Explore topic-wise MCQs in 8th Class.

This section includes 2318 Mcqs, each offering curated multiple-choice questions to sharpen your 8th Class knowledge and support exam preparation. Choose a topic below to get started.

1051.

The factors of \[{{x}^{2}}-16\] are __.

A.  \[({{x}^{2}}+2)({{x}^{2}}-2)\]
B.  \[(x+4)(x-4)\]
C.  \[(x+2)(x-2)\]
D.  Does not exist
Answer» C.  \[(x+2)(x-2)\]
1052.

What are the factors of \[{{x}^{2}}+xy-2xxz-2yz\]?

A.  \[(x-y)\] and \[(x+2z)\]
B.  \[(x+y)\] and \[(x-2z)\]
C.  \[(x-y)\]and \[(x-2z)\]
D.  \[(x+y)\] and \[(x+2z)\]
Answer» C.  \[(x-y)\]and \[(x-2z)\]
1053.

Identify the factors of\[18-32{{p}^{2}}\].

A.  \[2(4p+3)\,(4p-3)\]
B.  \[2(3+4p)\,(3-4p)\]
C.  \[4(3+4p)\,(3-4p)\]
D.  \[4(3+2p)\,(3-2p)\]
Answer» C.  \[4(3+4p)\,(3-4p)\]
1054.

What is the quotient when \[12ab\,{{(9{{a}^{2}}-16b)}^{2}}\] is divided by \[4ab\,(3a+4b)\]?

A.          \[4\,(3a+4b)\] 
B.         \[3\,(3a-4b)\]                  
C.                  \[3\,(3a+4b)\] 
D.         \[4\,(3a-4b)\]
Answer» C.                  \[3\,(3a+4b)\] 
1055.

What is the factor form of \[{{\left( {{p}^{2}}+{{q}^{2}}-{{r}^{2}} \right)}^{2}}-4{{p}^{2}}{{q}^{2}}\]?

A.  \[(p+q+r)\,(p+q-r)\]\[(p-q+r)\,(p-q-r)\]
B.  \[(p-q-r)\,({{p}^{2}}-{{q}^{2}}-{{r}^{2}})\]
C.  \[(p-q-r)\] \[(2p-2q-2r)\]
D.  \[(p+q-r)\,({{p}^{2}}-{{q}^{2}}-{{r}^{2}})\]
Answer» B.  \[(p-q-r)\,({{p}^{2}}-{{q}^{2}}-{{r}^{2}})\]
1056.

Find the factors of \[{{x}^{2}}+\frac{{{a}^{2}}-1}{a}x-1\]from the following.

A.  \[\left( x-\frac{1}{a} \right)\] and \[(x+a)\]
B.  \[\left( x-\frac{1}{{{a}^{2}}} \right)\] and \[(x+a)\]
C.  \[\left( x-\frac{1}{{{a}^{2}}} \right)\] and \[(x-a)\]
D.  \[\left( x+\frac{1}{{{a}^{2}}} \right)\] and \[(x+a)\]
Answer» B.  \[\left( x-\frac{1}{{{a}^{2}}} \right)\] and \[(x+a)\]
1057.

Choose the factors of \[a{{(x-y)}^{2}}-by+bx+3x-3y.\]

A.  \[(x-y)\] and \[\left[ a(x-y)+b+3 \right]\]
B.  \[(a-b)\] and \[(3x-3y)\]
C.  \[(x-y)\] and \[({{x}^{2}}+a+1)\] and \[({{y}^{2}}+b+1)\]
D.  \[(ax-y)\] and \[[a(x-y)+b+3]\]
Answer» B.  \[(a-b)\] and \[(3x-3y)\]
1058.

What is the perfect square form of \[9{{a}^{2}}-\frac{12}{5}a+\frac{4}{25}\]?

A.  \[{{\left( a-\frac{2}{5} \right)}^{2}}\]     
B.  \[{{\left( 3a-\frac{2}{5} \right)}^{2}}\]   
C.  \[{{\left( 2a-\frac{2}{5} \right)}^{2}}\]   
D.         \[{{\left( 3a+\frac{2}{5} \right)}^{2}}\]                  
Answer» C.  \[{{\left( 2a-\frac{2}{5} \right)}^{2}}\]   
1059.

