Solved papers for JEE Main & Advanced JEE Main Paper (Held On 10 April 2016)

done JEE Main Paper (Held On 10 April 2016) Total Questions - 30

• question_answer1)           Let C be a curve given by\[y(x)=1+\sqrt{4x-3},x>\frac{3}{4}\]. If P is a point on C, such that the tangent at P has slope\[\frac{2}{3}\], then a point through which the normal at P passes, is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  (3, - 4)                     
  done clear
  B)
  (1, 7)
  done clear
  C)
  (4, - 3)                     
  done clear
  D)
  (2, 3)
  done clear
  View Answer play_arrow

• question_answer2) Let \[a{{  }_{1}},{{a}_{2}},{{a}_{3}}........\,\,{{a}_{n}}..........\]be in A.P. If \[{{a}_{3}}+{{a}_{7}}+{{a}_{11}}+{{a}_{15}}=72\] then the sum of its first 17 terms is equal to   JEE Main Online Paper (Held On 10 April 2016)
  A)
  153                                           
  done clear
  B)
  306
  done clear
  C)
  612                                           
  done clear
  D)
  204
  done clear
  View Answer play_arrow

• question_answer3) If \[A>0,\,B>0\]and \[B=\frac{\pi }{6}\], then the minimum value of tanA + tanB is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[2-\sqrt{3}\]       
  done clear
  B)
  \[\frac{2}{\sqrt{3}}\]
  done clear
  C)
  \[\sqrt{3}-\sqrt{2}\]                          
  done clear
  D)
  \[4-2\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer4) The contrapositive of the following statement, ?If the side of a square doubles, then its area increases four times", is                   JEE Main Online Paper (Held On 10 April 2016)
  A)
  If the area of a square does not increase four times, then its side is not doubled.
  done clear
  B)
  If the area of a square increases four times, then its side is not doubled.                
  done clear
  C)
  If the area of a square increases four times, then its side is doubled.                
  done clear
  D)
  If the side of a square is not doubled, then its area does not increase four times.
  done clear
  View Answer play_arrow

• question_answer5) Let A be a \[3\times 3\] matrix such that \[{{A}^{2}}-5A+7I=0\]. Statement. - I : \[{{A}^{-1}}=\frac{1}{7}(5I-A)\]. Statement -II : The polynomial \[{{A}^{3}}-2{{A}^{2}}-3A+I\] can be reduced to \[5(A-41)\]. Then   JEE Main Online Paper (Held On 10 April 2016)
  A)
  Statement- I is false, but Statement-II is true.
  done clear
  B)
  Both the statements are false.
  done clear
  C)
  Both the statements are true.
  done clear
  D)
  Statement-I is true, but Statement-II is false.
  done clear
  View Answer play_arrow

• question_answer6) Equation of the tangent to the circle, at the point (1, - 1), whose centre is the point of intersection of the straight lines \[x-y=1\] and \[2x+y=3\] is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[3x-y-4=0\]         
  done clear
  B)
  \[x+4y+3=0\]
  done clear
  C)
  \[x-3y-4=0\]         
  done clear
  D)
  \[4x+y-3=0\]
  done clear
  View Answer play_arrow

• question_answer7) The sum\[\sum\limits_{r=1\grave{\ }}^{10}{({{r}^{2}}+1)\times (r!)}\]is equal to   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[10\times (11!)\]              
  done clear
  B)
  \[101\times (10!)\]
  done clear
  C)
  \[(11!)\]                                 
  done clear
  D)
  \[11\times (11!)\]
  done clear
  View Answer play_arrow

• question_answer8) Let ABC be a triangle whose circumventer is at P. If the position vectors of A,B,C and P are \[\overrightarrow{a}\,,\,\overrightarrow{b},\,\,\overrightarrow{c}\]and\[\frac{\overrightarrow{a}\,,\,+\overrightarrow{b},\,+\,\overrightarrow{c}}{4}\]respectively, then the position vector of the orthocenter of this triangle, is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[\overrightarrow{0}\]                                     
  done clear
  B)
  \[-\left( \frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{2} \right)\]
  done clear
  C)
  \[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\]                   
  done clear
  D)
  \[\left( \frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer9) Let \[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x\]. Then f is an increasing function in the interval   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[\left] \frac{\pi }{4},\frac{\pi }{2} \right[\]
  done clear
  B)
  \[\left] \frac{5\pi }{8},\frac{3\pi }{4} \right[\]
  done clear
  C)
  \[\left] 0,\frac{\pi }{4} \right[\]                         
  done clear
  D)
  \[\left] \frac{\pi }{2},\frac{5\pi }{8} \right[\]
  done clear
  View Answer play_arrow

• question_answer10) Let \[z=1+ai\]be a complex number, a > 0 such that \[{{z}^{3}}\] is a real number. Then the sum \[1+z+{{z}^{2}}+.....+{{z}^{11}}\]is equal to   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[-1250\sqrt{3}\,i\]                            
  done clear
  B)
  \[1250\sqrt{3}\,i\]
  done clear
  C)
  \[-1350\sqrt{3}\,i\]            
  done clear
  D)
  \[1365\sqrt{3}\,i\]
  done clear
  View Answer play_arrow

