Solved papers for JEE Main & Advanced JEE Main Paper (Held On 9 April 2016)

done JEE Main Paper (Held On 9 April 2016) Total Questions - 30

• question_answer1) If A and B are any two events such that P(A) =2/5 and \[P(A\cap B)=3/20,\]then the conditional probability, \[P(A/(A'\cap B')),\]where A' denotes the complement of A, is equal to :
  A)
  \[\frac{8}{17}\]                                
  done clear
  B)
  \[\frac{1}{4}\]
  done clear
  C)
  \[\frac{5}{17}\]
  done clear
  D)
  \[\frac{11}{20}\]
  done clear
  View Answer play_arrow

• question_answer2) For \[x\in R,x\ne 0,x\ne 1,\]let\[{{f}_{0}}(x)=\frac{1}{1-x}\]and\[{{f}_{n+1}}(x)={{f}_{0}}(f{{(}_{n}}(X)),\]n = 0, 1, 2, ........ Then the value of \[{{f}_{100}}(3)+{{f}_{1}}\left( \frac{2}{3} \right)+{{f}_{2}}\left( \frac{3}{2} \right)\]is equal to:   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\frac{4}{3}\]   
  done clear
  B)
  \[\frac{1}{3}\]
  done clear
  C)
  \[\frac{5}{3}\]                                   
  done clear
  D)
  \[\frac{8}{3}\]
  done clear
  View Answer play_arrow

• question_answer3) The distance of the point (1, .2, 4) from the plane passing through the point (1, 2, 2) and perpendicular to the planes \[x-y+2z=3\] and \[2x-2y+z+12=0\], is     JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\frac{1}{\sqrt{2}}\]                                     
  done clear
  B)
  2
  done clear
  C)
  \[\sqrt{2}\]                                        
  done clear
  D)
  \[2\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer4) If the equations \[{{x}^{2}}+bx-1=0\]and \[{{x}^{2}}+x+b=0\]have a common root different from . 1, then | b | is equal to   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\sqrt{2}\]                                        
  done clear
  B)
  2
  done clear
  C)
  \[\sqrt{3}\]        
  done clear
  D)
  3
  done clear
  View Answer play_arrow

• question_answer5) If \[2\int\limits_{0}^{1}{{{\tan }^{-1}}xdx}=\int\limits_{0}^{1}{{{\cot }^{-1}}}(1-x+{{x}^{2}})dx\]then\[\int\limits_{0}^{1}{{{\tan }^{-1}}}(1-x+{{x}^{2}})dx\]is equal to:   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\log 2\]
  done clear
  B)
  \[\frac{\pi }{2}+\log 2\]
  done clear
  C)
  \[\log 4\]                            
  done clear
  D)
  \[\frac{\pi }{2}-\log 4\]
  done clear
  View Answer play_arrow

• question_answer6) If \[P=\left[ \begin{matrix}    \frac{\sqrt{3}}{2} & \frac{1}{2}  \\    -\frac{1}{2} & \frac{\sqrt{3}}{2}  \\ \end{matrix} \right],A=\left[ \begin{matrix}    1 & 1  \\    0 & 1  \\ \end{matrix} \right]\]and\[Q=PA{{P}^{T}},\]then\[{{P}^{T}}{{Q}^{2015}}P\]is     JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\left[ \begin{matrix}    2015 & 1  \\    0 & 2015  \\ \end{matrix} \right]\]                   
  done clear
  B)
  \[\left[ \begin{matrix}    1 & 2015  \\    0 & 1  \\ \end{matrix} \right]\]
  done clear
  C)
  \[\left[ \begin{matrix}    0 & 2015  \\    0 & 0  \\ \end{matrix} \right]\]                                   
  done clear
  D)
  \[\left[ \begin{matrix}    2015 & 0  \\    1 & 2015  \\ \end{matrix} \right]\]
  done clear
  View Answer play_arrow

