Solved papers for JEE Main & Advanced JEE Main Paper (Held on 7 May 2012)

done JEE Main Paper (Held on 7 May 2012) Total Questions - 30

• question_answer1) If\[A=\left( \begin{matrix}    \alpha -1  \\    0  \\    0  \\ \end{matrix} \right),B=\left( \begin{matrix}    \alpha +1  \\    0  \\    0  \\ \end{matrix} \right)\]be two matrices, then \[A{{B}^{T}}\]is a non-zero matrix for |a| not equal to   JEE Main Online Paper (Held On 07 May 2012)
  A)
  2                                             
  done clear
  B)
                         0
  done clear
  C)
                         1     
  done clear
  D)
                         3
  done clear
  View Answer play_arrow

• question_answer2) If a circular iron sheet of radius 30 cm is heated such that its area increases at the uniform rate of\[6\pi c{{m}^{2}}hr,\]then the rate (in mm/hr) at which the radius of the circular sheet increases is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  1.0                                         
  done clear
  B)
                         0.1
  done clear
  C)
                         1.1                                         
  done clear
  D)
                         2.0
  done clear
  View Answer play_arrow

• question_answer3) The difference between the fourth term and the first term of a Geometrical Progresssion is 52. If the sum of its first three terms is 26, then the sum of the first six terms of the progression is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  63                                          
  done clear
  B)
                         189
  done clear
  C)
                         728      
  done clear
  D)
                         364
  done clear
  View Answer play_arrow

• question_answer4) The value of k for which the equation\[(k-2){{x}^{2}}+8x+k+4=0\]has both roots real, distinct and negative is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  6                                             
  done clear
  B)
                         3
  done clear
  C)
                         4                             
  done clear
  D)
                         1      
  done clear
  View Answer play_arrow

• question_answer5) Let y (x) be a solution of \[\frac{\left( 2+\sin x \right)}{\left( 1+y \right)}\frac{dy}{dx}=\cos x.\] If \[y(0)=2,\]then \[y\left( \frac{\pi }{2} \right)\]equals     JEE Main Online Paper (Held On 07 May 2012)
  A)
  \[\frac{5}{2}\]                                   
  done clear
  B)
                         2
  done clear
  C)
                         \[\frac{7}{2}\]
  done clear
  D)
                         3
  done clear
  View Answer play_arrow

• question_answer6) If the eccentricity of a hyperbola \[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]which passes through (k, 2), is \[\frac{\sqrt{13}}{3},\] then the value of \[{{k}^{2}}\] is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  18  
  done clear
  B)
                         8
  done clear
  C)
                         1                                             
  done clear
  D)
                         2
  done clear
  View Answer play_arrow

• question_answer7) If \[\int\limits_{e}^{x}{tf(t)dt}=\sin x-x\cos x-\frac{{{x}^{2}}}{2},\]for all\[x\in R-\{0\},\]then the value of\[f\left( \frac{\pi }{6} \right)\] is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  1/2                                        
  done clear
  B)
                         1
  done clear
  C)
                         0                                             
  done clear
  D)
                         -1/2
  done clear
  View Answer play_arrow

• question_answer8) If the number of 5-element subsets of the set\[A=\{{{a}_{1}},{{a}_{2}},....,{{a}_{20}}\}\] of 20 distinct elements is k times the number of 5-element subsets containing\[{{a}_{4}},\]then k is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  5                                             
  done clear
  B)
                         \[\frac{20}{7}\]
  done clear
  C)
                          4            
  done clear
  D)
                         \[\frac{10}{3}\]
  done clear
  View Answer play_arrow

• question_answer9) If the system of equations \[x+y+z=6\] \[x+2y+3z=10\] \[x+2y+\lambda z=0\] has a unique solution, then \[\lambda \] is not equal to   JEE Main Online Paper (Held On 07 May 2012)
  A)
  1                                             
  done clear
  B)
                         0
  done clear
  C)
                         2                                             
  done clear
  D)
                         3
  done clear
  View Answer play_arrow

• question_answer10) If the straight lines \[\text{x}+\text{3y}=\text{4},\text{3x}+\text{y}=\text{4}\]and \[\text{x}+\text{y}=0\]form a triangle, then the triangle is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  scalene
  done clear
  B)
                         equilateral triangle        
  done clear
  C)
                         isosceles
  done clear
  D)
                         right angled isosceles
  done clear
  View Answer play_arrow

• question_answer11) Let fix)be an indefinite integral of \[{{\cos }^{3}}x.\] Statement 1:f(x) is a periodic function of period\[\pi .\] Statement 2: \[{{\cos }^{3}}x\] is a periodic function.   JEE Main Online Paper (Held On 07 May 2012)
  A)
  Statement 1 is true, Statement 2 is false.
  done clear
  B)
                         Both the Statements are true, but Statement2 is not the correct explanation of Statement1.
  done clear
  C)
                         Both the Statements are true, and Statement2 is correct explanation of Statement 1.
  done clear
  D)
                         Statement 1 is false, Statement 2 is true.
  done clear
  View Answer play_arrow

