# 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

B)
a = 3, b = 4

C)
a = 0, b = 7

D)
a = 5, b = 2

• 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)
$\alpha =2,\,\,\beta =1$

B)
$\alpha =1,\,\,\beta =1$

C)
$\alpha =2,\,\,\beta =2$

D)
$\alpha =1,\,\,\beta =2$

• 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)
$\frac{\pi }{2}$

B)
$\pi$

C)
0

D)
$\frac{\pi }{4}$

• 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

B)
a = 8, b = 2

C)
a = 2, b = 8

D)
a = 4, b = 6

• 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

B)
- 2

C)
- 5

D)
5

• 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)
${{\left( y-2 \right)}^{2}}y{{'}^{2}}=25-{{\left( y-2 \right)}^{2}}$

B)
${{\left( x-2 \right)}^{2}}y{{'}^{2}}=25-{{\left( y-2 \right)}^{2}}$

C)
$\left( x-2 \right)y{{'}^{2}}=25-{{\left( y-2 \right)}^{2}}$

D)
$\left( y-2 \right)y{{'}^{2}}=25-{{\left( y-2 \right)}^{2}}$

• 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

B)
1

C)
2

D)
- 1

• 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

B)
If det$A=\pm 1$, then ${{A}^{-1}}$ need not exist

C)
If det $A=\pm 1$, then ${{A}^{-1}}$ exists but all its entries are not necessarily integers

D)
If det $A=\pm 1$, then ${{A}^{-1}}$ exists and all its entries are non-integers

• 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

B)
2

C)
1

D)
4

• 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)
$6.8.\,{{\,}^{7}}{{C}_{4}}$

B)
$7.{{\,}^{6}}{{C}_{4}}.{{\,}^{8}}{{C}_{4}}$

C)
$8.{{\,}^{6}}{{C}_{4}}.{{\,}^{7}}{{C}_{4}}$

D)
$6.7.{{\,}^{8}}{{C}_{4}}$

• 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 $J<2$

B)
$I>\frac{2}{3}$ and $J<2$

C)
$I>\frac{2}{3}$ and $J>2$

D)
$I<\frac{2}{3}$ and $J>2$

• 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)
$\frac{2}{3}$

B)
$\frac{4}{3}$

C)
$\frac{5}{3}$

D)
$\frac{1}{3}$

• question_answer13) The value of $\sqrt{2}\int{\frac{\sin xdx}{\sin \left( x-\frac{\pi }{4} \right)}}$ is       AIEEE  Solved  Paper-2007

A)
$x+\log \left| \sin \left( x-\frac{\pi }{4} \right) \right|+c$

B)
$x-\log \left| \cos \left( x-\frac{\pi }{4} \right) \right|+c$

C)
$x+\log \left| \cos \left( x-\frac{\pi }{4} \right) \right|+c$

D)
$x-\log \left| \sin \left( x-\frac{\pi }{4} \right) \right|+c$

• question_answer14) The statement $p\to \left( q\to p \right)$ is equivalent to       AIEEE  Solved  Paper-2007

A)
$p\to \left( p\wedge q \right)$

B)
$p\to \left( p\leftrightarrow q \right)$

C)
$p\to \left( p\to q \right)$

D)
$p\to \left( p\vee q \right)$

• 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)
$\frac{4}{17}$

B)
$\frac{5}{17}$

C)
$\frac{6}{17}$

D)
$\frac{3}{17}$

• 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.

B)
Statement-1 is true, Statement-2 is false.

C)
Statement-1 is false, Statement-2 is true.

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.

B)
Statement-1 is true, Statement-2 is false.

C)
Statement-1 is false, Statement-2 is true.

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.

B)
Statement-1 is true, Statement-2 is false.

C)
Statement-1 is false, Statement-2 is true.

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.  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.

B)
Statement-1 is true, Statement-2 is false.

C)
Statement-1 is false, Statement-2 is true.

D)
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

• 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)} AIEEE Solved Paper-2007 A) Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1. B) Statement-1 is true, Statement-2 is false. C) Statement-1 is false, Statement-2 is true. D) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. 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)
$\frac{-1}{i+1}$

B)
$\frac{1}{i-1}$

C)
$\frac{-1}{i-1}$

D)
$\frac{1}{i+1}$

• 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?

A)
S is an equivalence relation on R but T is not

B)
T is an equivalence relation on R but S is not

C)
Neither S nor T is an equivalence relation on R

D)
Both S and T are equivalence relations on R

• 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)
$g\left( y \right)=\frac{y+3}{4}$

B)
$g\left( y \right)=\frac{y-3}{4}$

C)
$g\left( y \right)=\frac{3y+4}{3}$

D)
$g\left( y \right)=4+\frac{y+3}{4}$

• 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)
$\frac{7\sqrt{3}}{2}\left( \sqrt{3}-1 \right)m$

B)
$\frac{7\sqrt{3}}{2}\frac{1}{\sqrt{3}+1}m$

C)
$\frac{7\sqrt{3}}{2}\frac{1}{\sqrt{3}-1}m$

D)
$\frac{7\sqrt{3}}{2}\left( \sqrt{3}+1 \right)m$

• 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

B)
$\frac{2}{5}$

C)
$\frac{3}{5}$

D)
0

• 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)
$\frac{2}{3}$

B)
$\frac{1}{2}$

C)
$\frac{1}{6}$

D)
$\frac{1}{3}$

• 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)
$\frac{4}{3}$

B)
$\frac{5}{3}$

C)
$\frac{8}{3}$

D)
$\frac{2}{3}$

• 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)

B)
(2, 0)

C)
(0, 2)

D)
(1, 0)

• 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)
$\left( -3,-4 \right)$

B)
$\left( 3,\,4 \right)$

C)
$\left( 3,\,-4 \right)$

D)
$\left( -3,\,\,4 \right)$

• 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

B)
- 4

C)
1

D)
2

• 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

B)
4

C)
- 4

D)
- 12

• 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 $-\sqrt{\frac{p}{3}}$

B)
The cubic has maxima at both $\sqrt{\frac{p}{3}}$and $-\sqrt{\frac{p}{3}}$

C)
The cubic has minima at $\sqrt{\frac{p}{3}}$ and maxima at $-\sqrt{\frac{p}{3}}$

D)
The cubic has minima at $-\sqrt{\frac{p}{3}}$ and maxima at $\sqrt{\frac{p}{3}}$

• 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

B)
5

C)
7

D)
1

• 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 $x=1$

B)
$f$ is differentiable at $x=1$ but not at $x=0$

C)
$f$ is neither differentiable at $x=0$ nor at $x=1$

D)
$f$ is differentiable at $x=0$ and 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

A)
$y=x{{e}^{\left( x-1 \right)}}$

B)
$y=x\ln x+x$

C)
$y=\ln x+x$

D)
$y=x\ln x+{{x}^{2}}$