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

### done AIEEE Solved Paper-2008 Total Questions - 105

• 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)
$y=x\ln x+{{x}^{2}}$

• question_answer36) Which one of the following is the correct statement?       AIEEE  Solved  Paper-2007

A)
Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase.

B)
${{B}_{2}}{{H}_{6}}.2N{{H}_{3}}$ is known as ?inorganic benzene?.

C)
Boric acid is a protonic acid.

D)
Beryllium exhibits coordination number of six.

• question_answer37) The treatment of $C{{H}_{3}}MgX$ with $C{{H}_{3}}C\equiv C-H$ produces       AIEEE  Solved  Paper-2007

A)
$C{{H}_{3}}-\overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{C}}\,=\overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}$

B)
$C{{H}_{4}}$

C)
$C{{H}_{3}}-CH=C{{H}_{2}}$

D)
$C{{H}_{3}}C\equiv C-C{{H}_{3}}$

• question_answer38) The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is       AIEEE  Solved  Paper-2007

A)
$-CHO,-COOH,-S{{O}_{3}}H,-CON{{H}_{2}}$

B)
$-CON{{H}_{2}},-CHO,-S{{O}_{3}}H,-COOH$

C)
$-COOH,-S{{O}_{3}}H,-CON{{H}_{2}},-CHO$

D)
$-S{{O}_{3}}H,-COOH,-CON{{H}_{2}},-CHO$

• question_answer39) The $p{{K}_{a}}$ of a weak acid, HA is 4.80. The $p{{K}_{b}}$ of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be       AIEEE  Solved  Paper-2007

A)
7.01

B)
9.22

C)
9.58

D)
4.79

• question_answer40) The hydrocarbon which can react with sodium in liquid ammonia is       AIEEE  Solved  Paper-2007

A)
$C{{H}_{3}}CH=CHC{{H}_{3}}$

B)
$C{{H}_{3}}C{{H}_{2}}C\equiv CC{{H}_{2}}C{{H}_{3}}$

C)
$C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C\equiv CC{{H}_{2}}C{{H}_{2}}C{{H}_{3}}$

D)
$C{{H}_{3}}C{{H}_{2}}C\equiv CH$

• question_answer41) Given $E_{C{{r}^{3+}}/Cr}^{o}=-0.72\,V,\,\,E_{F{{e}^{2+}}/Fe}^{o}=-0.42\,V$. The potential for the cell $Cr\left| C{{r}^{3+}}(0.1\,M)\, \right|\left| F{{e}^{2+}}(0.1\,M)\, \right|$ Fe is       AIEEE  Solved  Paper-2007

A)
- 0.339 V

B)
- 0.26 V

C)
0.26 V

D)
0.339 V

• question_answer42) Amount of oxalic acid present in a solution can be determined by its titration with $KMn{{O}_{4}}$ solution in the presence of ${{H}_{2}}S{{O}_{4}}$. The titration gives unsatisfactory result when carried out in the presence of HCl, because HCl       AIEEE  Solved  Paper-2007

A)
reduces permanganate to $M{{n}^{2+}}$.

B)
oxidises oxalic acid to carbon dioxide and water.

C)
gets oxidised by oxalic acid to chlorine.

D)
furnishes ${{H}^{+}}$ ions in addition to those from oxalic acid.

• question_answer43) Among the following substituted silanes the one which will give rise to cross linked silicone polymer on hydrolysis is       AIEEE  Solved  Paper-2007

A)
${{R}_{2}}SiC{{l}_{2}}$

B)
${{R}_{3}}SiCl$

C)
${{R}_{4}}Si$

D)
$RSiC{{l}_{3}}$

• question_answer44) Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below:  $\frac{1}{2}C{{l}_{2}}(g)\xrightarrow{\frac{1}{2}{{\Delta }_{diss}}{{H}^{\Theta }}}Cl(g)\xrightarrow{{{\Delta }_{eg}}{{H}^{\Theta }}}C{{l}^{-}}$$(g)\xrightarrow{\frac{1}{2}{{\Delta }_{hyd}}{{H}^{\Theta }}}C{{l}^{-}}(aq)$ The energy involved in the conversion of $\frac{1}{2}C{{l}_{2}}(g)$ to $C{{l}^{-}}(aq)$ (using the data, ${{\Delta }_{diss}}H_{C{{l}_{2}}}^{\Theta }=240\,kJ\,mo{{l}^{-1}},\,{{\Delta }_{eg}}H_{Cl}^{\Theta }=-349$$kJ\,mo{{l}^{-1}},{{\Delta }_{hyd}}{{H}_{C{{l}^{-}}}}=-381\,kJ\,mo{{l}^{-1}})$ will be
AIEEE  Solved  Paper-2007

