Solved papers for JEE Main & Advanced AIEEE Solved Paper-2008

done AIEEE Solved Paper-2008 Total Questions - 35

• question_answer1) The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?       AIEEE  Solved  Paper-2008
  A)
  a = 1, b = 6                          
  done clear
  B)
  a = 3, b = 4          
  done clear
  C)
         a = 0, b = 7          
  done clear
  D)
         a = 5, b = 2
  done clear
  View Answer play_arrow

• question_answer2) The vector \[\vec{a}=\alpha \hat{i}+2\hat{j}+\beta \hat{k}\] lies in the plane of the vectors \[\vec{b}=\hat{i}+\hat{j}\] and \[\vec{c}=\hat{j}+\hat{k}\] and bisects the angle between \[\vec{b}\] and \[\vec{c}\]. Then which one of the following gives possible values of \[\alpha \] and\[\beta \]?         AIEEE  Solved  Paper-2008
  A)
  \[\alpha =2,\,\,\beta =1\]                           
  done clear
  B)
  \[\alpha =1,\,\,\beta =1\]           
  done clear
  C)
         \[\alpha =2,\,\,\beta =2\]           
  done clear
  D)
         \[\alpha =1,\,\,\beta =2\]
  done clear
  View Answer play_arrow

• question_answer3) The non-zero vectors \[\vec{a},\,\vec{b}\], and \[\vec{c}\] are related by \[\vec{a}=8\vec{b}\] and \[\vec{c}=-7\vec{b}\]. Then the angle between \[\vec{a}\] and \[\vec{c}\] is       AIEEE  Solved  Paper-2008
  A)
  \[\frac{\pi }{2}\]              
  done clear
  B)
                         \[\pi \]                 
  done clear
  C)
                         0                                             
  done clear
  D)
                         \[\frac{\pi }{4}\]
  done clear
  View Answer play_arrow

• question_answer4) The line passing through the points \[\left( 5,1,\,a \right)\] and \[\left( 3,b,\,1 \right)\] crosses the yz-plane at the point \[\left( 0,\frac{17}{2},\frac{-13}{2} \right)\]. Then       AIEEE  Solved  Paper-2008
  A)
  a = 6, b = 4          
  done clear
  B)
         a = 8, b = 2          
  done clear
  C)
         a = 2, b = 8          
  done clear
  D)
         a = 4, b = 6
  done clear
  View Answer play_arrow

• question_answer5) If the straight lines \[\frac{x-1}{k}=\frac{y-2}{2}=\frac{z-3}{3}\] and \[\frac{x-2}{3}=\frac{y-3}{k}=\frac{z-1}{2}\] intersect at a point, then the integer k is equal to       AIEEE  Solved  Paper-2008
  A)
  2             
  done clear
  B)
  - 2                          
  done clear
  C)
  - 5                          
  done clear
  D)
  5
  done clear
  View Answer play_arrow

• question_answer6) The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is       AIEEE  Solved  Paper-2008
  A)
  \[{{\left( y-2 \right)}^{2}}y{{'}^{2}}=25-{{\left( y-2 \right)}^{2}}\]
  done clear
  B)
  \[{{\left( x-2 \right)}^{2}}y{{'}^{2}}=25-{{\left( y-2 \right)}^{2}}\]
  done clear
  C)
  \[\left( x-2 \right)y{{'}^{2}}=25-{{\left( y-2 \right)}^{2}}\]
  done clear
  D)
  \[\left( y-2 \right)y{{'}^{2}}=25-{{\left( y-2 \right)}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer7) Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that \[x=cy+bz=az+cx\] and \[z=bx+ay\]. Then \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc\] is equal to       AIEEE  Solved  Paper-2008
  A)
  0                             
  done clear
  B)
  1                             
  done clear
  C)
  2                             
  done clear
  D)
  - 1
  done clear
  View Answer play_arrow

