Solved papers for JEE Main & Advanced JEE Main Solved Paper-2014

done JEE Main Solved Paper-2014 Total Questions - 30

• question_answer1) The image of the line \[\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}\]in the plane \[2x-y+z+3=0\]is the line:   JEE Main  Solved  Paper-2014
  A)
  \[\frac{x+3}{3}=\frac{y-5}{1}=\frac{z-2}{-5}\]
  done clear
  B)
  \[\frac{x+3}{-3}=\frac{y-5}{-1}=\frac{z+2}{5}\]
  done clear
  C)
  \[\frac{x-3}{3}=\frac{y+5}{1}=\frac{z-2}{-5}\]
  done clear
  D)
  \[\frac{x-3}{-3}=\frac{y+5}{-1}=\frac{z-2}{5}\]
  done clear
  View Answer play_arrow

• question_answer2) If the coefficients of \[{{x}^{3}}\]and \[{{x}^{4}}\] in the expansion of \[(1+ax+b{{x}^{2}}){{(1-2x)}^{18}}\]in powers of x are both zero, then (a, b) is equal to:   JEE Main  Solved  Paper-2014
  A)
  \[\left( 16,\frac{251}{3} \right)\]                              
  done clear
  B)
  \[\left( 14,\frac{251}{3} \right)\]
  done clear
  C)
  \[\left( 14,\frac{272}{3} \right)\]                              
  done clear
  D)
  \[\left( 16,\frac{272}{3} \right)\]
  done clear
  View Answer play_arrow

• question_answer3) If \[a\in R\]and the equation \[-3{{(x-[x])}^{2}}+2(x-[x])+{{a}^{2}}=0\](where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of alie in the interval:   JEE Main  Solved  Paper-2014
  A)
  \[(-1,0)\cup (0,1)\]         
  done clear
  B)
  \[(-2,-1)\]                           
  done clear
  C)
  \[(-\infty ,-2)\cup (2,\infty )\]
  done clear
  View Answer play_arrow

• question_answer4) If \[\left[ \vec{a}\times \vec{b}\,\vec{b}\times \vec{c}\,\vec{c}\times \vec{a} \right]=\lambda {{\left[ \vec{a}\,\vec{b}\,\,\vec{c} \right]}^{2}}\]then\[\lambda \]is equal to:   JEE Main  Solved  Paper-2014
  A)
  2                                             
  done clear
  B)
  3
  done clear
  C)
  0                                             
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer5) The variance of first 50 even natural numbers is:   JEE Main  Solved  Paper-2014
  A)
  \[\frac{833}{4}\]                                              
  done clear
  B)
  \[833\]
  done clear
  C)
  \[437\]                                 
  done clear
  D)
  \[\frac{437}{4}\]
  done clear
  View Answer play_arrow

• question_answer6) A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is \[45{}^\circ\]. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30°. Then the speed (in m/s) of the bird is:   JEE Main  Solved  Paper-2014
  A)
  \[40\left( \sqrt{2}-1 \right)\]                      
  done clear
  B)
  \[40\left( \sqrt{3}-\sqrt{2} \right)\]
  done clear
  C)
   \[20\sqrt{2}\]                  
  done clear
  D)
  \[20\left( \sqrt{3}-1 \right)\]
  done clear
  View Answer play_arrow

• question_answer7) The integral\[\int\limits_{0}^{\pi }{\sqrt{1+4{{\sin }^{2}}\frac{x}{2}-4\sin \frac{x}{2}}dx}\]equals:   JEE Main  Solved  Paper-2014
  A)
  \[\pi -4\]                             
  done clear
  B)
  \[\frac{2\pi }{3}-4-4\sqrt{3}\]
  done clear
  C)
   \[4\sqrt{3}-4\]                 
  done clear
  D)
   \[4\sqrt{3}-4-\frac{\pi }{3}\]
  done clear
  View Answer play_arrow