Choose the factors of \[{{x}^{4}}-13{{x}^{2}}{{y}^{2}}+36{{y}^{4}}\] from the following.

A.  \[(x+4y),(x-4y),(x+2y)\]and \[(x-2y)\]
B.  \[({{x}^{2}}+2x-8)\] and \[({{x}^{2}}+2x-3)\]
C.  \[(x+3y),(x-3y),(x+2y)\]and \[(x-2y)\]
D.  \[({{x}^{2}}-2x-8)\] and \[({{x}^{2}}+2x+3)\]
Answer» D.  \[({{x}^{2}}-2x-8)\] and \[({{x}^{2}}+2x+3)\]
1060.

Which of the following factorizations is incorrect?

A.  \[200{{y}^{2}}-2=2(10y+1)\,(10y-1)\]
B.  \[49{{x}^{2}}-36=(7x+6)\,(7x-6)\]
C.  \[200{{y}^{2}}-2=2(10y+1)\,(10y+1)\]
D.  \[36-100{{k}^{2}}=(6+10k)\,(6-10k)\]
Answer» D.  \[36-100{{k}^{2}}=(6+10k)\,(6-10k)\]
1061.

The factors of \[15{{x}^{2}}-26x+8\]are __.

A.  \[(3x-4)(5x+2)\]         
B.  \[(3x-4)(5x-2)\]           
C.  \[(3x+4)(5x-2)\]         
D.  \[(3x+4)(5x+2)\]       
Answer» C.  \[(3x+4)(5x-2)\]         
1062.

For \[{{x}^{2}}+2x+5\]to be a factor of \[{{x}^{4}}+\text{ }p{{x}^{2}}+q,\]what must the respective values of p and q be?

A.  \[-2\] and \[5\]                               
B.  \[5\] and \[25\]
C.  \[10\] and \[20\]   
D.  \[6\] and \[25\]
Answer» E.
1063.

Which of the following is the correct factorization?

A.  \[64-{{x}^{2}}=(64-x)\,(64+x)\]
B.  \[27{{x}^{2}}-48=3(3x+4)\,(3x-4)\]
C.  \[{{y}^{2}}-81=(y+9)\,(y+9)\]
D.  \[36-{{p}^{2}}=(p-6)\,(p+6)\]
Answer» C.  \[{{y}^{2}}-81=(y+9)\,(y+9)\]
1064.

The area of a square is\[({{x}^{2}}+8x+16)c{{m}^{2}}\]. Find the length of its side.

A.  \[(x-8)\,cm\]                                    
B.  \[(x-4)\,cm\]    
C.         \[(x+4)\,cm\]                   
D.         \[(x+2)\,cm\]                                                   
Answer» D.         \[(x+2)\,cm\]                                                   
1065.

Find the factors of \[3{{z}^{2}}+9z+6\].

A.  \[3(z+1)\,(z+2)\]
B.  \[4(z+2)(z+3)\]
C.  \[2(z+3)\,(z+1)\]
D.  \[3(z+5)\,(z+5)\]
Answer» B.  \[4(z+2)(z+3)\]
1066.

Factorize\[49{{x}^{2}}-36\].

A.  \[(7x-6)\,(7x+6)\]
B.  \[(7x+36)7\]
C.  \[(7x+6)6\]
D.  \[(7x+6)\,(7x+36)\]
Answer» B.  \[(7x+36)7\]
1067.

Divide \[44({{m}^{4}}-5{{m}^{3}}-24{{m}^{2}})\] by \[11m(m-8)\].

A.  \[4{{m}^{2}}(m-3)\]
B.  \[4m(m-3)\]
C.  \[4{{m}^{2}}(m+3)\]
D.  \[4m(m+3)\]
Answer» E.
1068.

Divide \[q(5{{q}^{2}}-80)\] by \[5q(q+4)\].

