Aieee 2007 Solved Paper 3k685g
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AIEEE 2007 Solved Paper Mathematics Q. 1. In a geometric progression consisting of positive , each term equals the sum of the next two . Then the common ratio of this progression equals
a.
b. c.
d. Sol: Let geometric progression is a, ar, ar2,………….;(a, r > 0)
Correct choice: (4)
Q. 2. If sin
a. b. c. d.
1 3 4 5
Sol: Correct choice: (2) Q. 3. In the binomial expansion of
a. www.cbseguess.com
then a value of x is.
b.
c.
d.
Sol: orrect choice: (4) Q. 4. The set S : = {1, 2, 3, ……, 12} is to be partitioned into three sets A, B, C of equal size. Thus,
The number of ways to partition S is
a.
b.
c.
d. Sol:
12 different objects are to be divided into 3 groups of equal size, which are named as set A, B and
C.
Q. 5. The largest interval lying in
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Correct choice: (3)
for which the function
a.
b.
c.
d. a. Sol:
Correct choice: (4) Q. 6. A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are
a. b. c. d.
12 kg and 13 kg 5 kg and 5 kg 5kg and 12 kg 5 kg and 13 kg
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Sol: So tension in the strings are 5 kg and 12 kg. Correct choice: (3) Q. 7. A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is
a.
b.
c.
d.
Sol: Probability of getting sum of nine in a single throw
Probability of getting sum nine exactly two times out of three draws
.
orrect choice: (4) Q. 8. Consider a family of circles which are ing through the point (- 1, 1) and are tangent to x-axis. If (h, k), are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval
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a.
b.
c.
d. Sol: Centre of circle is (h, k) and x-axis is tangent. Also circle es through
Radius of the family of circle
Correct choice: (2) Q. 9. Let L be the line of intersection of the planes 2x + 3y +z = 1 and x + 3y +2z = 2. If L makes an angle positive x-axis, then
a.
b. c. 1
d. Sol:
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equals
with the
Correct choice: (1) Q. 10. The differential equation of all circles ing through the origin and having their centres on the x-axis is
a.
b.
c.
d. Sol: Equation of family of circles ing through origin and having their centres on x-axis is
Correct choice: (3) Q. 11. If p and q are positive real numbers such that then
a. 2 b. c. d.
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the maximum value of (p + q) is
Sol: Correct choice: (4) Q. 12. A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that subtends an angle of 600 at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 300. The height of the tower is
a. b.
c. d.
Sol:
Correct choice: (3)
Q. 13. The sum of the series
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a.
b. c. 0 d. Sol:
Correct choice: (2) Q. 14. The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a
a. b. c. d.
ellipse parabola circle hyperbola
Sol:
Correct choice: (1, 4)
Q. 15.
a. b. c. d.
4 10 6 0
Sol:
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Correct choice: (3) Q. 16. The resultant of two forces P N and 3 N is a force of 7 N. If the direction of 3 N force were reversed, the resultant would be
a. b. c. d.
. The value of P is
5N 6N 3N 4N
Sol:
Correct choice: (1) Q. 17. Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
a. b. c. d.
0.06 0.14 0.2 0.7
Sol:
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No choice is correct
Q. 18.
a. b. c. d.
divisible by neither x nor y divisible by both x and y divisible by x but not y divisible by y but not x
Sol:
Correct choice: (2)
Q. 19. For the hyperbola
a. b. c. d.
Eccentricity Directrix Abscissae of vertices Abscissae of foci
Sol:
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which of the following remains constant when α varies?
Correct choice: (4)
Q. 20. If a line makes an angle of with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is
a.
b.
c.
d. Sol:
Correct choice: (4) Q. 21. A value of C for which the conclusion of Mean Value Theorem holds for the function interval [1, 3] is
a.
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on the
b. c. d.
Sol: Correct choice: (1) Q. 22. The function
a.
b.
c.
d. Sol:
Correct choice: (2)
.
a. b. 1 www.cbseguess.com
is an increasing function in
c. d. 5 Sol:
Correct choice: (3)
Q. 24.
a. b. c. d. Sol:
Correct choice: (2) Q. 25. If
are unit vectors and θ is the acute angle between them, then
a. Exactly two values of b. More than two values of c. No value of d. Exactly one value of www.cbseguess.com
is a unit vector for
Sol:
Correct choice: (4) Q. 26. A particle just clears a wall of height b at a distance a and strikes the ground at a distance c from the point of projection. The angle of projection is
a. b.
c.
d. Sol:
Correct choice: (3) Q. 27. The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is
a. b. c. d.
40 20 80 60
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Sol: Let there are x boys and y girls in the class. So, total marks are 52 x + 42 y and according to second condition total marks = (x + y) 50 Now, So percentage of boys is 80. Correct choice: (3) Q. 28. The equation of a tangent to the parabola tangent to the parabola is perpendicular to the given tangent is
a. b. c. d.
The point on this line from which the other
(- 1, 1) (0, 2) (2, 4) (- 2, 0)
Sol: Point of intersection of two perpendicular tangents to the parabola lies on directrix of the parabola. Equation of directrix is x + 2 = 0 So point is (- 2, 0) Correct choice: (4) Q.29. If (2, 3, 5) is one end of a diameter of the sphere coordinates of the other end of the diameter are
a. b. c. d.
(4, 9, - 3) (4, - 3, 3) (4, 3, 5) (4, 3, - 3)
Sol: Centre (3, 6, 1)
Let other end is Correct choice: (1)
Q. 30.
a. b. c. d.
0 1 –4 –2
Sol:
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then the
Correct choice: (4) Q. 31. Let A (h, k), B (1, 1) and C (2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which ‘k’ can take is given by
a. b. c. d.
Sol: Correct choice: (3) Q. 32. angle PQR is
a.
b.
c. d. Sol:
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be three points. The equation of the bisector of the
Correct choice: (1) Q. 33. If one of the lines of then m is
a. b. – 2 c. 1 d. 2 Sol:
Correct choice: (3)
Q. 34.
a. b. 0 c. 1 d. 2 Sol:
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is a bisector of the angle between the lines xy = 0,
Correct choice: (1)
Q. 35. is true?
Then which of the following
a. b. f (x) is not differentiable at x = 1. c. f (x) is differentiable everywhere d. f (x) is not differentiable at x = 0. Sol: Correct choice: (3)
Q. 36. defining f (0) as
a. b. c. d.
2 –1 0 1
Sol:
Correct choice: (4)
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can be made continuous at x = 0 by
37.
a.
b.
c.
d. Sol:
Correct choice: (1)
Q. 38. The area enclosed between the curves
a. b. 1
c.
d.
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Sol:
Correct choice: (3) Q. 39. If the difference between the roots of the equation values of a is
then the set of possible
a. (- 3, 3) b. c. d. Sol:
Correct choice: (1)
AIEEE 2007 Solved Paper Physics Q. 1. The displacement of an object attached to a spring and executing simple harmonic motion is given by
metres. The time at which the maximum speed first occurs is
a. 0.5 s b. 0.75 s c. 0.125 s www.cbseguess.com
d. 0.25 s
Sol: Correct choice: (1) Q. 2. In an a.c. circuit the voltage applied is
is
. The resulting current in the circuit
. The power consumption in the circuit is given by
a. b. P = zero
c. d. Sol.
