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9142x is multiple of 4 

=> 9 + 1 + 4 + 2 + x is a multiple of 4 

=> 16 + x = 0, 4, 8, ……… 

x = -8, -4, 0, 4, 8 

Since, x is a digit 

4, 8

Students must solve the important Class 8 Maths MCQ Questions of Algebraic Expressions and Identities with Answers. This will help them to keep up with what is being taught in class and what might appear in the exams. A significant chunk of questions from this subject comes within the type of MCQ Questions. Therefore, by practicing more objective-type questions, the students will ensure securing better marks from this chapter.

MCQ Questions for class 8 Maths allow the students to study in-depth and prepare well in advance. They contain only the questions which are most likely to appear in the examinations. These questions are carefully curated based on the current syllabus, and curriculum, previous year questions papers.

Practice the MCQ Questions for Class 8 Algebraic Expressions and Identities with answers which are given here. 

Practice MCQ Question for Class 8 Maths chapter-wise

1. The expression x + 3 is in

(a) one variable
(b) two variables
(c) no variable
(d) none of these

2. The value of the expression x³ + y³ when x=2 and y=-2 is 

(a) 0
(b) 8
(c) 16
(d) -16

3. The expression 4xy + 7 is in

(a) one variable
(b) two variables
(c) no variable
(d) none of these

4. The value of 5x when x = 5 is

(a) 5
(b) 10
(c) 25
(d) -5

5. The value of x² – 2x + 1 when x = 1 is

(a) 1
(b) 2
(c) -2
(d) 0

6. The value of x² + y² when x = 1, y = 2 is

(a) 1
(b)2
(c) 4
(d) 5

7. The sum of 7x, 10x and 12x is

(a) 17x
(b) 22x
(c) 19x
(d) 29x

8. The sum of 8pq and -17 pq is

(a) pq
(b) 9pq
(c) -9pq
(d) -pq

9. The sum of 5x², -7x², 8x², 11x² and -9x² is

(a) 2x²
(b) 4x²
(c) 6x²
(d) 8x²

10. The result of subtraction of 3x from -4x is

(a) -7x
(b) 7x
(c) x
(d) -x

11. The product of 7x and -12x is

(a) 84x²
(b) -84x²
(c) x²
(d) -x²

12. The area of a rectangle whose length and breadth are 9y and 4y² respectively is

(a) 4y³
(b) 9y³
(c) 36y³
(d) 13y³

13. The volume of a cube of side 2a is

(a) 4a²
(b) 2a
(c) 8a³
(d) 8

14. The algebraic expression 3x + 2y + 6 is

(a) monomial
(b) Binomial
(c) Trinomial
(d) None of the above

15. If we add, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and -3xz + 5x – 2xy, then the answer is:

(a) 5xy + 9yz + 3zx + 5x – 4y
(b) 5xy – 9yz + 3zx – 5x – 4y
(c) 5xy + 10yz + 3zx + 15x – 4y
(d) 5xy + 10yz + 3zx + 5x – 6y

16. If we subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3, then the answer is:

(a) 8a + 2ab + 2b + 15
(b) 8a + 2ab + 2b – 15
(c) 8a – 2ab + 2b – 15
(d) 8a – 2ab – 2b – 15

17. The volume of a rectangle with length, breadth and height as 5x, 3x² and 7x⁴ respectively is:

(a) 105x⁷
(b) 105x²
(c) 105x⁴
(d) 105x

18. The area of a rectangle that has length = 2a²b and breadth = 3ab² is::

(a) 6a³b³
(b) a³b³
(c) 8a³b³
(d) 6a³b⁰

19. Expressions consists of _____________ and _______________.

(a) variables, constants
(b) identities
(c) expressions
(d) none of these

20. An algebraic expression consisting of three terms is called a ______ expression.

(a) monomial
(b) trinomial
(c) binomial
(d) polynomial

21. Value of expression a(a²+a +1)+5 for ‘ a’ = 0 is

(a) a+5      
(b) 1
(c) 6
(d) 5

22. Identify the coefficient of xy² in xy – 4xy² – 5x²y

(a) -5      
(b) 5
(c) -4
(d) 4

23. Obtain the volume of rectangle boxes with length, breadth and height are. 6a, 3b², 7a⁴

(a) 15a³ b⁵   
(b)  216 b³
(c) 126 a⁵ b²
(d) 17a² b³

24. Which of the following is like term as 7xy?

(a) 9
(b) 9x
(c) 9y
(d) 9xy

25. If a + b + c = 9 and ab + bc + ca = 26, then the value of a³ + b³ + c³ – 3abc

(a) 27
(b) 29
(c) 729
(d) 495

Answer:

1. Answer: (a) one variable

Explanation:  The only variable is x.

