25365 + Interview Questions in Mathematics Page 181 InterviewSolution

9001.	Fill in the blank with the correct option. A linear equation in one variable is _________.
Answer» Fill in the blank with the correct option. A linear equation in one variable is _________.

Discussion

9002.	If 152+a2=b2, then find a and b respectively.
Answer» If $15^{2} + a^{2} = b^{2},$ then find $a$ and $b$ respectively.

Discussion

9003.	Question 3In a huge park people are concentrated at three points (see the given figure)A: where there are different slides and swings for children,B: near which a man-made lake is situated,C: which is nearto a large parking and exit.Where should an ice-cream parlour be set up so that maximum number of persons can approach it?
Answer» Question 3 In a huge park people are concentrated at three points (see the given figure) A: where there are different slides and swings for children, B: near which a man-made lake is situated, C: which is nearto a large parking and exit. Where should an ice-cream parlour be set up so that maximum number of persons can approach it?

Discussion

9004.	If area of trapezium is 45cm2 if distance betweebetween parallel sides is 6cm and of the parallel sides is 10cm. Find the other??
Answer» If area of trapezium is 45cm² if distance betweebetween parallel sides is 6cm and of the parallel sides is 10cm. Find the other??

Discussion

9005.	Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Then which of the following options is correct?
Answer» Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Then which of the following options is correct?

Discussion

9006.	Is it possible to construct a rhombus AJUN with AU = 24 cm and JN = 10 cm? If yes, what is the length of the side of the rhombus?
Answer» Is it possible to construct a rhombus AJUN with AU = 24 cm and JN = 10 cm? If yes, what is the length of the side of the rhombus?

Discussion

9007.	If ∣∣∣z−z1z−z2∣∣∣ = 3, Where z1 and z2 are fixed complex numbers and z is a variable complex number, then 'z' lies on a:
Answer» If $∣ ∣ ∣ \frac{z - z_{1}}{z - z_{2}} ∣ ∣ ∣$ = 3, Where $z_{1}$ and $z_{2}$ are fixed complex numbers and z is a variable complex number, then 'z' lies on a:

Discussion

9008.	How to do square root while using pythogoras property
Answer» How to do square root while using pythogoras property

Discussion

9009.	A number is called a triangular number if its dot pattern can be arranged in
Answer» A number is called a triangular number if its dot pattern can be arranged in

Discussion

9010.	If a + b = 7 and ab = 12, find the value of a2 + b2
Answer» If a + b = 7 and ab = 12, find the value of a² + b²

Discussion

9011.	Salma runs 7 rounds of a circular field and covered a distance of 5.6 km. Find the diameter of the field (upto 3 decimal places) if perimeter is 3.14 times the diameter.
Answer» Salma runs 7 rounds of a circular field and covered a distance of 5.6 km. Find the diameter of the field (upto 3 decimal places) if perimeter is 3.14 times the diameter.

Discussion

9012.	The factorisation of x2−5x+6 is
Answer» The factorisation of $x^{2} - 5 x + 6$ is

Discussion

9013.	Question 7Write the correct answer from the given four options. The one's digit of the cube of 23 isa) 6b) 7c) 3d) 9
Answer» Question 7 Write the correct answer from the given four options. The one's digit of the cube of 23 is a) 6 b) 7 c) 3 d) 9

9013.

Question 7Write the correct answer from the given four options. The one's digit of the cube of 23 isa) 6b) 7c) 3d) 9

Answer»

Question 7

Write the correct answer from the given four options.

The one's digit of the cube of 23 is

a) 6

b) 7

c) 3

d) 9

Discussion

9014.	In the given figure, ABCD is a parallelogram. E is a point on DC. If AE bisects ∠A and BE bisects ∠B, then BC : AB = ___.
Answer» In the given figure, ABCD is a parallelogram. E is a point on DC. If AE bisects $∠$ A and BE bisects $∠$ B, then BC : AB = ___.

9014.

