Solved papers for JEE Main & Advanced AIEEE Solved Paper-2013

done AIEEE Solved Paper-2013 Total Questions - 30

• question_answer1) Distance between two parallel planes\[2x+y\] \[+2z=8\] and\[4x+2y+4z+5=0\text{ }is:\]     AIEEE Solevd Paper-2013
  A)
  \[\frac{3}{2}\]                   
  done clear
  B)
         \[\frac{5}{2}\]                   
  done clear
  C)
         \[\frac{7}{2}\]                   
  done clear
  D)
         \[\frac{9}{2}\]
  done clear
  View Answer play_arrow

• question_answer2) At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by\[\frac{dp}{dx}=100-12\sqrt{x}\]. If the firm employs 25 more workers, then the new level of production of items is:     AIEEE Solevd Paper-2013
  A)
  2500
  done clear
  B)
                         3000      
  done clear
  C)
         3500      
  done clear
  D)
         4500
  done clear
  View Answer play_arrow

• question_answer3) Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of\[A\times B\] having 3 or more elements is:     AIEEE Solevd Paper-2013
  A)
  256        
  done clear
  B)
                         220                        
  done clear
  C)
  219                        
  done clear
  D)
         211
  done clear
  View Answer play_arrow

• question_answer4) If the lines\[\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}\]and\[\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}\]are coplanar, then k can have:     AIEEE Solevd Paper-2013
  A)
  any value                            
  done clear
  B)
  exactly one value
  done clear
  C)
  exactly two values          
  done clear
  D)
  exactly three values
  done clear
  View Answer play_arrow

• question_answer5) If the vectors \[\overrightarrow{AB}=3\hat{i}+4\hat{k}\]and \[\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\]are the sides of a triangle ABC, then the length of the median through A is:     AIEEE Solevd Paper-2013
  A)
  \[\sqrt{18}\]                      
  done clear
  B)
  \[\sqrt{72}\]      
  done clear
  C)
         \[\sqrt{33}\]      
  done clear
  D)
         \[\sqrt{45}\]
  done clear
  View Answer play_arrow

• question_answer6) The real number k for which the equation, \[2{{x}^{3}}+3x+k=0\]has two distinct real roots in [0, 1]     AIEEE Solevd Paper-2013
  A)
  lies between 1 and 2
  done clear
  B)
  lies between 2 and 3
  done clear
  C)
  lies between −1 and 0
  done clear
  D)
  does not exist
  done clear
  View Answer play_arrow

• question_answer7) The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ??, is :     AIEEE Solevd Paper-2013
  A)
  \[\frac{7}{81}(179-{{10}^{-20}})\]
  done clear
  B)
  \[\frac{7}{9}(99-{{10}^{-20}})\]
  done clear
  C)
  \[\frac{7}{81}(179+{{10}^{-20}})\]            
  done clear
  D)
  \[\frac{7}{9}(99+{{10}^{-20}})\]
  done clear
  View Answer play_arrow

• question_answer8) A ray of light along\[x+\sqrt{3}y=\sqrt{3}\]gets reflected upon reaching x−axis, the equation of the reflected ray is:     AIEEE Solevd Paper-2013
  A)
  \[y=x+\sqrt{3}\]                              
  done clear
  B)
  \[\sqrt{3y}=x-\sqrt{3}\]               
  done clear
  C)
  \[y=\sqrt{3}x-\sqrt{3}\]               
  done clear
  D)
  \[\sqrt{3}y=x-1\]
  done clear
  View Answer play_arrow

• question_answer9) The number of values of k, for which the system of equations: \[(k+1)x+8y=4k\] \[kx+(k+3)y=3k-1\] has no solution, is:     AIEEE Solevd Paper-2013
  A)
  in finite                                
  done clear
  B)
  1                             
  done clear
  C)
         2                             
  done clear
  D)
         3
  done clear
  View Answer play_arrow

• question_answer10) If the equations\[{{x}^{2}}+2x+3=0\]and\[a{{x}^{2}}+bx+\] \[c=0,\text{ }a,b,c\in R,\]have a common root, then \[a:b:c\] is     AIEEE Solevd Paper-2013
  A)
  1 : 2 : 3                 
  done clear
  B)
  3 : 2 : 1
  done clear
  C)
         1 : 3 : 2
  done clear
  D)
         3 : 1 : 2
  done clear
  View Answer play_arrow

• question_answer11) The circle passing through (1, −2) and touching the axis of\[x\]at (3, 0) also passes through the point :     AIEEE Solevd Paper-2013
  A)
  (−5, 2)                  
  done clear
  B)
  (2, −5)  
  done clear
  C)
         (5, −2)  
  done clear
  D)
         (−2, 5)
  done clear
  View Answer play_arrow

