Solved papers for JEE Main & Advanced JEE Main Solved Paper-2016

done JEE Main Solved Paper-2016 Total Questions - 30

• question_answer1) A value of\[\theta \] for which\[\frac{2+3i\sin \theta }{1-2i\sin \theta }\]is purely imaginary, is : [JEE Main Solved Paper-2016 ]
  A)
  \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]                  
  done clear
  B)
  \[\frac{\pi }{3}\]
  done clear
  C)
  \[\frac{\pi }{6}\]                                              
  done clear
  D)
  \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{4} \right)\]
  done clear
  View Answer play_arrow

• question_answer2) The system of linear equations \[x+\lambda y-z=0\] \[\lambda x-y-z=0\] \[x+y-\lambda z=0\] has a non-trivial solution for : [JEE Main Solved Paper-2016 ]
  A)
   exactly three values of\[\lambda .\]
  done clear
  B)
  infinitely many values of \[\lambda .\]
  done clear
  C)
   exactly one value of \[\lambda .\]
  done clear
  D)
  exactly two values of \[\lambda .\]
  done clear
  View Answer play_arrow

• question_answer3) A wire of length 2 units is cut into two parts  which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then : [JEE Main Solved Paper-2016 ]
  A)
  \[2x=r\]                               
  done clear
  B)
  \[2x=(\pi +4)r\]
  done clear
  C)
  \[(4-\pi )x=\pi r\]            
  done clear
  D)
  \[x=2r\]
  done clear
  View Answer play_arrow

• question_answer4) A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is \[30{}^\circ \]. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is \[60{}^\circ \]. Then the time taken (in minutes) by him, form B to reach the pillar, is : [JEE Main Solved Paper-2016 ]
  A)
  5                                             
  done clear
  B)
  6
  done clear
  C)
  10                                          
  done clear
  D)
  20
  done clear
  View Answer play_arrow

• question_answer5) Let two fair six-faced dice A and B be thrown simultaneously. If \[{{E}_{1}}\] is the event that die A  shows up four, \[{{E}_{2}}\]is the event that die B shows up two and \[{{E}_{3}}\] is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true ? [JEE Main Solved Paper-2016 ]
  A)
  \[{{E}_{1}},{{E}_{2}}\]and \[{{E}_{3}}\]are independent.
  done clear
  B)
  \[{{E}_{1}}\]and \[{{E}_{2}}\]are independent.
  done clear
  C)
  \[{{E}_{2}}\]and \[{{E}_{3}}\]are independent.
  done clear
  D)
  \[{{E}_{1}}\]and\[{{E}_{3}}\] are independent.
  done clear
  View Answer play_arrow

• question_answer6) If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true ? [JEE Main Solved Paper-2016 ]
  A)
  \[3{{a}^{2}}-23a+44=0\]               
  done clear
  B)
  \[3{{a}^{2}}-26a+55=0\]
  done clear
  C)
  \[3{{a}^{2}}-32a+84=0\]               
  done clear
  D)
  \[3{{a}^{2}}-34a+91=0\]
  done clear
  View Answer play_arrow

• question_answer7) For\[x\in R,f(x)=|\log 2-\sin x|\] and \[g(x)=f(f(x)),\]then : [JEE Main Solved Paper-2016 ]
  A)
  g is differentiable at x = 0 and g'(0) = -sin(log2)
  done clear
  B)
  g is not differentiable at x = 0
  done clear
  C)
  g'(0) = cos(log2)
  done clear
  D)
  g'(0) = - cos(log2)
  done clear
  View Answer play_arrow

• question_answer8) The distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along the line x = y = z is : [JEE Main Solved Paper-2016 ]
  A)
  \[\frac{20}{3}\]                                
  done clear
  B)
  \[3\sqrt{10}\]
  done clear
  C)
  \[10\sqrt{3}\]                   
  done clear
  D)
  \[\frac{10}{\sqrt{3}}\]
  done clear
  View Answer play_arrow

• question_answer9) The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is : [JEE Main Solved Paper-2016 ]
  A)
  \[\sqrt{3}\]                                        
  done clear
  B)
  \[\frac{4}{3}\]
  done clear
  C)
  \[\frac{4}{\sqrt{3}}\]                                     
  done clear
  D)
  \[\frac{2}{\sqrt{3}}\]
  done clear
  View Answer play_arrow

• question_answer10) Let P be the point on the parabola, y2 = 8x which is at a minimum distance from the center C of the circle, \[{{x}^{2}}+{{(y+6)}^{2}}=1\]. Then the equation of the circle, passing through C and having its centre at P is : [JEE Main Solved Paper-2016 ]
  A)
  \[{{x}^{2}}+{{y}^{2}}-4x+9y+18=0\]
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}-4x+8y+12=0\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}-x+4y-12=0\]
  done clear
  D)
  \[{{x}^{2}}+{{y}^{2}}-\frac{x}{4}+2y-24=0\]
  done clear
  View Answer play_arrow

