Solved papers for JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)

done JEE Main Paper (Held On 26 May 2012) Total Questions - 30

• question_answer1) The distance of the point \[-\hat{i}+2\hat{j}+6\hat{k}\]from the straight line that passes through the point \[2\hat{i}+3\hat{j}-4\hat{k}\] and is parallel to the vector \[6\hat{i}+3\hat{j}-4\hat{k}\] is   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  9                             
  done clear
  B)
                         8
  done clear
  C)
                         7     
  done clear
  D)
                         10
  done clear
  View Answer play_arrow

• question_answer2) Consider the following planes \[P:x+y-2z+7=0\] \[Q:x+y+2z+2=0\] \[R:3x+3y-6z-11=0\]   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  P and R are perpendicular
  done clear
  B)
                         Q and R are perpendicular
  done clear
  C)
                         P and g are parallel
  done clear
  D)
                          P and R are parallel
  done clear
  View Answer play_arrow

• question_answer3) If\[A=\left[ \begin{matrix}    1 & 0 & 0  \\    2 & 1 & 0  \\    -3 & 2 & 1  \\ \end{matrix} \right]\]and\[B=\left[ \begin{matrix}    1 & 0 & 0  \\    -2 & 1 & 0  \\    7 & -2 & 1  \\ \end{matrix} \right]\] then AB equals.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  I              
  done clear
  B)
                         A
  done clear
  C)
                         B                            
  done clear
  D)
                         0
  done clear
  View Answer play_arrow

• question_answer4) If the A.M. between \[{{\text{p}}^{\text{th}}}\]and \[{{\text{q}}^{\text{th}}}\]terms of an A.P. is equal to the A.M. between \[{{\text{r}}^{\text{th}}}\]and \[{{\text{s}}^{\text{th}}}\] terms of the same A.P., then p + q is equal to.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  r+s-1
  done clear
  B)
  r+s-2
  done clear
  C)
  r+s+1                    
  done clear
  D)
  r+s
  done clear
  View Answer play_arrow

• question_answer5) The value of cos \[225{}^\circ \] + sin \[195{}^\circ \] is'.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[\frac{\sqrt{3}-1}{2\sqrt{2}}\]                  
  done clear
  B)
  \[\frac{\sqrt{3}-1}{\sqrt{2}}\]
  done clear
  C)
  \[-\frac{\sqrt{3}-1}{\sqrt{2}}\]  
  done clear
  D)
  \[\frac{\sqrt{3}+1}{\sqrt{2}}\]
  done clear
  View Answer play_arrow

• question_answer6) The middle term in the expansion of \[{{\left( 1-\frac{1}{x} \right)}^{n}}{{\left( 1-x \right)}^{n}}\] in powers of x is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[{{-}^{2n}}{{C}_{n-1}}\]                              
  done clear
  B)
                         \[{{-}^{2n}}{{C}_{n}}\]
  done clear
  C)
                         \[^{2n}{{C}_{n-1}}\]                       
  done clear
  D)
                         \[^{2n}{{C}_{n}}\]
  done clear
  View Answer play_arrow

• question_answer7) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \left( \pi {{\cos }^{2}}x \right)}{{{x}^{2}}}\] equals.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[-\pi \]                               
  done clear
  B)
                         1
  done clear
  C)
                         \[-1\]                                    
  done clear
  D)
                         \[\pi \]
  done clear
  View Answer play_arrow

• question_answer8) The line parallel to x-axis and passing through the point of intersection of lines \[ax+2by+3b=0\]and \[bx-2ay-3a=0,\] where \[(a,b)\ne (0,0)\] is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  above x-oxis ata distance 2/3 from it
  done clear
  B)
                         above x-axis at a distance 3/2 from it
  done clear
  C)
                         below x-axis at a distance 3/2 from it                
  done clear
  D)
                         below x-axis at a distance 2/3 from it
  done clear
  View Answer play_arrow