• question_answer12) The parabola\[{{y}^{2}}=x\] divides the circle \[{{x}^{2}}+{{y}^{2}}=2\]into two parts whose areas are in the ratio   JEE Main Online Paper (Held On 07 May 2012)
  A)
  \[9\pi +2:3\pi -2\]           
  done clear
  B)
                         \[9\pi -2:3\pi +2\]
  done clear
  C)
                         \[7\pi -2:2\pi -3\]            
  done clear
  D)
                         \[7\pi +2:3\pi +2\]
  done clear
  View Answer play_arrow

• question_answer13) The equation of the circle passing through the point (1,2) and through the points of intersection of\[{{x}^{2}}+{{y}^{2}}-4x-6y-21=0\]and \[3x+4y+5=0\] is given by   JEE Main Online Paper (Held On 07 May 2012)
  A)
  \[{{x}^{2}}+{{y}^{2}}+2x=2y+11=0\]
  done clear
  B)
                         \[{{x}^{2}}+{{y}^{2}}-2x+2y-7=0\]
  done clear
  C)
                         \[{{x}^{2}}+{{y}^{2}}-2x-2y-3=0\]
  done clear
  D)
                         \[{{x}^{2}}+{{y}^{2}}+2x+2y-11=0\]
  done clear
  View Answer play_arrow

• question_answer14) The frequency distribution of daily working expenditure of families in a locality is as follows:

  Expenditure in Rs. (x):	0-50	50-100	100-150	150-200	200-250
  No. of families (f):	24	33	37	B	25

  If the mode of the distribution is " 140, then the value of b is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  34                                          
  done clear
  B)
  31
  done clear
  C)
  26                                          
  done clear
  D)
  36
  done clear
  View Answer play_arrow

• question_answer15) The sum of the series\[{{\text{1}}^{\text{2}}}+\text{2}.{{\text{2}}^{\text{2}}}+{{\text{3}}^{\text{2}}}+\text{2}.{{\text{4}}^{\text{2}}}+{{\text{5}}^{\text{2}}}+\text{2}.{{\text{6}}^{\text{2}}}+....+\text{2(2m}{{\text{)}}^{\text{2}}}\]is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  \[m{{(2m+1)}^{2}}\]                      
  done clear
  B)
                         \[{{m}^{2}}(m+2)\]
  done clear
  C)
                         \[{{m}^{2}}(2m+1)\]                      
  done clear
  D)
                         \[m{{(m+2)}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer16) The point of intersection of the lines\[({{a}^{3}}+3)x+ay+a-3=0\]and\[({{a}^{5}}+2)x+(a+2)y+2a+3=0\](a real) lies on they-axis for   JEE Main Online Paper (Held On 07 May 2012)
  A)
  no value of a
  done clear
  B)
                         more than two values of a
  done clear
  C)
                         exactly one value of a
  done clear
  D)
                         exactly two values of a
  done clear
  View Answer play_arrow

• question_answer17) ABCD is parallelogram. The position vectors of A and C are respectively,\[3\hat{i}+3\hat{j}+5\hat{k}\] and\[\hat{i}-5\hat{j}-5\hat{k}\].If M is the midpoint of the diagonal\[\overset{\to }{\mathop{OM}}\,\]then the magnitude of the projection of on\[\overset{\to }{\mathop{OC}}\,,\] where O is the origin, is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  \[7\sqrt{51}\]                   
  done clear
  B)
                         \[\frac{7}{\sqrt{50}}\]
  done clear
  C)
                         \[7\sqrt{50}\]                   
  done clear
  D)
                         \[\frac{7}{\sqrt{51}}\]
  done clear
  View Answer play_arrow

• question_answer18) The range of the function \[f\left( x \right)=\frac{x}{1+|x|},x\in R,\]is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  R                                            
  done clear
  B)
                         -1,1
  done clear
  C)
                         R- {0}                    
  done clear
  D)
                         [-1, 1]  
  done clear
  View Answer play_arrow

• question_answer19) If two vertical poles 20 m and 80 m high stand apart on a horizontal plane, then the height (in m)of the point of intersection of the lines joining the top of each pole to the foot of other is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  16           
  done clear
  B)
                         18
  done clear
  C)
                         50                                          
  done clear
  D)
                         15
  done clear
  View Answer play_arrow

• question_answer20) If \[\vec{a}=\hat{i}-2\hat{j}+3\hat{k},\vec{b}=2\hat{i}+3\hat{j}-\hat{k}\]and\[\vec{c}=\lambda \hat{i}+\hat{j}+(2\lambda -1)\hat{k}\]are coplanar vectors, then\[\lambda \]is equal to
  A)
  0      
  done clear
  B)
                         -1
  done clear
  C)
                         2                             
  done clear
  D)
                         1
  done clear
  View Answer play_arrow

