Solved papers for JEE Main & Advanced JEE Main Paper (Held On 9 April 2014)

done JEE Main Paper (Held On 9 April 2014) Total Questions - 30

• question_answer1) Let P be the relation defined on the set of all real numbers such that \[P=\{(a,b):se{{c}^{2}}a-ta{{n}^{2}}b=1\}.\]Then P is:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  reflexive and symmetric but not transitive.
  done clear
  B)
  reflexive and transitive but not symmetric.
  done clear
  C)
  symmetric and transitive but not reflexive.
  done clear
  D)
  an equivalence relation.
  done clear
  View Answer play_arrow

• question_answer2) Let \[w(Imw\ne 0)\]be a complex number. Then the set of all complex number z satisfying the equation\[w-\overline{w}z=k(1-z),\]for some real number k, is   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[\left\{ z:\left| z \right|=1 \right\}\]                     
  done clear
  B)
  \[\left\{ z:z=\overline{z} \right\}\]
  done clear
  C)
  \[\left\{ z:z\ne 1 \right\}\]                          
  done clear
  D)
  \[\left\{ z:\left| z \right|=1,z\ne 1 \right\}\]
  done clear
  View Answer play_arrow

• question_answer3) If equations \[a{{x}^{2}}+bx+c=0(a,b,c\in R,a\ne 0)\]and \[2{{x}^{2}}+3x+4=0\]have a common root, then a : b : c equals:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  : 2 : 3                     
  done clear
  B)
  2 : 3 : 4
  done clear
  C)
  4 : 3 : 2                 
  done clear
  D)
  3 : 2 : 1
  done clear
  View Answer play_arrow

• question_answer4) If\[\frac{1}{\sqrt{\alpha }}\]and\[\frac{1}{\sqrt{\beta }}\] are the roots of the equation,\[a{{x}^{2}}+bx+1=0\]\[(a\ne 0,a,b,\in R),\]then the equation,\[x\left( x+{{b}^{3}} \right)+\left( {{a}^{3}}-3abx \right)=0\]has roots:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[{{\alpha }^{{}^{3}/{}_{2}}}\]and\[{{\beta }^{{}^{3}/{}_{2}}}\]  
  done clear
  B)
  \[\alpha {{\beta }^{{}^{1}/{}_{2}}}\]and\[{{\alpha }^{{}^{1}/{}_{2}}}\beta \]
  done clear
  C)
   \[\sqrt{\alpha \beta }\]and\[\alpha \beta \]      
  done clear
  D)
  \[{{\alpha }^{-\frac{3}{2}}}\]and\[{{\beta }^{-\frac{3}{2}}}\]
  done clear
  View Answer play_arrow

• question_answer5) If a, b, c are non-zero real numbers and if the system of equations

  (a - 1) x = y + z

  (b - 1) y = z + x

  (c - 1) z = x + y

  has a non-trivial solution, then ab + bc + ca equals:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  a + b + c                               
  done clear
  B)
  abc
  done clear
  C)
  1                                             
  done clear
  D)
  - 1
  done clear
  View Answer play_arrow

• question_answer6) If B is a \[3\times 3\]matrix such that \[{{B}^{2}}=0,\]then det. \[[{{(I+B)}^{50}}-50B]\]is equal to:     [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  1             
  done clear
  B)
  2
  done clear
  C)
  3                                             
  done clear
  D)
  50
  done clear
  View Answer play_arrow

• question_answer7) The number of terms in the expansion of\[{{(1+x)}^{101}}{{(1+{{x}^{2}}-x)}^{100}}\]in powers of x is:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  302                                        
  done clear
  B)
  301
  done clear
  C)
  202                                        
  done clear
  D)
  101
  done clear
  View Answer play_arrow

• question_answer8) The sum of the digits in the unit's place of all the 4-digitnumbers formed by using the numbers 3, 4, 5 and 6, without repetition, is:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  432                        
  done clear
  B)
  108
  done clear
  C)
  36                                          
  done clear
  D)
  18
  done clear
  View Answer play_arrow

• question_answer9) Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4th term is:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  8             
  done clear
  B)
  16
  done clear
  C)
  20          
  done clear
  D)
  24
  done clear
  View Answer play_arrow

• question_answer10) If the sum\[\frac{3}{{{1}^{2}}}+\frac{5}{{{1}^{2}}+{{2}^{2}}}+\frac{7}{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}+.......+\]up to 20 terms is equalto\[\frac{k}{21},\]then k is equal to:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  120        
  done clear
  B)
  180
  done clear
  C)
  240                                        
  done clear
  D)
  60
  done clear
  View Answer play_arrow