A)
- 850 kJ $mo{{l}^{-1}}$

B)
+120 kJ $mo{{l}^{-1}}$

C)
+152 kJ $mo{{l}^{-1}}$

D)
- 610 kJ $mo{{l}^{-1}}$

• question_answer45) Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly?       AIEEE  Solved  Paper-2007

A)
Metal sulphides are less stable than the corresponding oxides.

B)
$C{{O}_{2}}$ is more volatile than$C{{S}_{2}}$.

C)
Metal sulphides are thermodynamically more stable than $C{{S}_{2}}$.

D)
$C{{O}_{2}}$ is thermodynamically more stable than$C{{S}_{2}}$.

• question_answer46) Which one of the following constitutes a group of the isoelectronic species?       AIEEE  Solved  Paper-2007

A)
$C{{N}^{-}},{{N}_{2}},O_{2}^{2-},C_{2}^{2-}$

B)
${{N}_{2}},O_{2}^{-},N{{O}^{+}},CO$

C)
$C_{2}^{2-},O_{2}^{-},CO,NO$

D)
$N{{O}^{+}},C_{2}^{2-},C{{N}^{-}},{{N}_{2}}$

• question_answer47) Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives       AIEEE  Solved  Paper-2007

A)
p-nitrophenol

B)
nitrobenzene

C)
2, 4, 6-trinitrobenzene

D)
o-nitrophenol

• question_answer48)   The ionization enthalpy of hydrogen atom is$1.312\times {{10}^{6}}J\,mo{{l}^{-1}}$. The energy required to excite the electron in the atom from $n=1$to $n=2$ is       AIEEE  Solved  Paper-2007

A)
$7.56\times {{10}^{5}}J\,mo{{l}^{-1}}$

B)
$9.84\times {{10}^{5}}J\,mo{{l}^{-1}}$

C)
$8.51\times {{10}^{5}}J\,mo{{l}^{-1}}$

D)
$6.56\times {{10}^{5}}J\,mo{{l}^{-1}}$

• question_answer49) The organic chloro compound, which shows complete stereochemical inversion during a ${{S}_{N}}2$ reaction, is       AIEEE  Solved  Paper-2007

A)
${{(C{{H}_{3}})}_{2}}CHCl$

B)
$C{{H}_{3}}Cl$

C)
${{({{C}_{2}}{{H}_{5}})}_{2}}CHCl$

D)
${{(C{{H}_{3}})}_{3}}CCl$

• question_answer50) Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotized and then heated with cuprous bromide. The reaction mixture so formed contains       AIEEE  Solved  Paper-2007

A)
mixture of o - and p - bromoanilines

B)
mixture of o - and m - bromotoluenes

C)
mixture of o - and p - bromotoluenes

D)
mixture of o - and p - dibromobenzenes

• question_answer51) In the following sequence of reactions, the alkene affords the compound 'B' $C{{H}_{3}}CH=CHC{{H}_{3}}\xrightarrow{{{O}_{3}}}A\,\xrightarrow[Zn]{{{H}_{2}}O}\,B$. The compound B is       AIEEE  Solved  Paper-2007

A)
$C{{H}_{3}}C{{H}_{2}}COC{{H}_{3}}$

B)
$C{{H}_{3}}CHO$

C)
$C{{H}_{3}}C{{H}_{2}}CHO$

D)
$C{{H}_{3}}COC{{H}_{3}}$

• question_answer52) Which one of the following pairs of species have the same bond order?       AIEEE  Solved  Paper-2007