• question_answer7) If\[\int_{{}}^{{}}{\frac{dx}{{{\cos }^{3}}x\sqrt{2\sin 2x}}={{(\tan x)}^{A}}}+C{{(\tan x)}^{B}}+k,\] where k is a constant of integration, then A + B + C equals   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\frac{16}{5}\]
  done clear
  B)
  \[\frac{21}{5}\]
  done clear
  C)
  \[\frac{7}{10}\]
  done clear
  D)
  \[\frac{27}{10}\]
  done clear
  View Answer play_arrow

• question_answer8) The point (2, 1) is translated parallel to the line \[L:x-y=4\]by \[2\sqrt{3}\]units. If the new point Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is :   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[2x+2y=1-\sqrt{6}\]     
  done clear
  B)
  \[x=y=3-3\sqrt{6}\]
  done clear
  C)
  \[x+y=2-\sqrt{6}\]          
  done clear
  D)
  \[x+y=3-2\sqrt{6}\]
  done clear
  View Answer play_arrow

• question_answer9) If the function \[f(x)=\left\{ \begin{matrix}    -x, & x<1  \\    a+{{\cos }^{-1}} & (x+b),1\le x\le 2  \\ \end{matrix} \right.\] is differentiable at x = 1, then\[\frac{a}{b}\]is equal to :
  A)
  \[\frac{-\pi -2}{2}\]                         
  done clear
  B)
  \[-1-{{\cos }^{-1}}(2)\]
  done clear
  C)
  \[\frac{\pi +2}{2}\]         
  done clear
  D)
  \[\frac{\pi -2}{2}\]
  done clear
  View Answer play_arrow

• question_answer10) The value of\[\sum\limits_{r=1}^{15}{{{r}^{2}}}\left( \frac{^{15}{{C}_{r}}}{^{15}{{C}_{r-1}}} \right)\]is equal to   JEE Main Online Paper (Held On 09 April 2016)
  A)
  1085                                      
  done clear
  B)
  560                
  done clear
  C)
  680        
  done clear
  D)
  1240
  done clear
  View Answer play_arrow

• question_answer11) In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively \[3\hat{i}+\hat{j}-\hat{k},-\hat{i}+3\hat{j}+p\hat{k}\]and\[5\hat{i}+q\hat{j}-4\hat{k},\]then the point (p, q) lies on a line   JEE Main Online Paper (Held On 09 April 2016)
  A)
  parallel to y-axis
  done clear
  B)
  making an acute angle with the positive direction of x-axis
  done clear
  C)
  parallel to x-axis
  done clear
  D)
  making an obtuse angle with the position direction of x-axis.
  done clear
  View Answer play_arrow

• question_answer12) If\[\underset{x\to \infty }{\mathop{Lim}}\,{{\left( 1+\frac{a}{x}-\frac{4}{{{x}^{2}}} \right)}^{2x}}={{e}^{3}},\]then ?a? is equal to:   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\frac{2}{3}\]                                   
  done clear
  B)
  \[\frac{3}{2}\]
  done clear
  C)
  2                                             
  done clear
  D)
  \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer13) The number of \[x\in [0,2\pi ]\]for which\[\left| \sqrt{2{{\sin }^{4}}x+18{{\cos }^{2}}x}-\sqrt{2{{\cos }^{4}}x+18{{\sin }^{2}}x} \right|=1\]   JEE Main Online Paper (Held On 09 April 2016)
  A)
  6                                             
  done clear
  B)
  4
  done clear
  C)
  8             
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer14) If m and M are the minimum and the maximum values of \[4+\frac{1}{2}{{\sin }^{2}}2x-2{{\cos }^{4}}x,x\in R,\]then M-m is equal to   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\frac{7}{4}\]                   
  done clear
  B)
  \[\frac{15}{4}\]                
  done clear
  C)
  \[\frac{9}{4}\]   
  done clear
  D)
  \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer15) If a variable line drawn through the intersection of the lines\[\frac{x}{3}+\frac{y}{4}=1\]and\[\frac{x}{4}+\frac{y}{3}=1,\] meets the coordinate axes at A and B, \[(A\ne B),\] then the locus of the midpoint of AB is   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[7xy=6(x+y)\]
  done clear
  B)
  \[6xy=7(x+y)\]
  done clear
  C)
  \[4{{(x+y)}^{2}}-28(x+y)+49=0\]
  done clear
  D)
  \[14{{(x+y)}^{2}}-97(x+y)+168=0\]
  done clear
  View Answer play_arrow

