Solved papers for JEE Main & Advanced JEE Main Paper (Held On 12 May 2012)

done JEE Main Paper (Held On 12 May 2012) Total Questions - 30

• question_answer1) If a, b, c, d and are distinct real numbers such that \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}}){{p}^{2}}-2p\]\[(ab+bc+cd)+\]\[({{b}^{2}}+{{c}^{2}}+{{d}^{2}})\]\[\le 0,\]then   JEE Main Online Paper (Held On 12 May 2012)
  A)
  a, b, c, d are in A.P.
  done clear
  B)
  ab = cd
  done clear
  C)
  ac = bd
  done clear
  D)
  a, b, c, d are in G.P.
  done clear
  View Answer play_arrow

• question_answer2) The area of triangle formed by the lines joining the vertex of the parabola, \[{{x}^{2}}=8y,\]to the extremities of its latus rectum is   JEE Main Online Paper (Held On 12 May 2012)
  A)
  2                                             
  done clear
  B)
                         8
  done clear
  C)
                         1                                             
  done clear
  D)
                         4
  done clear
  View Answer play_arrow

• question_answer3) Let A and B be real matrices of the form \[\left[ \begin{matrix}   \alpha  & 0  \\   0 & \beta   \\ \end{matrix} \right]\]and \[\left[ \begin{matrix}    0 & \gamma   \\    \delta  & 0  \\ \end{matrix} \right],\]respectively. Statement 1: AB - BA is always an-invertible matrix. Statement 2: AB - BA is never an identity matrix.   JEE Main Online Paper (Held On 12 May 2012)
  A)
  Statement 1 is true. Statement 2 is false.
  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 a correct explanation of Statement!.
  done clear
  D)
                         Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement 1,
  done clear
  View Answer play_arrow

• question_answer4) If in a triangle \[ABC,\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13},\]then cos A is equal to     JEE Main Online Paper (Held On 12 May 2012)
  A)
  5/7                                        
  done clear
  B)
                         1/5
  done clear
  C)
                         35/19                                    
  done clear
  D)
                         19/35
  done clear
  View Answer play_arrow

• question_answer5) Statement 1: If A and B be two sets having p and q elements respectively, where q > p. Then the total number of functions from set A to set B is \[{{d}^{p}}.\]. Statement 2: The total number of selections of p different objects out of q objects is \[^{q}{{C}_{p}}.\]     JEE Main Online Paper (Held On 12 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 of 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 of Statement 1.
  done clear
  View Answer play_arrow

• question_answer6) A unit vector which is perpendicular to the vector \[2\hat{i}-\hat{j}+2\hat{k}\] and is coplanar with the vectors\[\hat{i}+\hat{j}-\hat{k}\]and \[2\hat{i}+2\hat{j}-\hat{k}\] is   JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[\frac{2\hat{j}+\hat{k}}{\sqrt{5}}\]                       
  done clear
  B)
                         \[\frac{3\hat{i}+2\hat{j}-2\hat{k}}{\sqrt{17}}\]
  done clear
  C)
                         \[\frac{3\hat{i}+2\hat{j}+2\hat{k}}{\sqrt{17}}\]                
  done clear
  D)
                         \[\frac{2\hat{i}+2\hat{j}-2\hat{k}}{3}\]
  done clear
  View Answer play_arrow

• question_answer7) The number of terms in the expansion of \[{{\left( {{y}^{1/5}}+{{x}^{1/10}} \right)}^{55}},\]in which powers of x and y are free from radical signs are     JEE Main Online Paper (Held On 12 May 2012)
  A)
  six       
  done clear
  B)
                         twelve
  done clear
  C)
                         seven                                   
  done clear
  D)
                         five
  done clear
  View Answer play_arrow

• question_answer8) If the point (1, a) lies between the straight lines  \[x+y=1\] and \[2(x+y)=3\]then a lies in interval     JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[\left( \frac{3}{2},\infty  \right)\]                           
  done clear
  B)
                         \[\left( 1,\frac{3}{2} \right)\]
  done clear
  C)
                         \[\left( -\infty ,0 \right)\]                            
  done clear
  D)
                         \[\left( 0,\frac{1}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer9) If two vertices of a triangle are (5, -1) and (-2,3) and its orthocentre is at (0, 0), then the third vertex is                JEE Main Online Paper (Held On 12 May 2012)             
  A)
  (4,-7)                                    
  done clear
  B)
                         (-4,-7)
  done clear
  C)
                         (-4,7)                                    
  done clear
  D)
                         (4,7)
  done clear
  View Answer play_arrow

• question_answer10) Statement 1: A function \[f:R\to R\] is continuous at \[{{x}_{0}}\]if and only if \[\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f(x)\] exists and \[\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f\left( x \right)=f\left( {{x}_{0}} \right)\] Statement 2: A function \[f:R\to R\] is discontinuous at \[{{x}_{0}}\] if and only if,\[\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f\left( x \right)\]exists and \[\underset{x\to {{x}_{0}}}{\mathop{\lim }}\,f\left( x \right)\ne f\left( {{x}_{0}} \right).\]     JEE Main Online Paper (Held On 12 May 2012)
  A)
  Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of 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 a correct explanation of Statement 1.
  done clear
  D)
                         Statement 1 is true. Statement 2 is false.
  done clear
  View Answer play_arrow

