Solved papers for JEE Main & Advanced JEE Main Solved Paper-2015

done JEE Main Solved Paper-2015 Total Questions - 30

• question_answer1) Let\[\vec{a},\vec{b}\]and\[\vec{c}\]be three non - zero vectors such that no two of them are collinear and\[\left( \vec{a}\times \vec{b} \right)\times \vec{c}=\frac{1}{3}\left| {\vec{b}} \right|\left| {\vec{c}} \right|\vec{a}.\]If \[\theta \]is the angle between vectors \[\vec{b}\]and \[\vec{c},\]then a value of \[\sin \theta \]is : [JEE Main Solved Paper-2015 ]
  A)
  \[\frac{2}{3}\]                                   
  done clear
  B)
  \[\frac{-2\sqrt{3}}{3}\]
  done clear
  C)
  \[\frac{2\sqrt{3}}{3}\]   
  done clear
  D)
  \[\frac{-\sqrt{2}}{3}\]
  done clear
  View Answer play_arrow

• question_answer2) Let O be the vertex and Q be any point on the parabola, \[{{x}^{2}}=8y.\]If the point P divides the line segment OQ internally in the ratio 1:3, then locus of P is : [JEE Main Solved Paper-2015 ]
  A)
  \[{{y}^{2}}=2x\]                               
  done clear
  B)
  \[{{x}^{2}}=2y\]
  done clear
  C)
  \[{{x}^{2}}=y\]                 
  done clear
  D)
  \[{{y}^{2}}=x\]
  done clear
  View Answer play_arrow

• question_answer3) If the angles of elevation of the top of a tower from three collinear points A,B and C, on a line leading to the foot of the tower, are 300, 450 and 600 respectively, then the ratio, AB : BC, is : [JEE Main Solved Paper-2015 ]
  A)
  \[1:\sqrt{3}\]                    
  done clear
  B)
  \[2:3\]
  done clear
  C)
  \[\sqrt{3}:1\]                    
  done clear
  D)
  \[\sqrt{3}:\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer4) The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices \[\left( 0,0 \right),\left( 0,41 \right)\] and \[\left( 41,0 \right),\] is [JEE Main Solved Paper-2015 ]
  A)
  820                                        
  done clear
  B)
  780
  done clear
  C)
  901                                        
  done clear
  D)
  861
  done clear
  View Answer play_arrow

• question_answer5) The equation of the plane containing the line \[2x-5y+z=3;x+y+4z=5,\] and parallel to the plane, \[x+3y+6z=1,\] is : [JEE Main Solved Paper-2015 ]
  A)
  \[x+3y+6z=7\]
  done clear
  B)
  \[x+6y+12z=-13\]
  done clear
  C)
  \[2x+6y+12z=13\]
  done clear
  D)
  \[x+3y+6z=-7\]
  done clear
  View Answer play_arrow

• question_answer6) Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set \[A\times B,\] each having at least three elements is : [JEE Main Solved Paper-2015 ]
  A)
  done clear
  B)
  275                                        
  done clear
  C)
  510
  done clear
  D)
  219                                        
  done clear
  E)
  256
  done clear
  View Answer play_arrow

• question_answer7) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\left( 1-\cos 2x \right)\left( 3+\cos x \right)}{x\tan 4x}\]is equal to : [JEE Main Solved Paper-2015 ]
  A)
  2             
  done clear
  B)
  \[\frac{1}{2}\]
  done clear
  C)
   4                                            
  done clear
  D)
  3
  done clear
  View Answer play_arrow

• question_answer8) The distance of the point \[\left( 1,0,2 \right)\]from the point of intersection of the line \[\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\]and the plane \[x-y+z=16,\] is : [JEE Main Solved Paper-2015 ]
  A)
  \[3\sqrt{21}\]                                   
  done clear
  B)
  13
  done clear
  C)
  \[2\sqrt{14}\]                                   
  done clear
  D)
  8
  done clear
  View Answer play_arrow