A)
$O_{2}^{-}$ and $C{{N}^{-}}$

B)
$N{{O}^{+}}$and $C{{N}^{+}}$

C)
$C{{N}^{-}}$ and $N{{O}^{+}}$

D)
$C{{N}^{-}}$and $C{{N}^{+}}$

• question_answer53) At ${{80}^{o}}C$, the vapour pressure of pure liquid  'A' is 520 mm Hg and that of pure liquid 'B' is 1000 mm Hg. If a mixture solution of 'A' and 'B' boils at ${{80}^{o}}C$ and 1 atm pressure, the amount of 'A' in the mixture is (1 atm = 760 mm Hg)       AIEEE  Solved  Paper-2007

A)
48 mol percent

B)
50 mol percent

C)
52 mol percent

D)
34 mol percent

• question_answer54) For a reaction $\frac{1}{2}A\xrightarrow{{}}2B$, rate of disappearance of 'A' is related to the rate of appearance of 'B' by the expression       AIEEE  Solved  Paper-2007

A)
$-\frac{d[A]}{dt}=\frac{d[B]}{dt}$

B)
$-\frac{d[A]}{dt}=4\frac{d[B]}{dt}$

C)
$-\frac{d[A]}{dt}=\frac{1}{2}\frac{d[B]}{dt}$

D)
$-\frac{d[A]}{dt}=\frac{1}{4}\frac{d[B]}{dt}$

• question_answer55) The equilibrium constants ${{K}_{{{p}_{1}}}}$ and ${{K}_{{{p}_{2}}}}$ for the reactions $X2Y$ and $ZP+Q$, respectively are in the ratio of 1 : 9. If the degree of dissociation of X and Z be equal then the ratio of total pressures at these equilibria is       AIEEE  Solved  Paper-2007

A)
1 : 3

B)
1 : 9

C)
1 : 36

D)
1 : 1

• question_answer56) In context with the industrial preparation of hydrogen from water gas $(CO+{{H}_{2}})$, which of the following is the correct statement?       AIEEE  Solved  Paper-2007

A)
${{H}_{2}}$ is removed through occlusion with Pd.

B)
CO is oxidised to $C{{O}_{2}}$ with steam in the presence of a catalyst followed by absorption of $C{{O}_{2}}$ in alkali.

C)
CO and ${{H}_{2}}$ are fractionally separated using differences in their densities.

D)
CO is removed by absorption in aqueous $C{{u}_{2}}C{{l}_{2}}$ solution.

• question_answer57) In which of the following octahedral complexes of Co (atomic number 27), will the magnitude of ${{\Delta }_{o}}$be the highest?       AIEEE  Solved  Paper-2007

A)
${{[Co{{({{H}_{2}}O)}_{6}}]}^{3+}}$

B)
${{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}$

C)
${{[Co{{(CN)}_{6}}]}^{3-}}$

D)
${{[Co{{({{C}_{2}}{{O}_{4}})}_{3}}]}^{3-}}$

• question_answer58)   The coordination number and the oxidation state of the element 'E' in the complex $[E{{(en)}_{2}}({{C}_{2}}{{O}_{4}})]N{{O}_{2}}$ (where (en) is ethylene diamine) are, respectively,       AIEEE  Solved  Paper-2007

A)
4 and 3

B)
6 and 3

C)
6 and 2

D)
4 and 2

• question_answer59) Identify the wrong statement in the following:       AIEEE  Solved  Paper-2007

A)
Ozone layer does not permit infrared radiation from the sun to reach the earth.

B)
Acid rain is mostly because of oxides of nitrogen and sulphur.

C)
Chlorofluorocarbons are responsible for ozone layer depletion.

D)
Greenhouse effect is responsible for global warming.

• question_answer60) Larger number of oxidation states are exhibited by the actinoids than those by lanthanoids, the main reason being       AIEEE  Solved  Paper-2007

A)
more energy difference between 5f and 6d than between 4f and 5d orbitals.

B)
more reactive nature of the actinoids than the lanthanoids.

C)
4f orbitals more diffused than the 5f orbitals.

D)
lesser energy difference between 5f and 6d than between 4f and 5d orbitals.

