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

AIEEE Solved Paper-2008 Total Questions - 105

1) 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

View Answer
2) 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)

       \[\alpha =1,\,\,\beta =2\]

View Answer
3) 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)

                       \[\frac{\pi }{4}\]

View Answer
4) 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

View Answer
5) 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

View Answer
6) 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)

\[\left( y-2 \right)y{{'}^{2}}=25-{{\left( y-2 \right)}^{2}}\]

View Answer
7) 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

View Answer
8) 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

View Answer
9) 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

View Answer
10) 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)

                       \[6.7.{{\,}^{8}}{{C}_{4}}\]

View Answer
11) 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 \[J>2\]

View Answer
12) 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)

       \[\frac{1}{3}\]

View Answer
13) 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)

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

View Answer
14) 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)

       \[p\to \left( p\vee q \right)\]

View Answer
15) 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)

       \[\frac{3}{17}\]

View Answer
16) 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.

View Answer
17) 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.

View Answer

18) 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

Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.

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

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

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

View Answer

19) 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

Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.

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

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

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

View Answer

20) 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

Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.

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

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

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

View Answer

21) 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)

\[\frac{1}{i+1}\]

View Answer
22) 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

View Answer
23) 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)

       \[g\left( y \right)=4+\frac{y+3}{4}\]

View Answer
24) 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)

       \[\frac{7\sqrt{3}}{2}\left( \sqrt{3}+1 \right)m\]

View Answer
25) 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

View Answer
26) 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)

       \[\frac{1}{3}\]

View Answer
27) 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)

       \[\frac{2}{3}\]

View Answer
28) 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)

View Answer
29) 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)

       \[\left( -3,\,\,4 \right)\]

View Answer
30) 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

View Answer
31) 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

View Answer
32) 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 \[\sqrt{\frac{p}{3}}\]

View Answer
33) 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

View Answer
34) 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 \[x=1\]

View Answer
35) 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)

       \[y=x\ln x+{{x}^{2}}\]

View Answer
36) 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.

View Answer
37) 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)

\[C{{H}_{3}}C\equiv C-C{{H}_{3}}\]

View Answer
38) 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)

\[-S{{O}_{3}}H,-COOH,-CON{{H}_{2}},-CHO\]

View Answer
39) 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

View Answer
40) 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)

\[C{{H}_{3}}C{{H}_{2}}C\equiv CH\]

View Answer
41) 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

View Answer
42) 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.

View Answer
43) 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)

       \[RSiC{{l}_{3}}\]

View Answer

44) 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

- 850 kJ \[mo{{l}^{-1}}\]

+120 kJ \[mo{{l}^{-1}}\]

+152 kJ \[mo{{l}^{-1}}\]

- 610 kJ \[mo{{l}^{-1}}\]

View Answer

45) 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\[C{{S}_{2}}\].

View Answer
46) 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)

                       \[N{{O}^{+}},C_{2}^{2-},C{{N}^{-}},{{N}_{2}}\]

View Answer
47) 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

View Answer
48)   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)

       \[6.56\times {{10}^{5}}J\,mo{{l}^{-1}}\]

View Answer
49) 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)

       \[{{(C{{H}_{3}})}_{3}}CCl\]

View Answer
50) 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

View Answer
51) 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)

\[C{{H}_{3}}COC{{H}_{3}}\]

View Answer
52) 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 \[C{{N}^{+}}\]

View Answer
53) 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

View Answer
54) 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)

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

View Answer
55) 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

View Answer
56) 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.

View Answer
57) 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)

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

View Answer
58) 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

View Answer
59) 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.

View Answer
60) 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.

View Answer
61) 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)

       \[{{X}_{2}}{{Y}_{3}}\]

View Answer
62) 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)

View Answer
63) 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

View Answer
64) 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)

\[C{{H}_{3}}CHO\]

View Answer
65) The absolute configuration of                 is AIEEE Solved Paper-2007

A)

R, S

B)

       S, R

C)

S, S

D)

       R, R

View Answer

66) 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

\[{{K}_{3}}={{K}_{1}}{{K}_{2}}\]

\[{{K}_{3}}\,.\,\,K_{2}^{3}=K_{1}^{2}\]

\[{{K}_{1}}\sqrt{{{K}_{2}}}={{K}_{3}}\]

\[{{K}_{2}}{{K}_{3}}={{K}_{1}}\]

View Answer

67) 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

View Answer
68) 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)

View Answer
69) \[\alpha \] - D - (+) - glucose and \[\beta \] - D - (+) - glucose are AIEEE Solved Paper-2007

A)

anomers

B)

enantiomers

C)

conformers

D)

epimers

View Answer
70) 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)

View Answer
71) 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

View Answer
72) 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

View Answer
73) 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)

        \[\frac{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}{{{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}}\]

View Answer
74) 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)

View Answer
75) 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)

\[\frac{\rho I}{a}-\frac{\rho I}{\left( a+b \right)}\]

View Answer
76) 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)

\[\frac{\rho I}{{{r}^{2}}}\]

View Answer
77) 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)

\[\frac{1}{12}m{{a}^{2}}\]

View Answer
78) 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.

View Answer
79) 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

View Answer
80) 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 \[m{{s}^{-1}}\]

View Answer
81) 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 \[{{P}_{2}}\]

View Answer
82) 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 \[m{{s}^{-1}}\]

View Answer
83) 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

View Answer
84) 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

View Answer
85) 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)

                       \[\alpha =\frac{0.08}{\pi },\,\beta =\frac{2.0}{\pi }\]

View Answer
86) 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)

       \[4.8\,\,\pi \times {{10}^{-4}}H\]

View Answer
87) 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)



View Answer
88) 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)

       \[{{\rho }_{1}}>{{\rho }_{3}}>{{\rho }_{2}}\]

View Answer
89) 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 \[n,\,{{r}_{n}}\propto n\]

View Answer
90) 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

View Answer
91) 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)

\[2d\cos i=n{{\lambda }_{dB}}\]

View Answer
92) 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)

View Answer
93) 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

View Answer
94) 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)

View Answer
95) 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)



View Answer
96) 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)

       \[{{\varepsilon }_{r}}=1.5,\,{{\mu }_{r}}=0.5\]

View Answer
97) 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 \[km\,{{s}^{-1}}\]

View Answer
98) 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)

View Answer
99) 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)

       \[M{{T}^{2}}{{C}^{-2}}\]

View Answer
100) 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

View Answer
101) 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)

\[2\times {{10}^{5}}J-3\times {{10}^{5}}J\]

View Answer
102) 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)

                       \[\frac{Vg{{\rho }_{1}}}{k}\]

View Answer
103) 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 \[\Omega \]

View Answer
104)   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)

       \[x>54\]

View Answer
105) 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

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