Solved papers for JEE Main & Advanced JEE Main Paper (Held On 19 April 2014)

done JEE Main Paper (Held On 19 April 2014) Total Questions - 30

• question_answer1) Let \[f:R\to R\]be defined by \[f(x)=\frac{\left| x \right|-1}{\left| x \right|+1}\]then f is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  both one-one and onto
  done clear
  B)
  one-one but not onto
  done clear
  C)
  onto but not one-one
  done clear
  D)
  neither one-one nor onto.
  done clear
  View Answer play_arrow

• question_answer2) For all complex numbers z of the form \[1+i\alpha ,\alpha \in R,\]if \[{{z}^{2}}=x+iy,\]then     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[{{y}^{2}}-4x+2=0\]      
  done clear
  B)
  \[{{y}^{2}}+4x-4=0\]
  done clear
  C)
  \[{{y}^{2}}-4x-4=0\]       
  done clear
  D)
  \[{{y}^{2}}+4x+2=0\]
  done clear
  View Answer play_arrow

• question_answer3) The equation \[\sqrt{3{{x}^{2}}+x+5}x-3,\]where x is real, has;     JEE Main Online Paper (Held On 19 April 2016)
  A)
  no solution
  done clear
  B)
  exactly one solution
  done clear
  C)
  exactly two solution
  done clear
  D)
  exactly four solution
  done clear
  View Answer play_arrow

• question_answer4) Let A and B be any two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB - BA is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  skewsymmetric
  done clear
  B)
  Symmetric
  done clear
  C)
   neither symmetric nor skewsymmetric
  done clear
  D)
  I or - I, where I is an identity matrix.
  done clear
  View Answer play_arrow

• question_answer5) If \[\Delta r=\left| \begin{matrix}   r & 2r-1 & 3r-2  \\    \frac{n}{2} & n-1 & a  \\    \frac{1}{2}n(n-1) & {{(n-1)}^{2}} & \frac{1}{2}(n-1)(3n-4)  \\ \end{matrix} \right|\]then the value of\[\sum\limits_{r=1}^{n-1}{{{\Delta }_{r}}}\]     JEE Main Online Paper (Held On 19 April 2016)
  A)
  depends only on a
  done clear
  B)
  depends only on n
  done clear
  C)
  depends both on a and n
  done clear
  D)
  is independent of both a and n
  done clear
  View Answer play_arrow

• question_answer6) Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  [8, 9]                     
  done clear
  B)
  [10, 12)
  done clear
  C)
  (11, 13]                                
  done clear
  D)
  (14, 17)
  done clear
  View Answer play_arrow

• question_answer7) The coefficient of \[{{x}^{1012}}\]in the expansion of \[{{(1+{{x}^{n}}+{{x}^{253}})}^{10}},\] (where \[n\le 22\]is any positive integer), is     JEE Main Online Paper (Held On 19 April 2016)
  A)
  1                                             
  done clear
  B)
  \[^{10}{{C}_{4}}\]
  done clear
  C)
  4n                                          
  done clear
  D)
  \[^{253}{{C}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer8) The number of terms in an A.P. is even; the sum of the odd terms in it is 24 and that the even terms is 30. If the last term exceeds the first term by \[10\frac{1}{2},\] then the number of terms in the A.P. is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  4                                             
  done clear
  B)
  8
  done clear
  C)
  12                                          
  done clear
  D)
  16
  done clear
  View Answer play_arrow

• question_answer9) Let \[f(n)=\left[ \frac{1}{3}+\frac{3n}{100} \right]n,\] where [n] denotes the greatest integer less than or equal to n. Then \[\sum\limits_{n=1}^{56}{f\left( n \right)}\]is equal to:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  56                                          
  done clear
  B)
  689
  done clear
  C)
  1287                      
  done clear
  D)
  1399
  done clear
  View Answer play_arrow

• question_answer10) If the function\[f\left( x \right)=\left\{ \begin{matrix}  \frac{\sqrt{2+\cos x}-1}{{{\left( \pi -x \right)}^{2}}}, & x\ne \pi   \\   k & ,x=\pi   \\ \end{matrix} \right.\]is continuous at \[x=\pi ,\] then k equals:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  0                                             
  done clear
  B)
  \[\frac{1}{2}\]
  done clear
  C)
  2                                             
  done clear
  D)
  \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer11) Let \[f:R\to R\]be a function such that \[\left| f\left( x \right) \right|\le {{x}^{2}},\]for all \[x\in R.\]Then, at x = 0, f is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  continuous but not differentiable.
  done clear
  B)
  continuous as well as differentiable.
  done clear
  C)
  neither continuous nor differentiable.
  done clear
  D)
  differentiable but not continuous.
  done clear
  View Answer play_arrow