• question_answer61) In a compound, atoms of element Y form $ccp$ lattice and those of element X occupy 2/3rd of tetrahedral voids. The formula of the compound will be       AIEEE  Solved  Paper-2007

A)
${{X}_{2}}Y$

B)
${{X}_{3}}{{Y}_{4}}$

C)
${{X}_{4}}{{Y}_{3}}$

D)
${{X}_{2}}{{Y}_{3}}$

• question_answer62) Gold numbers of protective colloids (A), (B), (C) and (D) are 0.50, 0.01, 0.10 and 0.005, respectively. The correct order of their protective powers is       AIEEE  Solved  Paper-2007

A)
(A) < (C) < (B) < (D)

B)
(B) < (D) < (A) < (C)

C)
(D) < (A) < (C) < (B)

D)
(C) < (B) < (D) < (A)

• question_answer63) The vapour pressure of water at ${{20}^{o}}C$ is 17.5 mm Hg. If 18 g of glucose $({{C}_{6}}{{H}_{12}}{{O}_{6}})$ is added to 178.2 g of water at ${{20}^{o}}C$, the vapour pressure of the resulting solution will be       AIEEE  Solved  Paper-2007

A)
16.500 mm Hg

B)
17.325 mm Hg

C)
17.675 mm Hg

D)
15.750 mm Hg

• question_answer64) Bakelite is obtained from phenol by reacting with       AIEEE  Solved  Paper-2007

A)
$C{{H}_{3}}COO{{H}_{3}}$

B)
$HCHO$

C)
${{(C{{H}_{2}}OH)}_{2}}$

D)
$C{{H}_{3}}CHO$

• question_answer65) The absolute configuration of                 is       AIEEE  Solved  Paper-2007

A)
R, S

B)
S, R

C)
S, S

D)
R, R

• question_answer66) For the following three reactions a, b, c equilibrium constants are given:  a. $CO(g)+{{H}_{2}}O(g)\underset{{}}{\overset{{}}{\longleftrightarrow}}C{{O}_{2}}(g)+{{H}_{2}}(g);{{K}_{1}}$ b. $C{{H}_{4}}(g)+{{H}_{2}}O(g)\underset{{}}{\overset{{}}{\longleftrightarrow}}CO(g)+3{{H}_{2}}(g);{{K}_{2}}$ c. $C{{H}_{4}}(g)+2{{H}_{2}}O(g)\underset{{}}{\overset{{}}{\longleftrightarrow}}C{{O}_{2}}(g)+4{{H}_{2}}(g);{{K}_{3}}$ Which of the following relations is correct?
AIEEE  Solved  Paper-2007

A)
${{K}_{3}}={{K}_{1}}{{K}_{2}}$

B)
${{K}_{3}}\,.\,\,K_{2}^{3}=K_{1}^{2}$

C)
${{K}_{1}}\sqrt{{{K}_{2}}}={{K}_{3}}$

D)
${{K}_{2}}{{K}_{3}}={{K}_{1}}$

• question_answer67) Standard entropy of ${{X}_{2}},{{Y}_{2}}$ and $X{{Y}_{3}}$ are 60, 40 and $50\,J{{K}^{-1}}mo{{l}^{-1}}$, respectively. For the reaction, $\frac{1}{2}{{X}_{2}}+\frac{3}{2}{{Y}_{2}}\xrightarrow{{}}X{{Y}_{3}}$, $\Delta H=-30\,kJ$, to be at equilibrium, the temperature will be       AIEEE  Solved  Paper-2007

A)
750 K

B)
1000 K

C)
1250 K

D)
500 K

• question_answer68) The electrophile, ${{E}^{\Theta }}$ attacks the benzene ring to generate the intermediate$\sigma$-complex. Of the following, which $\sigma$-complex is of lowest energy?       AIEEE  Solved  Paper-2007

A)

B)

C)

D)

• question_answer69) $\alpha$ - D - (+) - glucose and $\beta$ - D - (+) - glucose are       AIEEE  Solved  Paper-2007

A)
anomers

B)
enantiomers

C)
conformers

D)
epimers

• question_answer70) Four species are listed below:  $(i)\,\,\,HCO_{3}^{-}$ $(ii)\,\,\,{{H}_{3}}{{O}^{+}}$ $(iii)\,\,\,HSO_{4}^{-}$ $(iv)\,\,\,HS{{O}_{3}}F$
Which one of the following is the correct sequence of their acid strength?     AIEEE  Solved  Paper-2007