• question_answer12) If\[x,y,z\]are in A.P. and\[ta{{n}^{-1}}x,ta{{n}^{-1}}y\]and \[ta{{n}^{-1}}z\] are also in A.P., then :     AIEEE Solevd Paper-2013
  A)
  \[x=y=z\]                            
  done clear
  B)
  \[2x=3y=6z\]
  done clear
  C)
         \[6x=3y=2z\]
  done clear
  D)
         \[6x=4y=3z\]
  done clear
  View Answer play_arrow

• question_answer13) Consider: Statement − I:\[(p\wedge \sim q)\wedge (\sim p\wedge q)\]is a fallacy. Statement II:\[(p\to q)\leftrightarrow (\sim q\to \sim p)\]is a tautology.     AIEEE Solevd Paper-2013
  A)
  Statement − I is true; Statement − II is true; Statement − II is a correct explanation for Statement I.
  done clear
  B)
  Statement − I is true; Statement − II is true; Statement − II is not a correct explanation for Statement − I.
  done clear
  C)
  Statement − I is true; Statement − II is false.
  done clear
  D)
  Statement − I is false; Statement − II is true.
  done clear
  View Answer play_arrow

• question_answer14) If\[\int f(x)dx=\psi (x),\] then\[\int {{x}^{5}}f({{x}^{3}})dx\]is equal to:     AIEEE Solevd Paper-2013
  A)
  \[\frac{1}{3}\left[ {{x}^{3}}\psi ({{x}^{3}})-\int{{{x}^{2}}\psi ({{x}^{3}})dx} \right]+C\]
  done clear
  B)
  \[\frac{1}{3}{{x}^{3}}\psi ({{x}^{3}})-3\int{{{x}^{3}}\psi ({{x}^{3}})dx}+C\]
  done clear
  C)
  \[\frac{1}{3}{{x}^{3}}\psi ({{x}^{3}})-\int{{{x}^{3}}\psi ({{x}^{3}})dx}+C\]
  done clear
  D)
  \[\frac{1}{3}\left[ {{x}^{3}}\psi ({{x}^{3}})-\int{{{x}^{3}}\psi ({{x}^{3}})dx} \right]+C\]
  done clear
  View Answer play_arrow

• question_answer15) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}\]is equal to:     AIEEE Solevd Paper-2013
  A)
  \[-\frac{1}{4}\]                                 
  done clear
  B)
  \[\frac{1}{2}\]                   
  done clear
  C)
         1                             
  done clear
  D)
         2
  done clear
  View Answer play_arrow

• question_answer16) Statement − I: The value of the integral\[\int\limits_{\pi /6}^{\pi /3}{\frac{dx}{1+\sqrt{\tan x}}}\]is equal to \[\frac{\pi }{6}\] Statement − II: \[\int\limits_{a}^{b}{f(x)dx}\int\limits_{a}^{b}{f(a+b-x)dx}\]     AIEEE Solevd Paper-2013
  A)
  Statement − I is true; Statement − II is true; Statement − II is a correct explanation for Statement − I.
  done clear
  B)
  Statement − I is true; Statement − II is true; Statement − II is a not a correct explanation for Statement − I.
  done clear
  C)
  Statement − I is true; Statement − II is false.
  done clear
  D)
  Statement − I is false; Statement − II is true.
  done clear
  View Answer play_arrow

• question_answer17) The equation of the circle passing through the foci of the ellipse\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1,\]and having centre at (0, 3) is :     AIEEE Solevd Paper-2013
  A)
  \[{{x}^{2}}+{{y}^{2}}-6y-7=0\]
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}-6y+7=0\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}-6y-5=0\]
  done clear
  D)
  \[{{x}^{2}}+{{y}^{2}}-6y+5=0\]
  done clear
  View Answer play_arrow

• question_answer18) A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is:     AIEEE Solevd Paper-2013
  A)
  \[\frac{17}{{{3}^{5}}}\]                                 
  done clear
  B)
  \[\frac{13}{{{3}^{5}}}\]                 
  done clear
  C)
         \[\frac{11}{{{3}^{5}}}\]                 
  done clear
  D)
         \[\frac{10}{{{3}^{5}}}\]
  done clear
  View Answer play_arrow

• question_answer19) The x−coordinate of the in centre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is:     AIEEE Solevd Paper-2013
  A)
  \[2+\sqrt{2}\]   
  done clear
  B)
         \[2-\sqrt{2}\]
  done clear
  C)
  \[1+\sqrt{2}\]   
  done clear
  D)
         \[1-\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer20) The term independent of x in expansion of \[{{\left( \frac{x+1}{{{x}^{2/3}}-{{x}^{1/3}}+1}-\frac{x}{x-{{x}^{1/2}}} \right)}^{10}}\]is:     AIEEE Solevd Paper-2013
  A)
  4             
  done clear
  B)
                         120                        
  done clear
  C)
         210                        
  done clear
  D)
         310
  done clear
  View Answer play_arrow