In the given figure, ABCD is a parallelogram. E is a point on DC. If AE bisects ∠A and BE bisects ∠B, then BC : AB = ___.

Answer»

In the given figure, ABCD is a parallelogram. E is a point on DC. If AE bisects $∠$ A and BE bisects $∠$ B, then BC : AB = ___.

Discussion

9015.	Which of the following equations are linear equation in two variables?
Answer» Which of the following equations are linear equation in two variables?

Discussion

9016.	How many diagonals can a pentagon have?
Answer» How many diagonals can a pentagon have?

Discussion

9017.	Question 13In figure, arcs have been drawn with radii, 14 cm each and with centres P,Q and R. Find the area of the shaded region.
Answer» Question 13 In figure, arcs have been drawn with radii, 14 cm each and with centres P,Q and R. Find the area of the shaded region.

Discussion

9018.	A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
Answer» A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

Discussion

9019.	The number of integers n(
Answer» The number of integers n(<20) for which n 2 −3n+3 is a perfect square is

Discussion

9020.	The organizers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win, gets a prize of ₹25. The total prize money distributed is ₹3,000. Find the number of winners, if the total number of participants is 63.
Answer» The organizers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win, gets a prize of ₹25. The total prize money distributed is ₹3,000. Find the number of winners, if the total number of participants is 63.

Discussion

9021.	Question 106 (ii) The students of Anuj's class sold posters to raise money. Anuj wanted to create a ratio for finding the amount of money her class would make for different numbers of posters sold. She knew they could raise Rs. 250 for every 60 posters sold Could Anu's class raise exactly Rs. 2000? if so how any posters would they need to sell? if not , why?
Answer» Question 106 (ii) The students of Anuj's class sold posters to raise money. Anuj wanted to create a ratio for finding the amount of money her class would make for different numbers of posters sold. She knew they could raise Rs. 250 for every 60 posters sold Could Anu's class raise exactly Rs. 2000? if so how any posters would they need to sell? if not , why?

9021.

Question 106 (ii) The students of Anuj's class sold posters to raise money. Anuj wanted to create a ratio for finding the amount of money her class would make for different numbers of posters sold. She knew they could raise Rs. 250 for every 60 posters sold Could Anu's class raise exactly Rs. 2000? if so how any posters would they need to sell? if not , why?

Answer»

Question 106 (ii)

The students of Anuj's class sold posters to raise money. Anuj wanted to create a ratio for finding the amount of money her class would make for different numbers of posters sold. She knew they could raise Rs. 250 for every 60 posters sold
Could Anu's class raise exactly Rs. 2000? if so how any posters would they need to sell? if not , why?

Discussion

9022.	22. How many alternate faces are their in simple cube.
Answer» 22. How many alternate faces are their in simple cube.

Discussion

9023.	Find the product:
Answer» Find the product:

9023.

Find the product:

Answer»

Find the product:

Discussion

9024.	√288√128=? (a) √32 (b) 3√2 (c) 32 (d) 1.49
Answer» $\frac{\sqrt{288}}{\sqrt{128}} = ?$ (a) $\frac{\sqrt{3}}{2}$ (b) $\frac{3}{\sqrt{2}}$ (c) $\frac{3}{2}$ (d) 1.49

Discussion

9025.	A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find the total length of wire required and the area of each sector. [3 MARKS]
Answer» A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find the total length of wire required and the area of each sector. [3 MARKS]

9025.

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find the total length of wire required and the area of each sector. [3 MARKS]

Answer»

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find the total length of wire required and the area of each sector. [3 MARKS]

Discussion

9026.	In the given figure, AB is the chord to the circle centred at O. If AC = CB and ∠AOC=60∘, then find ∠CAO.
Answer» In the given figure, AB is the chord to the circle centred at O. If AC = CB and $∠ A O C = 60^{\circ}$ , then find $∠ C A O$ .