A.  \[5q(q-16)\]                     
B.  \[(q-4)\]             
C.         \[5q({{q}^{2}}+16)\]     
D.         \[(q+16)\]
Answer» C.         \[5q({{q}^{2}}+16)\]     
1069.

Simplify \[\frac{3lm}{8{{n}^{2}}}\times \frac{32{{\ln }^{3}}}{{{m}^{2}}}\div \frac{9{{\ln }^{2}}}{m}\].

A.  \[\frac{4l}{3n}\]                                              
B.  \[-\frac{4l}{3n}\]            
C.         \[\frac{4n}{3l}\]                              
D.         \[\frac{-4n}{3l}\]                            
Answer» B.  \[-\frac{4l}{3n}\]            
1070.

Give the factor form of \[3(2p-q+4r)+2p+15q-16r\]

A.  \[4\,(2p+3q+r)\]
B.  \[4\,(2p+3q-r)\]
C.  \[4\,(2p-3q+r)\]
D.  \[4\,(2p-3q-r)\]
Answer» C.  \[4\,(2p-3q+r)\]
1071.

What is the factorization of \[3xz-4yz-6xp+8yp\]?

A.  \[(3x+4y)\,(z+2p)\]
B.  \[(3x+4y)\,(z-2p)\]
C.  \[(3x-4y)\,(z+2p)\]
D.  \[(3x-4y)\,(z-2p)\]
Answer» E.
1072.

What are the factors of \[{{x}^{4}}+2{{x}^{2}}+9\]?

A.  \[({{x}^{2}}+2x+3),({{x}^{2}}-2x+3)\]
B.  \[({{x}^{2}}+3),({{x}^{2}}-3)\]
C.  \[({{x}^{2}}+2x+3),({{x}^{2}}+2x+3)\]
D.  \[({{x}^{2}}+3),({{x}^{2}}+3)\]
Answer» B.  \[({{x}^{2}}+3),({{x}^{2}}-3)\]
1073.

Simplify \[\frac{3(4+2{{m}^{2}}-m)-6(3{{m}^{2}}+m+2)}{2(2m-3)+3(m+2)}\]

A.                  \[\frac{3(3m+4)}{7}\]   
B.                  \[\frac{3(4m+3)}{7}\]
C.                  \[3\left( \frac{3m-4}{7} \right)\]
D.                  \[\frac{-3(4m+3)}{7}\]      
Answer» E.
1074.

Divide: \[4{{p}^{5}}-14{{p}^{4}}+6{{p}^{3}}-2{{p}^{2}}\] by \[2{{p}^{2}}\].

A.  \[2{{p}^{3}}+7{{p}^{2}}+3p+1\]
B.  \[2{{p}^{3}}-7{{p}^{2}}+3p-1\]
C.  \[2{{p}^{3}}-7{{p}^{2}}-3p-1\]
D.  \[2{{p}^{3}}+7{{p}^{2}}-3p-1\]
Answer» C.  \[2{{p}^{3}}-7{{p}^{2}}-3p-1\]
1075.

Find the quotient of the algebraic terms in \[\frac{36{{x}^{3}}{{y}^{2}}z}{-9{{x}^{2}}\,{{y}^{2}}z}\].

A.  \[4x\]                                  
B.  \[4x{{y}^{2}}z\]               
C.         \[-4x\]                
D.         \[4{{x}^{3}}{{y}^{2}}z\]
Answer» D.         \[4{{x}^{3}}{{y}^{2}}z\]
1076.

Simplify \[\frac{-3{{a}^{2}}b\times 15ca{{b}^{2}}}{-10\,cab}\].

A.  \[\frac{3}{2}{{a}^{2}}{{b}^{2}}\]                               
B.  \[\frac{9}{2}{{a}^{2}}{{b}^{2}}\]               
C.  \[\frac{3}{2}{{a}^{3}}{{b}^{3}}\]               
D.         \[\frac{7}{2}{{a}^{2}}{{b}^{2}}\]
Answer» C.  \[\frac{3}{2}{{a}^{3}}{{b}^{3}}\]               
1077.