• question_answer8) Let A be a square matrix all of whose entries are integers. Then which one of the following is true?       AIEEE  Solved  Paper-2008
  A)
  If det\[A=\pm 1\], then \[{{A}^{-1}}\] exists and all its entries are integers
  done clear
  B)
  If det\[A=\pm 1\], then \[{{A}^{-1}}\] need not exist
  done clear
  C)
  If det \[A=\pm 1\], then \[{{A}^{-1}}\] exists but all its entries are not necessarily integers
  done clear
  D)
  If det \[A=\pm 1\], then \[{{A}^{-1}}\] exists and all its entries are non-integers
  done clear
  View Answer play_arrow

• question_answer9) The quadratic equations \[{{x}^{2}}-6x+a=0\] and \[{{x}^{2}}-cx+6=0\] have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is       AIEEE  Solved  Paper-2008
  A)
  3                             
  done clear
  B)
         2                             
  done clear
  C)
         1                             
  done clear
  D)
         4
  done clear
  View Answer play_arrow

• question_answer10) How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?       AIEEE  Solved  Paper-2008
  A)
  \[6.8.\,{{\,}^{7}}{{C}_{4}}\]                         
  done clear
  B)
  \[7.{{\,}^{6}}{{C}_{4}}.{{\,}^{8}}{{C}_{4}}\]           
  done clear
  C)
                                         \[8.{{\,}^{6}}{{C}_{4}}.{{\,}^{7}}{{C}_{4}}\]                           
  done clear
  D)
                         \[6.7.{{\,}^{8}}{{C}_{4}}\]
  done clear
  View Answer play_arrow

• question_answer11) Let \[I=\int\limits_{0}^{1}{\frac{\sin x}{\sqrt{x}}dx}\] and \[J=\int\limits_{0}^{1}{\frac{\cos x}{\sqrt{x}}dx}\]. Then which one of the following is true?       AIEEE  Solved  Paper-2007
  A)
  \[I<\frac{2}{3}\] and \[J<2\]
  done clear
  B)
         \[I>\frac{2}{3}\] and \[J<2\]
  done clear
  C)
                         \[I>\frac{2}{3}\] and \[J>2\]       
  done clear
  D)
  \[I<\frac{2}{3}\] and \[J>2\]
  done clear
  View Answer play_arrow

• question_answer12) The area of the plane region bounded by the curves \[x+2{{y}^{2}}=0\] and \[x+3{{y}^{2}}=1\] is equal to       AIEEE  Solved  Paper-2007
  A)
  \[\frac{2}{3}\]                   
  done clear
  B)
         \[\frac{4}{3}\]   
  done clear
  C)
         \[\frac{5}{3}\]                   
  done clear
  D)
         \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer13) The value of \[\sqrt{2}\int{\frac{\sin xdx}{\sin \left( x-\frac{\pi }{4} \right)}}\] is       AIEEE  Solved  Paper-2007
  A)
  \[x+\log \left| \sin \left( x-\frac{\pi }{4} \right) \right|+c\]          
  done clear
  B)
  \[x-\log \left| \cos \left( x-\frac{\pi }{4} \right) \right|+c\]
  done clear
  C)
  \[x+\log \left| \cos \left( x-\frac{\pi }{4} \right) \right|+c\]
  done clear
  D)
                  \[x-\log \left| \sin \left( x-\frac{\pi }{4} \right) \right|+c\]
  done clear
  View Answer play_arrow

• question_answer14) The statement \[p\to \left( q\to p \right)\] is equivalent to       AIEEE  Solved  Paper-2007
  A)
  \[p\to \left( p\wedge q \right)\]              
  done clear
  B)
  \[p\to \left( p\leftrightarrow q \right)\]
  done clear
  C)
         \[p\to \left( p\to q \right)\]
  done clear
  D)
         \[p\to \left( p\vee q \right)\]
  done clear
  View Answer play_arrow

• question_answer15) The value of \[\cot \left( \cos e{{c}^{-1}}\frac{5}{3}+{{\tan }^{-1}}\frac{2}{3} \right)\] is       AIEEE  Solved  Paper-2007
  A)
  \[\frac{4}{17}\]
  done clear
  B)
                         \[\frac{5}{17}\]                
  done clear
  C)
         \[\frac{6}{17}\]
  done clear
  D)
         \[\frac{3}{17}\]
  done clear
  View Answer play_arrow

