Solved papers for JEE Main & Advanced JEE Main Paper (Held On 10 April 2015)

done JEE Main Paper (Held On 10 April 2015) Total Questions - 30

• question_answer1) A factory is operating in two shirts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is Rs. 54 and per day mean wage of all the workers is Rs. 60, then per day mean wage of the night shift workers (in Rs.) is: JEE Main Online Paper (Held On 10 April 2015)
  A)
   74
  done clear
  B)
   66
  done clear
  C)
    75
  done clear
  D)
   69
  done clear
  View Answer play_arrow

• question_answer2) If Rolle's theorem holds for the function \[f(x)=2{{x}^{3}}+b{{x}^{2}}+cx,x\in [-1,1],\]at the point \[x=\frac{1}{2},\]then 2b +c equals    JEE Main Online Paper (Held On 10 April 2015)
  A)
   2
  done clear
  B)
  - 1
  done clear
  C)
   -3
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer3) The area (in square units) of the region bounded by the curves \[y+2{{x}^{2}}=0\]and \[y+3{{x}^{2}}=1,\]is equal to : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[\frac{1}{3}\]                                   
  done clear
  B)
  \[\frac{3}{4}\]
  done clear
  C)
   \[\frac{3}{5}\]                                  
  done clear
  D)
  \[\frac{4}{3}\]
  done clear
  View Answer play_arrow

• question_answer4) The points \[\left( 0,\frac{8}{3} \right),(1,3)\]and (82, 30) : JEE Main Online Paper (Held On 10 April 2015)
  A)
   form an acute angled triangle.
  done clear
  B)
   form a right angled triangle.
  done clear
  C)
    form an obtuse angled triangle.
  done clear
  D)
   lie on a straight line.
  done clear
  View Answer play_arrow

• question_answer5) The least value of the product xyz for which the determinant \[\left| \begin{matrix}    x & 1 & 1  \\    1 & y & 1  \\    1 & 1 & z  \\ \end{matrix} \right|\]is non-negative, is : JEE Main Online Paper (Held On 10 April 2015)
  A)
   \[- 1\]
  done clear
  B)
  \[-2\sqrt{2}\]
  done clear
  C)
  \[-16\sqrt{2}\]
  done clear
  D)
  \[ - 8\]
  done clear
  View Answer play_arrow

• question_answer6) The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is: JEE Main Online Paper (Held On 10 April 2015)
  A)
   1120
  done clear
  B)
   1960
  done clear
  C)
    1880
  done clear
  D)
   1240
  done clear
  View Answer play_arrow

• question_answer7) If the points \[(1,1\lambda )\]and (-3, 0, 1) are equidistant    from    the    plane, \[3x+4y-12z+13=0,\]then \[\lambda \] satisfies the equation : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[3{{x}^{2}}-10x+21=0\]
  done clear
  B)
  \[3{{x}^{2}}-10x+7=0\]
  done clear
  C)
  \[3{{x}^{2}}+10x+7=0\]
  done clear
  D)
  \[3{{x}^{2}}+10x-13=0\]
  done clear
  View Answer play_arrow

• question_answer8) If \[f(x)=2ta{{n}^{-1}}x+{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right),x>1,\]then f(5) is equal to : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[\frac{\pi }{2}\]                                              
  done clear
  B)
  \[\pi \]
  done clear
  C)
  \[{{\tan }^{-1}}\left( \frac{65}{156} \right)\]                        
  done clear
  D)
  \[4{{\tan }^{-1}}(5)\]
  done clear
  View Answer play_arrow

• question_answer9) If \[2+3i\] is one of the roots of the equation \[2{{x}^{3}}-9{{x}^{2}}+kx-13=0,k\in R,\] then the real root of this equation : JEE Main Online Paper (Held On 10 April 2015)
  A)
   exists and is equal to 1.
  done clear
  B)
   does not exist.
  done clear
  C)
    exists and is equal to\[\frac{1}{2}\].
  done clear
  D)
  exists and is equal to\[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer10) An ellipse passes through the foci of the hyperbola, \[9{{x}^{2}}-4{{y}^{2}}=36\]and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is\[\frac{1}{2},\] then which of the following points does not lie on the ellipse? JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[(\sqrt{13},0)\]                               
  done clear
  B)
  \[\left( \sqrt{\frac{13}{2}},\sqrt{6} \right)\]
  done clear
  C)
   \[\left( \frac{1}{2}\sqrt{13},\frac{\sqrt{3}}{2} \right)\]                  
  done clear
  D)
  \[\left( \frac{\sqrt{39}}{2},\sqrt{3} \right)\]
  done clear
  View Answer play_arrow

• question_answer11) Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is : JEE Main Online Paper (Held On 10 April 2015)
  A)
   28                                         
  done clear
  B)
   31
  done clear
  C)
   29.5                                      
  done clear
  D)
   26.5
  done clear
  View Answer play_arrow

