Explore topic-wise MCQs in 9th Class.

This section includes 1900 Mcqs, each offering curated multiple-choice questions to sharpen your 9th Class knowledge and support exam preparation. Choose a topic below to get started.

651.

What is the valve of \[\left( lo{{g}_{\frac{1}{2}}}2 \right)\left( lo{{g}_{\frac{1}{3}}}3 \right)\left( lo{{g}_{\frac{1}{4}}}4 \right)........\left( lo{{g}_{\frac{1}{99}}}99 \right)\]

A.  1 
B.  -1             
C.  1 or -1                         
D.  0
Answer» B.  -1             
Discussion
652.

If \[\mathbf{x=}\frac{\sqrt{\mathbf{8}}\mathbf{+}\sqrt{\mathbf{2}}}{\mathbf{2}}\] and \[\mathbf{y=}\frac{\sqrt{\mathbf{8}}-\sqrt{\mathbf{2}}}{\mathbf{2}}\] then the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{121}}}\], \[\mathbf{(}{{\mathbf{x}}_{\mathbf{2}}}\mathbf{+4xy+}{{\mathbf{y}}_{\mathbf{2}}}\mathbf{)}\], equal to __________

A. 1                                                         
B. \[\frac{1}{2}\]    
C. \[\frac{13}{4}\]                                                 
D. 2
E. None of these
Answer» C. \[\frac{13}{4}\]                                                 
Discussion
653.

What is the value of \[lo{{g}_{100}}0.01\]?

A.  1/2                              
B. : \[-1\]  
C.  \[\frac{-1}{3}\]                        
D.  -3
Answer» C.  \[\frac{-1}{3}\]                        
Discussion
654.

If the sum of two numbers m and n is\[\sqrt{\mathbf{22}}\] and their difference  is \[\sqrt{\mathbf{18}}\] (where m > n), then the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{m}}}\mathbf{n}\] is equal to _____

A. 1                                                         
B. 0           
C. \[-1\]        
D. 2
E. None of these
Answer» D. 2
Discussion
655.

What is the value of\[\mathbf{2}\,\mathbf{log}(\mathbf{5}/\mathbf{8})+\mathbf{log}\left( \mathbf{l28}/\mathbf{125} \right)+\mathbf{log}\left( \mathbf{5}/\mathbf{2} \right)\]?

A.  0       
B.  -1             
C.  2                                
D.  5
Answer» B.  -1             
Discussion
656.

\[\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{x}}\mathbf{.}\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{x}}}\mathbf{27}}\mathbf{.}\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{9}}}\mathbf{x}}\mathbf{.}\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{x}}}\mathbf{729}}\]

A. \[\frac{1}{3}\]                                      
B. 3            
C.  9                                                        
D. \[\frac{1}{9}\] 
E. None of these
Answer» E. None of these
Discussion
657.

If \[{{\log }_{r}}6=m\] and \[lo{{g}_{r}}3=n\] then is \[lo{{g}_{r}}\left( r/2 \right)\]is equal to

A.  \[m-n+1\]        
B.  \[m+n-1\]           
C.  \[m-n-1\]                      
D.  \[m-n+1\]
Answer» E.
Discussion
658.

The value of the expression \[{{\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{2} \right)}^{\mathbf{3}}}\mathbf{+}\] \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{8}\,.\,\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{5}\text{ }\mathbf{+}\text{ }{{\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{5} \right)}^{\mathbf{3}}}\] is equal to _______

A. 0                                                         
B. 1            
C. 2                                                         
D. 3
E. None of these
Answer» C. 2                                                         
Discussion
659.

If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{16}}}\mathbf{m}=\mathbf{4}.\mathbf{5}\] and \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{4}}}\mathbf{n}=\mathbf{9},\]then m = ________

A. \[\sqrt{n}\]
B. \[{{n}^{2}}\]
C. n        
D. \[n\sqrt{n}\]
E. None of these
Answer» D. \[n\sqrt{n}\]
Discussion
660.

Simplify: \[\left[ \frac{1}{{{\log }_{xy}}(xyz)}+\frac{1}{{{\log }_{yz}}(xyz)}+\frac{1}{{{\log }_{zx}}(xyz)} \right]\]  

A.  1                                
B.  2
C.  3                                
D.  0
Answer» C.  3                                
Discussion
661.