• question_answer12) If non-zero real numbers b and c are such that min \[f(x)>\max g(x)\] where \[f(x)={{x}^{2}}+2bx+2{{c}^{2}}\]and \[g(x)=-{{x}^{2}}-2cx+{{b}^{2}}\]\[(x\in R);\] then\[\left| \frac{c}{b} \right|\]lies in the interval:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[\left( 0,\frac{1}{2} \right)\]                     
  done clear
  B)
  \[\left[ \frac{1}{2},\frac{1}{\sqrt{2}} \right)\]
  done clear
  C)
  \[\left[ \frac{1}{\sqrt{2},}\sqrt{2} \right]\]                           
  done clear
  D)
  \[\left( \sqrt{2},\infty  \right)\]
  done clear
  View Answer play_arrow

• question_answer13) If the volume of a spherical ball is increasing at the rate of \[4\pi cc/\sec ,\]then the rate of increase of its radius (in cm/sec), when the volume is \[288\pi cc,\]     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[\frac{1}{6}\]                                   
  done clear
  B)
  \[\frac{1}{9}\]
  done clear
  C)
  \[\frac{1}{36}\]
  done clear
  D)
  \[\frac{1}{24}\]
  done clear
  View Answer play_arrow

• question_answer14) If m is a non-zero number and \[\int_{{}}^{{}}{\frac{{{x}^{5m-1}}+2{{x}^{4m-1}}}{{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{3}}}}dx=f(x)+c,\]then f(x) is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[\frac{{{x}^{5m}}}{2m{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}\]   
  done clear
  B)
  \[\frac{{{x}^{4m}}}{2m{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}\]
  done clear
  C)
  \[\frac{2m\left( {{x}^{5m}}+{{x}^{4m}} \right)}{{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}\] 
  done clear
  D)
  \[\frac{\left( {{x}^{5m}}-{{x}^{4m}} \right)}{2m{{\left( {{x}^{2m}}+{{x}^{m}}+1 \right)}^{2}}}\]
  done clear
  View Answer play_arrow

• question_answer15) Let function F be defined as\[F(x)=\int\limits_{1}^{x}{\frac{{{e}^{t}}}{t}}dt,x>0\]then the value of the integral\[\int\limits_{1}^{x}{\frac{{{e}^{t}}}{t+a}}dt,\]where a > 0, is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[{{e}^{a}}\left[ F(x)-F(1+a) \right]\]
  done clear
  B)
  \[{{e}^{-a}}\left[ F(x+a)-F(a) \right]\]
  done clear
  C)
  \[{{e}^{a}}\left[ F(x+a)-F(1+a) \right]\]
  done clear
  D)
  \[{{e}^{-a}}\left[ F(x+a)-F(1+a) \right]\]
  done clear
  View Answer play_arrow

• question_answer16) The area of the region above the x-axis bounded by the curve \[y=\tan x,0\le x\le \frac{\pi }{2}\]and the tangent to the curve at \[x=\frac{\pi }{4}\] is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[\frac{1}{2}\left( \log 2-\frac{1}{2} \right)\]
  done clear
  B)
  \[\frac{1}{2}\left( \log 2+\frac{1}{2} \right)\]
  done clear
  C)
  \[\frac{1}{2}\left( 1-\log 2 \right)\]                          
  done clear
  D)
  \[\frac{1}{2}\left( 1+\log 2 \right)\]
  done clear
  View Answer play_arrow

• question_answer17) If\[\frac{dy}{dx}+y\tan x=\sin 2x\]and\[y(0)=1,\]then\[y(\pi )\] then y(p) is equal to:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  1                                             
  done clear
  B)
  -1
  done clear
  C)
  -5           
  done clear
  D)
  5
  done clear
  View Answer play_arrow

• question_answer18) The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points \[({{a}^{2}}+1,{{a}^{2}}+1)\]and \[(2a,-2a),a\ne 0.\]Then for any a, the orthocentre of this triangle lies on the line:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[y-2ax=0\]                        
  done clear
  B)
  \[y-({{a}^{2}}+1)x=0\]
  done clear
  C)
  \[y+x=0\]                           
  done clear
  D)
  \[{{(a-1)}^{2}}x-{{(a+1)}^{2}}y=0\]
  done clear
  View Answer play_arrow