• question_answer12) In a certain town, 25% of the families own a phone and 15% own a car; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :  5% families own both a car and a phone.   35% families own either a car or a phone.    40,000 families live in the town. Then, JEE Main Online Paper (Held On 10 April 2015)
  A)
   only  and  are correct.
  done clear
  B)
   Only  and  are correct.
  done clear
  C)
   All ,  and  are correct.
  done clear
  D)
   Only  and  are correct.
  done clear
  View Answer play_arrow

• question_answer13) For \[x>0,\]let \[f(x)=\int\limits_{1}^{x}{\frac{\log t}{1+t}}dt.\] Then  \[f(x)+f\left( \frac{1}{x} \right)\]is equal to: JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[\frac{1}{4}\log {{x}^{2}}\]                        
  done clear
  B)
  \[\frac{1}{4}{{(\log x)}^{2}}\]
  done clear
  C)
  \[\frac{1}{2}{{(\log x)}^{2}}\]                     
  done clear
  D)
   \[\log x\]
  done clear
  View Answer play_arrow

• question_answer14) If the coefficients of the three successive terms in the binomial expansion of \[{{(1+x)}^{n}}\]are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is : JEE Main Online Paper (Held On 10 April 2015)
  A)
   8th
  done clear
  B)
   6th
  done clear
  C)
   9th                                         
  done clear
  D)
   7th
  done clear
  View Answer play_arrow

• question_answer15) Let \[\overset{\to }{\mathop{a}}\,\] arid \[\overset{\to }{\mathop{b}}\,\] be two unit vectors such that|\[\left| \overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\, \right|=\sqrt{3}.\]If\[\overset{\to }{\mathop{c}}\,=\overset{\to }{\mathop{a}}\,+2\overset{\to }{\mathop{b}}\,+3\left( \overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\, \right),\]then \[2|\overset{\to }{\mathop{c}}\,|\]is equal to: JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[\sqrt{51}\]                                      
  done clear
  B)
  \[\sqrt{37}\]
  done clear
  C)
   \[\sqrt{43}\]                                     
  done clear
  D)
  \[\sqrt{55}\]
  done clear
  View Answer play_arrow

• question_answer16) Let L be the line passing through the point P(1, 2) such that its intercepted segment between the co-ordinate axes is bisected at P. If \[{{L}_{1}}\] is the line perpendicular to L and passing through the point (-2, 1),then the point of intersection of I and L JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[\left( \frac{3}{5},\frac{23}{10} \right)\]                              
  done clear
  B)
  \[\left( \frac{11}{20},\frac{29}{10} \right)\]
  done clear
  C)
  \[\left( \frac{4}{5},\frac{12}{5} \right)\]                
  done clear
  D)
  \[\left( \frac{3}{10},\frac{17}{5} \right)\]
  done clear
  View Answer play_arrow

• question_answer17) In a \[\Delta ABC,\frac{a}{b}=2+\sqrt{3}\]and \[\angle C={{60}^{o}}.\] Then the ordered pair \[(\angle A,\angle B)\]is equal to: JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[({{105}^{o}},{{15}^{o}})\]                         
  done clear
  B)
  \[({{45}^{o}},{{75}^{o}})\]
  done clear
  C)
  \[({{15}^{o}},{{105}^{o}})\]                         
  done clear
  D)
  \[({{75}^{o}},{{45}^{o}})\]
  done clear
  View Answer play_arrow

• question_answer18) Let the tangents drawn to the circle, \[{{x}^{2}}+{{y}^{2}}=16\]from the point P(0/ h) meet me r-axis at points A and B. If the area of \[\Delta APB\]is minimum, men h is equal to : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[4\sqrt{2}\]                                      
  done clear
  B)
  \[4\sqrt{3}\]
  done clear
  C)
  \[3\sqrt{2}\]                                      
  done clear
  D)
  \[3\sqrt{3}\]
  done clear
  View Answer play_arrow

• question_answer19) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{{{x}^{2}}}}-\cos x}{{{\sin }^{2}}x}\]is equal to : JEE Main Online Paper (Held On 10 April 2015)
  A)
   3                                            
  done clear
  B)
   \[\frac{3}{2}\]
  done clear
  C)
   2                                            
  done clear
  D)
   \[\frac{5}{4}\]
  done clear
  View Answer play_arrow

• question_answer20) The value of \[\sum\limits_{r=16}^{30}{(r+2)(r-3)}\]is equal to : JEE Main Online Paper (Held On 10 April 2015)
  A)
   7785                     
  done clear
  B)
   7775
  done clear
  C)
   7780                     
  done clear
  D)
   7770
  done clear
  View Answer play_arrow

• question_answer21) If \[y+3x=0\] is the equation of a chord of the circle, \[{{x}^{2}}+{{y}^{2}}-30x=0,\]then the equation of the circle with this chord as diameter is: JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[{{x}^{2}}+{{y}^{2}}+3x+9y=0\]
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}-3x+9y=0\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}-3x-9y=0\]
  done clear
  D)
  \[{{x}^{2}}+{{y}^{2}}+3x-9y=0\]
  done clear
  View Answer play_arrow

