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
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
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
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
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
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
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
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
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
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.
doneclear
B)
Statement-1 is true, Statement-2 is false.
doneclear
C)
Statement-1 is false, Statement-2 is true.
doneclear
D)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
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.
doneclear
B)
Statement-1 is true, Statement-2 is false.
doneclear
C)
Statement-1 is false, Statement-2 is true.
doneclear
D)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
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.
doneclear
B)
Statement-1 is true, Statement-2 is false.
doneclear
C)
Statement-1 is false, Statement-2 is true.
doneclear
D)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for = Statement-1.
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.
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.
doneclear
B)
Statement-1 is true, Statement-2 is false.
doneclear
C)
Statement-1 is false, Statement-2 is true.
doneclear
D)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
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?
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
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
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
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
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
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
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
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
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 \[-\sqrt{\frac{p}{3}}\]
doneclear
B)
The cubic has maxima at both \[\sqrt{\frac{p}{3}}\]and \[-\sqrt{\frac{p}{3}}\]
doneclear
C)
The cubic has minima at \[\sqrt{\frac{p}{3}}\] and maxima at \[-\sqrt{\frac{p}{3}}\]
doneclear
D)
The cubic has minima at \[-\sqrt{\frac{p}{3}}\] and maxima at \[\sqrt{\frac{p}{3}}\]
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 \[x=1\]
doneclear
B)
\[f\] is differentiable at \[x=1\] but not at \[x=0\]
doneclear
C)
\[f\] is neither differentiable at \[x=0\] nor at \[x=1\]
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