What is the value of \[{{[lo{{g}_{10}}(5lo{{g}_{10}}100)]}^{2}}_{b}\]

A.  4                    
B.  3             
C.  2                                
D.  1
Answer» E.
Discussion
662.

If log 2 = 0.3010, then the number of digits in \[{{\mathbf{2}}^{\mathbf{512}}}\] is _______

A. 150                                         
B. 154
C. 155     
D. 153
E. None of these
Answer» D. 153
Discussion
663.

What is \[lo{{g}_{10}}\left( \frac{3}{2} \right)+lo{{g}_{10}}\left( \frac{4}{3} \right)+lo{{g}_{10}}\left( \frac{5}{4} \right)+.......\]up to 10 terms equal to?

A.  0                                
B.  \[lo{{g}_{10}}6\]   
C.  \[lo{{g}_{10}}5\]                     
D.  None of these
Answer» C.  \[lo{{g}_{10}}5\]                     
Discussion
664.

If\[{{2}^{lo{{g}_{3}}^{9}}}+{{25}^{lo{{g}_{9}}^{3}}}={{8}^{lo{{g}_{x}}^{9}}}\], then x = _______.

A.  9                                
B.  8   
C.  3                                
D.  2
Answer» C.  3                                
Discussion
665.

If \[\mathbf{4a}\mathbf{.}{{\mathbf{b}}^{\mathbf{5log}}}{{_{\mathbf{b}}}^{\mathbf{a}}}\mathbf{=2916}\]then the value of a is _________

A.             1                                                         
B. 0           
C. 2                                                         
D. 3
E. None of these
Answer» E. None of these
Discussion
666.

If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{x}}}\mathbf{1/32=}\frac{-\,\mathbf{5}}{\mathbf{4}}\] then the value of x is __________

A. 8                                             
B. 16
C. 32                                            
D. 64
E. None of these
Answer» C. 32                                            
Discussion
667.

The value of \[\frac{1}{1+{{\log }_{ab}}c}+\frac{1}{1+{{\log }_{ac}}b}+\frac{1}{1+{{\log }_{bc}}a}\] equals

A.  2       
B.  0              
C.  1                                
D.  log abc
Answer» B.  0              
Discussion
668.

Solve for x, the equation: \[\mathbf{log}\,\,\left[ \mathbf{log}\,\mathbf{3}+\mathbf{log}\,\mathbf{3}\,\left( \mathbf{x}+\mathbf{1} \right) \right]=\mathbf{0}\]

A. \[{{2}^{8}}+1\]        
B. \[{{3}^{8}}+1\]       
C. \[{{2}^{7}}-1\]                                               
D. \[{{3}^{7}}-1\]
E. None of these
Answer» E. None of these
Discussion
669.

If \[l\mathbf{og}\left( \mathbf{0}.\mathbf{37} \right)=\overline{1}.\mathbf{756}\], then the value of \[\mathbf{log37}+\mathbf{log}{{\left( \mathbf{0}.\mathbf{37} \right)}^{\mathbf{3}}}+\mathbf{log}\sqrt{0.\mathbf{37}}\]Is:

A.  0.902                          
B.  \[\overline{2}.146\]          
C.  3.444   
D.  \[\overline{1}.146\]
Answer» D.  \[\overline{1}.146\]
Discussion
670.

Find the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\left( \frac{{{\mathbf{2}}^{\mathbf{2}}}\times {{\mathbf{3}}^{\mathbf{3}}}}{{{\mathbf{5}}^{\mathbf{3}}}} \right)\] where it is given that \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{2=0}\mathbf{.3010}\]and \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{3=0}\mathbf{.4771}\]

A. 0.2373                         
B. 2.0970      
C. 0.2070                                                 
D. 0.2273
E. None of these
Answer» B. 2.0970      
Discussion
671.