2. Answer: (a) 0

Explanation:  Value of x³+y³

=(2)³+(−2)³

=8−8

=0

3. Answer:(b) two variables

Explanation:  There are two variables x and y.

4. Answer: (c) 25

Explanation:  Value = 5 × 5 

= 25.

5. Answer: (d) 0

Explanation:  Value = (1)² – 2(1) + 1 

= 0

6. Answer: (d) 5

Explanation:  Value = (1)² + (2)² 

= 5.

7. Answer: (d) 29x

Explanation:  Sum = (7 + 10 + 12)x 

= 29x

8. Answer: (c) -9pq

Explanation:  Sum = {8 + (-17)} pq 

= -9pq

9. Answer: (d) 8x²

Explanation:  Sum = {5 + (-7) + 8 + 11 + (-9)} x²

 = 8x²

10. Answer: (a) -7x

Explanation:  -4x -3x 

= -7x

11. Answer: (b) -84x²

Explanation:  (7x) (-12x) 

= – 84x²

12. Answer: (c) 36y³

Explanation: Area of rectangle = l x b

= (9y)(4y²) 

= 36y³

13. Answer: (c) 8a³

Explanation: Volume = 2a × 2a × 2a

= 8a³

14. Answer: (c) Trinomial

Explanation:  The algebraic expression containing three terms is called a trinomial. Here, 3x, 2y and 6 are three terms.

15. Answer: (a) 5xy + 9yz + 3zx + 5x – 4y

Explanation:  Given, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and -3xz + 5x – 2xy.

If we add the three expressions, then we need to combine the like terms together.

(7xy – 2xy)+(5yz + 4yz) – 3zx + 9zx – 3xz – 4y + 5x

= 5y + 9yz + 3zx + 5x – 4y

16. Answer: (c) 8a – 2ab + 2b – 15

Explanation:  (12a – 9ab + 5b – 3) – (4a – 7ab + 3b + 12)

= 12a – 9ab + 5b – 3 – 4a + 7ab – 3b – 12

= (12 – 4)a – (9 – 7)ab + (5 – 3)b – 3 – 12

= 8a – 2ab + 2b – 15

17. Answer: (a) 105x⁷

Explanation:  Volume of rectangle = Length × breadth × height

V = 5x × 3x² × 7x⁴

V = 105 x¹⁺²⁺⁴

V = 105x⁷ cubic unit.

18. Answer: (a) 6a³b³

Explanation:  Area of rectangle (l x b)

= (2a²b)(3ab²) 

= 6a³b³

19. Answer: (a) variables, constants

Explanation: An expression is a combination of operators, constants and variables. An expression may consist of one or more operands, and zero or more operators to produce a value.

20. Answer: (b) trinomial

Explanation:  An algebraic Expression containing one term is monomial.

An algebraic Expression containing two terms is binomial.

An algebraic Expression containing three terms is trinomial.

21. Answer: (d) 5

Explanation: a(a²+a+1)+5

=a³+a²+a+5

Putting the value of a,we get,

a³+a²+a+5

=0+0+0+5

= 5

22. Answer: (c) -4

Explanation:  xy – 4xy² – 5x²y = 0

= (-4) xy² 

= Coefficient (-4)

23. Answer: (c)  126 a⁵ b²

Explanation: 6a × 3b² × 7a²

= 6 × a × 3 × b × b × 7 × a × a

= 126 a⁵ b²

24. Answer: (d) 9xy

Explanation: The terms which have the same literal coefficients raised to the same powers but may only differ in numerical coefficient are like terms.

25. Answer: (a) 27

Explanation: ⇒ (a + b + c)² = 81 [On squaring both sides of (i)]  

⇒ a² + b² + c² + 2(ab + bc + ac) = 81  

⇒ a² + b² + c² + 2 × 26 = 81 [∵ab + bc + ac = 26]  

⇒ a² + b² + c² = (81 - 52)  

⇒ a² + b² + 2 = 29.  

