20 \%$ simple interest per annum. He returned $€135000$ at the end of $10$ years. Find the amount of money borrowed by him.

A.	$€45000$
B.	$€47000$
C.	$€44000$
D.	$€46000$

Find compound interest on $€80000$ for $1$ year at $6 \%$ per annum compounded half yearly.

A.	$€ 4849$
B.	$€ 4884$
C.	$€ 4872$
D.	$€ 4934$

If F1 = -6y + 9, F2 = -7y and F3 = 6y + 3, simplify F1 × F2 + F3 in terms of y.

A.	42y2 - 57y + 3
B.	42y2 + 57y + 3
C.	-42y2 - 57y + 3
D.	42y2 - 57y - 3

Divide $16x^ { 3 } + 42x^ { 2 } + 12x-5$ by $2x^ { 2 } + 4x-1$.

A.	$8x + 5$
B.	$-3x^ { 2 }-3x-5$
C.	$2x^ { 2 }-7x-1$
D.	$-x-4$

A card is drawn from a shuffled deck of $52$ cards. What is the probability of getting a card greater than $4$ but lesser than $7$?

A.	$\dfrac { 2 } { 13 }$
B.	$\dfrac {1} { 52 }$
C.	$\dfrac { 4 } { 52 }$
D.	$\dfrac { 2 } { 52 }$

What is the next number in the series: 1, 2, 4, 3, 9, 4?

A.	16
B.	25
C.	4
D.	9