• question_answer22) The integral \[\int_{{}}^{{}}{\frac{dx}{{{(x+1)}^{\frac{3}{4}}}{{(x-2)}^{\frac{5}{4}}}}}\]is equal to: JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[4{{\left( \frac{x-2}{x+1} \right)}^{\frac{1}{4}}}+C\]       
  done clear
  B)
  \[-\frac{4}{3}{{\left( \frac{x+1}{x-2} \right)}^{\frac{1}{4}}}+C\]
  done clear
  C)
   \[4{{\left( \frac{x+1}{x-2} \right)}^{\frac{1}{4}}}+C\]      
  done clear
  D)
  \[-\frac{4}{3}{{\left( \frac{x-2}{x+1} \right)}^{\frac{1}{4}}}+C\]
  done clear
  View Answer play_arrow

• question_answer23) The distance, from the origin, of the normal to the curve, \[x=2\cos t+2t\sin t,\]\[y=2\sin t-2t\cos t\]at\[t=\frac{\pi }{4},\]is: JEE Main Online Paper (Held On 10 April 2015)
  A)
   2                                            
  done clear
  B)
  \[\sqrt{2}\]
  done clear
  C)
  \[2\sqrt{2}\]                                      
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer24) If the shortest distance between the lines \[\frac{x-1}{\alpha }=\frac{y+1}{-1}=\frac{z}{1},(\alpha \ne -1)\]and\[x+y+z+1=0=2x-y+z+3\]is\[\frac{1}{\sqrt{3}},\] a value of \[\alpha \] is : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[-\frac{16}{19}\]                                            
  done clear
  B)
  \[-\frac{19}{16}\]
  done clear
  C)
   \[\frac{19}{32}\]                                             
  done clear
  D)
  \[\frac{32}{19}\]
  done clear
  View Answer play_arrow

• question_answer25) If\[A=\left[ \begin{matrix}    0 & -1  \\    1 & 0  \\ \end{matrix} \right],\] then which one of the following statements is not correct ? JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[{{A}^{4}}-I={{A}^{2}}+I\]          
  done clear
  B)
  \[{{A}^{3}}+I=A({{A}^{3}}-I)\]
  done clear
  C)
   \[{{A}^{3}}-I=A(A-I)\]   
  done clear
  D)
  \[{{A}^{2}}+I=A({{A}^{2}}-I)\]
  done clear
  View Answer play_arrow

• question_answer26) Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[\frac{({{2}^{10}}-1)}{{{2}^{20}}}\]                         
  done clear
  B)
  \[\frac{({{2}^{10}}-1)}{{{2}^{10}}}\]
  done clear
  C)
  \[\frac{^{20}{{C}_{10}}}{{{2}^{10}}}\]                     
  done clear
  D)
  \[\frac{^{20}{{C}_{10}}}{{{2}^{20}}}\]
  done clear
  View Answer play_arrow

• question_answer27) If the tangent to the conic,\[y-6={{x}^{2}}\]at (2, 10) touches the circle, \[{{x}^{2}}+{{y}^{2}}+8x-2y=k\](for some fixed k) at a point \[(\alpha ,\beta );\] then \[(\alpha ,\beta )\]is : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[\left( -\frac{7}{17},\frac{6}{17} \right)\]                            
  done clear
  B)
  \[\left( -\frac{8}{17},\frac{2}{17} \right)\]
  done clear
  C)
  \[\left( -\frac{4}{17},\frac{1}{17} \right)\]                            
  done clear
  D)
  \[\left( -\frac{6}{17},\frac{10}{17} \right)\]
  done clear
  View Answer play_arrow

• question_answer28) The contrapositive of the statement "If it is raining, then I will not come", is : JEE Main Online Paper (Held On 10 April 2015)
  A)
  If I will come, then it is raining.
  done clear
  B)
   If I will not come, then it is raining.
  done clear
  C)
    I will come, then it is not raining.
  done clear
  D)
   If I will not come, then it is not raining.
  done clear
  View Answer play_arrow

• question_answer29) The largest value of r for which the region represented by the set\[\{\omega \in C/|\omega -4-i|\le r\}\]is contained in the region represented by the set \[\{z\in C/|z-1|\le |z+i|\},\]is equal to : JEE Main Online Paper (Held On 10 April 2015)
  A)
  \[2\sqrt{2}\]                                      
  done clear
  B)
  \[\sqrt{17}\]
  done clear
  C)
  \[\frac{5}{2}\sqrt{2}\]                   
  done clear
  D)
  \[\frac{3}{2}\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer30) If y(x) is the solution of the differential equation \[(x+2)\frac{dy}{dx}={{x}^{2}}+4x-9,x\ne -2\]and \[y(0)=0,\]then \[y(-4)\] is equal to : JEE Main Online Paper (Held On 10 April 2015)
  A)
  -1                                           
  done clear
  B)
  2
  done clear
  C)
  1                                             
  done clear
  D)
  0
  done clear
  View Answer play_arrow