Solved papers for JEE Main & Advanced JEE Main Paper (Held On 11 April 2015)

done JEE Main Paper (Held On 11 April 2015) Total Questions - 30

• question_answer1) Let \[A=\{{{x}_{1}},{{x}_{2}},...,{{x}_{7}}\}\]and \[B=\{{{y}_{1}},{{y}_{2}},{{y}_{3}}\}\]be two sets containing seven and three distinct elements respectively. Then the total number of functions\[f:A\to B\] that are onto, if there exist exactly three elements x in A such that\[f(x)={{y}_{2}},\] is equal to : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[14.{{\,}^{7}}{{C}_{2}}\]
  done clear
  B)
  \[16.{{\,}^{7}}{{C}_{3}}\]
  done clear
  C)
  \[12.{{\,}^{7}}{{C}_{2}}\]
  done clear
  D)
  \[14.{{\,}^{7}}{{C}_{3}}\]
  done clear
  View Answer play_arrow

• question_answer2) If z is a non-real complex number, then the minimum value of \[\frac{\operatorname{Im}\,{{z}^{5}}}{{{(Im\,z)}^{5}}}\]is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   -1
  done clear
  B)
   -2
  done clear
  C)
   -4
  done clear
  D)
   -5
  done clear
  View Answer play_arrow

• question_answer3) If the two roots of the equation, \[(a-1)({{x}^{4}}+{{x}^{2}}+1)+(a+1){{({{x}^{2}}+x+1)}^{2}}=0\]are real and distinct, then the set of all values of 'a' is: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\left( -\frac{1}{2},0 \right)\]
  done clear
  B)
  \[(-\infty ,-2)\cup (2,\infty )\]
  done clear
  C)
  \[\left( -\frac{1}{2},0 \right)\cup \left( 0,\frac{1}{2} \right)\]
  done clear
  D)
  \[\left( 0,\frac{1}{2} \right)\]
  done clear
  View Answer play_arrow

• question_answer4) If A is a \[3\times 3\] matrix such that |5. adjA| = 5, then A| is equal to : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\pm \frac{1}{5}\]
  done clear
  B)
  \[\pm \,5\]
  done clear
  C)
  \[\pm \,1\]
  done clear
  D)
  \[\pm \,\frac{1}{25}\]
  done clear
  View Answer play_arrow

• question_answer5) \[\left| \begin{matrix}    {{x}^{2}}+x & x+1 & x-2  \\    2{{x}^{2}}+3x-1 & 3x & 3x-3  \\    {{x}^{2}}+2x+3 & 2x-1 & 2x-1  \\ \end{matrix} \right|=ax-12,\]then 'a' is equal to : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   12
  done clear
  B)
   24
  done clear
  C)
   -12
  done clear
  D)
   -24
  done clear
  View Answer play_arrow

• question_answer6) If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   10
  done clear
  B)
   12
  done clear
  C)
   9
  done clear
  D)
   6
  done clear
  View Answer play_arrow

• question_answer7) The term independent of x in the binomial expansion of\[\left( 1-\frac{1}{x}+3{{x}^{5}} \right){{\left( 2{{x}^{2}}-\frac{1}{x} \right)}^{8}}\]is: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   400
  done clear
  B)
   406
  done clear
  C)
   -400
  done clear
  D)
   -496
  done clear
  View Answer play_arrow

• question_answer8) The sum of the 3rd and the 4th terms of a G.P. is 60 and the product of its first three terms is 1000. If the first term of this G.P. is positive, then its 7th term is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   7290
  done clear
  B)
   320
  done clear
  C)
   640
  done clear
  D)
   2430
  done clear
  View Answer play_arrow

• question_answer9) If \[\sum\limits_{n=1}^{5}{\frac{1}{n(n+1)(n+2)(n+3)}=\frac{k}{3},}\]then k is equal to : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{55}{336}\]
  done clear
  B)
  \[\frac{17}{105}\]
  done clear
  C)
  \[\frac{1}{6}\]
  done clear
  D)
  \[\frac{19}{112}\]
  done clear
  View Answer play_arrow

• question_answer10) Let k be a non-zero real number. If\[\begin{align}   & f(x)=\left\{ \frac{{{({{e}^{x}}-1)}^{2}}}{\sin \left( \frac{x}{k} \right)\log \left( 1+\frac{x}{4} \right)},x\ne 0 \right. \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,12\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,\,\,\,\,x=0 \\ \end{align}\] is a continuous function, then the value of k is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   1
  done clear
  B)
   2
  done clear
  C)
   3
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer11) The equation of a normal to the curve,\[\sin y=x\sin \left( \frac{\pi }{3}+y \right)\] at \[x=0,\]is: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[2x+\sqrt{3}y=0\]
  done clear
  B)
  \[2x-\sqrt{3}x=0\]
  done clear
  C)
  \[2y+\sqrt{3}x=0\]
  done clear
  D)
  \[2x-\sqrt{3}y=0\] \[x=0\Rightarrow y=0\]
  done clear
  View Answer play_arrow