• question_answer9) The sum of coefficients of integral powers of x in the binomial expansion of \[{{\left( 1-2\sqrt{x} \right)}^{50}}\]is [JEE Main Solved Paper-2015 ]
  A)
  \[\frac{1}{2}\left( {{3}^{50}}-1 \right)\]                 
  done clear
  B)
  \[\frac{1}{2}\left( {{2}^{50}}+1 \right)\]
  done clear
  C)
  \[\frac{1}{2}\left( {{3}^{50}}+1 \right)\]
  done clear
  D)
  \[\frac{1}{2}\left( {{3}^{50}} \right)\]
  done clear
  View Answer play_arrow

• question_answer10) The sum of first 9 terms of the series\[\frac{{{1}^{3}}}{1}+\frac{{{1}^{3}}+{{2}^{3}}}{1+3}+\frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}{1+3+5}\]...............is: [JEE Main Solved Paper-2015 ]
  A)
  142                                        
  done clear
  B)
  192
  done clear
  C)
  71                                          
  done clear
  D)
  96
  done clear
  View Answer play_arrow

• question_answer11) athematics The area (in sq. units ) of the region described by [JEE Main Solved Paper-2015 ]
  A)
  \[\frac{15}{64}\]                                              
  done clear
  B)
  \[\frac{9}{32}\]
  done clear
  C)
  \[\frac{7}{32}\]                                
  done clear
  D)
  \[\frac{5}{64}\]
  done clear
  View Answer play_arrow

• question_answer12) The set of all values of \[\lambda \]for which the system of linear equations: \[2{{x}_{1}}-2{{x}_{2}}+{{x}_{3}}=\lambda {{x}_{1}}\] \[2{{x}_{1}}-3{{x}_{2}}+2{{x}_{3}}=\lambda {{x}_{2}}\] \[-{{x}_{1}}+2{{x}_{2}}=\lambda {{x}_{3}}\]has a non- trivial solution, [JEE Main Solved Paper-2015 ]
  A)
  Contains two elements
  done clear
  B)
  Contains more than two elements.
  done clear
  C)
  Is an empty set                
  done clear
  D)
  Is a singleton.
  done clear
  View Answer play_arrow

• question_answer13) A complex number z is said to be unimodular if \[\left| z \right|=1.\]Suppose \[{{z}_{1}}\] and \[{{z}_{2}}\] are complex numbers such that \[\frac{{{z}_{1}}-2{{z}_{2}}}{2-{{z}_{1}}{{\overline{z}}_{2}}}\]is unimodular and \[{{z}_{2}}\] is not unimodular. Then the point \[{{z}_{1}}\] lies on a : [JEE Main Solved Paper-2015 ]
  A)
  Circle of radius 2              
  done clear
  B)
  Circle of radius 2
  done clear
  C)
  Straight line parallel to x-axis
  done clear
  D)
  Straight line parallel to y-axis Solut
  done clear
  View Answer play_arrow

• question_answer14) The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\] and \[{{x}^{2}}+{{y}^{2}}+6y+18y+26=0,\] is [JEE Main Solved Paper-2015 ]
  A)
  3
  done clear
  B)
  4
  done clear
  C)
  1                                             
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer15) The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8, without repetition is : [JEE Main Solved Paper-2015 ]
  A)
  120                                        
  done clear
  B)
  72
  done clear
  C)
   216                                       
  done clear
  D)
  192
  done clear
  View Answer play_arrow

• question_answer16) Let y(x) be the solution of the differential equation \[\left( x\log x \right)\frac{dy}{dx}+y=2x\log x,(x\ge 1).\] The y (e)is equal to [JEE Main Solved Paper-2015 ]
  A)
  2             
  done clear
  B)
  2e                
  done clear
  C)
  e                                                            
  done clear
  D)
  0
  done clear
  View Answer play_arrow