A)
(i) < (iii) < (ii) < (iv)

B)
(iii) < (i) < (iv) < (ii)

C)
(iv) < (ii) < (iii) < (i)

D)
(ii) < (iii) < (i) < (iv)

• question_answer71) This question contains Statement-1 and Statement -2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement -1: For a mass M kept at the canter of a cube of side 'a' the flux of gravitational field passing through its sides is $4\pi$ GM. and Statement -2: If the direction of a field due to a point source is radial and its dependence on the distance 'r' from the source is given as $\frac{1}{{{r}^{2}}}$, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.       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_answer72) Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on circular scale is 50. Further, it is found that screw gauge has a zero error of - 0.03mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3mm and the number of circular scale divisions in line with the main scale as 35. The diameter of wire is       AIEEE  Solved  Paper-2007

A)
3.67 mm

B)
3.38 mm

C)
3.32 mm

D)
3.73 mm

• question_answer73) An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume ${{V}_{1}}$ and contains ideal gas at pressure ${{P}_{1}}$ and temperature ${{T}_{1}}$. The other chamber has volume ${{V}_{2}}$ and contains ideal gas at pressure ${{P}_{2}}$ and temperature ${{T}_{2}}$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be       AIEEE  Solved  Paper-2007

A)
$\frac{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}{{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}}$

B)
$\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}$

C)
$\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}$

D)
$\frac{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}{{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}}$

• question_answer74) A student measures the focal length of a convex lens by putting an object pin at a distance 'u' from the lens and measuring the distance 'v' of the image pin. The graph between 'u' and 'v' plotted by the student should look like       AIEEE  Solved  Paper-2007

A)

B)

C)

D)

• question_answer75) Directions: Questions No. 75 are based on the following paragraph Consider a block of conducting material of resistivity '$\rho$' shown in the figure. Current 'I' enters at 'A' and leaves from 'D' . We apply superposition principal to find voltage '$\Delta V$' developed between 'B' and 'C' .  The calculation is done in the following steps: (i) Take current 'I' entering from 'A' and assume it to spread over a hemispherical surface in the block. (ii) Calculate field E(r) at distance 'r' from A by using Ohm's law $E=\rho j$, where 'j' is the current per unit area at 'r'. (iii) From the 'r' dependence of E(r), obtain the potential V(r) at 'r'. (iv) Repeat (i), (ii) and (iii) for current 'I' leaving 'D' and superpose results for 'A' and 'D'.        $\Delta V$ measured between B and C is     AIEEE  Solved  Paper-2007

A)
$\frac{\rho I}{2\pi a}-\frac{\rho I}{2\pi \left( a+b \right)}$

B)
$\frac{\rho I}{2\pi \left( a-b \right)}$

C)
$\frac{\rho I}{\pi a}-\frac{\rho I}{\pi \left( a+b \right)}$

D)
$\frac{\rho I}{a}-\frac{\rho I}{\left( a+b \right)}$

• question_answer76) Directions: Questions No. 76 are based on the following paragraph Consider a block of conducting material of resistivity '$\rho$' shown in the figure. Current 'I' enters at 'A' and leaves from 'D' . We apply superposition principal to find voltage '$\Delta V$' developed between 'B' and 'C' .  The calculation is done in the following steps: (i) Take current 'I' entering from 'A' and assume it to spread over a hemispherical surface in the block. (ii) Calculate field E(r) at distance 'r' from A by using Ohm's law $E=\rho j$, where 'j' is the current per unit area at 'r'. (iii) From the 'r' dependence of E(r), obtain the potential V(r) at 'r'. (iv) Repeat (i), (ii) and (iii) for current 'I' leaving 'D' and superpose results for 'A' and 'D'.        For current entering at A, the electric field at a distance 'r' from A is     AIEEE  Solved  Paper-2007

A)
$\frac{\rho I}{2\pi {{r}^{2}}}$

B)
$\frac{\rho I}{4\pi {{r}^{2}}}$

C)
$\frac{\rho I}{8\pi {{r}^{2}}}$

D)
$\frac{\rho I}{{{r}^{2}}}$

• question_answer77) Consider a uniform square plate of side 'a' and mass 'm' . The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is     AIEEE  Solved  Paper-2007

A)
$\frac{7}{12}m{{a}^{2}}$

B)
$\frac{2}{3}m{{a}^{2}}$

C)
$\frac{5}{6}m{{a}^{2}}$

D)
$\frac{1}{12}m{{a}^{2}}$

• question_answer78) An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by       AIEEE  Solved  Paper-2007

A)
a meter scale provided on the microscope

B)
a screw gauge provided on the microscope

C)
a vernier scale provided on the microscope

D)
a standard laboratory scale.