• question_answer21) Statement 1:\[y=mx-\frac{1}{m}\]is always a tangent to the parabola, \[{{y}^{2}}=-4x\]for all non-zero values of w. Statement 2: Every tangent to the parabola, \[{{y}^{2}}=-4x\] will meet its axis at a point whose abscissa is non-negative.   JEE Main Online Paper (Held On 07 May 2012)
  A)
  Statement 1 is true, Statement 2 is true; Statement 2 is 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 false.
  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_answer22) Let \[{{Z}_{1}}\]and \[{{Z}_{2}}\]be any two complex number. Statement1:\[\left| {{Z}_{1}}-{{Z}_{2}} \right|\ge \left| {{Z}_{1}} \right|-\left| {{Z}_{2}} \right|\] Statement 2: \[\left| {{Z}_{1}}+{{Z}_{2}} \right|\le \left| {{Z}_{1}} \right|+\left| {{Z}_{2}} \right|\]   JEE Main Online Paper (Held On 07 May 2012)
  A)
  Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
  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 true. Statement 2 is false.
  done clear
  D)
                         Statement 1 is false. Statement 2 is true.
  done clear
  View Answer play_arrow

• question_answer23) Let X and Y are two events such that\[P\left( X\cup Y \right)=P(X\cap Y).\] Statement1:\[P(X\cap Y')=P\left( X'\cap Y \right)=0\] Statement 2; \[P(X)+P=2P\left( X\cap Y \right)\]   JEE Main Online Paper (Held On 07 May 2012)
  A)
  Statement 1 is false. Statement 2 is true. Statement 1 is true. Statement 2 is true,
  done clear
  B)
                         Statement 2 is not a correct explanation of Statement 1.
  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_answer24) If\[f(y)=1-(y-1)+{{(y-1)}^{2}}-{{(y-1)}^{3}}\]\[+...-{{(y-1)}^{17}},\]then the coefficient of \[{{y}^{2}}\] in it is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  \[^{17}{{C}_{2}}\]                                           
  done clear
  B)
  \[^{17}{{C}_{3}}\]
  done clear
  C)
  \[^{18}{{C}_{2}}\]                                           
  done clear
  D)
  \[^{18}{{C}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer25) The values of a for which the two points (1, a, 1)and (-3, 0, a) lie on the opposite sides of the plane \[\text{3x}+\text{4y}-\text{12z}+\text{13}=0,\] satisfy   JEE Main Online Paper (Held On 07 May 2012)
  A)
  \[0<a<\frac{1}{3}\]                         
  done clear
  B)
                         \[-1<a<0\]
  done clear
  C)
                         \[a<-1\]or    \[a<\frac{1}{3}\]     
  done clear
  D)
                         \[a=0\]
  done clear
  View Answer play_arrow

• question_answer26) \[\underset{x\to 0}{\mathop{\lim }}\,\left( \frac{x-\sin x}{x} \right)\sin \left( \frac{1}{x} \right)\]   JEE Main Online Paper (Held On 07 May 2012)
  A)
  equals 1              
  done clear
  B)
                         equals 0
  done clear
  C)
                         does not exist                  
  done clear
  D)
                         equals? 1
  done clear
  View Answer play_arrow

• question_answer27) A line with positive direction cosines passes through the point P (2, - 1, 2) and makes equal angles with the coordinate axes. If the line meets the plane \[2x+y+z=9\] at point Q, then the length PQ equals   JEE Main Online Paper (Held On 07 May 2012)
  A)
  \[\sqrt{2}\]                                        
  done clear
  B)
  2
  done clear
  C)
  \[\sqrt{3}\]                        
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer28) Let\[f(x)=\sin x,g(x)=x.\] Statement1:\[f(x)\le g(x)\] for x in \[(0,\infty )\] Statement2:\[f(x)\le 1\] for x in \[(0,\infty )\] but \[g(x)\to \infty \]as\[x\to \infty .\]   JEE Main Online Paper (Held On 07 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 a correct explanation for Statement!.
  done clear
  D)
                         Statement 1 is false. Statement 2 is true.
  done clear
  View Answer play_arrow

• question_answer29) The Statement that is TRUE among the following is   JEE Main Online Paper (Held On 07 May 2012)
  A)
  The contrapositive of\[3x+2=8\Rightarrow x=2\]is\[x\ne 2\]\[\Rightarrow \]\[3x+2\ne 8.\]
  done clear
  B)
                         The converse of \[=0\Rightarrow x=0\] is \[x\ne 0\Rightarrow \tan x=0.\]
  done clear
  C)
                         \[p\Rightarrow q\] is equivalent to\[p\vee \tilde{\ }q.\]
  done clear
  D)
                         \[p\vee q\]and\[p\wedge q\] have the same truth table.
  done clear
  View Answer play_arrow

• question_answer30) If\[x+|y|=2y,\] then y as a function of x, at x = 0 is
  A)
  differentiable but not continuous
  done clear
  B)
                         continuous but not differentiable
  done clear
  C)
                         continuous as well as differentiable
  done clear
  D)
                         neither continuous nor differentiable
  done clear
  View Answer play_arrow