• question_answer8) The statement \[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\] is:   JEE Main  Solved  Paper-2014
  A)
  equivalent to \[p\leftrightarrow q\]
  done clear
  B)
  equivalent to \[\tilde{\ }p\leftrightarrow q\]
  done clear
  C)
  a tautology                        
  done clear
  D)
  a fallacy
  done clear
  View Answer play_arrow

• question_answer9) If A is an \[3\times 3\] non ? singular matrix such that AA′ = A′A and B = A−1 A′, then BB′ equals:   JEE Main  Solved  Paper-2014
  A)
  \[I+B\]                 
  done clear
  B)
  \[I\]
  done clear
  C)
  \[{{B}^{-1}}\]                                    
  done clear
  D)
  \[({{B}^{-1}})'\]
  done clear
  View Answer play_arrow

• question_answer10) The integral\[\int_{{}}^{{}}{\left( 1+x-\frac{1}{x} \right)}{{e}^{x+\frac{1}{x}}}dx\]is equal to   JEE Main  Solved  Paper-2014
  A)
  \[(x-1){{e}^{x+\frac{1}{x}}}+c\]
  done clear
  B)
  \[x{{e}^{x+\frac{1}{x}}}+c\]
  done clear
  C)
  \[(x+1){{e}^{x+\frac{1}{x}}}+c\]               
  done clear
  D)
  \[-x{{e}^{x+\frac{1}{x}}}+c\]
  done clear
  View Answer play_arrow

• question_answer11) If z is a complex number such that\[|z|\ge 2,\]then the minimum value of \[\left| z+\frac{1}{2} \right|:\]   JEE Main  Solved  Paper-2014
  A)
  is equal to \[\frac{5}{2}\]
  done clear
  B)
  lies in the interval (1, 2)
  done clear
  C)
  is strictly greater than \[\frac{5}{2}\]
  done clear
  D)
  is strictly greater than \[\frac{3}{2}\]but less than \[\frac{5}{2}\]
  done clear
  View Answer play_arrow

• question_answer12) If g is the inverse of a function f and \[(x)=\frac{1}{1+{{x}^{5}}},\]then g′ (x) is equal to :   JEE Main  Solved  Paper-2014
  A)
  \[1+{{x}^{5}}\]                 
  done clear
  B)
  \[5{{x}^{4}}\]
  done clear
  C)
  \[\frac{1}{1+{{\left\{ g(x) \right\}}^{5}}}\]                           
  done clear
  D)
  \[1+{{\{g(x)\}}^{5}}\]
  done clear
  View Answer play_arrow

• question_answer13) If\[\alpha ,\beta \ne 0,\]and\[f(n)={{\alpha }^{n}}+{{\beta }^{n}}\]and\[\left| \begin{matrix}    3 & 1+f(1) & 1+f(2)  \\    1+f(1) & 1+f(2) & 1+f(3)  \\    1+f(2) & 1+f(3) & 1+f(4)  \\ \end{matrix} \right|=K\]\[{{(1-\alpha )}^{2}}{{(1-\beta )}^{2}}{{(\alpha -\beta )}^{2}},\]then K is equal to:   JEE Main  Solved  Paper-2014
  A)
  \[\alpha \beta \]                                             
  done clear
  B)
  \[\frac{1}{\alpha \beta }\]
  done clear
  C)
  \[1\]            
  done clear
  D)
  \[-1\]
  done clear
  View Answer play_arrow

• question_answer14) Let \[{{f}_{k}}(x)=\frac{1}{k}(si{{n}^{k}}x+co{{s}^{k}}x),\]where\[x\in R\]and\[k\ge 1.\]Then\[{{f}_{4}}(x)-{{f}_{6}}(x)\]equals:   JEE Main  Solved  Paper-2014
  A)
  \[\frac{1}{6}\]                                   
  done clear
  B)
  \[\frac{1}{3}\]
  done clear
  C)
  \[\frac{1}{4}\]                                   
  done clear
  D)
  \[\frac{1}{12}\]
  done clear
  View Answer play_arrow