• question_answer11) If\[A=\left[ \begin{matrix}    5a & -b  \\    3 & 2  \\ \end{matrix} \right]\]and A adj A = A\[{{\text{A}}^{\text{T}}},\]then \[5a+b\]is equal to: [JEE Main Solved Paper-2016 ]
  A)
  13                                          
  done clear
  B)
  -1
  done clear
  C)
  5                                             
  done clear
  D)
  4
  done clear
  View Answer play_arrow

• question_answer12) Consider \[f(x)={{\tan }^{-1}}\left( \sqrt{\frac{1+\sin x}{1-\sin x}} \right),x\in \left( 0,\frac{\pi }{2} \right).\] A normal to \[y=f(x)at\,x=\frac{\pi }{6}\]also passes through the point : [JEE Main Solved Paper-2016 ]
  A)
  \[\left( \frac{\pi }{4},0 \right)\]                 
  done clear
  B)
  \[\left( 0,\text{ }0 \right)\]
  done clear
  C)
  \[\left( 0,\frac{2\pi }{3} \right)\]                               
  done clear
  D)
  \[\left( \frac{\pi }{6},0 \right)\]
  done clear
  View Answer play_arrow

• question_answer13) Two sides of a rhombus are along the lines, \[x-v+1=0\]and \[\text{7x}\text{y}\text{5}=0.\] If its diagonals intersect at (-1, -2), then which one of the following is a vertex of this rhombus ? [JEE Main Solved Paper-2016 ]
  A)
  \[\left( -\frac{10}{3},\frac{7}{3} \right)\]                               
  done clear
  B)
  \[(-3,-9)\]
  done clear
  C)
  \[(-3,-8)\]                           
  done clear
  D)
  \[\left( \frac{1}{3},\frac{8}{3} \right)\]
  done clear
  View Answer play_arrow

• question_answer14) If a curve y = f(x) passes through the point (1, -1) and satisfies the differential equation, \[y(1+xy)dx=xdy,\]then \[f\left( -\frac{1}{2} \right)\] is equal to : [JEE Main Solved Paper-2016 ]
  A)
  \[\frac{4}{5}\]                                   
  done clear
  B)
  \[-\frac{2}{5}\]
  done clear
  C)
  \[-\frac{4}{5}\]                                 
  done clear
  D)
  \[\frac{2}{5}\]
  done clear
  View Answer play_arrow

• question_answer15) If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is : [JEE Main Solved Paper-2016 ]
  A)
  58th
  done clear
  B)
  46th
  done clear
  C)
  59th                      
  done clear
  D)
  52nd
  done clear
  View Answer play_arrow

• question_answer16) If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :- [JEE Main Solved Paper-2016 ]
  A)
  \[\frac{7}{4}\]                                   
  done clear
  B)
  \[\frac{8}{5}\]
  done clear
  C)
  \[\frac{4}{3}\]                                   
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer17) If the number of terms in the expansion of \[{{\left( 1-\frac{2}{x}+\frac{4}{{{x}^{2}}} \right)}^{n}},x\ne 0,\] , is 28, then the sum of the coefficients of all the terms in this expansion, is :- [JEE Main Solved Paper-2016 ]
  A)
  729        
  done clear
  B)
  64
  done clear
  C)
  2187                      
  done clear
  D)
  243
  done clear
  View Answer play_arrow

• question_answer18) If the sum of the first ten terms of the series \[{{\left( 1\frac{3}{5} \right)}^{2}}+{{\left( 2\frac{2}{5} \right)}^{2}}+{{\left( 3\frac{1}{5} \right)}^{2}}+....,\]is\[\frac{16}{5}m,\]then m is equal to :- [JEE Main Solved Paper-2016 ]
  A)
   99                                         
  done clear
  B)
  102
  done clear
  C)
  101                                        
  done clear
  D)
  100
  done clear
  View Answer play_arrow

• question_answer19) If the line,\[\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}\]lies in the plane, \[1x+my-z=9,\]then\[{{1}^{2}}{{+}^{2}}\] is equal to :- [JEE Main Solved Paper-2016 ]
  A)
  2                                             
  done clear
  B)
  26
  done clear
  C)
  18                                          
  done clear
  D)
  5
  done clear
  View Answer play_arrow

• question_answer20) The Boolean Expression \[(p\wedge \tilde{\ }q)\vee q\vee (\tilde{\ }p\wedge q)\] is equivalent to :- [JEE Main Solved Paper-2016 ]
  A)
  \[p\vee \tilde{\ }q\]                      
  done clear
  B)
  \[\tilde{\ }p\wedge q\]
  done clear
  C)
  \[p\wedge q\]                 
  done clear
  D)
  \[p\vee q\]
  done clear
  View Answer play_arrow

• question_answer21) The integral\[\int_{{}}^{{}}{\frac{2{{x}^{12}}+5{{x}^{9}}}{{{x}^{5}}+{{x}^{3}}+1{{)}^{3}}}}dx\]is equal to :-
  A)
  \[\frac{-{{x}^{10}}}{2{{{{(}^{5}}+{{x}^{3}}+1)}^{2}}}+C\]
  done clear
  B)
  \[\frac{-{{x}^{5}}}{{{{{(}^{5}}+{{x}^{3}}+1)}^{2}}}+C\]
  done clear
  C)
  \[\frac{{{x}^{10}}}{2{{({{x}^{5}}+{{x}^{3}}+1)}^{2}}}+C\]
  done clear
  D)
  \[\frac{{{x}^{5}}}{2{{({{x}^{5}}+{{x}^{3}}+1)}^{2}}}+C\]
  done clear
  View Answer play_arrow