Discussion

9027.	A point (2,4) is translated through a distance of 5 units horizontally along positive x - axis. The new point is
Answer» A point $(2, 4)$ is translated through a distance of $5$ units horizontally along positive x - axis. The new point is

Discussion

9028.	The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the difference between the measure of the largest angle and the smallest angle.
Answer» The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the difference between the measure of the largest angle and the smallest angle.

Discussion

9029.	A can do a piece of work in 12 days. B can do this work in 16 days. A started the work alone. After how many days should B join him, so that the work is finished in 9 days?
Answer» $A$ can do a piece of work in $12$ days. $B$ can do this work in $16$ days. $A$ started the work alone. After how many days should $B$ join him, so that the work is finished in $9$ days?

Discussion

9030.	The polynomial x2 + y2 – z2 – 2xy on factorization gives _____________.
Answer» The polynomial x² + y² – z² – 2xy on factorization gives _____________.

Discussion

9031.	For the function y=6−5x, the value of y, when x=1 can be given by .
Answer» For the function $y = 6 - 5 x$ , the value of $y$ , when $x = 1$ can be given by .

Discussion

9032.	The number of squares on a coordinate plane with one vertex at A(-2, 2)and atleast one of the coordinate axes as axis of symmetry of the square is
Answer» The number of squares on a coordinate plane with one vertex at A(-2, 2) and atleast one of the coordinate axes as axis of symmetry of the square is

Discussion

9033.	Arun makes a cuboid of wood of sides 7cm, 4cm, 3cm How many such minimum number of cuboids will he need to form a cube?
Answer» Arun makes a cuboid of wood of sides 7cm, 4cm, 3cm How many such minimum number of cuboids will he need to form a cube?

Discussion

9034.	The total number of parallelograms in this figure is ___
Answer» The total number of parallelograms in this figure is ___

9034.

The total number of parallelograms in this figure is ___

Answer»

The total number of parallelograms in this figure is

___

Discussion

9035.	PQNM and ZYXW are two rectangular doors used for the main door and a cupboard. Find the ratio of their sides.
Answer» PQNM and ZYXW are two rectangular doors used for the main door and a cupboard. Find the ratio of their sides.

Discussion

9036.	Prepare a continuous grouped frequency distribution from the following data.Mid-PointFrequency5415825133512456Also, find the size of class intervals.
Answer» Prepare a continuous grouped frequency distribution from the following data. $\begin{matrix} Mid-Point & Frequency 5 & 4 15 & 8 25 & 13 35 & 12 45 & 6 \end{matrix}$ Also, find the size of class intervals.

Discussion

9037.	Evaluate : (i) (3x+12)(2x+13) (ii) (2a+0.5)(7a−0.3) (iii) (9−y)(7+y) (iv) (2−z)(15−z) (v) (a2+5)(a2−3) (vi) (4−ab)(8+ab) (vii) (5xy−7)(7xy+9) (viii) (3a2−4b2)(8a2−3b2)
Answer» Evaluate : (i) $(3 x + \frac{1}{2}) (2 x + \frac{1}{3})$ (ii) $(2 a + 0.5) (7 a - 0.3)$ (iii) $(9 - y) (7 + y)$ (iv) $(2 - z) (15 - z)$ (v) $(a^{2} + 5) (a^{2} - 3)$ (vi) $(4 - a b) (8 + a b)$ (vii) $(5 x y - 7) (7 x y + 9)$ (viii) $(3 a^{2} - 4 b^{2}) (8 a^{2} - 3 b^{2})$

9037.