• question_answer16) Directions: Questions number 16 to 20 are Assertion-Reason type questions. Each of these questions contains two statements: Statement-I (Assertion) and Statement-2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let A be a \[2\times 2\] matrix with real entries. Let I be the \[2\times 2\] identity matrix. Denote by tr(A), the sum of diagonal entries of A. Assume that \[{{A}^{2}}=I\]. Statement-1: If \[A\ne I\] and \[A\ne -I\], then det\[A=-I\]. Statement-2: If \[A\ne I\] and \[A\ne -I\], then \[tr\left( A \right)\ne 0\].       AIEEE  Solved  Paper-2007
  A)
  Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
  done clear
  B)
  Statement-1 is true, Statement-2 is false.
  done clear
  C)
  Statement-1 is false, Statement-2 is true.
  done clear
  D)
  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  done clear
  View Answer play_arrow

• question_answer17) Directions: Questions number 16 to 20 are Assertion-Reason type questions. Each of these questions contains two statements: Statement-I (Assertion) and Statement-2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Let p be the statement "x is an irrational number", q be the statement "y is transcendental number", and r be the statement "x is a rational number if y is a transcendental number".  

  Statement-1: r is equivalent to either q or p.

  Statement-2: r is equivalent to \[\sim \left( p\leftrightarrow \,\sim q \right)\].

      AIEEE  Solved  Paper-2007
  A)
  Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
  done clear
  B)
  Statement-1 is true, Statement-2 is false.
  done clear
  C)
  Statement-1 is false, Statement-2 is true.
  done clear
  D)
  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  done clear
  View Answer play_arrow

• question_answer18) Directions: Questions number 16 to 20 are Assertion-Reason type questions. Each of these questions contains two statements: Statement-I (Assertion) and Statement-2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

  In a shop there are five types of ice-creams available. A child buys six ice-creams.

  Statement-1: The number of different ways the child can buy the six ice-creams is \[^{10}{{C}_{5}}\].

  Statement-2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A"s and 4 B"s in a row.

    AIEEE  Solved  Paper-2007  
  A)
  Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
  done clear
  B)
  Statement-1 is true, Statement-2 is false.
  done clear
  C)
  Statement-1 is false, Statement-2 is true.
  done clear
  D)
  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for = Statement-1.
  done clear
  View Answer play_arrow

• question_answer19) Directions: Questions number 16 to 20 are Assertion-Reason type questions. Each of these questions contains two statements: Statement-I (Assertion) and Statement-2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

  Statement-1: \[\sum\limits_{r=0}^{n}{{{\left( r+1 \right)}^{n}}{{C}_{r}}=\left( n+2 \right){{2}^{n-1}}}\].

  Statement-2: \[\sum\limits_{r=0}^{n}{{{\left( r+1 \right)}^{n}}{{C}_{r}}{{x}^{r}}={{\left( 1+x \right)}^{n}}+nx{{\left( 1+x \right)}^{n-1}}}\].

      AIEEE  Solved  Paper-2007 
  A)
  Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
  done clear
  B)
  Statement-1 is true, Statement-2 is false.
  done clear
  C)
  Statement-1 is false, Statement-2 is true.
  done clear
  D)
  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  done clear
  View Answer play_arrow

• question_answer20) Directions: Questions number 16 to 20 are Assertion-Reason type questions. Each of these questions contains two statements: Statement-I (Assertion) and Statement-2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

  Statement-1: For every natural number \[\ge 2,\,\,\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+.....+\frac{1}{\sqrt{n}}>\sqrt{n}\].

  Statement-2: For every natural number \[n\ge 2,\sqrt{n\left( n+1 \right)}<n+1\].