• question_answer11) The sum of the series\[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...\] upto 15 terms is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  1                                             
  done clear
  B)
                         2
  done clear
  C)
                         3   
  done clear
  D)
                         4
  done clear
  View Answer play_arrow

• question_answer12) The coordinates of the foot perpendicular from the point (1,0,0) to the line \[\frac{x-1}{2}=\frac{y+1}{-3}=\frac{z+10}{8}\]are     JEE Main Online Paper (Held On 12 May 2012)
  A)
                  (2.-3.8)                                
  done clear
  B)
                         (1,-1,-10)
  done clear
  C)
                         (5,-8,-4)                               
  done clear
  D)
                         (3,-4,-2)
  done clear
  View Answer play_arrow

• question_answer13) If\[\vec{u}=\hat{j}+4\hat{k},\vec{v}=\hat{i}+3\hat{k}\] and \[\vec{w}=\cos \theta \hat{i}+\sin \theta \hat{j}\] are vectors in 3-dimensional space, then the maximum possible value of \[\left| \vec{u}\times \vec{v}.\vec{w} \right|\] is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[\sqrt{3}\]                                        
  done clear
  B)
                         \[5\]
  done clear
  C)
                         \[\sqrt{14}\]                                      
  done clear
  D)
                         \[7\]
  done clear
  View Answer play_arrow

• question_answer14) If the mean of 4,7,2,8,6 and a is 7, then the mean deviation from the median of these observations is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  8                                             
  done clear
  B)
                         5
  done clear
  C)
                         1                                             
  done clear
  D)
                         3
  done clear
  View Answer play_arrow

• question_answer15) Consider a rectangle whose length is increasing at the uniform rate of 2 m/sec, breadth is decreasing at the uniform rate of 3 m/sec and the area is decreasing at the uniform rate of it \[5\,{{m}^{2}}/\sec .\] If after some time the breadth of the rectangle is 2 m then the length of the rectangle is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  2m                                         
  done clear
  B)
                         4m
  done clear
  C)
                         1m                                         
  done clear
  D)
                         3m
  done clear
  View Answer play_arrow

• question_answer16) If \[f'(x)=\sin (\log x)\]and \[y=f\left( \frac{2x+3}{3-2x} \right),\] then\[\frac{dy}{dx}\] equals     JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[\sin \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]\]
  done clear
  B)
                         \[\frac{12}{{{\left( 3-2x \right)}^{2}}}\]
  done clear
  C)
                         \[\frac{12}{{{\left( 3-2x \right)}^{2}}}\sin \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]\]
  done clear
  D)
                         \[\frac{12}{{{\left( 3-2x \right)}^{2}}}\cos \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]\]
  done clear
  View Answer play_arrow

• question_answer17) The area of the triangle whose vertices are complex numbers z, iz, z + iz in the Argand diagram is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[2|z{{|}^{2}}\]                
  done clear
  B)
                         \[1/2|z{{|}^{2}}\]
  done clear
  C)
                         \[4|z{{|}^{2}}\]                
  done clear
  D)
                         \[|z{{|}^{2}}\]  
  done clear
  View Answer play_arrow

• question_answer18) Statement 1: The degrees of the differential equations \[\frac{dy}{dx}+{{y}^{2}}=x\] and \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+y\sin x\]are equal. Statement 2: The degree of a differential equation, when it is a polynomial equation in derivatives, is the highest positive integral power of the highest order derivative involved in the differential equation, otherwise degree is not defined.     JEE Main Online Paper (Held On 12 May 2012)
  A)
  Statement 1 is true. Statement 2 is true, Statement 2 is not a correct explanation of Statement!.
  done clear
  B)
                         Statement 1 is false, Statement 2 is true.
  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 a correct explanation of Statement 1.
  done clear
  View Answer play_arrow

• question_answer19) Statement 1: If the points (1,2,2), (2,1,2) and (2,2, z) and (1,1,1) are coplanar, then z= 2. Statement 2: If the 4 points P, Q, R and S are coplanar, then the volume of the tetrahedron PQRS is O.     JEE Main Online Paper (Held On 12 May 2012)
  A)
  Statement 1 is false,. Statement 2 is true.
  done clear
  B)
                         Statement 1 is true. Statement 2 is false.
  done clear
  C)
                         Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
  done clear
  D)
                         Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement!.
  done clear
  View Answer play_arrow

• question_answer20) If \[{{P}_{1}}\]and \[{{P}_{2}}\] are two points on the ellipse \[\frac{{{x}^{2}}}{4}+{{y}^{2}}=1\]at which the tangents are parallel to the chord joining the points (0,1) and (2,0), then the distance between \[{{P}_{1}}\] and \[{{P}_{2}}\] is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[2\sqrt{2}\]                                      
  done clear
  B)
                         \[\sqrt{5}\]
  done clear
  C)
                         \[2\sqrt{3}\]                                      
  done clear
  D)
                         \[\sqrt{10}\]
  done clear
  View Answer play_arrow