• question_answer22) If one of the diameters of the circle, given by the equation, \[\text{x2}+\text{y2}\text{4x}+\text{6y}\text{12}=0,\]is a chord of a circle S, whose centre is at (-3, 2), then the radius of S is :- [JEE Main Solved Paper-2016 ]
  A)
  10                                          
  done clear
  B)
   52
  done clear
  C)
  53                                          
  done clear
  D)
  5
  done clear
  View Answer play_arrow

• question_answer23) \[\underset{n\to \infty }{\mathop{\lim }}\,{{\left( \frac{(n+1)(n+2)....3n}{{{n}^{2n}}} \right)}^{1/n}}\]is equal to: [JEE Main Solved Paper-2016 ]
  A)
  \[3\log 3-2\]                      
  done clear
  B)
  \[\frac{18}{{{e}^{4}}}\]
  done clear
  C)
  \[\frac{27}{{{e}^{2}}}\]                                 
  done clear
  D)
  \[\frac{9}{{{e}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer24) The centres of those circles which touch the circle, \[{{\text{x}}^{\text{2}}}+{{\text{y}}^{\text{2}}}\text{8x}\text{8y}\text{4}=0,\]externally and also touch the x-axis, lie on :- [JEE Main Solved Paper-2016 ]
  A)
   A parabola                        
  done clear
  B)
  A circle
  done clear
  C)
  An ellipse which is not a circle
  done clear
  D)
  A hyperbola
  done clear
  View Answer play_arrow

• question_answer25) Let\[\overrightarrow{a},\overrightarrow{b}\]\[\overrightarrow{c}\]be three unit vectors such that\[\overrightarrow{a}\times \left( \overrightarrow{b}\times \overrightarrow{c} \right)=\frac{\sqrt{3}}{2}\left( \overrightarrow{b}+\overrightarrow{c} \right).\]If \[\overrightarrow{b}\]is not parallel to \[\overrightarrow{c}\], then the angle between \[\overrightarrow{a}\]and\[\overrightarrow{b}\]is :- [JEE Main Solved Paper-2016 ]
  A)
  \[\frac{5\pi }{6}\]                                            
  done clear
  B)
  \[\frac{3\pi }{4}\]
  done clear
  C)
  \[\frac{\pi }{2}\]                                              
  done clear
  D)
  \[\frac{2\pi }{3}\]
  done clear
  View Answer play_arrow

• question_answer26) Let\[p=\underset{x\to 0+}{\mathop{\lim }}\,{{\left( 1+{{\tan }^{2}}\sqrt{x} \right)}^{\frac{1}{2x}}}\] then log p is equal to :- [JEE Main Solved Paper-2016 ]
  A)
  \[\frac{1}{4}\]                                   
  done clear
  B)
   2
  done clear
  C)
  1                                             
  done clear
  D)
  \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer27) If \[0\le x<2\pi ,\]then the number of real values of x, which satisfy the equation \[\cos x+\cos 2x+\cos 3x+\cos 4x=0,\]is :- [JEE Main Solved Paper-2016 ]
  A)
  9                                             
  done clear
  B)
   3
  done clear
  C)
   5                                            
  done clear
  D)
   7
  done clear
  View Answer play_arrow

• question_answer28) The sum of all real values of x satisfying the equation \[{{\left( {{x}^{2}}-5x+5 \right)}^{{{x}^{2}}+4x-60}}=1\]is :- [JEE Main Solved Paper-2016 ]
  A)
  5                                             
  done clear
  B)
   3
  done clear
  C)
  - 4                                         
  done clear
  D)
  6
  done clear
  View Answer play_arrow

• question_answer29) The area (in sq. units) of the region \[\{(x,y):{{y}^{2}}\ge 2x\]and\[{{x}^{2}}+{{y}^{2}}\le 4x,x\ge 0,y\ge 0\]\[\}\] is :- [JEE Main Solved Paper-2016 ]
  A)
  \[\frac{\pi }{2}=\frac{2\sqrt{2}}{3}\]                       
  done clear
  B)
  \[\pi -\frac{4}{3}\]
  done clear
  C)
  \[\pi -\frac{4}{3}\]                          
  done clear
  D)
  \[\pi -\frac{4\sqrt{2}}{3}\]
  done clear
  View Answer play_arrow

• question_answer30) If\[f(x)+2f\left( \frac{1}{x} \right)=3x,x\ne 0,\]and \[S=\{x\in R;f(x)=f(-x)\};\]then [JEE Main Solved Paper-2016 ]
  A)
  contains more than two elements.
  done clear
  B)
   is an empty set.
  done clear
  C)
  contains exactly one element
  done clear
  D)
  contains exactly two elements
  done clear
  View Answer play_arrow