      AIEEE  Solved  Paper-2007
  A)
  Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
  done clear
  B)
  Statement-1 is true, Statement-2 is false.
  done clear
  C)
  Statement-1 is false, Statement-2 is true.
  done clear
  D)
  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  done clear
  View Answer play_arrow

• question_answer21) The conjugate of a complex number is \[\frac{1}{i-1}\]. Then that complex number is       AIEEE  Solved  Paper-2007
  A)
  \[\frac{-1}{i+1}\]
  done clear
  B)
                         \[\frac{1}{i-1}\]                
  done clear
  C)
         \[\frac{-1}{i-1}\]                              
  done clear
  D)
  \[\frac{1}{i+1}\]
  done clear
  View Answer play_arrow

• question_answer22) Let R be the real line. Consider the following subsets of the plane \[R\times R\]:D5)                 \[S=\left\{ \left( x,y \right):y=x+1\,\,and\,\,0<x<2 \right\}\]                 \[T=\left\{ \left( x,y \right):x-y\,is\,an\,\operatorname{int}eget \right\}\] Which one of the following is true?
  A)
  S is an equivalence relation on R but T is not
  done clear
  B)
  T is an equivalence relation on R but S is not
  done clear
  C)
  Neither S nor T is an equivalence relation on R
  done clear
  D)
  Both S and T are equivalence relations on R
  done clear
  View Answer play_arrow

• question_answer23) Let \[f:N\to Y\] be a function defined as\[f\left( x \right)=4x+3\], where \[Y=\{y\in N:y=4x+3\]for some \[x\in N\}\]. Show that f is invertible and its inverse is       AIEEE  Solved  Paper-2007
  A)
  \[g\left( y \right)=\frac{y+3}{4}\]             
  done clear
  B)
  \[g\left( y \right)=\frac{y-3}{4}\]
  done clear
  C)
                         \[g\left( y \right)=\frac{3y+4}{3}\]
  done clear
  D)
         \[g\left( y \right)=4+\frac{y+3}{4}\]
  done clear
  View Answer play_arrow

• question_answer24) AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60°. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is \[{{45}^{o}}\]. Then the height of the pole is       AIEEE  Solved  Paper-2007
  A)
  \[\frac{7\sqrt{3}}{2}\left( \sqrt{3}-1 \right)m\]
  done clear
  B)
          \[\frac{7\sqrt{3}}{2}\frac{1}{\sqrt{3}+1}m\]
  done clear
  C)
         \[\frac{7\sqrt{3}}{2}\frac{1}{\sqrt{3}-1}m\]
  done clear
  D)
         \[\frac{7\sqrt{3}}{2}\left( \sqrt{3}+1 \right)m\]
  done clear
  View Answer play_arrow

• question_answer25) A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then \[P\left( A\cup B \right)\] is       AIEEE  Solved  Paper-2007
  A)
  1                             
  done clear
  B)
         \[\frac{2}{5}\]                   
  done clear
  C)
         \[\frac{3}{5}\]                   
  done clear
  D)
         0
  done clear
  View Answer play_arrow

• question_answer26) It is given that the events A and B are such that \[P\left( A \right)=\frac{1}{4},\,P\left( A|B \right)=\frac{1}{2}\] and \[\,P\left( B|A \right)=\frac{2}{3}\]. Then \[P\left( B \right)\] is       AIEEE  Solved  Paper-2007
  A)
  \[\frac{2}{3}\]
  done clear
  B)
                                         \[\frac{1}{2}\]
  done clear
  C)
  \[\frac{1}{6}\]                  
  done clear
  D)
         \[\frac{1}{3}\]
  done clear
  View Answer play_arrow

• question_answer27) A focus of an ellipse is at the origin. The directrix is the line \[x=4\] and the eccentricity is \[\frac{1}{2}\]. Then the length of the semimajor axis is       AIEEE  Solved  Paper-2007
  A)
  \[\frac{4}{3}\]                   
  done clear
  B)
         \[\frac{5}{3}\]                   
  done clear
  C)
         \[\frac{8}{3}\]   
  done clear
  D)
         \[\frac{2}{3}\]
  done clear
  View Answer play_arrow