Evaluate : (i) (3x+12)(2x+13) (ii) (2a+0.5)(7a−0.3) (iii) (9−y)(7+y) (iv) (2−z)(15−z) (v) (a2+5)(a2−3) (vi) (4−ab)(8+ab) (vii) (5xy−7)(7xy+9) (viii) (3a2−4b2)(8a2−3b2)

Answer»

Evaluate :

(i) $(3 x + \frac{1}{2}) (2 x + \frac{1}{3})$

(ii) $(2 a + 0.5) (7 a - 0.3)$

(iii) $(9 - y) (7 + y)$

(iv) $(2 - z) (15 - z)$

(v) $(a^{2} + 5) (a^{2} - 3)$

(vi) $(4 - a b) (8 + a b)$

(vii) $(5 x y - 7) (7 x y + 9)$

(viii) $(3 a^{2} - 4 b^{2}) (8 a^{2} - 3 b^{2})$

Discussion

9038.	A solid cylindrical party popper having radius 7 cm and length 20 cm needs to be gift wrapped by a paper sheet. What is the area of sheet required to cover it completely ?
Answer» A solid cylindrical party popper having radius 7 cm and length 20 cm needs to be gift wrapped by a paper sheet. What is the area of sheet required to cover it completely ?

Discussion

9039.	In the given figure which of the following relations between area of rectangles and squares forms an identity (a−b)(a+b)=(a2−b2)?
Answer» In the given figure which of the following relations between area of rectangles and squares forms an identity $(a - b) (a + b) = (a^{2} - b^{2})$ ?

Discussion

9040.	Fill in the Blanks Question 12 The relation between dependent and independent variable is shown through a ______.
Answer» Fill in the Blanks Question 12 The relation between dependent and independent variable is shown through a ______.

Discussion

9041.	Solve 46 (x-2) + 4 < 10 and represent its solution on a number line. Given replacement set is {-8, -2, 9, 11, 12}
Answer» Solve $\frac{4}{6}$ (x-2) + 4 < 10 and represent its solution on a number line. Given replacement set is {-8, -2, 9, 11, 12}

Discussion

9042.	Tick (\checkmark) the correct answer in each of the following: (x+4)(x+4)=? (a) (x2+16) (b) (x2+4x+16) (c) (x2+8x+16) (d) (x2+16x)
Answer» Tick (\checkmark) the correct answer in each of the following: $(x + 4) (x + 4) = ?$ (a) $(x^{2} + 16)$ (b) $(x^{2} + 4 x + 16)$ (c) $(x^{2} + 8 x + 16)$ (d) $(x^{2} + 16 x)$

9042.

Tick (\checkmark) the correct answer in each of the following: (x+4)(x+4)=? (a) (x2+16) (b) (x2+4x+16) (c) (x2+8x+16) (d) (x2+16x)

Answer»

Tick (\checkmark) the correct answer in each of the following:
$(x + 4) (x + 4) = ?$

(a) $(x^{2} + 16)$
(b) $(x^{2} + 4 x + 16)$
(c) $(x^{2} + 8 x + 16)$
(d) $(x^{2} + 16 x)$

Discussion

9043.	f(x)=x+1x then f(x3)equal to where x3is cube of x
Answer» f(x)=x+1x then f(x3)equal to where x3is cube of x

Discussion

9044.	Question 18 Bulbs are packed in cartons each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs and the results are given in the following table. Number of0123456Moredefectivethan 6bulbsFrequency400180484118832 One carton was selected at random. What is the probability that it has (i) No defective bulb? (ii) Defective bulbs from 2 - 6? (iii) Defective bulbs less than 4?
Answer» Question 18 Bulbs are packed in cartons each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs and the results are given in the following table. $\begin{matrix} N u m b e r o f & 0 & 1 & 2 & 3 & 4 & 5 & 6 & M o r e d e f e c t i v e & t h a n 6 b u l b s F r e q u e n c y & 400 & 180 & 48 & 41 & 18 & 8 & 3 & 2 \end{matrix}$ One carton was selected at random. What is the probability that it has (i) No defective bulb? (ii) Defective bulbs from 2 - 6? (iii) Defective bulbs less than 4?