Divide  \[-15{{a}^{2}}b{{c}^{3}}\] by \[-5ab{{c}^{2}}\].

A.  \[3{{a}^{1}}c\]                                 
B.  \[3{{a}^{2}}c\] 
C.  \[3{{a}^{3}}c\] 
D.         \[4{{a}^{2}}c\]
Answer» C.  \[3{{a}^{3}}c\] 
1078.

What are the factors of \[{{a}^{2}}{{b}^{2}}+{{c}^{2}}{{d}^{2}}-{{a}^{2}}{{c}^{2}}-{{b}^{2}}{{d}^{2}}\]?

A.  \[(a+d),\,(a-d),(b+c)\] and \[(b-c)\]
B.  \[({{a}^{2}}-{{b}^{2}})\]
C.  \[({{a}^{2}}-{{d}^{2}})\] and \[({{b}^{2}}+{{c}^{2}})\]
D.  \[({{a}^{2}}+{{d}^{2}})\] and \[({{b}^{2}}-{{c}^{2}})\]
Answer» B.  \[({{a}^{2}}-{{b}^{2}})\]
1079.

What is the result when \[{{x}^{3}}+6{{x}^{2}}+9x\]is factorized?

A.  \[{{x}^{2}}{{(x+2)}^{2}}\]                            
B.  \[x{{(x+3)}^{2}}\]           
C.         \[x(x+3)\]          
D.         \[{{x}^{2}}(x+3)\]
Answer» C.         \[x(x+3)\]          
1080.

Do as directed. (i) Factorise: \[{{x}^{2}}+\frac{1}{{{x}^{2}}}-3\] (ii) Find the greatest common factors of \[14{{x}^{2}}{{y}^{3}},21{{x}^{3}}{{y}^{2}}\] and \[35{{x}^{4}}{{y}^{5}}z\]. (iii) Divide \[z(5{{z}^{2}}-80)\]by \[5z(z+4)\].

A. (i) (ii) (iii) \[\left( x-\frac{1}{x} \right)\left( x-\frac{1}{x}-2 \right)\] \[7x{{y}^{2}}\] \[z-4\]                
B. (i) (ii) (iii) \[\left( x+\frac{1}{x} \right)\left( x+\frac{1}{x}+2 \right)\] \[7{{x}^{2}}y\] \[z-4\]                
C. (i) (ii) (iii) \[\left( x-\frac{1}{x}+1 \right)\left( x-\frac{1}{x}-1 \right)\] \[7{{x}^{2}}{{y}^{2}}\] \[z-4\]                
D. (i) (ii) (iii) \[\left( x-\frac{1}{x}-1 \right)\left( x+\frac{1}{x}+1 \right)\] \[7{{x}^{2}}{{y}^{2}}\] \[z-2\]
Answer» D. (i) (ii) (iii) \[\left( x-\frac{1}{x}-1 \right)\left( x+\frac{1}{x}+1 \right)\] \[7{{x}^{2}}{{y}^{2}}\] \[z-2\]
1081.

Which of the following is the exponential form of factors of \[{{a}^{2}}+4a+4\]?        

A.  \[{{(a+2)}^{2}}\]                             
B.  \[{{(a+1)}^{2}}\]             
C.         \[{{(a-2)}^{2}}\]              
D.         \[{{(a-1)}^{2}}\]                                                              
Answer» B.  \[{{(a+1)}^{2}}\]             
1082.

Find the factors of\[6\text{ }mn-4n+6-9m\].  

A.  \[(2m-1)\] and \[(2n-4)\]
B.  \[(4m-1)\] and \[(n-3)\]
C.  \[(3m-2)\] and \[(2n-3)\]
D.  \[(4m-4)\] and \[(n-1)\]            
Answer» D.  \[(4m-4)\] and \[(n-1)\]            
1083.

If \[({{x}^{2}}+3x+5)({{x}^{2}}-3x+5)={{m}^{2}}-{{n}^{2}}\]then m=_____.