• question_answer17) If \[A=\left[ \begin{matrix}    1 & 2 & 2  \\    2 & 1 & -2  \\    a & 2 & b  \\ \end{matrix} \right]\]is a matrix satisfying the equation \[A{{A}^{T}}=9I,\] where I is \[3\times 3\] identity matrix, then the ordered pair (a,b) is equal to : [JEE Main Solved Paper-2015 ]
  A)
  (2,1)                                      
  done clear
  B)
  -(-2,-1)
  done clear
  C)
  (2,-1)                    
  done clear
  D)
  (-2,1)
  done clear
  View Answer play_arrow

• question_answer18) ) If m is the A.M. of two distinct real numbers \[l\] and \[n\left( l,n>1 \right)\]and \[{{G}_{1}},{{G}_{2}}\]and \[{{G}_{3}}\] are three geometric means between \[l\] and n, then \[G_{1}^{4}+2G_{2}^{4}+G_{3}^{4}\]equals. [JEE Main Solved Paper-2015 ]
  A)
  \[4lm{{n}^{2}}\]                               
  done clear
  B)
  \[4{{l}^{2}}{{m}^{2}}{{n}^{2}}\]
  done clear
  C)
  \[4{{l}^{2}}mn\]                               
  done clear
  D)
  \[4l{{m}^{2}}n\]
  done clear
  View Answer play_arrow

• question_answer19) The negation of \[\tilde{\ }s\vee \left( \tilde{\ }r\wedge s \right)\]is equivalent to : [JEE Main Solved Paper-2015 ]
  A)
  \[s\vee \left( r\vee \tilde{\ }s \right)\]  
  done clear
  B)
  \[s\wedge r\]
  done clear
  C)
  \[s\wedge \tilde{\ }r\]                  
  done clear
  D)
  \[s\wedge \left( r\wedge \tilde{\ }s \right)\]
  done clear
  View Answer play_arrow

• question_answer20) The integral\[\int_{{}}^{{}}{\frac{dx}{{{x}^{2}}{{\left( {{x}^{4}}+1 \right)}^{{}^{3}/{}_{4}}}}}\]equals: [JEE Main Solved Paper-2015 ]
  A)
  \[-{{\left( {{x}^{4}}+1 \right)}^{\frac{1}{4}}}+c\]
  done clear
  B)
  \[-{{\left( \frac{{{x}^{4}}+1}{{{x}^{4}}} \right)}^{\frac{1}{4}}}+c\]
  done clear
  C)
  \[{{\left( \frac{{{x}^{4}}+1}{{{x}^{4}}} \right)}^{\frac{1}{4}}}+c\]
  done clear
  D)
  \[{{\left( {{x}^{4}}+1 \right)}^{\frac{1}{4}}}+c\]
  done clear
  View Answer play_arrow

• question_answer21) The normal to the curve \[{{x}^{2}}+2xy-3{{y}^{2}}=0,\] at (1, 1) : [JEE Main Solved Paper-2015 ]
  A)
  meets the curve again in the third quadrant.                
  done clear
  B)
  meets the curve again in the fourth quadrant.
  done clear
  C)
  does not meet the curve again.                
  done clear
  D)
  meets the curve again in the second quadrant.
  done clear
  View Answer play_arrow