Discussion

9045.	Number of soldiers in a battalion is 4. So, total number of soldiers in 3 battalions is ____
Answer» Number of soldiers in a battalion is 4. So, total number of soldiers in 3 battalions is ____

Discussion

9046.	ABCD and ABFE are parallelograms as shown in the figure. If ar (ABCD) = 36 cm2 and ar(ABFE) = 18 cm2, then ar (EFCD) [in cm2] is: ___
Answer» ABCD and ABFE are parallelograms as shown in the figure. If ar (ABCD) = 36 $c m^{2}$ and ar(ABFE) = 18 $c m^{2}$ , then ar (EFCD) [in $c m^{2}$ ] is: ___

9046.

ABCD and ABFE are parallelograms as shown in the figure. If ar (ABCD) = 36 cm2 and ar(ABFE) = 18 cm2, then ar (EFCD) [in cm2] is: ___

Answer»

ABCD and ABFE are parallelograms as shown in the figure. If ar (ABCD) = 36 $c m^{2}$ and ar(ABFE) = 18 $c m^{2}$ , then ar (EFCD) [in $c m^{2}$ ] is:

___

Discussion

9047.	If 4x = 64, then which of the following is/are true?
Answer» If $4^{x}$ = 64, then which of the following is/are true?

Discussion

9048.	Rajdhani Express met with an accident while crossing the bridge on the Krishna River. 1114th of the length of the train was found hanging off the rails on the river. If the length of the train was 322 m, find out what length of the train was found hanging?
Answer» Rajdhani Express met with an accident while crossing the bridge on the Krishna River. ${\frac{11}{14}}^{t h}$ of the length of the train was found hanging off the rails on the river. If the length of the train was 322 m, find out what length of the train was found hanging?

Discussion

9049.	Question 1(i) The following graph shows the temperature of a patient in a hospital, recorded every hour What was the patient’s temperature at 1 p.m.?
Answer» Question 1(i) The following graph shows the temperature of a patient in a hospital, recorded every hour What was the patient’s temperature at 1 p.m.?

Discussion

9050.	A stationery shop costs Rs. 4 for a pencil. Pavan wants to buy 3 pencils. How much will it cost him? I answered Rs. 12 and I am marked wrong. And the solution said 12. Can one write cost as number only , without any unit? Why am I wrong? Please help.
Answer» A stationery shop costs Rs. 4 for a pencil. Pavan wants to buy 3 pencils. How much will it cost him? I answered Rs. 12 and I am marked wrong. And the solution said 12. Can one write cost as number only , without any unit? Why am I wrong? Please help.

9050.

A stationery shop costs Rs. 4 for a pencil. Pavan wants to buy 3 pencils. How much will it cost him? I answered Rs. 12 and I am marked wrong. And the solution said 12. Can one write cost as number only , without any unit? Why am I wrong? Please help.

Answer»

A stationery shop costs Rs. 4 for a pencil. Pavan wants to buy 3 pencils. How much will it cost him?

I answered Rs. 12 and I am marked wrong. And the solution said 12. Can one write cost as number only , without any unit? Why am I wrong? Please help.

Discussion

Explore topic-wise InterviewSolutions in .

Fill in the blank with the correct option. A linear equation in one variable is _________.

If 152+a2=b2, then find a and b respectively.

If area of trapezium is 45cm2 if distance betweebetween parallel sides is 6cm and of the parallel sides is 10cm. Find the other??

Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Then which of the following options is correct?

Is it possible to construct a rhombus AJUN with AU = 24 cm and JN = 10 cm? If yes, what is the length of the side of the rhombus?

If ∣∣∣z−z1z−z2∣∣∣ = 3, Where z1 and z2 are fixed complex numbers and z is a variable complex number, then 'z' lies on a:

How to do square root while using pythogoras property

A number is called a triangular number if its dot pattern can be arranged in

If a + b = 7 and ab = 12, find the value of a2 + b2

Salma runs 7 rounds of a circular field and covered a distance of 5.6 km. Find the diameter of the field (upto 3 decimal places) if perimeter is 3.14 times the diameter.

The factorisation of x2−5x+6 is

Question 7Write the correct answer from the given four options. The one's digit of the cube of 23 isa) 6b) 7c) 3d) 9

In the given figure, ABCD is a parallelogram. E is a point on DC. If AE bisects ∠A and BE bisects ∠B, then BC : AB = ___.