• question_answer9) The chord PQ of the parabola \[{{y}^{2}}=x,\]where one end P of the chord is at point (4, - 2), is perpendicular to the axis of the parabola. Then the slope of the normal at Q is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[-4\]    
  done clear
  B)
                         \[-\frac{1}{4}\]
  done clear
  C)
                          4                                            
  done clear
  D)
                         \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer10) Let p and q denote the following statements p : The sun is shining q: I shall play tennis in the afternoon The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[q\Rightarrow \tilde{\ }p\]                        
  done clear
  B)
                         \[q\wedge \tilde{\ }p\]
  done clear
  C)
                         \[p\wedge \tilde{\ }q\]                
  done clear
  D)
                         \[\tilde{\ }q\Rightarrow \tilde{\ }p\]
  done clear
  View Answer play_arrow

• question_answer11) If the sum of the series \[{{\text{1}}^{\text{2}}}+\text{2}.{{\text{2}}^{\text{2}}}+{{\text{3}}^{\text{2}}}+\text{2}.{{\text{4}}^{\text{2}}}+{{\text{5}}^{\text{2}}}+\]\[~...\text{ 2}.{{\text{6}}^{\text{2}}}+...\] upto n terms, when n is even, is\[\frac{n{{\left( n+1 \right)}^{2}}}{2},\]then the sum of the series, when n is odd, is  ,   JEE Main Online Paper (Held On 26-May-2012)      
  A)
  \[{{n}^{2}}(n+1)\]                           
  done clear
  B)
                          \[\frac{{{n}^{2}}(n-1)}{2}\]
  done clear
  C)
                         \[\frac{{{n}^{2}}(n+1)}{2}\]                        
  done clear
  D)
                         \[{{n}^{2}}(n-1)\]
  done clear
  View Answer play_arrow

• question_answer12) The area bounded by the parabola \[{{y}^{2}}=4x\] and the line \[\text{2x}-\text{3y}+\text{4}=0,\] in square unit, is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[\frac{2}{5}\]                                   
  done clear
  B)
                         \[\frac{1}{3}\]
  done clear
  C)
                         \[1\]                                     
  done clear
  D)
                         \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer13) Let \[f;\left( -\infty ,\infty  \right)\to \left( -\infty ,\infty  \right)\] be defined by \[f(x)={{x}^{3}}+1.\] Statement 1: The function f has a local extremumatx=0 Statement 2: The function f is continuous and differentiable on \[\left( -\infty ,\infty  \right)\] and f'(0)=0.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   Statement 1 is true. Statement 2 is false.
  done clear
  B)
                         Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  done clear
  C)
                          Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.
  done clear
  D)
                         Statement 1 is false, Statement 2 is true.
  done clear
  View Answer play_arrow

• question_answer14) Let A and B be nonempty sets in R and\[f:A\to B\] is a objective function. Statement 1: fis an onto function. Statement 2: There exists a function \[g:B\to A\] such that \[fog={{I}_{B}}.\].   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  Statement 1 is true, Statement 2 is false.
  done clear
  B)
                         Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
  done clear
  C)
                         Statement 1 is false. Statement 2 is true.
  done clear
  D)
                         Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.
  done clear
  View Answer play_arrow

• question_answer15) The number of common tangents of the circles given by\[{{x}^{2}}+{{y}^{2}}-8x-2y+1=0\]and\[{{x}^{2}}+{{y}^{2}}+6x+8y=0\]is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  one                                       
  done clear
  B)
                         four
  done clear
  C)
                         two    
  done clear
  D)
                         three
  done clear
  View Answer play_arrow