• question_answer79) A horizontal overhead power line is at a height of 4m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is $({{\mu }_{0}}=4\pi \times {{10}^{-7}}T\,m\,{{A}^{-1}})$       AIEEE  Solved  Paper-2007

A)
$5\times {{10}^{-6}}T$ southward

B)
$2.5\times {{10}^{-7}}T$ northward

C)
$2.5\times {{10}^{-7}}T$ southward

D)
$5\times {{10}^{-6}}T$ northward

• question_answer80) The speed of sound in oxygen $({{O}_{2}})$ at a certain temperature is 460 $m{{s}^{-1}}$. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal)       AIEEE  Solved  Paper-2007

A)
650 $m{{s}^{-1}}$

B)
330 $m{{s}^{-1}}$

C)
460 $m{{s}^{-1}}$

D)
500 $m{{s}^{-1}}$

• question_answer81) A 5V battery with internal resistance $2\,\Omega$ and a 2V battery with internal resistance $1\,\Omega$ are connected to a $10\,\,\Omega$ resistor as shown in the figure. The current in the $10\,\,\Omega$ resistor is                     AIEEE  Solved  Paper-2007

A)
0.03 A ${{P}_{2}}$ to ${{P}_{1}}$

B)
0.27 A ${{P}_{1}}$ to ${{P}_{2}}$

C)
0.27 A ${{P}_{2}}$ to ${{P}_{1}}$

D)
0.03 A ${{P}_{1}}$ to ${{P}_{2}}$

• question_answer82) A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 $m{{s}^{-1}}$. The magnitude of its momentum is recorded as       AIEEE  Solved  Paper-2007

A)
17.56 kg $m{{s}^{-1}}$

B)
17.57 kg $m{{s}^{-1}}$

C)
17. 6 kg $m{{s}^{-1}}$

D)
17.565 kg $m{{s}^{-1}}$

• question_answer83) A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found between P and Q. By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q, some resistance is seen on the multimeter. Which of the following is true for the transistor?       AIEEE  Solved  Paper-2007

A)
It is a pnp transistor with R as emitter

B)
It is an npn transistor with R as collector

C)
It is an npn transistor with R as base

D)
It is a pnp transistor with R as collector

• question_answer84) A block of mass 0.50 kg is moving with a speed of 2.00 $m{{s}^{-1}}$ on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is       AIEEE  Solved  Paper-2007

A)
0.67 J

B)
0.34 J

C)
0.16 J

D)
1.00 J

• question_answer85) A wave travelling along the x-axis is described by the equation $y\left( x,\,t \right)=0.005\cos \left( \alpha x-\beta t \right)$. If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then $\alpha$ and $\beta$ in appropriate units are       AIEEE  Solved  Paper-2007

A)
$\alpha =\frac{0.04}{\pi },\,\beta =\frac{1.0}{\pi }$

B)
$\alpha =12.50\pi ,\,\beta =\frac{\pi }{2.0}$

C)
$\alpha =25.00\pi ,\,\beta =\pi$

D)
$\alpha =\frac{0.08}{\pi },\,\beta =\frac{2.0}{\pi }$

• question_answer86) Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area A = 10 $c{{m}^{2}}$ and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is $({{\mu }_{0}}=4\pi \times {{10}^{-7}}T\,m\,{{A}^{-1}})$       AIEEE  Solved  Paper-2007

A)
$4.8\,\,\pi \times {{10}^{-5}}H$

B)
$2.4\,\,\pi \times {{10}^{-4}}H$

C)
$2.4\,\,\pi \times {{10}^{-5}}H$

D)
$4.8\,\,\pi \times {{10}^{-4}}H$

• question_answer87) A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?       AIEEE  Solved  Paper-2007