Which of the following equations are linear equation in two variables?

How many diagonals can a pentagon have?

Question 13In figure, arcs have been drawn with radii, 14 cm each and with centres P,Q and R. Find the area of the shaded region.

A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

The number of integers n(

The organizers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win, gets a prize of ₹25. The total prize money distributed is ₹3,000. Find the number of winners, if the total number of participants is 63.

22. How many alternate faces are their in simple cube.

Find the product:

√288√128=? (a) √32 (b) 3√2 (c) 32 (d) 1.49

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find the total length of wire required and the area of each sector. [3 MARKS]

In the given figure, AB is the chord to the circle centred at O. If AC = CB and ∠AOC=60∘, then find ∠CAO.

A point (2,4) is translated through a distance of 5 units horizontally along positive x - axis. The new point is

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the difference between the measure of the largest angle and the smallest angle.

A can do a piece of work in 12 days. B can do this work in 16 days. A started the work alone. After how many days should B join him, so that the work is finished in 9 days?

The polynomial x2 + y2 – z2 – 2xy on factorization gives _____________.

For the function y=6−5x, the value of y, when x=1 can be given by .

The number of squares on a coordinate plane with one vertex at A(-2, 2)and atleast one of the coordinate axes as axis of symmetry of the square is

Arun makes a cuboid of wood of sides 7cm, 4cm, 3cm How many such minimum number of cuboids will he need to form a cube?

The total number of parallelograms in this figure is ___

PQNM and ZYXW are two rectangular doors used for the main door and a cupboard. Find the ratio of their sides.

Prepare a continuous grouped frequency distribution from the following data.Mid-PointFrequency5415825133512456Also, find the size of class intervals.

Evaluate : (i) (3x+12)(2x+13) (ii) (2a+0.5)(7a−0.3) (iii) (9−y)(7+y) (iv) (2−z)(15−z) (v) (a2+5)(a2−3) (vi) (4−ab)(8+ab) (vii) (5xy−7)(7xy+9) (viii) (3a2−4b2)(8a2−3b2)

A solid cylindrical party popper having radius 7 cm and length 20 cm needs to be gift wrapped by a paper sheet. What is the area of sheet required to cover it completely ?

In the given figure which of the following relations between area of rectangles and squares forms an identity (a−b)(a+b)=(a2−b2)?

Fill in the Blanks Question 12 The relation between dependent and independent variable is shown through a ______.

Solve 46 (x-2) + 4 &lt; 10 and represent its solution on a number line. Given replacement set is {-8, -2, 9, 11, 12}

Tick (\checkmark) the correct answer in each of the following: (x+4)(x+4)=? (a) (x2+16) (b) (x2+4x+16) (c) (x2+8x+16) (d) (x2+16x)

f(x)=x+1x then f(x3)equal to where x3is cube of x

Number of soldiers in a battalion is 4. So, total number of soldiers in 3 battalions is ____

ABCD and ABFE are parallelograms as shown in the figure. If ar (ABCD) = 36 cm2 and ar(ABFE) = 18 cm2, then ar (EFCD) [in cm2] is: ___

If 4x = 64, then which of the following is/are true?

Rajdhani Express met with an accident while crossing the bridge on the Krishna River. 1114th of the length of the train was found hanging off the rails on the river. If the length of the train was 322 m, find out what length of the train was found hanging?

Question 1(i) The following graph shows the temperature of a patient in a hospital, recorded every hour What was the patient’s temperature at 1 p.m.?

A stationery shop costs Rs. 4 for a pencil. Pavan wants to buy 3 pencils. How much will it cost him? I answered Rs. 12 and I am marked wrong. And the solution said 12. Can one write cost as number only , without any unit? Why am I wrong? Please help.

Solve 46 (x-2) + 4 < 10 and represent its solution on a number line. Given replacement set is {-8, -2, 9, 11, 12}