Solved papers for JEE Main & Advanced JEE Main Paper (Held On 19 May 2012)

done JEE Main Paper (Held On 19 May 2012) Total Questions - 30

• question_answer1) The equation of the normal to the parabola, \[{{x}^{2}}=8y\]at \[x=4\]is     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[x+2y=0\]                         
  done clear
  B)
                         \[x+y=2\]
  done clear
  C)
                         \[x-2y=0\]                          
  done clear
  D)
                         \[x+y=6\]
  done clear
  View Answer play_arrow

• question_answer2) The value of the integral\[\int\limits_{0}^{0.9}{\left[ x-2\left[ x \right] \right]dx,}\]where [.] denotes the greatest integer function is     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  0.9                         
  done clear
  B)
                         1.8
  done clear
  C)
                         -0.9                                       
  done clear
  D)
                         0
  done clear
  View Answer play_arrow

• question_answer3) If a, b, c, are non zero complex numbers satisfying \[{{\text{a}}^{\text{2}}}+{{\text{b}}^{\text{2}}}+{{\text{c}}^{\text{2}}}=0\]and\[\left| \begin{matrix}    {{b}^{2}}+{{c}^{2}} & ab & ac  \\    ab & {{c}^{2}}+{{a}^{2}} & bc  \\    ac & bc & {{a}^{2}}+{{b}^{2}}  \\ \end{matrix} \right|=k{{a}^{2}}{{b}^{2}}{{c}^{2}},\]is equal to     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  1                             
  done clear
  B)
                         3
  done clear
  C)
                         4     
  done clear
  D)
                         2
  done clear
  View Answer play_arrow

• question_answer4) If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is.     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[\frac{8}{15}\]                                
  done clear
  B)
  \[\frac{4}{15}\]
  done clear
  C)
  \[\frac{2}{15}\]                                           
  done clear
  D)
  \[\frac{1}{15}\]
  done clear
  View Answer play_arrow

• question_answer5) The sum of the series \[1+\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+...\]upto n terms is.     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[\frac{7}{6}n+\frac{1}{6}-\frac{2}{{{3.2}^{n-1}}}\]           
  done clear
  B)
                         \[\frac{5}{3}n-\frac{7}{6}+\frac{2}{{{2.3}^{n-1}}}\]
  done clear
  C)
                         \[n+\frac{1}{2}-\frac{1}{{{2.3}^{n}}}\]    
  done clear
  D)
                         \[n-\frac{1}{3}-\frac{1}{{{3.2}^{n-1}}}\]
  done clear
  View Answer play_arrow

• question_answer6) If\[a+b+c=0,\left| \overset{\to }{\mathop{a}}\, \right|=3,\left| \overset{\to }{\mathop{b}}\, \right|=5\]and\[\left| \overset{\to }{\mathop{c}}\, \right|=7,\]then the angle between \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,\]is then f(1) equals.     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[\frac{\pi }{3}\]                                              
  done clear
  B)
                         \[\frac{\pi }{4}\]
  done clear
  C)
                         \[\frac{\pi }{6}\]                                              
  done clear
  D)
                         \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer7) If\[f\left( x \right)=\int_{{}}^{{}}{\left( \frac{{{x}^{2}}+{{\sin }^{2}}x}{1+{{x}^{2}}} \right)}\sec x\,dx\]and\[f(0)=0,\]then f(1) equals.     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[\tan 1-\frac{\pi }{4}\] 
  done clear
  B)
                         \[\tan 1+1\]
  done clear
  C)
                         \[\frac{\pi }{4}\]                                              
  done clear
  D)
                         \[1-\frac{\pi }{4}\]
  done clear
  View Answer play_arrow