Correct choice: (2)
Q. 3. An electric charge situated at
a. b. c. d.
is placed at the origin (0, 0) of X – Y co-ordinate system. Two points A and B are
and (2, 0) respectively. The potential difference between the points A and B will be
9 volt zero 2 volt 4.5 volt
Sol: Correct choice: (2) www.cbseguess.com
Q. 4. A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be
a. 1 b. 2
c.
d. Sol: Work done by battery
Energy stored in capacitor
Correct choice: (4) Q. 5. An ideal coil of 10 H is connected in series with a resistance of connection is made, the current flowing in amperes in the circuit is
and a battery of 5V. 2 seconds after the
a. (1 - e) b. e c. d.
Sol: Correct choice: (4) Q. 6. A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its cross
section. The ratio of the magnetic field at
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and 2a is
b. 4 c. 1
d.
Sol: Correct choice: (3) Q. 7. A current I flows along the length of an infinitely long, straight, thin walled pipe. Then
a. b. c. d.
the magnetic field is zero only on the axis of the pipe the magnetic field is different at different points inside the pipe the magnetic field at any point inside the pipe is zero the magnetic field at all points inside the pipe is the same, but not zer
Sol: Magnetic field inside the infinitely long pipe is zero at all points. Correct choice: (3)
Q. 8. If is the mass of an oxygen isotope respectively, the nuclear binding energy of the isotope is
, are the masses of a proton and a neutron
a. b. c. d. Sol: Nuclear binding energy Correct choice: (2) Q. 9. In gamma ray emission from a nucleus
a. b. c. d.
both the neutron number and the proton number change there is no change in the proton number and the neutron number only the neutron number changes only the proton number changes
Sol: Gamma ray is electromagnetic radiation which does not involve any change in proton number or neutron number Correct choice: (2)
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Q. 10. If in p-n junction diode, a square input signal of 10 V is applied as shown. Then the output signal across will be
a.
b.
c.
d.
Sol: Diode is forward biased in first half cycle and amplitude of signal is www.cbseguess.com
Correct choice: (4) Q. 11. Photon of frequency v has a momentum associated with it. If c is the velocity of light, the momentum is
a. v / c b. hvc c. d. h v / c
Sol:
Correct choice: (4)
Q. 12. The velocity of a particle is time ( t = 1) is
. If its position is x = 0 at t = 0, then its displacement after unit
a. b. c. d.
Sol:
, Correct choice: (2)
Q. 13. For the given uniform square lamina ABCD, whose centre is O,
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a. b. c. d.
Sol: Correct choice: (3) Q. 14. A point mass oscillates along the x-axis according to the law of the particle is written as ,
a. b. c. d.
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. If the acceleration
Sol: Correct choice: (4) Q. 15. Charges are placed on the vertices of a square as shown. Let be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then
a.
remains unchanged, V changes
b. Both
and V change
c.
and V remain unchanged
d.
changes , V remain unchanged
Sol: In initial case, is along (1) whereas in final case is along (2). Potential at centre remains same.
Correct choice: (4) Q. 16. The half-life period of a radio-active element X is same as the mean life time of another radio-active element Y. Initially they have the same number of atoms. Then
a. b. c. d.
X will decay faster than Y Y will decay faster than X X and Y have same decay rate initially X and Y decay at same rate always
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Sol:
, Y will decay faster than X
Correct choice: (2) Q. 17. A Carnot engine, having an efficiency of as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is
a. b. c. d.
99 J 90 J 1J 100 J
Sol:
If same carnot engine is used as refrigerator then Correct choice: (2) Q. 18. Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate?
a. the number of free conduction electrons is significant in C but small in Si and Ge. b. the number of free conduction electrons is negligibly small in all the three. c. the number of free electrons for conduction is significant in all the three. www.cbseguess.com
d. the number of free electrons for conduction is significant only in Si and Ge but small in C. Sol: Correct choice: (4) Q. 19. A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields with a velocity
perpendicular to both
and
and
, and comes out without any change in magnitude or direction of
.
a. b. c. d.
Sol:
Magnitude of
and direction of
direction perpendicular to plane of
and
should be such that net force on charge particle be zero. and coming out of plane. So direction of
should be in the
is in the direction of
Correct choice: (1) Q. 20. The potential at a point x (measured in by
) due to some charges situated on the x-axis is given
. The electric field is
a. 5/3
and in the –ve x direction
b. 5/3
and in the +ve x direction
c. 10/9
and in the –ve x direction
d. 10/9
and in the +ve x direction
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given by
Sol: Correct choice: (4) Q. 21. Which of the following transitions in hydrogen atoms emit photons of highest frequency?
a. b. c. d.
n = 2 to n = 6 n = 6 to n = 2 n = 2 to n = 1 n = 1 to n = 2
Sol:
So photons of highest frequency will be emitted for n = 2 to n = 1 Correct choice: (3) Q. 22. A block of mass m is connected to another block of mass M by a spring (massless) of spring constant k. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force F starts acting on the block of mass M to pull it. Find the force on the block of mass m
a.
b.
c.
d. Sol: In the question the state of spring is not mentioned. We are assuming acceleration of both blocks to be same.
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Correct choice: (3) Q. 23. Two lenses of power –15 D and +5D are in with each other. The focal length of the combination is
a. b. c. d.
– 20 cm – 10 cm + 20 cm + 10 cm
Sol: Correct choice: (2) Q. 24. One end of a thermally insulated rod is kept at a temperature two sections of lengths and interface of the sections is
and thermal conductivities
and
and the other at
. The rod is composed of
respectively. The temperature at the
a. b. c. d.
Sol: Correct choice: (3) Q. 25. A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of
a. 1000 b. 10000 www.cbseguess.com
c. 10 d. 100
Sol: Correct choice: (4) Q. 26. If respectively, then
denote the specific heats of nitrogen per unit mass at constant pressure and constant volume
a. b. c. d. Sol:
are molar specific heat capacitates. For unit mass if specific heat
capacities are
Correct choice: (1)
Q. 27. A charged particle moves through a magnetic field perpendicular to its direction. Then
a. b. c. d.
the momentum changes but the kinetic energy is constant both momentum and kinetic energy of the particle are not constant both, momentum and kinetic energy of the particle are constant kinetic energy changes but the momentum is constant
Sol: Magnetic force can not do any work, so kinetic energy remains constant. Since initial velocity is perpendicular to magnetic field, hence momentum will change. Correct choice: (1) Q. 28. Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current and COD carries a current . The magnetic field on a point lying at a distance d from O, in a direction perpendicular to the plane of the wires AOB and COD, will be given by
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a.
b.
c.
d.
Sol: Magnetic field due to AB and CD are
direction
respectively and are in mutually perpendicular
.
Correct choice: (2) Q. 29. The resistance of a wire is 5 ohm at be
a. b. c. d.