• question_answer21) The area enclosed by the curves \[y={{x}^{2}},y={{x}^{3}},x=0\]and \[x=0\]where \[p>1,\]is 1/6. The p equals     JEE Main Online Paper (Held On 12 May 2012)
  A)
  8/3                        
  done clear
  B)
                         16/3
  done clear
  C)
                         2                                             
  done clear
  D)
                         4/3
  done clear
  View Answer play_arrow

• question_answer22) If \[f(x)=x{{e}^{x}}^{(1-x)},x\in R,\]then f(x) is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  decreasing on [-1/2,1]
  done clear
  B)
                         decreasing on R
  done clear
  C)
                         increasing on [-1/2,1]
  done clear
  D)
                         increasing on R
  done clear
  View Answer play_arrow

• question_answer23) The integral of \[\frac{{{x}^{2}}-x}{{{x}^{3}}-{{x}^{2}}+x-1}\]w.r.t.x is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[\frac{1}{2}\log \left( {{x}^{2}}+1 \right)+C\]
  done clear
  B)
                         \[\frac{1}{2}\log \left| {{x}^{2}}+1 \right|+C\]
  done clear
  C)
                         \[\log \left( {{x}^{2}}+1 \right)+C\]         
  done clear
  D)
                         \[\log \left| {{x}^{2}}-1 \right|+C\]
  done clear
  View Answer play_arrow

• question_answer24) The logically equivalent preposition of \[p\Leftrightarrow q\]is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[\left( p\Rightarrow q \right)\wedge \left( q\Rightarrow p \right)\]      
  done clear
  B)
                         \[p\wedge q\]
  done clear
  C)
                         \[\left( p\wedge q \right)\vee \left( q\Rightarrow p \right)\]     
  done clear
  D)
                         \[\left( p\wedge q \right)\Rightarrow \left( q\vee p \right)\]
  done clear
  View Answer play_arrow

• question_answer25) If\[\left| \begin{matrix} -2a & a+b & a+c  \\ b+a & -2b & b+c  \\ c+a & b+c & -2c  \\ \end{matrix} \right|\]\[=\alpha \left( a+b \right)\left( b+c \right)\left( c+a \right)\ne 0\]then \[\alpha \] is equal to     JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[a+b+c\]                           
  done clear
  B)
                         \[abc\]
  done clear
  C)
                          4
  done clear
  D)
                         1
  done clear
  View Answer play_arrow

• question_answer26) If \[A=\{x\in {{z}^{+}}:x<10\]and x is a multiple of 3 or 4}, where \[{{z}^{+}}\] is the set of positive integers, then the total number of symmetric relations on A is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  25                                           
  done clear
  B)
                         215
  done clear
  C)
                         210                                         
  done clear
  D)
                         220
  done clear
  View Answer play_arrow

• question_answer27) If the sum of the square of the roots of the equation \[{{x}^{2}}-(\sin \alpha -2)x-(1+\sin \alpha )=0\] is least, then \[\alpha \] is equal to     JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[\frac{\pi }{6}\]                                              
  done clear
  B)
                         \[\frac{\pi }{4}\]
  done clear
  C)
                         \[\frac{\pi }{3}\]                                              
  done clear
  D)
                         \[\frac{\pi }{2}\]
  done clear
  View Answer play_arrow

• question_answer28) If \[\frac{d}{dx}G(x)=\frac{{{e}^{\tan x}}}{x},x\in (0,\pi /2),\]then \[\int\limits_{1/4}^{1/2}{\frac{2}{x}.{{e}^{\tan (\pi {{x}^{2}})}}}dx\] is equal to     JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[G(\pi /4)-G(\pi /16)\]
  done clear
  B)
                         \[2[G(\pi /4)-G(\pi /16)]\]
  done clear
  C)
                         \[\pi [G(1/2)-G(1/4)]\]
  done clear
  D)
                         \[G(1/\sqrt{2})-G(1/2)\]
  done clear
  View Answer play_arrow

• question_answer29) A number w is randomly selected from the set {1,2,3,....., 1000}. The probability that\[\frac{\sum\limits_{i=1}^{n}{{{i}^{2}}}}{\sum\limits_{i=1}^{n}{i}}\] is  an integer is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  0.331                                    
  done clear
  B)
                         0333
  done clear
  C)
                         0334                                      
  done clear
  D)
                         0332
  done clear
  View Answer play_arrow

• question_answer30) If a straight line y - x = 2 divides the region \[{{x}^{2}}+{{y}^{2}}\le 4\]into two parts, then the ratio of the area of the smaller part to the area of the greater part is     JEE Main Online Paper (Held On 12 May 2012)
  A)
  \[3\pi -8:\pi +8\]                              
  done clear
  B)
                         \[\pi -3:3\pi +3\]
  done clear
  C)
                         \[3\pi -4:\pi +4\]                              
  done clear
  D)
                         \[\pi -2:3\pi +2\]
  done clear
  View Answer play_arrow