A)

B)

C)

D)

• question_answer88) A jar is filled with two non-mixing liquids 1 and 2 having densities ${{\rho }_{1}}$ and ${{\rho }_{2}}$, respectively. A solid ball, made of a material of density ${{\rho }_{3}}$, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ${{\rho }_{1}},{{\rho }_{2}}$ and${{\rho }_{3}}$?                     AIEEE  Solved  Paper-2007

A)
${{\rho }_{1}}<{{\rho }_{2}}<{{\rho }_{3}}$

B)
${{\rho }_{1}}<{{\rho }_{3}}<{{\rho }_{2}}$

C)
${{\rho }_{3}}<{{\rho }_{1}}<{{\rho }_{2}}$

D)
${{\rho }_{1}}>{{\rho }_{3}}>{{\rho }_{2}}$

• question_answer89) Suppose an electron is attracted towards the origin by a force $\frac{k}{r}$ where 'k' is a constant and 'r' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the ${{n}^{th}}$ orbital of the electron is found to be $'{{r}_{n}}'$ and the kinetic energy of the electron to be $'{{T}_{n}}'$. Then which of the following is true?       AIEEE  Solved  Paper-2007

A)
${{T}_{n}}\propto \frac{1}{n},\,{{r}_{n}}\propto n$

B)
${{T}_{n}}\propto \frac{1}{n},\,{{r}_{n}}\propto {{n}^{2}}$

C)
${{T}_{n}}\propto \frac{1}{{{n}^{2}}},\,{{r}_{n}}\propto {{n}^{2}}$

D)
${{T}_{n}}$ independent of $n,\,{{r}_{n}}\propto n$

• question_answer90) Directions: Questions No. 90 are based on the following paragraph. Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure).             Electrons accelerated by potential V are diffracted from a crystal. If $d=1\overset{o}{\mathop{A}}\,$ and$i={{30}^{o}}$, V should be about ($h=6.6\times {{10}^{-34}}Js$,${{m}_{e}}=9.1\times {{10}^{-31}}kg,\,e=1.6\times {{10}^{-19}}C$)     AIEEE  Solved  Paper-2007

A)
500 V

B)
1000 V

C)
2000 V

D)
50 V

• question_answer91) Directions: Questions No. 91 are based on the following paragraph. Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure).   If a strong diffraction peak is observed when electrons are incident at an angle 'I' from the normal to the crystal planes with distance 'd' between them (see figure), de Broglie wavelength ${{\lambda }_{dB}}$ of electrons can be calculated by the relationship (n is an integer)     AIEEE  Solved  Paper-2007

A)
$2\,d\sin i=n{{\lambda }_{dB}}$

B)
$d\cos i=n{{\lambda }_{dB}}$

C)
$d\sin i=n{{\lambda }_{dB}}$

D)
$2d\cos i=n{{\lambda }_{dB}}$

• question_answer92) Directions: Questions No. 92 are based on the following paragraph. Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure).                  In an experiment, electrons are made to pass through a narrow slit of width 'd' comparable to their de Broglie wavelength. They are detected on a screen at a distance 'D' from the slit (see figure). Which of the following graphs can be expected to represent the number of electrons 'N' detected as a function of the detector position 'y' (y = 0 corresponds to the middle of the slit)?       AIEEE  Solved  Paper-2007

A)

B)

C)

D)

• question_answer93) In the circuit shown, A and B represent two inputs and C represents the output. The circuit represents                     AIEEE  Solved  Paper-2007

A)
NAND gate

B)
OR gate

C)
NOR gate

D)
AND gate

• question_answer94) A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range $0\le r<\infty$, where r is the distance from the centre of the shell?       AIEEE  Solved  Paper-2007

A)

B)

C)

D)

• question_answer95) A body is at rest at $x=0$. At $t=0$, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through $x=0$ moving in the positive x direction with a constant speed. The position of the first body is given by ${{x}_{1}}(t)$after time t and that of the second body by ${{x}_{2}}(t)$ after the same time interval. Which of the following graphs correctly describes $({{x}_{1}}-{{x}_{2}})$ as a function of time t?       AIEEE  Solved  Paper-2007