2 ohm 1 ohm 4 ohm 3 ohm
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and 6 ohm at
. The resistance of the wire at
will
Sol: Correct choice: (3) Q. 30. A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is
a. b. c. d. zero Sol: No change in the energy of the system. Hence, not net work done by the system is zero. Correct choice: (4) Q. 31. If are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan’s oil drop experiment could be performed on the two surfaces, one will find the
ratio
a. 1 b. 0 c. d. Sol: Correct choice: (1) Q. 32. A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of
the discs coincide. The centre of mass of the new disc is
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from the centre of the bigger disc. The value of is
b.
c.
d.
Sol: If mass of circular disc is M, then mass of removed disc is distance x from centre, then
[In question x is given out to be be
. Let centre of mass of remaining disc is at a
. If we take that, then no choice is correct we believe in place of
, it should
] Correct choice: (1)
Q. 33. A round uniform body of radius R, mass M and moment of inertia I rolls down (without slipping) an inclined plane making an angle
a.
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with the horizontal. Then its acceleration is
c.
d.
Sol:
Correct choice: (1) Q. 34. Angular momentum of the particle rotating with a central force is constant due to
a. b. c. d.
constant force constant linear momentum zero torque constant torque
Sol: Central force is directed towards a point, therefore torque of the central force is zero. Correct choice: (3) Q. 35. s A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000 N/m. The spring compresses by
a. b. c. d.
5.5 cm 2.5 cm 11.0 cm 8.5 cm
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Sol: Correct choice: (1) Q. 36. A particle is projected at
a. b. c. d.
to the horizontal with a kinetic energy K. The kinetic energy at the highest point is
K Zero K/4 K/2
Sol: Correct choice: (3)
Q. 37. In Young’s double slit experiment the intensity at a point where the path difference is
wavelength of the light used) is I. If
a.
b.
c.
d.
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denotes the maximum intensity,
is equal to
being the
Sol: Let intensity of light from individual slits is
I’ Correct choice: (4) Q. 38. Two springs, of force constants k1 and k2, are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both k1 and k2 are made four times their original values, the frequency of oscillation becomes
a. b. c. d.
f/2 f/4 4f 2f
Sol:
Correct choice: (4)
Q. 39. When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path ibf Q = 36 cal. W along the path ibf is
a. b. c. d.
6 cal 16 cal 66 cal 14 cal
Sol:
Correct choice: (1)
Q. 40. A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is
a.
b. www.cbseguess.com
c. d.
Sol: Correct choice: (1)
AIEEE 2007 Solved Paper Chemistry
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Q. 1. The energies of activation for forward and reverse reactions for respectively. The presence of a catalyst lowers the activation energy of both (forward and reverse) reactions by 100 kJ mol–1. The enthalpy change of the in the presence of catalyst will be (in kJ mol–1)
reaction
a. b. c. d.
300 120 280 20
Sol: Enthalpy change of a reaction is not affected by the presence of a catalyst as it lowers the activation energy of the forward and reverse reaction by the same amount . None of the options given is correct but option (4) can be treated as correct in of magnitude. Correct choice: (4)
Q. 2. The cell,
, was allowed to be completely discharged at
298 K. The relative concentration of ZnocellE
a. antilog (24.08) b. 37.3 c. d.
Sol: Correct choice: (3) Q. 3. The pKa of a weak acid (HA) is 4.5. The pOH of an aqueous buffered solution of HA in which 50% of the acid is ionized is
a. 4.5 b. 2.5 c. 9.5 www.cbseguess.com
d. 7.0 Sol: If the given weak acid is 50% ionized, then its conjugate base will have the concentration same as that of weak acid.
Correct choice: (3) Q. 4. Consider the reaction, When concentration of B alone was doubled, the half−life did not change. When the concentration of A alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is
a. b. no unit c. d. Sol: The reaction would be first order with respect to A and first order with respect to B. The overall order of the reaction is 2.
Correct choice: (1) Q. 5.. Identify the incorrect statement among the following:
a. b. c. d.
d−Block elements show irregular and erratic chemical properties among themselves . La and Lu have partially filled d orbitals and no other partially filled orbitals. The chemistry of various lanthanoids is very similar. 4f and 5f orbitals are equally shielded.
Sol: 4f orbital electrons are shielded more than 5f orbital electrons. Correct choice: (4) Q. 6. Which one of the following has a square planar geometry?
a. b. www.cbseguess.com
c. d. (Atomic numbers: Co = 27, Ni = 28, Fe = 26, Pt = 78) Sol: Platinum(+II) only forms square planar complex. Correct choice: (4) Q. 7. Which of the following molecules is expected to rotate the plane of plane − polarised light?
a.
b.
c.
d.
Sol: Compound (1) does not have any plane of symmetry as well as centre of symmetry so it rotates the plane of plane−polarised light. Compound (2), (3) and (4) have a plane of symmetry, so they all are optically inactive. Correct choice: (1) Q. 8. The secondary structure of protein refers to:
a. helical backbone. b. hydrophobic interactions. c. sequence of amino acids. d. fixed configuration of the polypeptide backbone. Sol: Secondary structure of a protein refers to the fixed configuration of the polypeptide skeleton. structure results only when intramolecular H−bonds are formed between
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helix
of one amino acid residue and N−H
of fourth amino acid residue in polypeptide chain. formed between
pleated structure is formed when intermolecular H−bond is
of one polypeptide chain with N−H of the other chain. Correct choice: (4)
Q. 9. Which of the following reactions will yield 2,2−dibromopropane?
a. b. c. d.
Sol: Correct choice: (1) Q. 10. In the chemical reaction, (A) and (B) are respectively:
the compounds
a. b. c. d. Sol: choice: (4)
This is carbylamine reaction. Correct
Q. 11. The reaction of toluene with Cl2 in presence of FeCl3 gives predominantly:
a. b. c. d.
benzoyl chloride benzyl chloride o− and p−chlorotoluene m−chlorotoluene
Sol:
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The reaction proceeds by electrophilic substitution mechanism. Correct choice: (3 ) Q. 12. Presence of a nitro group in a benzene ring
a. b. c. d.
activates the ring towards electrophilic substitution. renders the ring basic. deactivates the ring towards nucleophilic substitution. deactivates the ring towards electrophilic substitution.
Sol: −NO2 group in benzene ring shows −I and −R effect, which deactivates the ring towards electrophilic substitution but activates it towards nucleophilic substitution. Correct choice: (4) Q. 13. In which of the following ionization processes, the bond order has increased and the magnetic behaviour has changed?
a. b. c. d. Sol:
Correct choice: (2) Q. 14. The actinoids exhibit more number of oxidation states in general than the lanthanoids. This is because
a. b. c. d.
the 5f orbitals are more buried than the 4f orbitals. there is a similarity between 4f and 5f orbitals in their angular part of the wave function. the actinoids are more reactive than the lanthanoids. the 5f orbitals extend further from the nucleus than the 4f orbitals.
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Sol: The actinoids exhibit more number of oxidation states than lanthanoids because they can loose more number of electrons as the 5f orbital electrons are held less strongly than the 4f orbital electrons. Correct choice: (4) Q. 15. Equal masses of methane and oxygen are mixed in an empty container at pressure exerted by oxygen is
. The fraction of the total
a.
b.
c.
d. Sol: Let the mass of methane and oxygen be x g each.