• question_answer22) Let \[{{\tan }^{-1}}y={{\tan }^{-1}}x+{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right),\]where \[|x|<\frac{1}{\sqrt{3}}.\]Then a value of y is : [JEE Main Solved Paper-2015 ]
  A)
  \[\frac{3x-{{x}^{3}}}{1+3{{x}^{2}}}\]                       
  done clear
  B)
  \[\frac{3x+{{x}^{3}}}{1+3{{x}^{2}}}\]
  done clear
  C)
  \[\frac{3x-{{x}^{3}}}{1-3{{x}^{2}}}\]        
  done clear
  D)
  \[\frac{3x+{{x}^{3}}}{1-3{{x}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer23) If the function. \[g\left( x \right)=\left\{ \begin{align}   & k\sqrt{x+1},\,\,\,\,\,\,0\le x\le 3 \\  & mx+2,\,\,\,\,\,\,\,\,3<x\le 5 \\ \end{align} \right.\]is differentiable, then the value of k + m is : [JEE Main Solved Paper-2015 ]
  A)
  \[\frac{10}{3}\]                                
  done clear
  B)
  4
  done clear
  C)
  2             
  done clear
  D)
  \[\frac{16}{5}\]
  done clear
  View Answer play_arrow

• question_answer24) The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3,4 and 5 are added to the data, then the mean of the resultant data, is: [JEE Main Solved Paper-2015 ]
  A)
  15.8                       
  done clear
  B)
  14.0
  done clear
  C)
  16.8                                       
  done clear
  D)
  16.0
  done clear
  View Answer play_arrow

• question_answer25) The integral \[\int\limits_{2}^{4}{\frac{\log {{x}^{2}}}{\log {{x}^{2}}+\log \left( 36-12x+{{x}^{2}} \right)}dx}\] is equal to : [JEE Main Solved Paper-2015 ]
  A)
  1                                             
  done clear
  B)
  6
  done clear
  C)
  2                                             
  done clear
  D)
  4
  done clear
  View Answer play_arrow

• question_answer26) Let \[\alpha \] and \[\beta \] be the roots of equation \[{{x}^{2}}-6x-2=0.\] If \[{{a}_{n}}={{\alpha }^{n}}-{{\beta }^{n}},\] for \[n\ge 1,\] then the value \[\frac{{{a}_{10}}-2{{a}_{8}}}{2{{a}_{9}}}\]is equal to : [JEE Main Solved Paper-2015 ]
  A)
  3             
  done clear
  B)
  -3
  done clear
  C)
  6                                             
  done clear
  D)
  -6
  done clear
  View Answer play_arrow

• question_answer27) Let f (x) be a polynomial of degree four having extreme values at x = 1 and x =2. If\[\underset{x\to 0}{\mathop{\lim }}\,\left( 1+\frac{f\left( x \right)}{{{x}^{2}}} \right)=3,\]then f(2) is equal to : [JEE Main Solved Paper-2015 ]
  A)
  0             
  done clear
  B)
  4
  done clear
  C)
  -8                                          
  done clear
  D)
  -4
  done clear
  View Answer play_arrow

• question_answer28) The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{5}=1,\]is: [JEE Main Solved Paper-2015 ]
  A)
   \[\frac{27}{2}\]                               
  done clear
  B)
   27
  done clear
  C)
  \[\frac{27}{4}\]                                
  done clear
  D)
  18
  done clear
  View Answer play_arrow

• question_answer29) If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is : [JEE Main Solved Paper-2015 ]
  A)
  \[220{{\left( \frac{1}{3} \right)}^{12}}\]                 
  done clear
  B)
  \[22{{\left( \frac{1}{3} \right)}^{11}}\]
  done clear
  C)
  \[\frac{55}{3}{{\left( \frac{2}{3} \right)}^{11}}\]
  done clear
  D)
  \[55{{\left( \frac{2}{3} \right)}^{10}}\]
  done clear
  View Answer play_arrow

• question_answer30) Locus of the image of the point \[\left( 2,3 \right)\]in the line\[\left( 2x-3y+4 \right)+k\left( x-2y+3 \right)=0,\]\[k\in R,\] is a : [JEE Main Solved Paper-2015 ]
  A)
  circle of radius \[\sqrt{2}\]
  done clear
  B)
  circle of radius \[\sqrt{3}\]
  done clear
  C)
  straight line parallel to x - axis
  done clear
  D)
  straight line parallel to y - axis
  done clear
  View Answer play_arrow