Railways Quantitative Aptitude Simplification Sample Paper

done Simplification Sample Test Paper-3 Total Questions - 20    [Download]

• question_answer1)
  If \[x=\frac{1}{2+\sqrt{3}},\] find the value of \[{{x}^{3}}-{{x}^{2}}-11x+3\]
  A)
   0        
  done clear
  B)
          3       
  done clear
  C)
   x                    
  done clear
  D)
   x+3
  done clear
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• question_answer2)
  If \[x=3\sqrt{3}+\sqrt{26}\]  find the value of \[\frac{1}{2}\left( x+\frac{1}{x} \right)\]
  A)
   \[\frac{1}{2}\]             
  done clear
  B)
   \[\sqrt{3}\]     
  done clear
  C)
   3        
  done clear
  D)
   \[3\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer3)
  If \[x=2+{{2}^{1/3}}+{{2}^{2/3}}\] find \[{{x}^{3}}-6{{x}^{2}}+6x-2.\]
  A)
   0                    
  done clear
  B)
   1         
  done clear
  C)
   2        
  done clear
  D)
   6
  done clear
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• question_answer4)
  Express \[1.272727.....=1.\overline{27}\] in the form \[\frac{p}{q},\]where p and q are integers and \[q\ne 0.\]
  A)
   \[\frac{1}{27}\]            
  done clear
  B)
   \[\frac{1}{11}\]
  done clear
  C)
   \[\frac{14}{11}\]                      
  done clear
  D)
   \[\frac{14}{27}\]
  done clear
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• question_answer5)
  The value of x, when \[{{2}^{x+4}}{{.3}^{x+1}}=288.\]                                                                                                                                     
  A)
   1                    
  done clear
  B)
   \[-1\]      
  done clear
  C)
   0        
  done clear
  D)
   None
  done clear
  View Answer play_arrow

• question_answer6)
  When simplified the product \[\left( 1+\frac{1}{2} \right)\left( 1+\frac{1}{3} \right)\left( 1+\frac{1}{4} \right).....\left( 1+\frac{1}{n} \right)\] becomes
  A)
   \[n\]                
  done clear
  B)
   \[\frac{n-1}{2}\]
  done clear
  C)
   \[\frac{n+1}{2}\]         
  done clear
  D)
   \[\frac{n}{2}\]
  done clear
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• question_answer7)
  If \[a=2+\sqrt{3}\] and & \[b=2-\sqrt{3}\] then \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}\] is equal to
  A)
   14                   
  done clear
  B)
   \[-14\]    
  done clear
  C)
   \[8\sqrt{3}\]     
  done clear
  D)
   \[-8\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer8)
  Rationalizing factor of \[(2+\sqrt{3})=\]
  A)
   \[2-\sqrt{3}\]    
  done clear
  B)
   \[\sqrt{3}\]
  done clear
  C)
   \[2+\sqrt{3}\]  
  done clear
  D)
   \[3+\sqrt{3}\]
  done clear
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• question_answer9)
  Which of the following is equal to x?
  A)
   \[{{x}^{\frac{12}{7}}}-{{x}^{\frac{5}{7}}}\]           
  done clear
  B)
   \[\sqrt[12]{{{\left( {{x}^{4}} \right)}^{\frac{1}{3}}}}\]
  done clear
  C)
   \[{{\left( \sqrt{{{x}^{3}}} \right)}^{\frac{2}{3}}}\]     
  done clear
  D)
          \[{{x}^{\frac{12}{19}}}+{{x}^{\frac{7}{19}}}\]
  done clear
  View Answer play_arrow

• question_answer10)
  If \[\frac{1}{x+1}+\frac{1}{x+4}=0\]then x=
  A)
   \[2\frac{1}{2}\]            
  done clear
  B)
   \[-2\frac{1}{2}\]
  done clear
  C)
   3                    
  done clear
  D)
   \[-\,3\]
  done clear
  View Answer play_arrow