Correct choice: (3) Q. 16. . A 5.25% solution of a substance is isotonic with a 1.5% solution of urea (molar mass = 60 g mol–1) in the same solvent. If the densities of both the solutions are assumed to be equal to 1.0 g cm–3, molar mass of the substance will be
a. b. c. d.
90.0 g mol–1 115.0 g mol–1 105.0 g mol–1 210.0 g mol–1
Sol: Since the two solutions are isotonic, their concentrations will be
same.
Correct choice: (4)
Q. 17. Assuming that water vapour is an ideal gas, the internal energy change when 1 mol of water is vapourised at 1 bar pressure and 1000C,(Given: Molar enthalpy of vapourisation of water at 1 bar and 373 K = 41 kJ mol−1 and R = 8.3 J mol−1K−1) will be:
a. 4.100 kJ mol−1 www.cbseguess.com
b. 3.7904 kJ mol−1 c. 37.904 kJ mol−1 d. 41.00 kJ mol−1 Sol:
Correct choice: (3) Q. 18. In a saturated solution of the sparingly soluble strong electrolyte AgIO3(Molecular mass = 283) the equilibrium which sets in is If the solubility product constant K spof AgIO3 at a given temperature is, what is the mass of AgIO3contained in 100 ml of its saturated solution?
a. b. c. d.
28.3 × 10–2 g 2.83 × 10–3 g 1.0 × 10–7 g 1.0 × 10–4 g
Sol:
If ‘s’ is the solubility of AglO3 in a saturated solution, then
Correct choice: (2) Q. 19. A radioactive element gets spilled over the floor of a room. Its half–life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?
a. b. c. d.
1000 days 300 days 10 days 100 days
Sol: Let the permissible activity limit of the radioactive element be x, then the initial activity would be 10 x.
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Correct choice: (4) Q. 20. Which one of the following conformations of cyclohexane is chiral?
a. b. c. d.
Twist boat Rigid Chair Boat
Sol: Twist boat conformation of cyclohexane is chiral because it has neither plane of symmetry nor centre of symmetry. Correct choice: (1) Q. 21. Which of the following is the correct order of decreasing SN2 reactivity?
a. b. c. d.
RCH2X > R3CX > R2CHX RCH2X > R2CHX > R3CX R3CX > R2CHX > RCH2X R2CHX > R3CX > RCH2X (X = a halogen)
Sol: The reactivity of a compound towards SN2 reaction decreases as the crowding at the C–atom containing leaving group increases. Correct choice: (2) Q. 22. In a following sequence of reactions,
a. b. c. d.
butanal n–butyl alcohol n–propyl alcohol propanal
Sol:
Correct choice: (3) Q. 23. Which of the following sets of quantum numbers represents the highest energy of an atom?
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Sol: An orbital having higher value of (n + l) has higher energy. Out of the four options given, the value of (n + l) is highest if n = 3 and l = 2. Correct choice: (2) Q. 24. Which of the following hydrogen bonds is the strongest?
a. b. c. d.
O–H.…N F–H.…F O–H.…O O–H.…F
Sol: Greater the difference in electronegativity of H–atom and the other electronegative atom with which H is covalently bonded, stronger is the hydrogen bond. Highest electronegativity difference exists in HF molecule. Correct choice: (2) Q. 25. In the reaction,
a. b. c. d.
6 L HCl(aq) is consumed for every 3 L H2(g) produced. 33.6 L H2(g) is produced regardless of temperature and pressure for every mole Al that reacts. 67.2 L H2(g) at STP is produced for every mole Al that reacts. 11.2 L H2(g) at STP is produced for every mole HCl(aq) consumed.
Sol: Given that, For each mole of Al reacted, 1.5 mol of H2 is formed; and for each mole of HCl(aq) consumed, 0.5 mol or 11.2 L of H2 at STP is formed. Correct choice: (4) Q. 26. Regular use of which of the following fertilizers increases the acidity of soil?
a. b. c. d.
Potassium nitrate Urea Superphosphate of lime Ammonium sulphate
Sol: Ammonium sulphate is a salt of weak base and strong acid. Its aqueous solution is acidic due to hydrolysis of ammonium ion. It will increase the acidity of soil. Correct choice: (4) Q. 27. Identify the correct statement regarding a spontaneous process:
a. b. c. d.
For a spontaneous process in an isolated system, the change in entropy is positive. Endothermic processes are never spontaneous. Exothermic processes are always spontaneous. Lowering of energy in the reaction process is the only criterion for spontaneity.
Sol: For a process to be spontaneous in an isolated system, the change in entropy is positive. Correct choice: (1) www.cbseguess.com
Q. 28. Which of the following nuclear reactions will generate an isotope?
a. neutron particle emission b. positron emission c.
particle emission
d.
particle emission
Sol: In a nuclear reaction, an isotope cannot be generated by the emission of positron , particle or particle because it will change the atomic number of the parent nuclei. An isotope can be generated when the nuclei of an element are bombarded with slow neutrons e.g., particle emission is a hypothetical process. Correct choice: (1)
. Formation of isotope by neutron
Q. 29. The equivalent conductances of two strong electrolytes at infinite dilution in H2O (where ions move freely through a solution) at 250C are given below: What additional information/quantity one needs to calculate of an aqueous solution of acetic acid?
a. b. c. (C) The limiting equivalent conducted of d. Sol:
Correct choice: (1) Q. 30. Which one of the following is the strongest base in aqueous solution?
a. b. c. d.
Trimethylamine Aniline Dimethylamine Methylamine
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Sol: Aliphatic amines are more basic than aromatic amines and among aliphatic amines, the order of basicity in aqueous solution is
Correct choice: (3)
Q. 31. The compound formed as a result of oxidation of ethyl benzene by KMnO4 is
a. b. c. d.
benzophenone acetophenone benzoic acid benzyl alcohol
Sol:
Correct choice: (3)
Q. 32. The IUPAC name of
a. b. c. d.
is
1,1–diethyl–2,2–dimethylpentane 4,4–dimethyl–5,5–diethylpentane 5,5–diethyl–4,4–dimethylpentane 3–ethyl–4,4–dimethylheptane
Sol: IUPAC name of the given compound is: 3–ethyl–4,4–dimethyl heptane. Correct choice: (4) Q. 33. Which of the following species exhibits the diamagnetic behaviour?
a. b. c. d. NO Sol: , and NO are paramagnetic due to the presence of 2, 1 and 1 unpaired electrons respectively. have no unpaired electron and is diamagnetic in nature. Correct choice: (1) Q. 34. The stability of dihalides of Si, Ge, Sn and Pb increases steadily in the sequence
a. GeX2 << SiX2 << SnX2 << PbX2 b. SiX2 << GeX2 << PbX2 << SnX2 c. SiX2 << GeX2 << SnX2 << PbX2 www.cbseguess.com
will
d. PbX2 << SnX2 << GeX2 << SiX2 Sol: The stability of the lower oxidation state increases down the group in group 14. SiX2 << GeX2 << SnX2 << PbX2 Correct choice: (3) Q. 35. Identify the incorrect statement among the following:
a. b. c. d.