A.  \[{{x}^{2}}-3x\]                 
B.  \[3x\]  
C.  \[{{x}^{2}}+5\]                 
D.  Both (a) and (b)
Answer» D.  Both (a) and (b)
1084.

Find the factors of \[{{b}^{2}}-7b+12\].

A.  \[(b-4),\,(b-8)\]
B.  \[(b-3),\,(b-4)\]
C.  \[(b-10),\,(b-1)\]
D.  \[(b-7),\,(b-9)\]
Answer» C.  \[(b-10),\,(b-1)\]
1085.

Divide \[6{{p}^{5}}+18{{p}^{4}}-3{{p}^{2}}\] by \[3{{p}^{2}}\].

A.  \[6{{p}^{3}}-6{{p}^{2}}+1\]
B.  \[2{{p}^{3}}-6{{p}^{2}}-1\]
C.  \[2{{p}^{3}}+6{{p}^{2}}-1\]
D.  \[2{{p}^{3}}+6{{p}^{2}}+1\]
Answer» D.  \[2{{p}^{3}}+6{{p}^{2}}+1\]
1086.

Fill in the blanks. (i) \[\frac{{{a}^{2}}-{{b}^{2}}}{a(a-b)}-\frac{a{{b}^{2}}+{{a}^{2}}b}{a{{b}^{2}}}\] is equal to    P   . (ii) \[\frac{64{{y}^{4}}+8{{y}^{3}}}{4{{y}^{3}}}\] is equal to     Q    . (iii) When we divide \[(38{{a}^{3}}{{b}^{3}}{{c}^{2}}-19{{a}^{4}}{{b}^{2}}c)\] by \[19{{a}^{2}}bc\], the result is \[ka{{b}^{2}}c-{{a}^{2}}b\]. Then \[k=\underline{\,\,\,R\,\,\,}\].

A. P Q R \[\frac{(a+b)(b-a)}{ab}\] \[3(8y+1)\] 1                
B. P Q R \[\frac{(a+b\,)(b-a)}{ab}\] \[3(8y+1)\] 1                
C. P Q R \[\frac{(a+b)(a-b)}{ab}\] \[2(8y+1)\] 1                
D. P Q R \[\frac{(a+b)(b-a)}{ab}\] \[2(8y+1)\] 2
Answer» E.
1087.

If \[({{x}^{2}}+3x+5)\,\,({{x}^{2}}-3x+5)={{m}^{2}}-{{n}^{2}},\]what is the value of m?

A.  \[{{x}^{2}}-3x\]                               
B.  \[3x\]                  
C.  \[{{x}^{2}}+5\]
D.         \[{{x}^{2}}+3x\]
Answer» D.         \[{{x}^{2}}+3x\]
1088.

Which is the correct statement in the following?

A.  \[{{(3m+4)}^{2}}=3{{m}^{2}}+6m+16\]
B.  \[n(3n+2)=3{{n}^{2}}+2n\]
C.  \[(x-2)\,(x-8)={{x}^{2}}-16\]
D.  \[(p+2)\,(p+4)={{p}^{2}}+8\]
Answer» C.  \[(x-2)\,(x-8)={{x}^{2}}-16\]
1089.

Simplify:- \[\frac{-14{{x}^{12}}y+8{{x}^{5}}z}{2{{x}^{2}}}\]

A. \[{{x}^{3}}(-7{{x}^{7}}y+4z)\] 
B.  \[{{x}^{2}}(7{{x}^{7}}y-4z)\]    
C.  \[{{x}^{2}}(-7{{x}^{6}}y+2z)\]
D.  \[{{x}^{3}}(-7{{x}^{7}}y+4z)\]
Answer» B.  \[{{x}^{2}}(7{{x}^{7}}y-4z)\]    
1090.

Factorise\[{{(2x+3y)}^{2}}-5(2x+3y)\]- 14.

A. \[4(2x+3y)(x+y-2)\]
B.  \[4(2x+3y)(x+y+2)\]
C.  \[(2x-3y+7)(2x-3y+2)\]
D.  \[(2x+3y-7)(2x+3y+2)\]
Answer» E.
1091.

                From the following, which are the factors of \[{{a}^{2}}+b-ab-a\]?                  