• question_answer15) Let \[\alpha \] and \[\beta \] be the roots of equation \[p{{x}^{2}}+qx+r=0,p\ne 0.\]If p, q, r are in A.P. and \[\frac{1}{\alpha }+\frac{1}{\beta }=4,\]then the value of \[|\alpha -\beta |\]is :   JEE Main  Solved  Paper-2014
  A)
  \[\frac{\sqrt{61}}{9}\]                   
  done clear
  B)
  \[\frac{2\sqrt{17}}{9}\]
  done clear
  C)
  \[\frac{\sqrt{34}}{9}\]                   
  done clear
  D)
  \[\frac{2\sqrt{13}}{9}\]
  done clear
  View Answer play_arrow

• question_answer16) Let A and B be two events such that \[P(\overline{A\cup B})=\frac{1}{16}.P(A\cap B)=\frac{1}{4}\]and\[P(\overline{A})=\frac{1}{4},\]where\[\overline{A}\]stands for the complement of the event A. Then the events A and B are :   JEE Main  Solved  Paper-2014
  A)
   mutually exclusive and independent.
  done clear
  B)
  equally likely but not independent.
  done clear
  C)
  independent but not equally likely.
  done clear
  D)
  independent and equally likely.
  done clear
  View Answer play_arrow

• question_answer17) If f and g are differentiable functions in [0, 1] satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6,then for some \[c\in \}0,1[:\]   JEE Main  Solved  Paper-2014
  A)
  \[2f'(c)=g'(c)\]  
  done clear
  B)
  \[2f'(c)=3g'(c)\]
  done clear
  C)
  \[f'(c)=g'(c)\]    
  done clear
  D)
  \[f'(c)=2g'(c)\]
  done clear
  View Answer play_arrow

• question_answer18) Let the population of rabbits surviving at a time t be governed by the differential equation\[\frac{dp(t)}{dt}=\frac{1}{2}p(t)-200.\] If \[p(0)=100,\]then p(t) equals :   JEE Main  Solved  Paper-2014
  A)
  \[400-300\,{{\text{e}}^{\text{t/2}}}\]    
  done clear
  B)
  \[300-200\,{{\text{e}}^{\text{-t/2}}}\]
  done clear
  C)
  \[600-500\,{{\text{e}}^{\text{t/2}}}\]    
  done clear
  D)
  \[400-300\,{{\text{e}}^{\text{-t/2}}}\]
  done clear
  View Answer play_arrow

• question_answer19) Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to :   JEE Main  Solved  Paper-2014
  A)
  \[\frac{\sqrt{3}}{\sqrt{2}}\]                                        
  done clear
  B)
  \[\frac{\sqrt{3}}{2}\]
  done clear
  C)
  \[\frac{1}{2}\]                                   
  done clear
  D)
  \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer20) The area of the region described by \[A=\{(x,\text{ }y):{{x}^{2}}+{{y}^{2}}\le 1\]and \[{{y}^{2}}\le 1-x\}\]is   JEE Main  Solved  Paper-2014
  A)
  \[\frac{\pi }{2}+\frac{4}{3}\]       
  done clear
  B)
  \[\frac{\pi }{2}-\frac{4}{3}\]
  done clear
  C)
  \[\frac{\pi }{2}-\frac{2}{3}\]                        
  done clear
  D)
  \[\frac{\pi }{2}+\frac{2}{3}\]
  done clear
  View Answer play_arrow

• question_answer21) Let a, b, c and d be non−zero numbers. If the point of intersection of the lines \[4ax+2ay+c=0\]and \[5bx+2by+d=\] lies in the fourth quadrant and is equidistant from the two axes then : JEE Main  Solved  Paper-2014
  A)
   2bc − 3ad = 0    
  done clear
  B)
  2bc + 3ad = 0
  done clear
  C)
  3bc − 2ad = 0
  done clear
  D)
  3bc + 2ad = 0
  done clear
  View Answer play_arrow