• question_answer12) Let k and K be the minimum and the maximum values of the function\[f(x)=\frac{{{(1+x)}^{0.6}}}{1+{{x}^{0.6}}}\]in \[[0,1]\]respectively, then the ordered pair (k, K) is equal to : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[(1,{{2}^{0.6}})\]
  done clear
  B)
  \[({{2}^{-0.4}}1,{{2}^{0.6}})\]
  done clear
  C)
  \[({{2}^{-0.6}},1)\]
  done clear
  D)
  \[({{2}^{-0.4}},1)\]
  done clear
  View Answer play_arrow

• question_answer13) From the top of a 64 metres high tower, a stone is thrown upwards vertically with the velocity of 48 m/s. The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration \[g=32\text{ }m/{{s}^{2}},\]is: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   100
  done clear
  B)
   88
  done clear
  C)
   128
  done clear
  D)
   112
  done clear
  View Answer play_arrow

• question_answer14) 2015 / If \[\int_{{}}^{{}}{\frac{\log \left( t+\sqrt{1+{{t}^{2}}} \right)}{\sqrt{1+{{t}^{2}}}}}dt=\frac{1}{2}{{\left( g(t) \right)}^{2}}+C,\]where C is a constant, then g(2) is equal to : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[2\log (2+\sqrt{5})\]
  done clear
  B)
  \[\log (2+\sqrt{5})\]
  done clear
  C)
  \[\frac{1}{\sqrt{5}}\log (2+\sqrt{5})\]
  done clear
  D)
  \[\frac{1}{2}\log (2+\sqrt{5})\]
  done clear
  View Answer play_arrow

• question_answer15) Let \[f:R\to R\]be a function such that\[f(2-x)=f\,(2+x)\] and\[f(4-x)=f\,(4+x),\]for all \[x\in R\]and \[\int\limits_{0}^{2}{f(x)}dx=5.\]Then the value of \[\int\limits_{10}^{50}{f(x)}\,dx\]is:
  A)
   80
  done clear
  B)
   100
  done clear
  C)
   125
  done clear
  D)
   200
  done clear
  View Answer play_arrow

• question_answer16) Let \[f:(-1,1)\to R\] be a continuous function. If \[\int\limits_{0}^{\sin x}{f(t)dt}=\frac{\sqrt{3}}{2}x,\] then\[f\left( \frac{\sqrt{3}}{2} \right)\]is equal to : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{\sqrt{3}}{2}\]
  done clear
  B)
  \[\sqrt{3}\]
  done clear
  C)
  \[\sqrt{\frac{3}{2}}\]
  done clear
  D)
  \[\frac{1}{2}\]
  done clear
  View Answer play_arrow

• question_answer17) The solution of the differential equation \[ydx-(x+2{{y}^{2}})dy=0\]is\[x=f(y).\] If \[f(-1)=1,\] then\[f(1)\]is equal to: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   4
  done clear
  B)
   3
  done clear
  C)
   2
  done clear
  D)
   1
  done clear
  View Answer play_arrow

• question_answer18) A straight line L through the point (3, - 2) is inclined at an angle of 60° to the line \[\sqrt{3}x+y=1.\]If L also intersects the x-axis, then the equation of L is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[y+\sqrt{3}x+2-3\sqrt{3}=0\]
  done clear
  B)
  \[y-\sqrt{3}x+2+3\sqrt{3}=0\]
  done clear
  C)
  \[\sqrt{3}y-x+3+2\sqrt{3}=0\]
  done clear
  D)
  \[\sqrt{3}y+x-3+2\sqrt{3}=0\]
  done clear
  View Answer play_arrow

• question_answer19) If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is \[3x+4y+3=0,\] then the equation of the circumcircle of this triangle is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[{{x}^{2}}+{{y}^{2}}-2x-2y-2=0\]
  done clear
  B)
  \[{{x}^{2}}+{{y}^{2}}-2x-2y-14=0\]
  done clear
  C)
  \[{{x}^{2}}+{{y}^{2}}-2x-2y+2=0\]
  done clear
  D)
  \[{{x}^{2}}+{{y}^{2}}-2x-2y-7=0\]
  done clear
  View Answer play_arrow

• question_answer20) If a circle passing through the point (-1, 0) touches y-axis at (0, 2), then the length of the chord of the circle along the x-axis is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{3}{2}\]
  done clear
  B)
  \[\frac{5}{2}\]
  done clear
  C)
   3
  done clear
  D)
   5
  done clear
  View Answer play_arrow

• question_answer21) If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{1}{2}\]
  done clear
  B)
  \[\frac{2\sqrt{2}-1}{2}\]
  done clear
  C)
  \[\sqrt{2}-1\]
  done clear
  D)
  \[\frac{\sqrt{2}-1}{2}\]
  done clear
  View Answer play_arrow