• question_answer28) A parabola has the origin as its focus and the line \[x=2\] as the directrix. Then the vertex of the parabola is at       AIEEE  Solved  Paper-2007
  A)
  (0, 1)
  done clear
  B)
                         (2, 0)     
  done clear
  C)
                         (0, 2)     
  done clear
  D)
         (1, 0)
  done clear
  View Answer play_arrow

• question_answer29) The point diametrically opposite to the point P(1, 0) on the circle \[{{x}^{2}}+{{y}^{2}}+2x+4y-3=0\] is
  A)
  \[\left( -3,-4 \right)\]
  done clear
  B)
                         \[\left( 3,\,4 \right)\]     
  done clear
  C)
         \[\left( 3,\,-4 \right)\]   
  done clear
  D)
         \[\left( -3,\,\,4 \right)\]
  done clear
  View Answer play_arrow

• question_answer30) The perpendicular bisector of the line segment joining \[P\left( 1,4 \right)\] and \[Q\left( k,3 \right)\] has y-intercept -4. Then a possible value of k is       AIEEE  Solved  Paper-2007
  A)
  - 2                          
  done clear
  B)
  - 4                          
  done clear
  C)
  1                             
  done clear
  D)
  2
  done clear
  View Answer play_arrow

• question_answer31) The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is       AIEEE  Solved  Paper-2007
  A)
  12          
  done clear
  B)
  4                             
  done clear
  C)
  - 4                          
  done clear
  D)
  - 12
  done clear
  View Answer play_arrow

• question_answer32) Suppose the cubic \[{{x}^{3}}-px+q\] has three distinct real roots where \[p>0\] and \[q>0\]. Then which one of the following holds?       AIEEE  Solved  Paper-2007
  A)
  The cubic has minima at both \[\sqrt{\frac{p}{3}}\] and \[-\sqrt{\frac{p}{3}}\]
  done clear
  B)
  The cubic has maxima at both \[\sqrt{\frac{p}{3}}\]and \[-\sqrt{\frac{p}{3}}\]
  done clear
  C)
  The cubic has minima at \[\sqrt{\frac{p}{3}}\] and maxima at \[-\sqrt{\frac{p}{3}}\]
  done clear
  D)
  The cubic has minima at \[-\sqrt{\frac{p}{3}}\] and maxima at \[\sqrt{\frac{p}{3}}\]
  done clear
  View Answer play_arrow

• question_answer33) How many real solutions does the equation \[{{x}^{7}}+14{{x}^{5}}+16{{x}^{3}}+30x-560=0\] have?       AIEEE  Solved  Paper-2007
  A)
  3                             
  done clear
  B)
         5                             
  done clear
  C)
         7                             
  done clear
  D)
         1
  done clear
  View Answer play_arrow

• question_answer34) Let \[f\left( x \right)=\left\{ \begin{matrix}    \left( x-1 \right)\sin \frac{1}{x-1} & if\,x\ne 1  \\    0 & if\,x=1  \\ \end{matrix} \right.\]. Then which one of the following is true?       AIEEE  Solved  Paper-2007
  A)
  \[f\] is differentiable at \[x=0\] but not at \[x=1\]
  done clear
  B)
  \[f\] is differentiable at \[x=1\] but not at \[x=0\]
  done clear
  C)
  \[f\] is neither differentiable at \[x=0\] nor at \[x=1\]
  done clear
  D)
  \[f\] is differentiable at \[x=0\] and at \[x=1\]
  done clear
  View Answer play_arrow

• question_answer35) The solution of the differential equation \[\frac{dy}{dx}=\frac{x+y}{x}\] satisfying the condition \[y\left( 1 \right)=1\] is       AIEEE  Solved  Paper-2007
  A)
  \[y=x{{e}^{\left( x-1 \right)}}\] 
  done clear
  B)
         \[y=x\ln x+x\]                  
  done clear
  C)
  \[y=\ln x+x\]     
  done clear
  D)
         \[y=x\ln x+{{x}^{2}}\]
  done clear
  View Answer play_arrow