• question_answer8) Let\[p,q,r\in R\]and \[r>p>0.\]If the quadratic equation\[p{{x}^{2}}+qx+r=0\] has two complex roots \[\alpha \]and \[\beta ,\]then\[|\alpha |+|\beta |\]is.       JEE Main  Online Paper (Held On 19  May  2012)
  A)
  equal to 1
  done clear
  B)
                         less than 2 but not equal to 1
  done clear
  C)
                         greater than 2  
  done clear
  D)
                         equal to 2
  done clear
  View Answer play_arrow

• question_answer9) If three distinct points A, B, C are given in the 2- dimensional coordinate plane such that the ratio of the distance of each one of them from the point (1, 0) to the distance from (- 1,0) is equal to \[\frac{1}{2},\]then the circum centre of the triangle ABC is at, the point.     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[\left( \frac{5}{3},0 \right)\]         
  done clear
  B)
                         (0,0)
  done clear
  C)
                         \[\left( \frac{1}{3},0 \right)\]                     
  done clear
  D)
                         (3,0)
  done clear
  View Answer play_arrow

• question_answer10) If the line \[y=mx+1\] meets the circle \[{{\text{x}}^{\text{2}}}+{{\text{y}}^{\text{2}}}+\text{3x}=0\]in two points equidistant from and on opposite sides of x-axis, then.     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  3m+2=0                               
  done clear
  B)
                         3m-2=0
  done clear
  C)
                         2m+3=0                               
  done clear
  D)
                         2m-3=0
  done clear
  View Answer play_arrow

• question_answer11) Let f: [1, 3]\[\to \] R be a function satisfying \[\frac{x}{[x]}\le f\left( x \right)\le \sqrt{6-x},\]for all \[x\ne 2\]and f(2) = 1, where R is the set of all real numbers and [x] denotes the largest integer less than or equal to x. Statement 1: \[\underset{x\to {{2}^{-}}}{\mathop{\lim }}\,f\left( x \right)\] exists. Statement 2: f is continuous at x = 2.     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  done clear
  B)
  Statement 1 is false. Statement 2 is true.
  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_answer12) The general solution of the differential equation \[\frac{dy}{dx}+\frac{2}{x}y={{x}^{2}}\]is     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[y=c{{x}^{-3}}-\frac{{{x}^{2}}}{4}\]        
  done clear
  B)
                         \[y=c{{x}^{3}}-\frac{{{x}^{2}}}{4}\]
  done clear
  C)
                         \[y=c{{x}^{2}}+\frac{{{x}^{3}}}{5}\]                         
  done clear
  D)
                         \[y=c{{x}^{-2}}+\frac{{{x}^{3}}}{5}\]
  done clear
  View Answer play_arrow

• question_answer13) A value of \[{{\tan }^{-1}}\left( \sin \left( {{\cos }^{-1}}\left( \sqrt{\frac{2}{3}} \right) \right) \right)\]is       JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[\frac{\pi }{4}\]                                              
  done clear
  B)
                         \[\frac{\pi }{2}\]
  done clear
  C)
                         \[\frac{\pi }{3}\]                                              
  done clear
  D)
                         \[\frac{\pi }{6}\]
  done clear
  View Answer play_arrow

• question_answer14) Let p and q be two Statements. Amongst the following, the Statement that is equivalent to \[p\to q\] is     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[p\wedge \tilde{\ }q\]                
  done clear
  B)
                         \[\tilde{\ }p\vee q\]
  done clear
  C)
                         \[\tilde{\ }p\wedge q\]                
  done clear
  D)
                         \[p\vee \tilde{\ }q\]
  done clear
  View Answer play_arrow

• question_answer15) If the three planes \[x=5,2x-5a+3z-2=0\]and \[3bx+y-3z=0\] contain a common line, then (a, b) is equal to     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[\left( \frac{8}{15},-\frac{1}{5} \right)\]
  done clear
  B)
                         \[\left( \frac{1}{5},-\frac{8}{15} \right)\]
  done clear
  C)
                         \[\left( -\frac{8}{15},\frac{1}{5} \right)\]                               
  done clear
  D)
                         \[\left( -\frac{1}{5},\frac{8}{15} \right)\]
  done clear
  View Answer play_arrow