• question_answer11) Let \[P=\{\theta \,:\,\sin \theta -\cos \theta =\sqrt{2}\cos \theta =\sqrt{2}\cos \theta \}\]and \[Q=\{\theta :\sin +\cos \theta =\sqrt{2}\,\sin \theta \}\] be two sets. Then   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[Q\,\not\subset P\]                        
  done clear
  B)
  \[P\,\not\subset Q\]
  done clear
  C)
  \[P\subset Q\,\]and \[Q-P\ne \phi \]        
  done clear
  D)
  P = Q
  done clear
  View Answer play_arrow

• question_answer12) The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1,2 and 6, then the mean deviation from the mean of the data is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  2.5                                                            
  done clear
  B)
  2.8                
  done clear
  C)
  2.6                                                            
  done clear
  D)
  2.4
  done clear
  View Answer play_arrow

• question_answer13) The number of distinct real values of \[\lambda \] for which the lines \[\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{2}=\frac{z+3}{{{}^{2}}}\]and\[\frac{x-3}{1}=\frac{y-2}{{{}^{2}}}=\frac{z-1}{2}\]are coplanar is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  3                
  done clear
  B)
  2
  done clear
  C)
  1                                                
  done clear
  D)
  4
  done clear
  View Answer play_arrow

• question_answer14) The angle of elevation of the top of a vertical tower from a point A, due east of it is \[{{45}^{o}}\]. The angle of elevation of the top of the same tower from a point B, due south of A is \[{{30}^{o}}\]. If the distance between A and B is \[54\sqrt{2}\]m, then the height of the tower (in metres), is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  54                                              
  done clear
  B)
  108
  done clear
  C)
  \[54\sqrt{3}\]                       
  done clear
  D)
  36 3
  done clear
  View Answer play_arrow

• question_answer15) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{(1-\cos 2x)}^{2}}}{2x\ \tan x-x{{\tan }^{2}}x}\]is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[2\]                                               
  done clear
  B)
  \[-\frac{1}{2}\]
  done clear
  C)
  \[\frac{1}{2}\]                                      
  done clear
  D)
  \[-2\]
  done clear
  View Answer play_arrow

• question_answer16) The solution of the differential equation\[\frac{dy}{dx}+y\frac{y}{2}\sec \,x=\frac{\tan x}{2y}\], where\[\le \,x<\frac{\pi }{2}\] and y(0) = 1, is given by   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[{{y}^{2}}=1-\frac{x}{\sec x\,+\tan x}\]  
  done clear
  B)
  \[{{y}^{2}}=1+\frac{x}{\sec x\,+\tan x}\]
  done clear
  C)
  \[y=1+\frac{x}{\sec x\,+\tan x}\]
  done clear
  D)
  \[y=1-\frac{x}{\sec x\,+\tan x}\]
  done clear
  View Answer play_arrow

• question_answer17) P and Q are two distinct points on the parabola, \[{{y}^{2}}=4x\], with parameters t and \[{{t}_{1}}\] respectively. If the normal at p passes through Q, then the minimum value of \[t_{1}^{2}\] is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  4                                
  done clear
  B)
  6
  done clear
  C)
  8                
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer18) A hyperbola whose transverse axis is along the major axis of the conic,\[\frac{{{x}^{2}}}{3}+\frac{{{y}^{2}}}{4}=4\] and has vertices at the foci of this conic. If the eccentricity of the hyperbola is\[\frac{3}{2}\], then which of the following points does NOT lie on it?   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[\left( \sqrt{5},2\sqrt{2} \right)\]                              
  done clear
  B)
  \[\left( 5,2\sqrt{3} \right)\]
  done clear
  C)
  \[\left( 0,\,\,2 \right)\]     
  done clear
  D)
  \[\left( \sqrt{10},\,\,2\sqrt{3} \right)\]
  done clear
  View Answer play_arrow

• question_answer19) For \[x\,\in \,R,\,x\,\ne 0\], if y(x) is a differentiable function such that\[x\int\limits_{1}^{x}{y(t)dt=(x+1)\int\limits_{1}^{x}{ty(t)dt}}\], then y(x) equals(where C is a constant)   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[C{{x}^{3}}{{e}^{\frac{1}{x}}}\]                   
  done clear
  B)
  \[\frac{C}{x}{{e}^{\frac{-1}{x}}}\]
  done clear
  C)
  \[\frac{C}{{{x}^{2}}}{{e}^{-\frac{1}{x}}}\]                 
  done clear
  D)
  \[\frac{C}{{{x}^{3}}}{{e}^{-\frac{1}{x}}}\]
  done clear
  View Answer play_arrow

• question_answer20) ABC is a triangle in a plane with vertices A(2,3,5), B(-1,3,2) and C\[(\lambda ,\,\,5,\,\,\mu )\]. If the median through A is equally inclined to the coordinate axes, then the value of (\[({{\lambda }^{3}}+{{\mu }^{3}}+5)\]is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  676                                           
  done clear
  B)
  1130
  done clear
  C)
  1348         
  done clear
  D)
  1077
  done clear
  View Answer play_arrow