Ozone reacts with SO2 to give SO3. Silicon reacts with NaOH(aq) in the presence of air to give Na2SiO3 and H2O. Cl2 reacts with excess of NH3 to give N2 and HCl. Br2 reacts with hot and strong NaOH solution to give NaBr, NaBrO4 and H2O.
Sol: O3 + SO2
SO3 + O2
Si + 2NaOH + O2 3Cl2 + 2NH3
Na2SiO3 + H2O
N2 + 6HCl
3Br2 + 6NaOH
5NaBr + NaBrO3 + 3H2O Correct choice: (4)
Q. 36. The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizing power of the cationic species, K+, Ca2+, Mg2+, Be2+?
a. b. c. d. e. Sol: Greater the charge/size ratio of a cation, size but charge of all those ions is same. Thus, polarising power of these ions is in the order: K+ has a 1 unit charge less than that of Ca2+ and its size 2+ + is larger than that of Ca , thus polarising power of K is less than that of Ca2+. So, the correct order is Correct choice: (3) Q. 37. The density (in g mL–1) of a 3.60 M sulphuric acid solution that is 29% H2SO4 (Molar mass = 98 g mol–1) by mass will be
a. b. c. d.
.64 1.88 1.22 1.45
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Sol: Let the mass of solution be x g.
Correct choice: (3) Q. 38. The first and second dissociation constants of an acid H2A are 1.0 × 10–5 and 5.0 × 10–10respectively. The overall dissociation constant of the acid will be
a. b. c. d.
5.0 × 10–5 5.0 × 1015 5.0 × 10–15 0.2 × 105
Sol: Correct choice: (3) Q. 39. A mixture of ethyl alcohol and propyl alcohol as vapour pressure of 290 mm at 300 K. The vapour pressure of propyl alcohol is 200 mm. If the mole fraction of ethyl alcohol is 0.6, its vapour pressure (in mm) at the same temperature will be
a. b. c. d.
350 300 700 360
Sol:
Correct choice: (1) Q. 40. In conversion of lime–stone to lime, The values of that and be spontaneous is
and
are +179.1 kJ mol–1 and 160.2 J/K respectively at 298 K and 1 bar. Assuming
do not change with temperature, temperature above which conversion of limestone to lime will
a. 1008 K b. 1200 K www.cbseguess.com
c. 845 K d. 1118 K Sol: when
The decomposition of CaCO3 to CaO and CO2 would become spontaneous would be –ve. But limiting condition can be arrived at when
zero. Correct choice: (4)
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would become
a.
b. c.
d. Sol: Let geometric progression is a, ar, ar2,………….;(a, r > 0)
Correct choice: (4)
Q. 2. If sin
a. b. c. d.
1 3 4 5
Sol: Correct choice: (2) Q. 3. In the binomial expansion of
a. www.cbseguess.com
then a value of x is.
b.
c.
d.
Sol: orrect choice: (4) Q. 4. The set S : = {1, 2, 3, ……, 12} is to be partitioned into three sets A, B, C of equal size. Thus,
The number of ways to partition S is
a.
b.
c.
d. Sol:
12 different objects are to be divided into 3 groups of equal size, which are named as set A, B and
C.
Q. 5. The largest interval lying in
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Correct choice: (3)
for which the function
a.
b.
c.
d. a. Sol:
Correct choice: (4) Q. 6. A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are
a. b. c. d.
12 kg and 13 kg 5 kg and 5 kg 5kg and 12 kg 5 kg and 13 kg
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Sol: So tension in the strings are 5 kg and 12 kg. Correct choice: (3) Q. 7. A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is
a.
b.
c.
d.
Sol: Probability of getting sum of nine in a single throw
Probability of getting sum nine exactly two times out of three draws
.
orrect choice: (4) Q. 8. Consider a family of circles which are ing through the point (- 1, 1) and are tangent to x-axis. If (h, k), are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval
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a.
b.
c.
d. Sol: Centre of circle is (h, k) and x-axis is tangent. Also circle es through
Radius of the family of circle
Correct choice: (2) Q. 9. Let L be the line of intersection of the planes 2x + 3y +z = 1 and x + 3y +2z = 2. If L makes an angle positive x-axis, then
a.
b. c. 1
d. Sol:
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equals
with the
Correct choice: (1) Q. 10. The differential equation of all circles ing through the origin and having their centres on the x-axis is
a.
b.
c.
d. Sol: Equation of family of circles ing through origin and having their centres on x-axis is
Correct choice: (3) Q. 11. If p and q are positive real numbers such that then
a. 2 b. c. d.
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the maximum value of (p + q) is
Sol: Correct choice: (4) Q. 12. A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that subtends an angle of 600 at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 300. The height of the tower is
a. b.
c. d.
Sol:
Correct choice: (3)
Q. 13. The sum of the series
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a.
b. c. 0 d. Sol:
Correct choice: (2) Q. 14. The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a
a. b. c. d.
ellipse parabola circle hyperbola
Sol:
Correct choice: (1, 4)
Q. 15.
a. b. c. d.
4 10 6 0
Sol:
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Correct choice: (3) Q. 16. The resultant of two forces P N and 3 N is a force of 7 N. If the direction of 3 N force were reversed, the resultant would be
a. b. c. d.
. The value of P is
5N 6N 3N 4N
Sol:
Correct choice: (1) Q. 17. Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is
a. b. c. d.
0.06 0.14 0.2 0.7
Sol:
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No choice is correct
Q. 18.
a. b. c. d.
divisible by neither x nor y divisible by both x and y divisible by x but not y divisible by y but not x
Sol:
Correct choice: (2)
Q. 19. For the hyperbola
a. b. c. d.
Eccentricity Directrix Abscissae of vertices Abscissae of foci
Sol:
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which of the following remains constant when α varies?
Correct choice: (4)
Q. 20. If a line makes an angle of with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is
a.
b.
c.
d. Sol:
Correct choice: (4) Q. 21. A value of C for which the conclusion of Mean Value Theorem holds for the function interval [1, 3] is
a.
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on the
b. c. d.
Sol: Correct choice: (1) Q. 22. The function
a.
b.
c.
d. Sol:
Correct choice: (2)
.
a. b. 1 www.cbseguess.com
is an increasing function in
c. d. 5 Sol:
Correct choice: (3)
Q. 24.
a. b. c. d. Sol:
Correct choice: (2) Q. 25. If
are unit vectors and θ is the acute angle between them, then
a. Exactly two values of b. More than two values of c. No value of d. Exactly one value of www.cbseguess.com
is a unit vector for
Sol:
Correct choice: (4) Q. 26. A particle just clears a wall of height b at a distance a and strikes the ground at a distance c from the point of projection. The angle of projection is
a. b.
c.
d. Sol:
Correct choice: (3) Q. 27. The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is
a. b. c. d.
40 20 80 60
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Sol: Let there are x boys and y girls in the class. So, total marks are 52 x + 42 y and according to second condition total marks = (x + y) 50 Now, So percentage of boys is 80. Correct choice: (3) Q. 28. The equation of a tangent to the parabola tangent to the parabola is perpendicular to the given tangent is
a. b. c. d.