• question_answer22) Let PS be the median of the triangle with vertices P(2, 2), Q(6, −1) and R (7, 3). The equation ofthe line passing through (1, −1) and parallel to PS is :   JEE Main  Solved  Paper-2014cc
  A)
  \[4x-7y-11=0\] 
  done clear
  B)
  \[2x+9y+7=0\]
  done clear
  C)
   \[4x+7y+3=0\] 
  done clear
  D)
  \[2x-9y-11=0\]
  done clear
  View Answer play_arrow

• question_answer23) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin (\pi co{{s}^{2}}x)}{{{x}^{2}}}\]is equal to:   JEE Main  Solved  Paper-2014
  A)
  \[\frac{\pi }{2}\]                                              
  done clear
  B)
  1
  done clear
  C)
  \[-\pi \]                               
  done clear
  D)
  \[\pi \]
  done clear
  View Answer play_arrow

• question_answer24) If \[X=\{{{4}^{n}}-1:n\varepsilon N\}\] and\[Y=\{9(n-1):n\varepsilon N\},\] where N is the set of natural numbers, then \[X\cup Y\] is equal to :   JEE Main  Solved  Paper-2014
  A)
  N                                            
  done clear
  B)
  Y − X
  done clear
  C)
  X                                            
  done clear
  D)
  Y
  done clear
  View Answer play_arrow

• question_answer25) The locus of the foot of perpendicular drawn from the centre of the ellipse \[{{x}^{2}}+3{{y}^{2}}=6\] on any tangent to it is :   JEE Main  Solved  Paper-2014
  A)
  \[{{({{x}^{2}}-{{y}^{2}})}^{2}}=6{{x}^{2}}+2{{y}^{2}}\]
  done clear
  B)
  \[{{({{x}^{2}}-{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}\]
  done clear
  C)
  \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}+2{{y}^{2}}\]
  done clear
  D)
  \[{{({{x}^{2}}+{{y}^{2}})}^{2}}=6{{x}^{2}}-2{{y}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer26) Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is :   JEE Main  Solved  Paper-2014
  A)
  \[\sqrt{2}+\sqrt{3}\]                      
  done clear
  B)
  \[3+\sqrt{2}\]
  done clear
  C)
  \[2-\sqrt{3}\]                    
  done clear
  D)
  \[2+\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer27) If \[{{(10)}^{9}}+2{{(11)}^{1}}{{(10)}^{8}}+3{{(11)}^{2}}{{(10)}^{7}}+...+10\]\[{{(11)}^{9}}=k{{(10)}^{9}},\]then k is equal to :   JEE Main  Solved  Paper-2014
  A)
  \[\frac{121}{10}\]                                            
  done clear
  B)
  \[\frac{441}{100}\]
  done clear
  C)
  \[100\]                 
  done clear
  D)
  \[110\]
  done clear
  View Answer play_arrow

• question_answer28) The angle between the lines whose direction cosines satisfy the equations \[\ell +m+n=0\]and\[{{\ell }^{2}}={{m}^{2}}+{{n}^{2}}\]is :   JEE Main  Solved  Paper-2014
  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_answer29) The slope of the line touching both the parabolas \[{{y}^{2}}=4x\]and \[{{x}^{2}}=-32y\]is :   JEE Main  Solved  Paper-2014
  A)
  \[\frac{1}{2}\]   
  done clear
  B)
  \[\frac{3}{2}\]
  done clear
  C)
  \[\frac{1}{8}\]                                   
  done clear
  D)
  \[\frac{2}{3}\]
  done clear
  View Answer play_arrow

• question_answer30) If x = −1 and x = 2 are extreme points of \[f(x)=\alpha log|x|+\beta {{x}^{2}}+x\]then :   JEE Main  Solved  Paper-2014
  A)
  \[\alpha =-6,\beta =\frac{1}{2}\]              
  done clear
  B)
  \[\alpha =-6,\beta =-\frac{1}{2}\]
  done clear
  C)
  \[\alpha =2,\beta =-\frac{1}{2}\]              
  done clear
  D)
  \[\alpha =2,\beta =\frac{1}{2}\]
  done clear
  View Answer play_arrow