• question_answer19) If a line L is perpendicular to the line \[5x-y=1\], and the area of the triangle formed by the line L and the coordinate axes is 5, then the distance of line L from the line \[x+5y=0\] is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[\frac{7}{\sqrt{5}}\]                                     
  done clear
  B)
  \[\frac{5}{\sqrt{13}}\]
  done clear
  C)
  \[\frac{7}{\sqrt{13}}\]                   
  done clear
  D)
  \[\frac{5}{\sqrt{7}}\]
  done clear
  View Answer play_arrow

• question_answer20) The equation of circle described on the chord \[3x+y+5=0\]of the circle \[{{x}^{2}}+{{y}^{2}}=16\]as diameter is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[{{x}^{2}}+{{y}^{2}}+3x+y-11=0\]
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}+3x+y+1=0\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}+3x+y-2=0\]
  done clear
  D)
  \[{{x}^{2}}+{{y}^{2}}+3x+y-22=0\]
  done clear
  View Answer play_arrow

• question_answer21) A chord is drawn through the focus of the parabola \[{{y}^{2}}=6x\]such that its distance from the vertex of this parabola is \[\frac{\sqrt{5}}{2},\]then its slope can be:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[\frac{\sqrt{5}}{2}\]     
  done clear
  B)
  \[\frac{\sqrt{3}}{2}\]
  done clear
  C)
  \[\frac{2}{\sqrt{5}}\]                                     
  done clear
  D)
  \[\frac{2}{\sqrt{3}}\]
  done clear
  View Answer play_arrow

• question_answer22) The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{5}=1,\] meet x-axis and y-axis at A and B respectively. Then \[{{(OA)}^{2}}-{{(OB)}^{2}},\]where O is the origin, equals:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[-\frac{20}{9}\]               
  done clear
  B)
  \[\frac{19}{9}\]
  done clear
  C)
  4                                             
  done clear
  D)
  \[-\frac{4}{3}\]
  done clear
  View Answer play_arrow

• question_answer23) Equation of the line of the shortest distance between the lines \[\frac{x}{1}=\frac{y}{-1}=\frac{z}{1}\]and \[\frac{x-1}{0}=\frac{y+1}{-2}=\frac{z}{1}\]is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  \[\frac{x}{1}=\frac{y}{-1}=\frac{z}{-2}\]
  done clear
  B)
  \[\frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{-2}\]
  done clear
  C)
  \[\frac{x-1}{1}=\frac{y+1}{-1}=\frac{z}{1}\]         
  done clear
  D)
  \[\frac{x}{-2}=\frac{y}{1}=\frac{z}{2}\]
  done clear
  View Answer play_arrow

• question_answer24) If the angle between the line  and the plane is then the value of  is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
                                        
  done clear
  B)
  
  done clear
  C)
          
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer25) If andthen the magnitude of the projection ofon is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  12                                          
  done clear
  B)
  15
  done clear
  C)
  14                                          
  done clear
  D)
  13
  done clear
  View Answer play_arrow

• question_answer26) Let A and E be any two events with positive probabilities: Statement - 1: Statement ? 2:     JEE Main Online Paper (Held On 19 April 2016)
  A)
  Both the statements are true
  done clear
  B)
  Both the statements are false
  done clear
  C)
  Statement-1 is true, Statement-2 is false
  done clear
  D)
  Statement-1 is false, Statement-2 is true
  done clear
  View Answer play_arrow

• question_answer27) Let and be respectively the mean, mode and variance of n observations andwhere   is any number. Statement I: Variance of  is Statement II: Mean and mode of areand ? M ? a, respectively.     JEE Main Online Paper (Held On 19 April 2016)
  A)
  Statement I and Statement II are both false
  done clear
  B)
  Statement I and Statement II are both true
  done clear
  C)
  Statement I is true and Statement II is false
  done clear
  D)
  Statement I is false and Statement II is true
  done clear
  View Answer play_arrow

• question_answer28) The function is a periodic function with period:     JEE Main Online Paper (Held On 19 April 2016)
  A)
                                         
  done clear
  B)
  
  done clear
  C)
           
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer29) The principal value of is:     JEE Main Online Paper (Held On 19 April 2016)
  A)
                      
  done clear
  B)
  
  done clear
  C)
                        
  done clear
  D)
  
  done clear
  View Answer play_arrow

• question_answer30) The contrapositive of the statement 'if I am not feeling well, then I will go to the doctor' is     JEE Main Online Paper (Held On 19 April 2016)
  A)
  If I am feeling well, then I will not go to the doctor
  done clear
  B)
  If I will go to the doctor, then I am feeling well
  done clear
  C)
  If I will not go to the doctor, then I am feeling well
  done clear
  D)
  If I will go to the doctor, then I am not feeling well.
  done clear
  View Answer play_arrow