The point on this line from which the other
(- 1, 1) (0, 2) (2, 4) (- 2, 0)
Sol: Point of intersection of two perpendicular tangents to the parabola lies on directrix of the parabola. Equation of directrix is x + 2 = 0 So point is (- 2, 0) Correct choice: (4) Q.29. If (2, 3, 5) is one end of a diameter of the sphere coordinates of the other end of the diameter are
a. b. c. d.
(4, 9, - 3) (4, - 3, 3) (4, 3, 5) (4, 3, - 3)
Sol: Centre (3, 6, 1)
Let other end is Correct choice: (1)
Q. 30.
a. b. c. d.
0 1 –4 –2
Sol:
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then the
Correct choice: (4) Q. 31. Let A (h, k), B (1, 1) and C (2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which ‘k’ can take is given by
a. b. c. d.
Sol: Correct choice: (3) Q. 32. angle PQR is
a.
b.
c. d. Sol:
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be three points. The equation of the bisector of the
Correct choice: (1) Q. 33. If one of the lines of then m is
a. b. – 2 c. 1 d. 2 Sol:
Correct choice: (3)
Q. 34.
a. b. 0 c. 1 d. 2 Sol:
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is a bisector of the angle between the lines xy = 0,
Correct choice: (1)
Q. 35. is true?
Then which of the following
a. b. f (x) is not differentiable at x = 1. c. f (x) is differentiable everywhere d. f (x) is not differentiable at x = 0. Sol: Correct choice: (3)
Q. 36. defining f (0) as
a. b. c. d.
2 –1 0 1
Sol:
Correct choice: (4)
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can be made continuous at x = 0 by
37.
a.
b.
c.
d. Sol:
Correct choice: (1)
Q. 38. The area enclosed between the curves
a. b. 1
c.
d.
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Sol:
Correct choice: (3) Q. 39. If the difference between the roots of the equation values of a is
then the set of possible
a. (- 3, 3) b. c. d. Sol:
Correct choice: (1)
AIEEE 2007 Solved Paper Physics Q. 1. The displacement of an object attached to a spring and executing simple harmonic motion is given by
metres. The time at which the maximum speed first occurs is
a. 0.5 s b. 0.75 s c. 0.125 s www.cbseguess.com
d. 0.25 s
Sol: Correct choice: (1) Q. 2. In an a.c. circuit the voltage applied is
is
. The resulting current in the circuit
. The power consumption in the circuit is given by
a. b. P = zero
c. d. Sol.
Correct choice: (2)
Q. 3. An electric charge situated at
a. b. c. d.
is placed at the origin (0, 0) of X – Y co-ordinate system. Two points A and B are
and (2, 0) respectively. The potential difference between the points A and B will be
9 volt zero 2 volt 4.5 volt
Sol: Correct choice: (2) www.cbseguess.com
Q. 4. A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be
a. 1 b. 2
c.
d. Sol: Work done by battery
Energy stored in capacitor
Correct choice: (4) Q. 5. An ideal coil of 10 H is connected in series with a resistance of connection is made, the current flowing in amperes in the circuit is
and a battery of 5V. 2 seconds after the
a. (1 - e) b. e c. d.
Sol: Correct choice: (4) Q. 6. A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its cross
section. The ratio of the magnetic field at
a. www.cbseguess.com
and 2a is
b. 4 c. 1
d.
Sol: Correct choice: (3) Q. 7. A current I flows along the length of an infinitely long, straight, thin walled pipe. Then
a. b. c. d.
the magnetic field is zero only on the axis of the pipe the magnetic field is different at different points inside the pipe the magnetic field at any point inside the pipe is zero the magnetic field at all points inside the pipe is the same, but not zer
Sol: Magnetic field inside the infinitely long pipe is zero at all points. Correct choice: (3)
Q. 8. If is the mass of an oxygen isotope respectively, the nuclear binding energy of the isotope is
, are the masses of a proton and a neutron
a. b. c. d. Sol: Nuclear binding energy Correct choice: (2) Q. 9. In gamma ray emission from a nucleus
a. b. c. d.
both the neutron number and the proton number change there is no change in the proton number and the neutron number only the neutron number changes only the proton number changes
Sol: Gamma ray is electromagnetic radiation which does not involve any change in proton number or neutron number Correct choice: (2)
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Q. 10. If in p-n junction diode, a square input signal of 10 V is applied as shown. Then the output signal across will be
a.
b.
c.
d.
Sol: Diode is forward biased in first half cycle and amplitude of signal is www.cbseguess.com
Correct choice: (4) Q. 11. Photon of frequency v has a momentum associated with it. If c is the velocity of light, the momentum is
a. v / c b. hvc c. d. h v / c
Sol:
Correct choice: (4)
Q. 12. The velocity of a particle is time ( t = 1) is
. If its position is x = 0 at t = 0, then its displacement after unit
a. b. c. d.
Sol:
, Correct choice: (2)
Q. 13. For the given uniform square lamina ABCD, whose centre is O,
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a. b. c. d.
Sol: Correct choice: (3) Q. 14. A point mass oscillates along the x-axis according to the law of the particle is written as ,
a. b. c. d.
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. If the acceleration
Sol: Correct choice: (4) Q. 15. Charges are placed on the vertices of a square as shown. Let be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then
a.
remains unchanged, V changes
b. Both
and V change
c.
and V remain unchanged
d.
changes , V remain unchanged
Sol: In initial case, is along (1) whereas in final case is along (2). Potential at centre remains same.
Correct choice: (4) Q. 16. The half-life period of a radio-active element X is same as the mean life time of another radio-active element Y. Initially they have the same number of atoms. Then
a. b. c. d.
X will decay faster than Y Y will decay faster than X X and Y have same decay rate initially X and Y decay at same rate always
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Sol:
, Y will decay faster than X
Correct choice: (2) Q. 17. A Carnot engine, having an efficiency of as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is
a. b. c. d.
99 J 90 J 1J 100 J
Sol:
If same carnot engine is used as refrigerator then Correct choice: (2) Q. 18. Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate?
a. the number of free conduction electrons is significant in C but small in Si and Ge. b. the number of free conduction electrons is negligibly small in all the three. c. the number of free electrons for conduction is significant in all the three. www.cbseguess.com
d. the number of free electrons for conduction is significant only in Si and Ge but small in C. Sol: Correct choice: (4) Q. 19. A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields with a velocity
perpendicular to both
and
and
, and comes out without any change in magnitude or direction of
.
a. b. c. d.
Sol:
Magnitude of
and direction of
direction perpendicular to plane of
and
should be such that net force on charge particle be zero. and coming out of plane. So direction of
should be in the
is in the direction of
Correct choice: (1) Q. 20. The potential at a point x (measured in by
) due to some charges situated on the x-axis is given
. The electric field is
a. 5/3
and in the –ve x direction
b. 5/3
and in the +ve x direction
c. 10/9
and in the –ve x direction
d. 10/9
and in the +ve x direction
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given by
Sol: Correct choice: (4) Q. 21. Which of the following transitions in hydrogen atoms emit photons of highest frequency?
a. b. c. d.
n = 2 to n = 6 n = 6 to n = 2 n = 2 to n = 1 n = 1 to n = 2
Sol:
So photons of highest frequency will be emitted for n = 2 to n = 1 Correct choice: (3) Q. 22. A block of mass m is connected to another block of mass M by a spring (massless) of spring constant k. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force F starts acting on the block of mass M to pull it. Find the force on the block of mass m
a.
b.
c.
d. Sol: In the question the state of spring is not mentioned. We are assuming acceleration of both blocks to be same.