If \[\mathbf{x=lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{27}\] and \[\mathbf{y=lo}{{\mathbf{g}}_{\mathbf{9}}}\mathbf{27}\] then \[\frac{\mathbf{1}}{\mathbf{x}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{y}}\mathbf{=}\]______.

A.  \[\frac{1}{3}\]                         
B.  \[\frac{1}{9}\]              
C.  3                                
D.  1
Answer» E.
Discussion
672.

If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{x}-\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{y}=\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{5}-\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{10}\] and \[\mathbf{3x=y+2}\]then y is equal to _________

A. 4      
B. 3           
C. 2                                                         
D. 1
E. None of these
Answer» B. 3           
Discussion
673.

\[\frac{\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{6}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{2+1}}=\]

A.  \[lo{{g}_{2}}6\]                      
B.  \[lo{{g}_{2}}5\]           
C.  \[lo{{g}_{10}}6\]    
D.  \[lo{{g}_{10}}30\]
Answer» D.  \[lo{{g}_{10}}30\]
Discussion
674.

If \[{{\mathbf{5}}^{\mathbf{log}}}{{^{_{\mathbf{5}}}}^{\mathbf{4}}}\mathbf{+}{{\mathbf{4}}^{\mathbf{lo}{{\mathbf{g}}_{\mathbf{x}}}\mathbf{3}}}\mathbf{=7}\] then the value of x is _________

A. 1                                                         
B. 2            
C. 3                                                         
D. 4
E. None of these
Answer» E. None of these
Discussion
675.

If \[x={{y}^{x}},y={{z}^{y}}\]and \[z={{x}^{y}}\], then the value of xyz equal to;

A.  -1                               
B.  0             
C.  1      
D.  xyz
Answer» D.  xyz
Discussion
676.

\[\mathbf{log}\left( \frac{\mathbf{1}}{\mathbf{2}} \right)\mathbf{+log}\left( \frac{\mathbf{2}}{\mathbf{3}} \right)\mathbf{+log}\left( \frac{\mathbf{3}}{\mathbf{4}} \right)......\mathbf{+log}\left( \frac{\mathbf{999}}{\mathbf{1000}} \right)\]    

A. -3                    
B. -2          
C. -1                                                        
D. 0
E. None of these
Answer» B. -2          
Discussion
677.

Find the value of x which satisfies the relation\[lo{{g}_{10}}2+lo{{g}_{10}}(\mathbf{4x}+1)=\mathbf{lo}{{\mathbf{g}}_{10}}(\mathbf{x}+1)+1\]

A.  4                                
B.  \[-4\]
C.  1/4                              
D.  not defined
Answer» C.  1/4                              
Discussion
678.

Simplification of\[\mathbf{5}\text{ }\mathbf{log}\text{ }\mathbf{2}+\mathbf{4}\text{ }\mathbf{log}\text{ }\mathbf{3}+\mathbf{2}\text{ }\mathbf{log}\text{ }\mathbf{4}\] \[+\,\mathbf{log}\text{ }\mathbf{5}-\mathbf{2}\text{ }\mathbf{log}\text{ }\mathbf{9}\]is ________

A. \[\text{log 2156}\]                                                         
B. \[\text{log 256}\]     
C. \[\text{log 2560}\]         
D. \[\text{log 3162}\]
E. None of these
Answer» D. \[\text{log 3162}\]
Discussion
679.

If \[lo{{g}_{10}}8=x\], then \[lo{{g}_{10}}\left( \frac{1}{80} \right)\] is equal to:

A.  \[-\left( 1+x \right)\]   
B.  \[{{\left( 1+x \right)}^{-1}}\]
C.  \[\frac{a}{10}\]                           
D.  \[\frac{1}{10a}\]
Answer» B.  \[{{\left( 1+x \right)}^{-1}}\]
Discussion
680.