Now, we have 

a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - ab - bc - ac)   

= (a + b + c) [(a² + b² + c² ) - (ab + bc + ac)]   

= 9 × [(29 - 26)]   

= (9 × 3)   

= 27

Click here Practice MCQ Question for Algebraic Expressions and Identities Class 8

1/12 of the sheet was wasted.

=> 1 – 1/12 = 11/12 of the sheet was used in making the tank.

Let the metal sheet originally brought was = x m²

11/12 x = 87.12m² 

∴ x = 87.12 x 12/11 = 95.04m²

1. d) 404.25cm³

2. b) 89.83 cm³

3. d) Cylindrical glass, 314.42 cm³

4. c) 24m

5. b) 38.5m²

1. a) 19404 cu. m

2. b) \(\cfrac43\,\pi\,r^3\)

3. b) 1232 sq.m

4. c) 1392 sq.m

5. d) 192 m³

Sum of first n terms be S_n given as

S_n = 2n + 3n²

We have to find the r^th term that is a_r

Using the hint: the n^th term is given as a_n = S_n – S_n-1

⇒ a_r = S_r – S_r-1

Using S_n = 2n + 3n²

⇒ a_r = 2r + 3r² – (2(r – 1) + 3(r – 1)²)

⇒ a_r = 2r + 3r² – (2r – 2 + 3(r² – 2r + 1))

⇒ a_r = 2r + 3r² – (2r – 2 + 3r² – 6r + 3)

⇒ a_r = 6r – 1

Hence the r^th term is 6r – 1

We know that,

a_n = a + (n – 1)d

So, a₉ = a + (9 – 1)d

⇒ a₉ = a + 8d

and a₁₃ = a + 12d

According to the question,

9 times the 9^th term i.e. a₉ = 13 times the 13^th term i.e. a₁₃

⇒ 9 × a₉ = 13 × a₁₃

⇒ 9(a + 8d) = 13(a + 12d)

⇒ 9a + 72d = 13a + 156d

⇒ 9a – 13a = 156d – 72d

⇒ -4a = 84d

⇒ a = -21d …(i)

Now, we have to find the 22^nd term

∴ a₂₂ = a + 21d

⇒ a₂₂ = -21d + 21d [from (i)]

⇒ a₂₂ = 0

Hence, the correct option is (a)

(D) 4

Explanation:

To find: Common Difference of A.P that is d

Consider,

S_n = 3n + 2n²

Putting n = 1, we get

S₁ = 3(1) + 2(1)²

= 3 + 2

S₁ = 5

Putting n = 2, we get

S₂ = 3(2) + 2(2)²

= 6 + 2(4)

= 6 + 8

S₂ = 14

Now, we know that,

S₁ = a₁

⇒ a₁ = 5

And a₂ = S₂ – S₁

= 14 – 5

= 9

∴ Common Difference, d = a₂ – a₁

= 9 – 5

= 4

Hence, the correct option is (D)

The correct answer is False

(A) Ratio of 5 paise to 25 paise is the same as the ratio of 20 paise to 100 Paisa or 1 Rupee
(B) Saturn and Jupiter take 9 hours 56 minutes and 10 hours 40 minutes, respectively for one spin on their axes. The ratio of the time taken by Saturn and Jupiter in lowest form is 149 : 160
(C) 10g of caustic soda dissolved in 100mL of water makes a solution of caustic soda. Amount of caustic soda needed for 1 litre of water to make the same type of solution is 100 gm.

1. python 

2. giant 

3. casement

4. statue 

5. springing 

6. impressive 

7. nostalgic 

8. nature 

9. lamenting 

10. consecrates

11. sanctified 

12. forgotten

The creeper is compared to a lady love.

The creeper appears like a huge python.

B. create proper balance between study and hours of watching TV

Context: The poetess is watching the Casuarina tree from her window which looks very beautiful. 

Explanation: The poetess says that the Casuarina tree is very dear to her not because it is splendid but because it reminds her of those happy days when she used to play under the tree with her friends. The poetess says that the tree will always remain dear to her as it is associated with her friends whom she loves extremely. The poetess hopes that the tree will ever grow in memory of her friends but she will shed tears as she misses them all.

Nightingale sings in the poet’s garden.

At night, the garden overflows with endless melodious song sung by the dark king from the Casuarina Tree when the men are sleeping.

C. She generally doesn’t share anything with her.

D. more than one style of learning helps improve retention

According to Prof. Mackay, sharing between parents and children unites families.