• question_answer11)
  If \[\frac{x}{pq}+\frac{x}{qr}+\frac{x}{pr}=p+q+r,\] then x=
  A)
   \[pqr\]              
  done clear
  B)
   \[\frac{pq}{r}\]
  done clear
  C)
   \[\frac{p}{qr}\]            
  done clear
  D)
   \[\frac{q}{pr}\]
  done clear
  View Answer play_arrow

• question_answer12)
  The equation \[\frac{12x+1}{4}=\frac{13x-1}{5}+3\] is true for
  A)
   \[x=\frac{1}{8}\]         
  done clear
  B)
   \[x=2\]
  done clear
  C)
   \[x=5/8\]         
  done clear
  D)
   \[x=\frac{3}{4}\]
  done clear
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• question_answer13)
  If \[\frac{a}{2}+b=0.8\] and \[\frac{7}{a+\frac{b}{2}}=10,\] then (a, b) are
  A)
   (0.2, 0.4)         
  done clear
  B)
   (0.3, 0.5)
  done clear
  C)
   (0.4, 0.6)         
  done clear
  D)
   (0.4, 0.5)
  done clear
  View Answer play_arrow

• question_answer14)
  A bag contains 50P, 25P and 10P coins in the ratio 2 : 3 : 4 amounting to Rs. 129. Find the number of coins of each type
  A)
   120, 180, 240
  done clear
  B)
   180, 150, 200
  done clear
  C)
   200, 180, 120
  done clear
  D)
          180, 200, 140
  done clear
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• question_answer15)
  Monthly incomes of two persons are in the ratio 4 : 5 and their monthly expenses are in the ratio 7 : 9. If each saves Rs. 50 per month, their monthly incomes (in rupees) are :
  A)
   (500, 400)        
  done clear
  B)
   (300, 600)
  done clear
  C)
   (400, 500)        
  done clear
  D)
   none of these
  done clear
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• question_answer16)
  If \[6x+3y=7xy\] and \[3x+9y=11xy,\] then the value of x and y are
  A)
   \[\left( 1,\frac{3}{2} \right)\]      
  done clear
  B)
   \[\left( 2,\frac{3}{2} \right)\]
  done clear
  C)
   \[\left( \frac{3}{2},1 \right)\]      
  done clear
  D)
   \[\left( \frac{3}{2},2 \right)\]
  done clear
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• question_answer17)
  The angle A of a triangle ABC is equal to the sum of the two other angles. Also the ratio of the angle B to angle C is 4 : 5. The three angles are
  A)
   \[90{}^\circ ,\]\[40{}^\circ ,\]\[50{}^\circ \]     
  done clear
  B)
   \[90{}^\circ ,\]\[55{}^\circ ,\]\[35{}^\circ \]
  done clear
  C)
   \[90{}^\circ ,\]\[60{}^\circ ,\]\[30{}^\circ \]
  done clear
  D)
   None of these
  done clear
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• question_answer18)
  If a is a natural number then \[{{a}^{2}}+\frac{1}{{{a}^{2}}}\] is always greater than or equal to
  A)
   5                    
  done clear
  B)
   4         
  done clear
  C)
   3                    
  done clear
  D)
   2
  done clear
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• question_answer19)
  If \[\sqrt{0.04\times 0.4\times a}=0.4\times 0.04\times \sqrt{b},\] then value of \[\frac{b}{a}\] is
  A)
   0.016  
  done clear
  B)
   \[\frac{125}{2}\]
  done clear
  C)
   0.16    
  done clear
  D)
   None of these.
  done clear
  View Answer play_arrow

• question_answer20)
  If 'x' is any natural number, then \[{{x}^{3}}-\frac{1}{{{x}^{3}}^{{}}}\] will always be greater than or equal to
  A)
   \[x+\frac{1}{x}\]         
  done clear
  B)
   \[3\left( x-\frac{1}{x} \right)\]
  done clear
  C)
   \[3\left( x+\frac{1}{x} \right)\]   
  done clear
  D)
   \[\left( {{x}^{3}}+\frac{1}{{{x}^{3}}} \right)\]
  done clear
  View Answer play_arrow