• question_answer16) \[{{\left| {{z}_{1}}+{{z}_{2}} \right|}^{2}}+{{\left| {{z}_{1}}-{{z}_{2}} \right|}^{2}}\] is equal to.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[2\left( \left| {{z}_{1}}-{{z}_{2}} \right| \right)\]                             
  done clear
  B)
                         \[2\left( {{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}} \right)\]
  done clear
  C)
                         \[\left| {{z}_{1}} \right|\left| {{z}_{2}} \right|\]                
  done clear
  D)
                         \[{{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer17) \[f\left( x \right)=\frac{dx}{{{\sin }^{6}}x}\]is a polynomial of degree.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   5 in cot x            
  done clear
  B)
                         5 in tan x
  done clear
  C)
                          3 in tan x            
  done clear
  D)
                         3 in cot x
  done clear
  View Answer play_arrow

• question_answer18) The equation of a plane containing the line \[\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}\] and the point (0,7, - 7) is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[x+y+z=0\]                       
  done clear
  B)
                         \[x+2y+z=21\]
  done clear
  C)
                         \[3x-2y+5z+35=0\]
  done clear
  D)
                         \[3x+2y+5z+21=0\]
  done clear
  View Answer play_arrow

• question_answer19) Statement-1: The vectors \[\overset{\to }{\mathop{a}}\,,\overset{\to }{\mathop{b}}\,\]and \[\overset{\to }{\mathop{c}}\,\] lie in the same plane if and only if \[\overset{\to }{\mathop{a}}\,.\left( \overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{c}}\, \right)=0\] Statement-2: The vectors \[\overset{\to }{\mathop{u}}\,\]and \[\overset{\to }{\mathop{v}}\,\] are perpendicular if and only if \[\overset{\to }{\mathop{u}}\,.\overset{\to }{\mathop{v}}\,=0\]where\[\overset{\to }{\mathop{u}}\,\times \overset{\to }{\mathop{v}}\,\]is a vector perpendicular to the plane of.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  Statement 1 is false. Statement 2 is true.
  done clear
  B)
  Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation for Statement!.
  done clear
  C)
  Statement 1 is true, Statement 2 is false.
  done clear
  D)
  Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
  done clear
  View Answer play_arrow

• question_answer20) Statement 1: If the system of equations\[x+ky+3z=0,\]\[3x+ky-2z=0,\]\[2x+3y-4z=0\]has anon- trivial solution, then the value of k is\[\frac{31}{2}.\] Statement 2: A system of three homogeneous equations in three variables has a non trivial solution if the determinant of the coefficient matrix is zero.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  Statement 1 is false, Statement 2 is true.
  done clear
  B)
                         Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  done clear
  C)
                         Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
  done clear
  D)
                          Statement 1 is true, Statement 2 is false.
  done clear
  View Answer play_arrow

• question_answer21) The normal at  \[\left( 2,\frac{3}{2} \right)\]to the ellipse,\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{3}=1\] touches a parabola, whose equation is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[{{y}^{2}}=-104x\]                         
  done clear
  B)
                         \[{{y}^{2}}=14x\]
  done clear
  C)
                         \[{{y}^{2}}=26x\]                             
  done clear
  D)
                         \[{{y}^{2}}=-14x\]
  done clear
  View Answer play_arrow

• question_answer22) If [x] is the greatest integer \[\le x,\] then the value of the integral\[\int\limits_{-0.9}^{0.9}{\left( \left[ {{x}^{2}} \right]+\log \left( \frac{2-x}{2+x} \right) \right)dx}\]is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  0.486                                    
  done clear
  B)
                          0.243
  done clear
  C)
                          1.8                                        
  done clear
  D)
                          0
  done clear
  View Answer play_arrow

• question_answer23) If\[a,b,c\in R\] and 1 is a root of equation \[a{{x}^{2}}+bx+c=0,\]then the curve \[y=4a{{x}^{2}}+3bx+2c,a\ne 0\]intersect x-axis at.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  two distinct points whose coordinates are always rational numbers
  done clear
  B)
         no point
  done clear
  C)
                         exactly two distinct points
  done clear
  D)
                         exactly one point
  done clear
  View Answer play_arrow