C. he forgets most of what he reads

When children are not able to understand the intention of parents, it proves to be an obstacle in sharing.

B. an international counsellor

D. advise the students and their parents

Manipravalam - literally meaning, “diamonds and corals” refers to the two languages, Sanskrit and the regional language. Lilatilakam is a text in Manipravalam.

We know more about the cultural practices of rulers than about those of ordinary people because: 

• Only rulers could afford minstrels and historians for records and documentation. They could preserve their records at their palaces. 
• Ordinary people used to struggle to earn their livelihood. 
• Ordinary people did not have resources or wealth to preserve their memories and cultural practices.

• The important architectural features of the temples in Bengal were the double-roof (dochala) and the four-roof (chauchala). 
• In the comparatively more complex four-roofed structure, four triangular roofs placed on the four walls move up to converge on a curved line or a point. 
• Temples were usually built on a square platform. The outer walls of many temples were decorated with paintings, ornamental tiles or terracotta tablets. 
• In some temples, particularly in Vishnupur in the Bankura district of West Bengal, such decorations reached a high degree of excellence.

Stories about Rajput heroes were recorded in poems and songs, which were recited by specially trained minstrels. These poems and songs preserved the memories of heroes and were expected to inspire others to follow their examples. Ordinary people were also attracted by these stories – which often depicted dramatic situations, and a range of strong emotions – loyalty, friendship, love, valour, anger, etc.

The major patrons of Kathak were the Mughal emperors and the Nawabs of Lucknow, especially Wajid Ali Shah.

Conquerors tried to gain control over the Jagannatha temple at Puri because: 

• it would make their rule acceptable to the local people since the temple was important as a place of pilgrimage. 
• the temple was also a centre of authority in social and political matters.

Bengal also witnessed a temple-building spree from the late fifteenth century, which culminated in the nineteenth century. 

• Temples were built in Bengal to house the local deities who had gained the recognition of the Brahmanas. 
• Many of the modest brick and terracotta temples in Bengal were built with the support of several “low” social groups, such as the Kolu (oil pressers) and the Kansari (bell metal workers). 
• The coming of the European trading companies created new economic opportunities; many families belonging to these social groups availed of these. As their social and economic position improved, they proclaimed their status by constructing temples.

The founder of the Awadh state was _Burhan-ul-Mulk Sa’adat Khan_.

The Marathas wanted to expand beyond the Deccan to receive tribute and control trade and agriculture. They had built a rich and effective administrative system, so they could think of expanding beyond the Deccan for more power and resources.

In the eighteenth century, the Sikhs organized themselves into a number of bands called jathas, and later misls. Their combined forces were known as the grand army (dal khalsa). The entire body used to meet at Amritsar at the time of Baisakhi and Diwali to take collective decisions known as “resolutions of the Guru (gurmatas)”. A system called rakhi was introduced, offering protection to cultivators on the payment of a tax of 20 per cent of the produce. Guru Gobind Singh created the khalsa that helped Sikhs defeat the Mughal governors first and then Ahmad Shah Abdali who had seized the rich province of the Punjab and the Sarkar of Sirhind from the Mughals.

The offices held by Sa’adat Khan included subadari, diwani and faujdari.

A major theme in ‘The Lake Isle of Innisfree’, is nature versus civilization. What we value in life is often the exact opposite of what civilization brings with it. Nature allows us to explore the various forms of life but civilization has certain set rules with which we have to abide.

Umara and jagirdars constituted powerful sections of the Mughal _administration_.

Plant cells differ from those of animals in having an additional layer around the cell membrane termed cell wall.

Cytoplasm: That part of a cell’s protoplasm that lies outside of its nucleus.

Cell Wall: Cells, the outermost non-living cellulose layer that surrounds the entire cell, including the cell membrane.

Cell membrane: The thin, flexible layer that surrounds a cell and which controls all that enters and leaves the cell.

Reproduction: The biological process by which an organism produces its own kind to maintain the race. Reproduction enables the continuity of species generation after generation.

Types of Reproduction:

(a)  Asexual reproduction

(b)  Sexual reproduction

Asexual reproduction:- When single parent produces offspring without the involvement of gamete formation . Such offspring is morphologically and genetically similar to the parent.