• question_answer16) If\[f(x)=3{{x}^{10}}-7{{x}^{8}}+5{{x}^{6}}-21{{x}^{3}}+3{{x}^{2}}-7,\]then \[\underset{\alpha \to 0}{\mathop{\lim }}\,\frac{f\left( 1-\alpha  \right)-f\left( 1 \right)}{{{\alpha }^{3}}+3\alpha }\]is     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[-\frac{53}{3}\]                                               
  done clear
  B)
                         \[\frac{53}{3}\]
  done clear
  C)
                         \[-\frac{55}{3}\]                                               
  done clear
  D)
                         \[\frac{55}{3}\]
  done clear
  View Answer play_arrow

• question_answer17) Let Z and? F be complex numbers such that \[|Z|=|W|,\] and arg Z denotes the principal argument of Z. Statement 1. If arg Z+ arg \[W=\pi ,\]then \[Z=-\overline{W}.\] Statement1: \[|Z|=|W|,\]implies arg Z- arg \[\overline{W}=\pi .\]     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  Statement 1 is true. Statement 2 is false. Statement 1 is true, Statement 2 is true,
  done clear
  B)
                         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 false, Statement 2 is true.
  done clear
  View Answer play_arrow

• question_answer18) Consider a quadratic equation \[\text{a}{{\text{x}}^{\text{2}}}+\text{bx}+\text{c}=0,\]where \[\text{2a}+\text{3b}+\text{6c}=0\] and let\[g\left( x \right)=a\frac{{{x}^{3}}}{3}+b\frac{{{x}^{2}}}{2}+cx.\] Statement 1: The quadratic equation has at least one root in the interval (0, 1). Statement 2: The Rolle's theorem is applicable to function g(x) on the interval [0, 1].     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  Statement 1 is false, Statement 2 is true.
  done clear
  B)
  Statement 1 is true. Statement 2 is false. Statement 1 is true, Statement 2 is true,
  done clear
  C)
  Statement 2 is not a correct explanation for Statement 1.
  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_answer19) Suppose \[\theta \] and \[\phi (\ne 0)\] are such that \[(\theta +\phi ),\sec \theta \]and \[\sec (\theta -\phi )\] are in A.P. If \[\cos \theta =k\cos \left( \frac{\phi }{2} \right)\] for some k, then A; is equal to     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[\pm \sqrt{2}\]                                              
  done clear
  B)
                         \[\pm 1\]
  done clear
  C)
                         \[\pm \frac{1}{\sqrt{2}}\]                            
  done clear
  D)
                         \[\pm 2\]
  done clear
  View Answer play_arrow

• question_answer20) Statement!: The shortest distance between the is lines \[\frac{x}{2}=\frac{y}{-1}=\frac{z}{2}\]and\[\frac{x-1}{4}=\frac{y-1}{-2}=\frac{z-1}{4}\]is\[\sqrt{2}.\] Statement 2: The shortest distance between two parallel lines is the perpendicular distance from any point on one of the lines to the other line.     JEE Main  Online Paper (Held On 19  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 a correct explanation for Statement 1.
  done clear
  View Answer play_arrow

• question_answer21) If \[n{{=}^{m}}{{C}_{2}},\]then the value of \[^{n}{{C}_{2}}\] is given by     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  \[3{{(}^{m+1}}{{C}_{4}})\]           
  done clear
  B)
                         \[^{m-1}{{C}_{4}}\]
  done clear
  C)
                         \[^{m+1}{{C}_{4}}\]                       
  done clear
  D)
                         \[2{{(}^{m+2}}{{C}_{4}})\]
  done clear
  View Answer play_arrow

