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

AIEEE Solved Paper-2008 Total Questions - 35

1) 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
2) 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
3) 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
4) 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
5) 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
6) 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
7) 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
8) 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
9) 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
10) 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
11) 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
12) 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
13) 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
14) 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
15) 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
16) 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
17) 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
18) 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
19) 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
20) 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
21) 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
22) 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
23) 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
24) 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
25) 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
26) 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
27) 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
28) 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
29) 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
30) 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
31) 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
32) 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
33) 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
34) 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
35)   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