• question_answer24) If\[f(x)=a|\sin x|+b{{e}^{|x|}}+c|x{{|}^{3}},\] where \[a,b,c\in R\], is differentiable at x = 0, then.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[a=0,b\]and c are any real numbers
  done clear
  B)
                         \[c=0,a=0,b\] is any real number
  done clear
  C)
                         \[b=0,c=0,a\] is any real number
  done clear
  D)
                         \[a=0,b=0,c\] is any real number
  done clear
  View Answer play_arrow

• question_answer25) The integrating factor of the differential equation \[\left( {{x}^{2}}-1 \right)\frac{dy}{dx}+2xy=x\] is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[\frac{1}{{{x}^{2}}-1}\]                
  done clear
  B)
                         \[{{x}^{2}}-1\]
  done clear
  C)
                         \[\frac{{{x}^{2}}-1}{x}\]                
  done clear
  D)
                         \[\frac{x}{{{x}^{2}}-1}\]
  done clear
  View Answer play_arrow

• question_answer26) Consider the straight lines \[{{L}_{1}}:x-y=1\] \[{{L}_{2}}:x+y=1\] \[{{L}_{3}}:2x+2y=5\] \[{{L}_{4}}:2x-2y=7\] The correct statement is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[{{L}_{1}}||{{L}_{4}},{{L}_{2}}||{{L}_{3}},{{L}_{1}}\]intersect \[{{L}_{4}}.\]
  done clear
  B)
  \[{{L}_{1}}\bot {{L}_{2}},{{L}_{1}}||{{L}_{3}},{{L}_{1}}\] intersect \[{{L}_{2}}.\]
  done clear
  C)
  \[{{L}_{1}}\bot {{L}_{2}},{{L}_{2}}||{{L}_{3}},{{L}_{1}}\] intersect \[{{L}_{4}}.\]
  done clear
  D)
  \[{{L}_{1}}\bot {{L}_{2}},{{L}_{1}}||{{L}_{3}},{{L}_{2}}\] intersect \[{{L}_{4}}.\]
  done clear
  View Answer play_arrow

• question_answer27) Statement-1: The variance of first n odd natural numbers is\[\frac{{{n}^{2}}-1}{3}\] Statement-2: The sum of first n odd natural number is n2 and the sum of square of first n odd natural numbers is \[\frac{n\left( 4{{n}^{2}}+1 \right)}{3}.\].   JEE Main Online Paper (Held On 26-May-2012)  
  A)
   Statement 1 is true, Statement 2 is false.
  done clear
  B)
  Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
  done clear
  C)
  Statement 1 is false, Statement 2 is true.
  done clear
  D)
  Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  done clear
  View Answer play_arrow

• question_answer28) If a metallic circular plate of radius 50 cm is heated so that its radius increases at the rate of 1 mm per hour, then the rate at which, the area of the plate increases (in \[\text{c}{{\text{m}}^{\text{2}}}\]/hour) is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[5\pi \]               
  done clear
  B)
                                         \[10\pi \]
  done clear
  C)
                         \[100\pi \]                          
  done clear
  D)
                         \[50\pi \]
  done clear
  View Answer play_arrow

• question_answer29) If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[6!7!\]                                
  done clear
  B)
                         \[{{(6!)}^{2}}\]
  done clear
  C)
                         \[{{(7!)}^{2}}\]                                 
  done clear
  D)
                         \[7!\]
  done clear
  View Answer play_arrow

• question_answer30) There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the um and there after a ball is drawn at random from the um, then the probability that it is white is.   JEE Main Online Paper (Held On 26-May-2012)  
  A)
  \[\frac{1}{4}\]                                   
  done clear
  B)
  \[\frac{2}{3}\]
  done clear
  C)
  \[\frac{1}{5}\]                                   
  done clear
  D)
  \[\frac{1}{3}\]
  done clear
  View Answer play_arrow