• question_answer11) If f(x) is continuous and\[f\left( \frac{9}{2} \right)=\frac{2}{9},\]then \[\underset{x\to 0}{\mathop{\lim }}\,f\left( \frac{1-\cos 3x}{{{x}^{2}}} \right)\]is equal to:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[\frac{9}{2}\]                                   
  done clear
  B)
  \[\frac{2}{9}\]
  done clear
  C)
  0                                             
  done clear
  D)
  \[\frac{8}{9}\]
  done clear
  View Answer play_arrow

• question_answer12) If\[y={{e}^{nx}},\]then\[\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)\left( \frac{{{d}^{2}}x}{d{{y}^{2}}} \right)\]is equal to:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[n{{e}^{nx}}\]                                 
  done clear
  B)
  \[n{{e}^{-nx}}\]
  done clear
  C)
  1                                             
  done clear
  D)
  \[-n{{e}^{-nx}}\]
  done clear
  View Answer play_arrow

• question_answer13) If the Rolle's theorem holds for the function\[f(x)=2{{x}^{3}}+a{{x}^{2}}+bx\] in the interval [-1, 1] for the point\[c=\frac{1}{2},\]then the value of 2a + b is:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[1\]                                            
  done clear
  B)
  \[-1\]
  done clear
  C)
  \[2\]                                            
  done clear
  D)
  \[- 2\]
  done clear
  View Answer play_arrow

• question_answer14) If \[f(x)={{\left( \frac{3}{5} \right)}^{x}}+{{\left( \frac{4}{5} \right)}^{x}}=-1,x\in R,\]then the equation f(x) =0 has :   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  no solution
  done clear
  B)
  one solution
  done clear
  C)
  two solutions
  done clear
  D)
  more than two solutions
  done clear
  View Answer play_arrow

• question_answer15) \[\int_{{}}^{{}}{\frac{{{\sin }^{8}}x-{{\cos }^{8}}x}{\left( 1-2\sin x{{\cos }^{2}}x \right)}}dx\]is equal to:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[\frac{1}{2}\sin 2x+c\]                 
  done clear
  B)
  \[-\frac{1}{2}\sin 2x+c\]
  done clear
  C)
  \[-\frac{1}{2}\sin x+c\]                 
  done clear
  D)
  \[-{{\sin }^{2}}x+c\]
  done clear
  View Answer play_arrow

• question_answer16) The integral \[\int\limits_{0}^{\frac{1}{2}}{\frac{\ln \left( 1+2x \right)}{1+4{{x}^{2}}}}dx,\]equals:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[\frac{\pi }{4}\ln 2\]                     
  done clear
  B)
  \[\frac{\pi }{8}\ln 2\]
  done clear
  C)
  \[\frac{\pi }{16}\ln 2\]   
  done clear
  D)
  \[\frac{\pi }{32}\ln 2\]
  done clear
  View Answer play_arrow

• question_answer17) Let \[A=\{(x,y):{{y}^{2}}\le 4x,y-2x\ge -4\}.\]The area (in square units) of the region A is:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  8                                             
  done clear
  B)
  9
  done clear
  C)
  10                                          
  done clear
  D)
  11
  done clear
  View Answer play_arrow

• question_answer18) If the differential equation representing the family of all circles touching x-axis at the origin is \[\left( {{x}^{2}}-{{y}^{2}} \right)\frac{dy}{dx}=g\left( x \right)y,\]then g(x) equals:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[\frac{1}{2}x\]                                
  done clear
  B)
  \[2{{x}^{2}}\]
  done clear
  C)
  \[2x\]                                   
  done clear
  D)
  \[\frac{1}{2}{{x}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer19) Let a and b be any two numbers satisfying\[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{4}.\] Then, the foot of perpendicular from the origin on the variable line,\[\frac{x}{a}+\frac{y}{b}=1,\]lies on:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  a hyperbola with each semi-axis \[=\sqrt{2}\]
  done clear
  B)
  a hyperbola with each semi-axis = 2
  done clear
  C)
  a circle of radius = 2
  done clear
  D)
  a circle of radius \[=\sqrt{2}\]
  done clear
  View Answer play_arrow

• question_answer20) Given three points \[P, Q, R\] with \[P(5, 3)\] and R lies on the x-axis. If equation of RQ is \[x - 2y = 2\] and PQ is parallel to the x-axis, then the centroid of \[DPQR\] lies on the line:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[2x+y-9=0\text{ }~\]  
  done clear
  B)
  \[x-2y+1=0\]
  done clear
  C)
  \[5x - 2y = 0\]
  done clear
  D)
  \[2x - 5y = 0\]
  done clear
  View Answer play_arrow

• question_answer21) If the point (1, 4) lies inside the circle \[{{x}^{2}}+{{y}^{2}}-6x-10y+p=0\] and the circle does not touch or intersect the coordinate axes, then the set of all possible values of p is the interval:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[(0, 25)\]                 
  done clear
  B)
  \[(25, 39)\]
  done clear
  C)
  \[(9, 25)\]                 
  done clear
  D)
  \[(25, 29)\]
  done clear
  View Answer play_arrow