If \[{{\mathbf{x}}^{\mathbf{3}}}\mathbf{-}{{\mathbf{y}}^{\mathbf{3}}}\mathbf{=1}\],  x > y, then find the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{(x-y)}}}\mathbf{ (}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+xy)}\]

A. 0                                                                     
B. 1
C. -1             
D. Cannot be determined
E.  None of these
Answer» D. Cannot be determined
Discussion
681.

\[\left[ \frac{1}{\left( {{\log }_{x}}yz \right)+1}+\frac{1}{\left( {{\log }_{y}}zx \right)+1}+\frac{1}{\left( {{\log }_{z}}xz \right)+1} \right]\]is equal to :

A.  1         
B.  \[\frac{3}{2}\]               
C.  2                                
D.  3
Answer» B.  \[\frac{3}{2}\]               
Discussion
682.

If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{4 + lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{7=x }-\mathbf{ 1}\], then find the value of\[\frac{\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{ 84}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{ 28}}\].

A. \[\frac{x}{x+1}\]          
B. \[\frac{x+1}{x}\]
C. \[\frac{x-1}{x}\]                                                
D. \[\frac{x}{x-1}\]
E. None of these
Answer» E. None of these
Discussion
683.

The value of \[{{16}^{{{\log }_{4}}5}}\]is:

A.  \[\frac{5}{64}\]                            
B.  5
C.  16                               
D.  25
Answer» E.
Discussion
684.

The value of \[\left( \mathbf{lo}{{\mathbf{g}}_{3}}\mathbf{4} \right)\left( \mathbf{lo}{{\mathbf{g}}_{4}}\mathbf{5} \right)\left( \mathbf{lo}{{\mathbf{g}}_{5}}\mathbf{6} \right)\left( \mathbf{lo}{{\mathbf{g}}_{6}}\mathbf{7} \right)\left( \mathbf{lo}{{\mathbf{g}}_{7}}\mathbf{8} \right)\left( \mathbf{lo}{{\mathbf{g}}_{8}}\mathbf{9} \right)\] is :

A.  2  
B.  7
C.  8                    
D.  33
Answer» B.  7
Discussion
685.

If \[\mathbf{log}\,\mathbf{[4}-\mathbf{6 lo}{{\mathbf{g}}_{\mathbf{64}}}\mathbf{ (x+5)]=0}\], then the value of x is _______

A. 0                                                                     
B. 1            
C. 2                                                                     
D. 3
E. None of these
Answer» E. None of these
Discussion
686.

\[{{\mathbf{2}}^{\mathbf{4}\,\mathbf{log}}}{{^{_{\mathbf{2}}}}^{\mathbf{5}}}\mathbf{ + }{{\mathbf{3}}^{\mathbf{2}\,\mathbf{log}}}{{^{_{\mathbf{3}}}}^{\mathbf{4}}}\mathbf{=}\]________

A.             641                                    
B. 5           
C. 25                                                                    
D. 625
E. None of these
Answer» B. 5           
Discussion
687.

The value of \[\left( \frac{1}{{{\log }_{3}}60}+\frac{1}{{{\log }_{4}}60}+\frac{1}{{{\log }_{5}}60} \right)\]  is:

A.  0                                
B.  1
C.  5                                
D.  60
Answer» C.  5                                
Discussion
688.

Solve: \[\frac{\mathbf{lo}{{\mathbf{g}}_{\mathbf{16}}}\mathbf{(lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{ 625)}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{512}}}\mathbf{(lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{ 6561)}}\]

A. \[\frac{1}{6}\]                                                              
B. \[\frac{5}{2}\]
C. \[\frac{2}{3}\]                                                  
D. \[\frac{3}{2}\]
E. None of these
Answer» E. None of these
Discussion
689.

if \[lo{{g}_{5}}({{x}^{2}}+x)-lo{{g}_{10}}(x+1)=2\], then the value of x is:

A.  5                                
B.  10
C.  25       
D.  32
Answer» D.  32
Discussion
690.

The value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{7}}}\mathbf{3}.\text{ }\mathbf{lo}{{\mathbf{g}}_{\mathbf{27}}}\mathbf{4}.\text{ }\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{7}.\text{ }\mathbf{lo}{{\mathbf{g}}_{\mathbf{64}}}\mathbf{5}\]is _________

A. \[\frac{1}{2}\]                                                              
B. \[\frac{1}{4}\]
C. \[\,\frac{1}{8}\]                                                            
D. \[\frac{1}{9}\]
E. None of these
Answer» E. None of these
Discussion
691.