• question_answer16) If f(x) is a differentiable function in the interval \[(0,\,\,\infty )\] such that f(1) = 1 and \[\underset{t\to x}{\mathop{Lim}}\,\frac{{{t}^{2}}f(x)-{{x}^{2}}f(t)}{t-x}=1,\]for each x > 0, then \[f\left( \frac{3}{2} \right)\] is equal to :   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\frac{13}{6}\]                                
  done clear
  B)
  \[\frac{23}{18}\]
  done clear
  C)
  \[\frac{25}{9}\]                                
  done clear
  D)
  \[\frac{31}{18}\]
  done clear
  View Answer play_arrow

• question_answer17) If the tangent at a point P, with parameter t, on the curve \[x=4{{t}^{2}}+3,y=8{{t}^{3}}-1,t\in R,\]meets the curve again at a point Q, then the coordinates of Q are :   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[({{t}^{2}}+3,-{{t}^{3}}-1)\]       
  done clear
  B)
  \[({{t}^{2}}+3,{{t}^{3}}-1)\]
  done clear
  C)
  \[(16{{t}^{2}}+3,-64{{t}^{3}}-1)\]              
  done clear
  D)
  \[(4{{t}^{2}}+3,-4{{t}^{3}}-1)\]
  done clear
  View Answer play_arrow

• question_answer18) If the tangent at a point on the ellipse\[\frac{{{x}^{2}}}{27}+\frac{{{y}^{2}}}{3}=1\]meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is :   JEE Main Online Paper (Held On 09 April 2016)
  A)
  9             
  done clear
  B)
  \[\frac{9}{2}\]
  done clear
  C)
  \[9\sqrt{3}\]                                      
  done clear
  D)
  \[3\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer19) The point represented by 2+i in the Arg and plane moves 1 unit eastwards, then 2 units northwards and finally from there 2 2 units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by :   JEE Main Online Paper (Held On 09 April 2016)
  A)
  2 + 2i                     
  done clear
  B)
  - 2 - 2i
  done clear
  C)
  1 + i       
  done clear
  D)
  - 1 - i
  done clear
  View Answer play_arrow

• question_answer20) A circle passes through (-2, 4). Which one of the following equations can represent a diameter of this circle?   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[4x+5y-6=0\]   
  done clear
  B)
  \[5x+2y+4=0\]
  done clear
  C)
  \[2x-3y+10=0\]
  done clear
  D)
  \[3x+4y-3=0\]
  done clear
  View Answer play_arrow

• question_answer21) The number of distinct real roots of the equation,\[\left| \begin{matrix}    \cos x & \sin x & \sin x  \\    \sin x & \cos x & \sin x  \\    \sin x & \sin x & \cos x  \\ \end{matrix} \right|=0\]in the interval \[\left[ -\frac{\pi }{4},\frac{\pi }{4} \right]\]is:   JEE Main Online Paper (Held On 09 April 2016)
  A)
  4
  done clear
  B)
  1
  done clear
  C)
  2                                             
  done clear
  D)
  3
  done clear
  View Answer play_arrow

• question_answer22) The shortest distance between the lines\[\frac{x}{2}=\frac{y}{2}=\frac{z}{1}\]and\[\frac{x+2}{-1}=\frac{y-4}{8}=\frac{z-5}{4}\]lies in the interval :   JEE Main Online Paper (Held On 09 April 2016)
  A)
  (2, 3]
  done clear
  B)
  [0, 1)
  done clear
  C)
  (3, 4]                     
  done clear
  D)
  [1, 2)
  done clear
  View Answer play_arrow