A)

B)

C)

D)

• question_answer96) Relative permittivity and permeability of a material are ${{\varepsilon }_{r}}$ and ${{\mu }_{r}}$, respectively. Which of the following values of these quantifies are allowed for a diamagnetic material?       AIEEE  Solved  Paper-2007

A)
${{\varepsilon }_{r}}=0.5,\,{{\mu }_{r}}=0.5$

B)
${{\varepsilon }_{r}}=1.5,\,{{\mu }_{r}}=1.5$

C)
${{\varepsilon }_{r}}=0.5,\,{{\mu }_{r}}=1.5$

D)
${{\varepsilon }_{r}}=1.5,\,{{\mu }_{r}}=0.5$

• question_answer97) A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 $km\,{{s}^{-1}}$, the escape velocity from the surface of the planet would be

A)
110 $km\,{{s}^{-1}}$

B)
0.11 $km\,{{s}^{-1}}$

C)
1.1 $km\,{{s}^{-1}}$

D)
11 $km\,{{s}^{-1}}$

• question_answer98) A thin rod of length ?L? is lying along the x-axis with its ends at $x=0$ and $x=L$. Its linear density (mass/length) varies with x as $k{{\left( \frac{x}{L} \right)}^{n}}$, where ?n? can be zero or any positive number. If the position ${{x}_{CM}}$ of the centre of mass of the rod is plotted against ?n?, which of the following graphs best approximates the dependence of ${{x}_{CM}}$ on n?       AIEEE  Solved  Paper-2007

A)

B)

C)

D)

• question_answer99) The dimension of magnetic field in M, L, T and C (Coulomb) is given as       AIEEE  Solved  Paper-2007

A)
$M{{T}^{-1}}{{C}^{-1}}$

B)
$M{{T}^{-2}}{{C}^{-1}}$

C)
$ML{{T}^{-1}}{{C}^{-1}}$

D)
$M{{T}^{2}}{{C}^{-2}}$

• question_answer100) A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is 'd'. The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant ${{\kappa }_{1}}=3$ and thickness $\frac{d}{3}$ while the other one has dielectric constant ${{\kappa }_{2}}=6$ and thickness $\frac{2d}{3}$. Capacitance of the capacitor is now       AIEEE  Solved  Paper-2007

A)
40.5 pF

B)
20.25 pF

C)
1.8 pF

D)
45 pF

• question_answer101) An athlete in the olympic games covers a distance of 100m in 10s. His kinetic energy can be estimated to be in the range       AIEEE  Solved  Paper-2007

A)
20,000 J - 50,000 J

B)
2,000 J - 5,000 J

C)
200 J - 500 J

D)
$2\times {{10}^{5}}J-3\times {{10}^{5}}J$

• question_answer102) A spherical solid ball of volume V is made of a material of density ${{\rho }_{1}}$. It is falling through a liquid of density ${{\rho }_{2}}\left( {{\rho }_{2}}<{{\rho }_{1}} \right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e.${{F}_{viscous}}=-k{{v}^{2}}(k>0)$. The terminal speed of the ball is       AIEEE  Solved  Paper-2007

A)
$\sqrt{\frac{Vg{{\rho }_{1}}}{k}}$

B)
$\frac{Vg\left( {{\rho }_{1}}-{{\rho }_{2}} \right)}{k}$

C)
$\sqrt{\frac{Vg\left( {{\rho }_{1}}-{{\rho }_{2}} \right)}{k}}$

D)
$\frac{Vg{{\rho }_{1}}}{k}$

• question_answer103) Shown in the figure is a meter-bridge set up with null deflection in the galvanometer. The value of the unknown resistor R is                       AIEEE  Solved  Paper-2007

A)
110 $\Omega$

B)
55 $\Omega$

C)
13.75 $\Omega$

D)
220 $\Omega$

• question_answer104)   While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. Then       AIEEE  Solved  Paper-2007

A)
$54>x>36$

B)
$36>x>18$

C)
$18>x$

D)
$x>54$

• question_answer105) This question contains Statement-1 and Statement -2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement -1: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. and Statement -2: For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decreases with increasing Z.       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