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Correct choice: (3) Q. 23. Two lenses of power –15 D and +5D are in with each other. The focal length of the combination is
a. b. c. d.
– 20 cm – 10 cm + 20 cm + 10 cm
Sol: Correct choice: (2) Q. 24. One end of a thermally insulated rod is kept at a temperature two sections of lengths and interface of the sections is
and thermal conductivities
and
and the other at
. The rod is composed of
respectively. The temperature at the
a. b. c. d.
Sol: Correct choice: (3) Q. 25. A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of
a. 1000 b. 10000 www.cbseguess.com
c. 10 d. 100
Sol: Correct choice: (4) Q. 26. If respectively, then
denote the specific heats of nitrogen per unit mass at constant pressure and constant volume
a. b. c. d. Sol:
are molar specific heat capacitates. For unit mass if specific heat
capacities are
Correct choice: (1)
Q. 27. A charged particle moves through a magnetic field perpendicular to its direction. Then
a. b. c. d.
the momentum changes but the kinetic energy is constant both momentum and kinetic energy of the particle are not constant both, momentum and kinetic energy of the particle are constant kinetic energy changes but the momentum is constant
Sol: Magnetic force can not do any work, so kinetic energy remains constant. Since initial velocity is perpendicular to magnetic field, hence momentum will change. Correct choice: (1) Q. 28. Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current and COD carries a current . The magnetic field on a point lying at a distance d from O, in a direction perpendicular to the plane of the wires AOB and COD, will be given by
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a.
b.
c.
d.
Sol: Magnetic field due to AB and CD are
direction
respectively and are in mutually perpendicular
.
Correct choice: (2) Q. 29. The resistance of a wire is 5 ohm at be
a. b. c. d.
2 ohm 1 ohm 4 ohm 3 ohm
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and 6 ohm at
. The resistance of the wire at
will
Sol: Correct choice: (3) Q. 30. A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is
a. b. c. d. zero Sol: No change in the energy of the system. Hence, not net work done by the system is zero. Correct choice: (4) Q. 31. If are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan’s oil drop experiment could be performed on the two surfaces, one will find the
ratio
a. 1 b. 0 c. d. Sol: Correct choice: (1) Q. 32. A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of
the discs coincide. The centre of mass of the new disc is
a. www.cbseguess.com
from the centre of the bigger disc. The value of is
b.
c.
d.
Sol: If mass of circular disc is M, then mass of removed disc is distance x from centre, then
[In question x is given out to be be
. Let centre of mass of remaining disc is at a
. If we take that, then no choice is correct we believe in place of
, it should
] Correct choice: (1)
Q. 33. A round uniform body of radius R, mass M and moment of inertia I rolls down (without slipping) an inclined plane making an angle
a.
b. www.cbseguess.com
with the horizontal. Then its acceleration is
c.
d.
Sol:
Correct choice: (1) Q. 34. Angular momentum of the particle rotating with a central force is constant due to
a. b. c. d.
constant force constant linear momentum zero torque constant torque
Sol: Central force is directed towards a point, therefore torque of the central force is zero. Correct choice: (3) Q. 35. s A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000 N/m. The spring compresses by
a. b. c. d.
5.5 cm 2.5 cm 11.0 cm 8.5 cm
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Sol: Correct choice: (1) Q. 36. A particle is projected at
a. b. c. d.
to the horizontal with a kinetic energy K. The kinetic energy at the highest point is
K Zero K/4 K/2
Sol: Correct choice: (3)
Q. 37. In Young’s double slit experiment the intensity at a point where the path difference is
wavelength of the light used) is I. If
a.
b.
c.
d.
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denotes the maximum intensity,
is equal to
being the
Sol: Let intensity of light from individual slits is
I’ Correct choice: (4) Q. 38. Two springs, of force constants k1 and k2, are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both k1 and k2 are made four times their original values, the frequency of oscillation becomes
a. b. c. d.
f/2 f/4 4f 2f
Sol:
Correct choice: (4)
Q. 39. When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path ibf Q = 36 cal. W along the path ibf is
a. b. c. d.
6 cal 16 cal 66 cal 14 cal
Sol:
Correct choice: (1)
Q. 40. A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is
a.
b. www.cbseguess.com
c. d.
Sol: Correct choice: (1)
AIEEE 2007 Solved Paper Chemistry
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Q. 1. The energies of activation for forward and reverse reactions for respectively. The presence of a catalyst lowers the activation energy of both (forward and reverse) reactions by 100 kJ mol–1. The enthalpy change of the in the presence of catalyst will be (in kJ mol–1)
reaction
a. b. c. d.
300 120 280 20
Sol: Enthalpy change of a reaction is not affected by the presence of a catalyst as it lowers the activation energy of the forward and reverse reaction by the same amount . None of the options given is correct but option (4) can be treated as correct in of magnitude. Correct choice: (4)
Q. 2. The cell,
, was allowed to be completely discharged at
298 K. The relative concentration of ZnocellE
a. antilog (24.08) b. 37.3 c. d.
Sol: Correct choice: (3) Q. 3. The pKa of a weak acid (HA) is 4.5. The pOH of an aqueous buffered solution of HA in which 50% of the acid is ionized is
a. 4.5 b. 2.5 c. 9.5 www.cbseguess.com
d. 7.0 Sol: If the given weak acid is 50% ionized, then its conjugate base will have the concentration same as that of weak acid.
Correct choice: (3) Q. 4. Consider the reaction, When concentration of B alone was doubled, the half−life did not change. When the concentration of A alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is
a. b. no unit c. d. Sol: The reaction would be first order with respect to A and first order with respect to B. The overall order of the reaction is 2.
Correct choice: (1) Q. 5.. Identify the incorrect statement among the following:
a. b. c. d.
d−Block elements show irregular and erratic chemical properties among themselves . La and Lu have partially filled d orbitals and no other partially filled orbitals. The chemistry of various lanthanoids is very similar. 4f and 5f orbitals are equally shielded.
Sol: 4f orbital electrons are shielded more than 5f orbital electrons. Correct choice: (4) Q. 6. Which one of the following has a square planar geometry?
a. b. www.cbseguess.com
c. d. (Atomic numbers: Co = 27, Ni = 28, Fe = 26, Pt = 78) Sol: Platinum(+II) only forms square planar complex. Correct choice: (4) Q. 7. Which of the following molecules is expected to rotate the plane of plane − polarised light?
a.
b.
c.
d.