Types of asexual reproduction:

a.  Binary fission: In Monerans and protists the single celled organisms divide equally to form two daughter cells.

e.g., Amoeba , Paramoecium

b.  Multiple fission : When an organism divides to form many daughter organisms .

e.g., Plasmodium.

c.  Budding : When parent organism gives rise to a small projection called the bud. The bud increases in size and gets detached from parent organism and matures into new organism.

e.g., Yeast & Hydra.

d.  Gemmule formation : In sponges a large number of buds are formed inside the body which are called gemmules . Gemmules are small bodies which consist of a mass of undifferentiated cells surrounded by protective covering of spicules and sycon.

e. Fragmentation : When parent body breaks into two or more pieces due to water current. Each piece or fragment develops to form new parent.

e.g., spirogyra ,sponges, flatworms. 

f. Vegetative propagules : In higher plants the vegetative parts are used to raise new plants.These vegetative parts are called propagules ,

these are as below 

(i)  Runner in Oxalis ad Marsilea

(ii)  Rhizome in ginger and turmeric

(iii)  Sucker in banana, pineapple,mint,etc

(iv) Tuber in Potato(EYES)

(v)  Offset in water hyacinth and pistia 

(vi)  Bulb in onion and Garlic.

(vii)  Leaf buds in bryophyllum

(viii)  Bulbil in Agave

g. Zoospores and conidia formation: In certain algae and fungi, asexual reproduction takes place by specialized reproduction structures called zoospores. Zoospores are flagellated oval structures.

e.g., Chlamydomonas.

In Aspergillus and penicillium a chain of non motile small spores are formed on fungal hyphae – Conidiophores. These small spores are called conidia which on return of favourable conditions germinate to form new plant body.

1. England had a number of iron mines. 

2. Therefore, it was necessary to advance the technique of smelting iron to acquire purified iron from it. 

3. The fuel for iron furnaces was replaced from wood to coal. 

4. Special machines were made to keep the furnaces at a set temperature and to maintain their aeration. 

5. In 1865, the process of producing steel from molten iron was invented and the nature of the iron industry underwent a major transformation. 

6. At about the same time, a method was adopted to pour the molten metal into casts for making iron bars (e.g. rails).

• Economic nationalism began the vicious circle of continuously capturing new marketplaces, searching for sources of a cheap supply of raw material, maintaining an unbroken chain supply of raw material), to attract more and more investors, to safeguard their investments. This resulted in limitless exploitation of the colonies.
• Extreme nationalism, industrialization, concepts of racial superiority, aggressive colonial policies further supported the growth of imperialism.
• The result was the immense expanse of the empires like England, France, Belgium, Germany, etc.

1. The European Renaissance began in the 14th century C.E. 

2. It reached its zenith in the 15th and 16th centuries.

3. These three centuries laid the foundations of a culture based on rationalism and science. 

4. This age gave a new direction to human intellect genius and way of life. 

5. People started writing poetry, drama, and fiction. 

6. Novel experiments were conducted in the field of science. 

7. In the pre-renaissance period, the thought about the existence of the universe revolved around ‘God’. 

8. In short, in this period new inventions, machinery, art, drama, literature, and geographical discoveries have taken place.

1. The two cities of Jerusalem and Bethlehem considered holy by the Jews, Christians, and Muslims were under Islamic rule in the 11th century. 

2. Christians of Europe wanted to regain hold over these cities and fought several wars known as ‘Crusaders’. 

3. The common people in Europe were highly inspired to be part of such religious wars. 

4. When the Pope announced that the sins of those who took part in such wars would be forgiven and would immediately go to Heaven, there was spontaneous participation by the common people in the crusaders. 

5. Besides social and political circumstances, the Roman emperors were also trying to bring Syria and Asia Minor under their control.

6. Moreover, the rich merchants in Genova and Venice in Italy were looking for Central Asian markets to establish their trade. 

7. The first crusade started in 1096 C.E.

8. A second call for the crusade was given by Pope Eugenius III who sought help from the French King Louis VII and the German King Conrad III. 

9. The crusaders were ultimately defeated by the Turks and in 1187 C.E. Saladin, the Sultan of Egypt defeated the crusaders by conquering Jerusalem. 

10. However, the crusaders failed for several reasons such as the attitude of the Pope and the European rulers common people losing faith, the rift between the Pope and the European kings, etc.

The scientists of the 17^th century emphasized the following things:

• To prove that scientific principles established by empirical experiments are true despite time and space.
• To convert the emergent scientific rules into scientific formulae.
• To create new scientific parlance and so on. These efforts helped the progress of science.