• question_answer22) If OB is the semi-minor axis of an ellipse, \[{{F}_{1}}\] and \[{{F}_{2}}\] are its foci and the angle between \[{{F}_{1}}B\]and \[{{F}_{2}}B\] is a right angle, then the square of the eccentricity of the ellipse is:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  (a)\[\frac{1}{2}\]             
  done clear
  B)
  \[\frac{1}{\sqrt{2}}\]
  done clear
  C)
  \[\frac{1}{2\sqrt{2}}\]                   
  done clear
  D)
  \[\frac{1}{4}\]
  done clear
  View Answer play_arrow

• question_answer23) Equation of the plane which passes through the point of inter section of lines \[\frac{x-1}{3}=\frac{y-2}{1}=\frac{z-3}{2}\]and\[\frac{x-3}{1}=\frac{y-1}{2}=\frac{z-2}{3}\]and has the largest distance from the origin is:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[7x\text{ }+\text{ }2y\text{ }+\text{ }4z\text{ }=\text{ }54~~\]            
  done clear
  B)
  \[3x\text{ }+\text{ }4y\text{ }+\text{ }5z\text{ }=\text{ }49\]
  done clear
  C)
  \[4x\text{ }+\text{ }3y\text{ }+\text{ }5z\text{ }=\text{ }50\]              
  done clear
  D)
  \[5x\text{ }+\text{ }4y\text{ }+\text{ }3z\text{ }=\text{ }57\]
  done clear
  View Answer play_arrow

• question_answer24) A line in the 3-dimensional space makes an angle\[\theta \left( 0<\theta \le \frac{\pi }{2} \right)\]with both the x and y axes. Then the set of all values of \[\theta \] is the interval:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[\left( 0,\frac{\pi }{4} \right]\]                 
  done clear
  B)
                  \[\left[ \frac{\pi }{6},\frac{\pi }{3} \right]\]
  done clear
  C)
  \[\left[ \frac{\pi }{4},\frac{\pi }{2} \right]\]
  done clear
  D)
  \[\left( \frac{\pi }{3},\frac{\pi }{2} \right]\]
  done clear
  View Answer play_arrow

• question_answer25) If\[\left| \overset{\to }{\mathop{a}}\, \right|=2,\left| \overset{\to }{\mathop{b}}\, \right|=3\]and\[\left| 2\overset{\to }{\mathop{a}}\,-\overset{\to }{\mathop{b}}\, \right|=5,\]then\[\left| 2\overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\, \right|\] equals:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  17                                          
  done clear
  B)
  7
  done clear
  C)
  5                                             
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer26) In a set of 2n distinct observations, each of the observations below the median of all the observations is increased by 5and each of the remaining observations is decreased by 3. Then the mean of the new set of observations:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  increases by 1
  done clear
  B)
  decreases by 1
  done clear
  C)
  decreases by 2
  done clear
  D)
  increases by 2
  done clear
  View Answer play_arrow

• question_answer27) If A and B are two events such that \[P\left( A\cup B \right)=P\left( A\cap B \right),\]then the incorrect statement amongst the following statements is:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  A and B are equally likely
  done clear
  B)
  \[P\left( A\cap B' \right)=0\]
  done clear
  C)
  \[P\left( A'\cap B \right)=0\]      
  done clear
  D)
  \[P(A)+P(B)=1\]
  done clear
  View Answer play_arrow

• question_answer28) The number of values of \[\alpha \] in \[[0,2\pi ]\]for which \[2{{\sin }^{3}}\alpha -7{{\sin }^{2}}\alpha +7\sin \alpha =2,\]is:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  6                                             
  done clear
  B)
  4
  done clear
  C)
  3             
  done clear
  D)
  1
  done clear
  View Answer play_arrow

• question_answer29) If\[\cos ec\theta =\frac{p+q}{p-w}(p\ne q\ne 0),\]then\[\left| \cot \left( \frac{\pi }{4}+\frac{\theta }{2} \right) \right|\]then cotto:   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  \[\sqrt{\frac{p}{q}}\]                                     
  done clear
  B)
  \[\sqrt{\frac{q}{p}}\]
  done clear
  C)
  \[\sqrt{pq}\]                     
  done clear
  D)
  \[pq\]
  done clear
  View Answer play_arrow

• question_answer30) The contrapositive of the statement "I go to school if it does not rain" is   [JEE Main Online Paper ( Held On 09 Apirl  2014  )
  A)
  If it rains, I do not go to school.
  done clear
  B)
  If I do not go to school, it rains.
  done clear
  C)
  If it rains, I go to school.
  done clear
  D)
  If I go to school, it rains.
  done clear
  View Answer play_arrow