A.  \[(a-1)\]and \[(a-b)\]             
B.  \[(a+b)\]and \[(a-1)\]     
C.  \[(a+1)\]and \[(a-b)\]     
D.  \[(a+b)\] and \[(a+1)\]                 
Answer» B.  \[(a+b)\]and \[(a-1)\]     
1092.

One of the factors of (\[{{(p+q)}^{2}}-{{(a-b)}^{2}}\]\[+p+q-a+b\] is

A.  \[(p+q+a+b)\]         
B.  \[(p+q-a+b)\]
C.  \[(p-q+a-b)\]
D.         \[(p-q+a+b)\]
Answer» C.  \[(p-q+a-b)\]
1093.

What is the coefficient of 'a' when \[9{{a}^{2}}+18a\]is divided by \[(a+2)\]?

A.  \[18\]                                  
B.  \[9\]                    
C.  \[\frac{1}{2}\]                  
D.         \[2\]                                    
Answer» C.  \[\frac{1}{2}\]                  
1094.

Divide \[(32{{x}^{4}}{{y}^{3}}-16{{x}^{3}}{{y}^{4}})\] by \[(-8{{x}^{2}}y)\]

A. \[4{{x}^{3}}{{y}^{2}}+2x{{y}^{3}}\]           
B.  \[4{{x}^{3}}y-2x{{y}^{3}}\]      
C.  \[-4{{x}^{2}}{{y}^{2}}+2x{{y}^{3}}\]
D.         \[-4x{{y}^{2}}+2x{{y}^{3}}\]   
Answer» D.         \[-4x{{y}^{2}}+2x{{y}^{3}}\]   
1095.

Which of the following are the factors of \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{9}\]?

A.  \[\left( \frac{x}{4}+\frac{y}{9} \right)\] and \[\left( \frac{x}{4}-\frac{y}{9} \right)\]
B.  \[\left( \frac{x}{2}+\frac{y}{9} \right)\] and \[\left( \frac{x}{2}-\frac{y}{9} \right)\]
C.  \[\left( \frac{x}{2}+\frac{y}{3} \right)\]and \[\left( \frac{x}{2}-\frac{y}{3} \right)\]
D.  \[\left( \frac{x}{2}-\frac{y}{3} \right)\] and \[\left( \frac{x}{4}-\frac{y}{9} \right)\]
Answer» D.  \[\left( \frac{x}{2}-\frac{y}{3} \right)\] and \[\left( \frac{x}{4}-\frac{y}{9} \right)\]
1096.

How many factors does \[({{x}^{9}}-x)\] have?

A.  \[5\]                                    
B.  \[4\]                    
C.         \[2\]                    
D.         \[9\]
Answer» B.  \[4\]                    
1097.

For \[{{x}^{2}}+2x+5\] to be a factor of\[x4+p{{x}^{2}}+q\], the values of p and q must be _____.

A.  -2, 5               
B.  5, 25  
C.  10, 20            
D.  6, 25  
Answer» E.
1098.

Choose the factors of \[15{{x}^{2}}-26x+8\] from the following.

A.  \[(3x-4),(5x+2)\]
B.  \[(3x-4),(5x-2)\]
C.  \[(3x+4),(5x-2)\]
D.  \[(3x+4),(5x+2)\]
Answer» C.  \[(3x+4),(5x-2)\]
1099.

Factorisation of \[xy-pq+qy-px\]is ______.

A.  \[(y-p)(x+q)\] 
B.  \[(y-p)(x-q)\]
C.         \[(y+p)(x+q)\]
D.         \[(y+p)(x-q)\] 
Answer» B.  \[(y-p)(x-q)\]
1100.

What are the factors of \[ax+by+bx+az+ay+bz\]?

A.  \[(bx+ay),(ax+by)\]
B.  \[(a+b),(2x+2y+2z)\]
C.  \[(x+y+z),(a+b)\]
D.  \[(x+y-z),(a-b)\]
Answer» D.  \[(x+y-z),(a-b)\]