If \[lo{{g}_{10}}5+lo{{g}_{10}}(5x+1)=log\left( x+5 \right)+1,\] then x is equal to:

A.  1                                
B.  3
C.  5                                
D.  10
Answer» C.  5                                
Discussion
692.

Which of the following is least among the following? \[\text{lo}{{\text{g}}_{4}}260,\,\,{{\log }_{2}}18,\,\,{{\log }_{7}}2300,\,\,{{\log }_{5}}630,\,\,{{\log }_{3}}200\]

A. \[{{\log }_{4}}260\]                                                      
B. \[{{\log }_{2}}18\]
C. \[{{\log }_{7}}2300\]
D. \[{{\log }_{3}}225\]
E. None of these
Answer» D. \[{{\log }_{3}}225\]
Discussion
693.

If \[lo{{g}_{5}}x+2{{\log }_{25}}x+3lo{{g}_{12}}x=9,\] then x = ________.

A.  6                                
B.  36              
C.  125     
D.  None of these
Answer» D.  None of these
Discussion
694.

If \[lo{{g}_{8}}x+lo{{g}_{8}}\frac{1}{6}=\frac{1}{3}\], then the value of s Is:

A.  12     
B.  16
C.  18                               
D.  24
Answer» B.  16
Discussion
695.

If \[\frac{\mathbf{log x}}{\mathbf{log y}}\mathbf{=}\frac{\mathbf{log 121}}{\mathbf{log 11}}\], then the relation between x and Y is __________

A. \[x=\sqrt{y}\]                                                   
B. \[{{x}^{2}}=y\]
C. \[x={{y}^{2}}\]         
D. \[x=2y\]
E. None of these
Answer» D. \[x=2y\]
Discussion
696.

If \[log2=x,log3=y\] and log\[\mathbf{7}=\mathbf{z}\], then the value of \[\mathbf{log}\left( \mathbf{8}.\sqrt[3]{\mathbf{21}} \right)\]is:

A.  \[2x+\frac{2}{3}y-\frac{1}{3}z\]          
B.  \[2x+\frac{2}{3}y+\frac{1}{3}z\]
C.  \[2x-\frac{2}{3}y+\frac{1}{3}z\]         
D.  \[3x+\frac{1}{3}y+\frac{1}{3}z\]
Answer» E.
Discussion
697.

If \[lo{{g}_{a}}(ab)=x,\]then \[lo{{g}_{b}}(ab)\]is:

A.  \[\frac{1}{x}\]                         
B.  \[\frac{x}{1+x}\]
C.  \[\frac{x}{1-x}\]                       
D.  \[\frac{x}{x-1}\]
Answer» E.
Discussion
698.

\[\log \mathbf{l60}\]is equal to:

A.  \[2\,log2+3\,log3\]        
B.  \[3\,log2+2\,log3\]
C.  \[3\,log2+2\,log3-log5\]           
D.  \[5\,log2+log5\]
Answer» E.
Discussion
699.

If \[{{\mathbf{a}}^{\mathbf{6}}}=\text{ }{{\mathbf{b}}^{\mathbf{6}}}+{{\mathbf{c}}^{\mathbf{6}}}\], then the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{c}}}({{\mathbf{a}}^{\mathbf{2}}}-{{\mathbf{b}}^{\mathbf{2}}})+\mathbf{lo}{{\mathbf{g}}_{\mathbf{c}}}({{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}+\mathbf{ab})\]\[+\text{ }\mathbf{lo}{{\mathbf{g}}_{\mathbf{c}}}\left( {{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}+\mathbf{ab} \right)\] is equal to ________

A. 1                                                         
B. 3           
C. 6           
D. 0
E. None of these
Answer» D. 0
Discussion
700.

Evaluate: \[lo{{g}_{16}}64~-lo{{g}_{64}}16\]

A.  6                                
B.  \[\frac{1}{6}\]
C.  \[\frac{6}{5}\]                         
D.  \[\frac{5}{6}\]
Answer» E.
Discussion