• question_answer22) If P(5) denotes the set of all subsets of a given set S, then the number of one-to-one functions from the set 5'= {1,2,3} to the set P(5) is     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  24                                          
  done clear
  B)
                         8
  done clear
  C)
                         336    
  done clear
  D)
                         320
  done clear
  View Answer play_arrow

• question_answer23) The number of arrangements that can be formed from the letters a, b, c, d, e, /taken 3 at a time without repetition and each arrangement containing at least one vowel, is     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  96                                          
  done clear
  B)
                         128
  done clear
  C)
                         24                                          
  done clear
  D)
                         72
  done clear
  View Answer play_arrow

• question_answer24) The weight W of a certain stock of fish is given by W=nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as \[n=2{{t}^{2}}+3\]and \[w={{t}^{2}}-t+2,\]then the rate of change of W with respect to t at t = 1 is     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  1                             
  done clear
  B)
                         8
  done clear
  C)
                         13        
  done clear
  D)
                         5
  done clear
  View Answer play_arrow

• question_answer25) The area of the region bounded by the curve \[y={{x}^{3}},\] and the lines, y= 8, and x = 0, is     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  8                                             
  done clear
  B)
                         12
  done clear
  C)
                         10                                          
  done clear
  D)
                         16
  done clear
  View Answer play_arrow

• question_answer26) If \[\overset{\to }{\mathop{a}}\,=\hat{i}-2\hat{j}+3\hat{k},\overset{\to }{\mathop{b}}\,=2\hat{i}+3\hat{j}-\hat{k}\]and \[\overset{\to }{\mathop{c}}\,=r\hat{i}+\hat{j}+\left( 2r-1 \right)\hat{k}\]are three vectors such  that \[\overset{\to }{\mathop{c}}\,\] is parallel to the plane of \[\overset{\to }{\mathop{a}}\,\] and \[\overset{\to }{\mathop{b}}\,,\] then r is equal to     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  1                                             
  done clear
  B)
                         -1
  done clear
  C)
                         0  
  done clear
  D)
                         2
  done clear
  View Answer play_arrow

• question_answer27) Let L be the liney = 2x, in the two dimensional plane. Statement 1: The image of the point (0,1) in L is the point \[\left( \frac{4}{5},\frac{3}{5} \right).\] Statement 2: The points (0,1) and\[\left( \frac{4}{5},\frac{3}{5} \right)\] lie on opposite sides of the line L and are at equal distance from it.     JEE Main  Online Paper (Held On 19  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 true. Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  done clear
  D)
                         Statement 1 is false. Statement 2 is true.
  done clear
  View Answer play_arrow

• question_answer28) The median of 100 observations grouped in classes of equal width is 25. If the median class interval is 20 - 30 and the number of observations less than 20 is 45, then the frequency of median class is     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  10
  done clear
  B)
                         20
  done clear
  C)
                         15                          
  done clear
  D)
                         12
  done clear
  View Answer play_arrow

• question_answer29) If the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]coincide with the foci of the hyperbola \[\frac{{{x}^{2}}}{144}-\frac{{{y}^{2}}}{81}=\frac{1}{25},\]then \[{{b}^{2}}\] is equal to     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  8                                             
  done clear
  B)
                         10
  done clear
  C)
                         7     
  done clear
  D)
                         9
  done clear
  View Answer play_arrow

• question_answer30) If \[{{A}^{T}}\]denotes the transpose of the matrix\[A=\left[ \begin{matrix}    0 & 0 & a  \\    0 & b & c  \\    d & e & f  \\ \end{matrix} \right],\]where a, b, c, d, e and f are integers such that \[abd\ne 0,\] then the number of such matrices for which \[{{A}^{-1}}={{A}^{T}}\]is     JEE Main  Online Paper (Held On 19  May  2012)
  A)
  2(3!)                                     
  done clear
  B)
                         3(2!)
  done clear
  C)
                         23         
  done clear
  D)
                         32
  done clear
  View Answer play_arrow