• question_answer23) If the four letter words (need not be meaningful) are to be formed using the letters from the word MEDITERRANEAN. such that the first letter is R and the fourth letter is E, then the total number of all such words is :   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\frac{11!}{{{(2!)}^{3}}}\]
  done clear
  B)
  59                
  done clear
  C)
  110                                                        
  done clear
  D)
  56
  done clear
  View Answer play_arrow

• question_answer24) Let a and b respectively be the semi-transverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation \[\text{9e}{{\text{-}}^{\text{2}}}\text{-18e}+\text{5}=0.\] If S(5, 0) is a focus and 5x = 9 is the corresponding directrix of hyperbola, then \[{{a}^{2}}-{{b}^{2}}\]is equal to   JEE Main Online Paper (Held On 09 April 2016)
  A)
  - 7          
  done clear
  B)
  - 5
  done clear
  C)
  5                                             
  done clear
  D)
  7
  done clear
  View Answer play_arrow

• question_answer25) Consider the following two statements : P : If 7 is an odd number, then 7 is divisible by 2. Q : If 7 is a prime number, then 7 is an odd number. If \[{{V}_{1}}\]is the truth value of contrapositive of P and \[{{V}_{2}}\] is the truth value of contrapositive of Q, then the ordered pair \[({{V}_{1}},{{V}_{2}})\] equals :   JEE Main Online Paper (Held On 09 April 2016)
  A)
  (F, T)
  done clear
  B)
  (T, F)
  done clear
  C)
  (F, F)                     
  done clear
  D)
  (T, T)
  done clear
  View Answer play_arrow

• question_answer26) The minimum distance of a point on the curve \[y={{x}^{2}}-4\] from the origin is :   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\frac{\sqrt{15}}{2}\]                                   
  done clear
  B)
  \[\frac{\sqrt{19}}{2}\]                
  done clear
  C)
  \[\sqrt{\frac{15}{2}}\]                                                   
  done clear
  D)
  \[\sqrt{\frac{19}{2}}\]
  done clear
  View Answer play_arrow

• question_answer27) Let x, y, z be positive real numbers such that  \[\text{x}+\text{y}+\text{z}=\text{12}\]and \[{{x}^{3}}{{y}^{4}}{{z}^{5}}=(0.1){{(600)}^{3}}.\]Then \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}\] is equal to   JEE Main Online Paper (Held On 09 April 2016)
  A)
  270                                        
  done clear
  B)
  258
  done clear
  C)
  216        
  done clear
  D)
  342
  done clear
  View Answer play_arrow

• question_answer28) If the mean deviation of the numbers 1, 1 + d, ..., 1 + 100d from their mean is 255, then a value of d is :   JEE Main Online Paper (Held On 09 April 2016)
  A)
  10                                          
  done clear
  B)
  20.2
  done clear
  C)
  5.05                                       
  done clear
  D)
  10.1
  done clear
  View Answer play_arrow

• question_answer29) For\[x\in R,x=-1,\]if \[{{(1+x)}^{2016}}+x{{(1+x)}^{2015}}+{{x}^{2}}\]\[{{(1+x)}^{2014}}+...........+{{x}^{2016}}=\]\[\sum\limits_{i=0}^{2016}{{{a}_{i}}{{x}^{i}},}\]then\[{{a}_{17}}\]is equal to:   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\frac{2016!}{16!}\]                      
  done clear
  B)
  \[\frac{2017!}{2000!}\]
  done clear
  C)
  \[\frac{2017!}{17!2000!}\]
  done clear
  D)
  \[\frac{2016!}{17!1999!}\]
  done clear
  View Answer play_arrow

• question_answer30) The area (in sq. units) of the region described by \[A=\{(x,y)|y\ge {{x}^{2}}-5x+4,x+y\ge 1,y\le 0\}\]is :   JEE Main Online Paper (Held On 09 April 2016)
  A)
  \[\frac{7}{2}\]                                   
  done clear
  B)
  \[\frac{13}{6}\]
  done clear
  C)
  \[\frac{17}{6}\]                                
  done clear
  D)
  \[\frac{19}{6}\]
  done clear
  View Answer play_arrow