• question_answer22) Let PQ be a double ordinate of the parabola, \[{{y}^{2}}=-4x,\]where P lies in the second quadrant. If R divides PQ in the ratio 2 : 1, then the locus of R is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   \[9{{y}^{2}}=4x\]
  done clear
  B)
   \[9{{y}^{2}}=-4x\]
  done clear
  C)
  \[3{{y}^{2}}=2x\]
  done clear
  D)
  \[3{{y}^{2}}=-2x\]
  done clear
  View Answer play_arrow

• question_answer23) The shortest distance between the z-axis and the line \[x+y+2z-3=0=2x+3y+4z-4,\] is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   1
  done clear
  B)
   2
  done clear
  C)
   3
  done clear
  D)
   4
  done clear
  View Answer play_arrow

• question_answer24) A plane containing the point (3, 2, 0) and the line \[\frac{x-1}{1}=\frac{y-2}{5}=\frac{z-3}{4}\]also contains the point : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
   (0, -3, 1)
  done clear
  B)
   (0, 7, 10)
  done clear
  C)
   (0, 7, -10)
  done clear
  D)
   (0, 3, 1)
  done clear
  View Answer play_arrow

• question_answer25) In a parallelogram \[ABCD,\left| \overrightarrow{AB} \right|=a,\left| \overrightarrow{AD} \right|=b\]and \[\left| \overrightarrow{AC} \right|=c,\] then \[\overrightarrow{AB}.\overrightarrow{AB}\] has the value : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{1}{2}\left( {{a}^{2}}-{{b}^{2}}+{{c}^{2}} \right)\]
  done clear
  B)
  \[\frac{1}{4}\left( {{a}^{2}}+{{b}^{2}}-{{c}^{2}} \right)\]
  done clear
  C)
  \[\frac{1}{3}\left( {{b}^{2}}+{{c}^{2}}-{{a}^{2}} \right)\]
  done clear
  D)
  \[\frac{1}{2}\left( {{a}^{2}}+{{b}^{2}}+{{c}^{2}} \right)\]
  done clear
  E)
  None of these
  done clear
  View Answer play_arrow

• question_answer26) If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{1}{26}\]
  done clear
  B)
  \[\frac{1}{27}\]
  done clear
  C)
  \[\frac{1}{21}\]
  done clear
  D)
  \[\frac{1}{15}\]
  done clear
  View Answer play_arrow

• question_answer27) If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to one is : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{1}{16}\]
  done clear
  B)
  \[\frac{9}{16}\]
  done clear
  C)
  \[\frac{3}{4}\]
  done clear
  D)
  \[\frac{15}{16}\]
  done clear
  View Answer play_arrow

• question_answer28) If \[\cos \alpha +\cos \beta =\frac{3}{2}\]and \[\sin \alpha +\sin \beta =\frac{1}{2}\]and \[\theta \]is the arithmetic mean of \[\alpha \] and \[\beta ,\] then \[\sin 2\theta +\cos 2\theta \]is equal to: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{3}{5}\]
  done clear
  B)
  \[\frac{4}{5}\]
  done clear
  C)
  \[\frac{7}{5}\]
  done clear
  D)
  \[\frac{8}{5}\]
  done clear
  View Answer play_arrow

• question_answer29) Let 10 vertical poles standing at equal distances on a straight line, subtend the same angle of elevation \[\alpha \]at a point O on this line and all the poles are on the same side of O. If the height of the longest pole is 'h' and the distance of the foot of the smallest pole from 0 is 'a' ; then the distance between two consecutive poles, is: [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\frac{h\sin \alpha +a\cos \alpha }{9\sin \alpha }\]
  done clear
  B)
  \[\frac{h\cos \alpha -a\sin \alpha }{9\cos \alpha }\]
  done clear
  C)
  \[\frac{h\cos \alpha -a\sin \alpha }{9\sin \alpha }\]
  done clear
  D)
  \[\frac{h\sin \alpha +a\cos \alpha }{9\cos \alpha }\]
  done clear
  View Answer play_arrow

• question_answer30) Consider the following statements : P : Suman is brilliant. Q : Suman is rich. R : Suman is honest. The negation of the statement, "Suman is brilliant and dishonest if and only if Suman is rich" can be equivalently expressed as : [JEE Main Online Paper (Held On 11 April 2015)]  
  A)
  \[\tilde{\ }Q\leftrightarrow \tilde{\ }P\wedge R\]
  done clear
  B)
  \[\tilde{\ }Q\leftrightarrow \tilde{\ }P\vee R\]
  done clear
  C)
  \[\tilde{\ }Q\leftrightarrow \tilde{\ }P\vee \tilde{\ }R\]
  done clear
  D)
  \[\tilde{\ }Q\leftrightarrow P\wedge \tilde{\ }R\]
  done clear
  View Answer play_arrow