• question_answer21) The area (in square units) bounded by the curves\[y=\sqrt{x},\text{ }2y-x+3=0,\]x−axis, and lying in the first quadrant is:     AIEEE Solevd Paper-2013
  A)
  9                             
  done clear
  B)
  36                          
  done clear
  C)
         18                          
  done clear
  D)
         \[\frac{27}{4}\]
  done clear
  View Answer play_arrow

• question_answer22) Let\[{{T}_{n}}\]be the number of all possible triangles formed by joining vertices of a n−sided regular polygon. If\[{{T}_{n+1}}-{{T}_{n}}=1\]then the value of n is:     AIEEE Solevd Paper-2013
  A)
  7                                             
  done clear
  B)
  5                             
  done clear
  C)
         10                          
  done clear
  D)
         8
  done clear
  View Answer play_arrow

• question_answer23) If z is a complex number of unit modulus and argument \[\theta \], then \[\arg \left( \frac{1+z}{1+z} \right)\] equals:     AIEEE Solevd Paper-2013
  A)
  \[-\theta \]                                        
  done clear
  B)
  \[\frac{\pi }{2}-\theta \]               
  done clear
  C)
         \[\theta \]                          
  done clear
  D)
         \[\pi -\theta \]
  done clear
  View Answer play_arrow

• question_answer24) ABCD is a trapezium such that AB and CD are parallel and\[BC\bot CD\]. If\[\angle ADB=\theta ,\text{ }BC=p\] and\[CD=q,\]then AB is equal to:     AIEEE Solevd Paper-2013
  A)
  \[\frac{({{p}^{2}}\text{+}{{q}^{2}})sin\theta }{p\,cos\,\theta +q\,sin\,\theta }\]
  done clear
  B)
         \[\frac{{{p}^{2}}+{{q}^{2}}cos}{p\,cos\,\theta +q\,sin\,\theta }\]
  done clear
  C)
  \[\frac{{{p}^{2}}+{{q}^{2}}}{{{p}^{2}}cos\,\theta +{{q}^{2}}sin\,\theta }\]
  done clear
  D)
         \[\frac{({{p}^{2}}+{{q}^{2}})\sin \theta }{{{(pcos\,\theta +qsin\,\theta )}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer25) If\[P=\left[ \begin{matrix}    1 & \alpha  & 3  \\    1 & 3 & 3  \\    2 & 4 & 4  \\ \end{matrix} \right]\]is the ad joint of\[3\times 3\]matrix A and \[|A|=4,\] then \[\alpha \] is equal to:     AIEEE Solevd Paper-2013
  A)
  4             
  done clear
  B)
                         11                          
  done clear
  C)
         5                             
  done clear
  D)
         0
  done clear
  View Answer play_arrow

• question_answer26) The intercepts on x−axis made by tangents to the curve,\[y=\int\limits_{0}^{x}{|t|}dt,x\in R,\]which are parallel to the line\[y=2x,\]are equal to     AIEEE Solevd Paper-2013
  A)
  \[\pm 1\]
  done clear
  B)
  \[\pm 2\]
  done clear
  C)
  \[\pm 3\]
  done clear
  D)
  \[\pm 4\]
  done clear
  View Answer play_arrow

• question_answer27) Given: A circle,\[2{{x}^{2}}+2{{y}^{2}}=5\]and a parabola, \[{{y}^{2}}=4\sqrt{5}x.\] Statement − I: An equation of a common tangent to these curves is\[y=x+5.\] Statement − II: If the line,\[y=mx+\frac{\sqrt{5}}{m}(m\ne 0)\]is their common tangent, then ?m? satisfies\[{{m}^{4}}-3{{m}^{2}}+2=0.\]     AIEEE Solevd Paper-2013
  A)
  Statement−I is true; Statement−II is true; Statement − II is a correct explanation for Statement − I.
  done clear
  B)
  Statement−I is true; Statement−II is true; Statement − II is not a correct explanation for Statement − I.
  done clear
  C)
  Statement−I is true; Statement−II is false.
  done clear
  D)
  Statement−I is false; Statement−II is true.
  done clear
  View Answer play_arrow

• question_answer28) If\[y=sec(ta{{n}^{-1}}x),\]then\[\frac{dy}{dx}\]at\[x=1\]is equal to:     AIEEE Solevd Paper-2013
  A)
  \[\frac{1}{\sqrt{2}}\]                     
  done clear
  B)
         \[\frac{1}{2}\]                   
  done clear
  C)
         1                             
  done clear
  D)
         \[\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer29) The expression\[\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}\]can be written as:     AIEEE Solevd Paper-2013
  A)
  \[sinA\text{ }cosA+1\]  
  done clear
  B)
   \[secA\text{ }cosecA+1\]           
  done clear
  C)
  \[tanA+cotA\]  
  done clear
  D)
  \[secA+cosecA\]
  done clear
  View Answer play_arrow

• question_answer30) All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?     AIEEE Solevd Paper-2013
  A)
  mean   
  done clear
  B)
         median                
  done clear
  C)
         mode   
  done clear
  D)
         variance
  done clear
  View Answer play_arrow