• question_answer21) A ray of light is incident along a line which meets another line, \[7x-y+1=0\], at the point (0, 1). The ray is then reflected from this point along the line, \[y+2x=1\]. Then the equation of the line of incidence of the ray of light is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[41x+38y-38=0\]               
  done clear
  B)
  \[41x-38y+38=0\]
  done clear
  C)
  \[41x+25y-25=0\]0             
  done clear
  D)
  \[41x-25y+25=0\]
  done clear
  View Answer play_arrow

• question_answer22) A straight line through origin O meets the line \[3y=10-4x\] and \[8x+6y+5=0\] at points A and Respectively. Then O divides the segment AB in the ratio   JEE Main Online Paper (Held On 10 April 2016)
  A)
  3 : 4                                          
  done clear
  B)
  1 : 2
  done clear
  C)
  2 : 3                             
  done clear
  D)
  4 : 1
  done clear
  View Answer play_arrow

• question_answer23) The value of the integral\[\int\limits_{4}^{10}{\frac{[{{x}^{2}}]dx}{[{{x}^{2}}-28x+196]+[{{x}^{2}}]}}\] , where [x] denotes the greatest integer less than or equal to x, is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  3
  done clear
  B)
         7
  done clear
  C)
                  6                                             
  done clear
  D)
                  \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer24) If \[\frac{^{n+2}{{C}_{6}}}{^{n-2}{{P}_{2}}}=11\], then n satisfies the equation   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[{{n}^{2}}+n-110=0\]                      
  done clear
  B)
  \[{{n}^{2}}+5n-84=0\]                
  done clear
  C)
  \[{{n}^{2}}+3n-180=0\]
  done clear
  D)
  \[{{n}^{2}}+2n-80=0\]
  done clear
  View Answer play_arrow

• question_answer25) If the coefficients of \[{{x}^{-2}}\] and \[{{x}^{-4}}\] in the expansion of, \[{{\left( {{x}^{\frac{1}{3}}}\frac{1}{2{{x}^{\frac{1}{3}}}} \right)}^{18}}\] , (x > 0) )are m and n respectively, then \[\frac{m}{n}\] is equal to   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[\frac{5}{4}\]                 
  done clear
  B)
  \[\frac{4}{5}\]   
  done clear
  C)
  \[27\]                                             
  done clear
  D)
  \[182\]
  done clear
  View Answer play_arrow

• question_answer26) If \[A=\left[ \begin{matrix} -4 & -1  \\  3 & 1  \\ \end{matrix} \right]\], then the determinant of the matrix \[({{A}^{2016}}-2{{A}^{2015}}-{{A}^{2014}})\] is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[2014\]                                        
  done clear
  B)
  \[2016\]
  done clear
  C)
  \[-175\]                                         
  done clear
  D)
  \[- 25\]
  done clear
  View Answer play_arrow

• question_answer27) If x is a solution of the equation, \[\sqrt{2x+1}-\sqrt{2x-1}=1\,,\,\,\left( x\le \frac{1}{2} \right)\] , then \[\sqrt{4{{x}^{2}}-1}\] is equal to   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[2\]                                               
  done clear
  B)
  \[\frac{3}{4}\]
  done clear
  C)
  \[2\sqrt{2}\]
  done clear
  D)
  \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer28) An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[\frac{192}{729}\]
  done clear
  B)
  \[\frac{256}{729}\]
  done clear
  C)
  \[\frac{240}{729}\]                                             
  done clear
  D)
  \[\frac{496}{729}\]
  done clear
  View Answer play_arrow

• question_answer29) The integral \[\int{\frac{dx}{\left( 1+\sqrt{x} \right)\sqrt{x-{{x}^{2}}}}}\] is equal to (where C is a constant of integration)   JEE Main Online Paper (Held On 10 April 2016)
  A)
  \[-2\sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+C\]            
  done clear
  B)
  \[-2\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+C\]
  done clear
  C)
  \[-\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}+C\]   
  done clear
  D)
  \[2\sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}+C\]
  done clear
  View Answer play_arrow

• question_answer30) Let a,b \[\in \] R, \[(a\ne 0)\] If the function f defined as \[f(x)=\left\{ \begin{matrix}    2{{x}^{2}}, & 0\le x<1  \\    a, & {}  \\    a, & 1\le x<\sqrt{2}  \\    \frac{2{{b}^{2}}-4b}{{{x}^{3}}} & \sqrt{2}\le x<\infty   \\ \end{matrix} \right.\]
  A)
  \[\left( \sqrt{2},1-\sqrt{3} \right)\]                         
  done clear
  B)
  \[\left( \sqrt{2},1-\sqrt{3} \right)\]
  done clear
  C)
  \[\left( \sqrt{2},-1+\sqrt{3} \right)\]       
  done clear
  D)
  \[\left( -\sqrt{2},1+\sqrt{3} \right)\]
  done clear
  View Answer play_arrow