Sol: Compound (1) does not have any plane of symmetry as well as centre of symmetry so it rotates the plane of plane−polarised light. Compound (2), (3) and (4) have a plane of symmetry, so they all are optically inactive. Correct choice: (1) Q. 8. The secondary structure of protein refers to:
a. helical backbone. b. hydrophobic interactions. c. sequence of amino acids. d. fixed configuration of the polypeptide backbone. Sol: Secondary structure of a protein refers to the fixed configuration of the polypeptide skeleton. structure results only when intramolecular H−bonds are formed between
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helix
of one amino acid residue and N−H
of fourth amino acid residue in polypeptide chain. formed between
pleated structure is formed when intermolecular H−bond is
of one polypeptide chain with N−H of the other chain. Correct choice: (4)
Q. 9. Which of the following reactions will yield 2,2−dibromopropane?
a. b. c. d.
Sol: Correct choice: (1) Q. 10. In the chemical reaction, (A) and (B) are respectively:
the compounds
a. b. c. d. Sol: choice: (4)
This is carbylamine reaction. Correct
Q. 11. The reaction of toluene with Cl2 in presence of FeCl3 gives predominantly:
a. b. c. d.
benzoyl chloride benzyl chloride o− and p−chlorotoluene m−chlorotoluene
Sol:
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The reaction proceeds by electrophilic substitution mechanism. Correct choice: (3 ) Q. 12. Presence of a nitro group in a benzene ring
a. b. c. d.
activates the ring towards electrophilic substitution. renders the ring basic. deactivates the ring towards nucleophilic substitution. deactivates the ring towards electrophilic substitution.
Sol: −NO2 group in benzene ring shows −I and −R effect, which deactivates the ring towards electrophilic substitution but activates it towards nucleophilic substitution. Correct choice: (4) Q. 13. In which of the following ionization processes, the bond order has increased and the magnetic behaviour has changed?
a. b. c. d. Sol:
Correct choice: (2) Q. 14. The actinoids exhibit more number of oxidation states in general than the lanthanoids. This is because
a. b. c. d.
the 5f orbitals are more buried than the 4f orbitals. there is a similarity between 4f and 5f orbitals in their angular part of the wave function. the actinoids are more reactive than the lanthanoids. the 5f orbitals extend further from the nucleus than the 4f orbitals.
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Sol: The actinoids exhibit more number of oxidation states than lanthanoids because they can loose more number of electrons as the 5f orbital electrons are held less strongly than the 4f orbital electrons. Correct choice: (4) Q. 15. Equal masses of methane and oxygen are mixed in an empty container at pressure exerted by oxygen is
. The fraction of the total
a.
b.
c.
d. Sol: Let the mass of methane and oxygen be x g each.
Correct choice: (3) Q. 16. . A 5.25% solution of a substance is isotonic with a 1.5% solution of urea (molar mass = 60 g mol–1) in the same solvent. If the densities of both the solutions are assumed to be equal to 1.0 g cm–3, molar mass of the substance will be
a. b. c. d.
90.0 g mol–1 115.0 g mol–1 105.0 g mol–1 210.0 g mol–1
Sol: Since the two solutions are isotonic, their concentrations will be
same.
Correct choice: (4)
Q. 17. Assuming that water vapour is an ideal gas, the internal energy change when 1 mol of water is vapourised at 1 bar pressure and 1000C,(Given: Molar enthalpy of vapourisation of water at 1 bar and 373 K = 41 kJ mol−1 and R = 8.3 J mol−1K−1) will be:
a. 4.100 kJ mol−1 www.cbseguess.com
b. 3.7904 kJ mol−1 c. 37.904 kJ mol−1 d. 41.00 kJ mol−1 Sol:
Correct choice: (3) Q. 18. In a saturated solution of the sparingly soluble strong electrolyte AgIO3(Molecular mass = 283) the equilibrium which sets in is If the solubility product constant K spof AgIO3 at a given temperature is, what is the mass of AgIO3contained in 100 ml of its saturated solution?
a. b. c. d.
28.3 × 10–2 g 2.83 × 10–3 g 1.0 × 10–7 g 1.0 × 10–4 g
Sol:
If ‘s’ is the solubility of AglO3 in a saturated solution, then
Correct choice: (2) Q. 19. A radioactive element gets spilled over the floor of a room. Its half–life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?
a. b. c. d.
1000 days 300 days 10 days 100 days
Sol: Let the permissible activity limit of the radioactive element be x, then the initial activity would be 10 x.
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Correct choice: (4) Q. 20. Which one of the following conformations of cyclohexane is chiral?
a. b. c. d.
Twist boat Rigid Chair Boat
Sol: Twist boat conformation of cyclohexane is chiral because it has neither plane of symmetry nor centre of symmetry. Correct choice: (1) Q. 21. Which of the following is the correct order of decreasing SN2 reactivity?
a. b. c. d.
RCH2X > R3CX > R2CHX RCH2X > R2CHX > R3CX R3CX > R2CHX > RCH2X R2CHX > R3CX > RCH2X (X = a halogen)
Sol: The reactivity of a compound towards SN2 reaction decreases as the crowding at the C–atom containing leaving group increases. Correct choice: (2) Q. 22. In a following sequence of reactions,
a. b. c. d.
butanal n–butyl alcohol n–propyl alcohol propanal
Sol:
Correct choice: (3) Q. 23. Which of the following sets of quantum numbers represents the highest energy of an atom?
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Sol: An orbital having higher value of (n + l) has higher energy. Out of the four options given, the value of (n + l) is highest if n = 3 and l = 2. Correct choice: (2) Q. 24. Which of the following hydrogen bonds is the strongest?
a. b. c. d.
O–H.…N F–H.…F O–H.…O O–H.…F
Sol: Greater the difference in electronegativity of H–atom and the other electronegative atom with which H is covalently bonded, stronger is the hydrogen bond. Highest electronegativity difference exists in HF molecule. Correct choice: (2) Q. 25. In the reaction,
a. b. c. d.
6 L HCl(aq) is consumed for every 3 L H2(g) produced. 33.6 L H2(g) is produced regardless of temperature and pressure for every mole Al that reacts. 67.2 L H2(g) at STP is produced for every mole Al that reacts. 11.2 L H2(g) at STP is produced for every mole HCl(aq) consumed.
Sol: Given that, For each mole of Al reacted, 1.5 mol of H2 is formed; and for each mole of HCl(aq) consumed, 0.5 mol or 11.2 L of H2 at STP is formed. Correct choice: (4) Q. 26. Regular use of which of the following fertilizers increases the acidity of soil?
a. b. c. d.
Potassium nitrate Urea Superphosphate of lime Ammonium sulphate
Sol: Ammonium sulphate is a salt of weak base and strong acid. Its aqueous solution is acidic due to hydrolysis of ammonium ion. It will increase the acidity of soil. Correct choice: (4) Q. 27. Identify the correct statement regarding a spontaneous process:
a. b. c. d.
For a spontaneous process in an isolated system, the change in entropy is positive. Endothermic processes are never spontaneous. Exothermic processes are always spontaneous. Lowering of energy in the reaction process is the only criterion for spontaneity.
Sol: For a process to be spontaneous in an isolated system, the change in entropy is positive. Correct choice: (1) www.cbseguess.com
Q. 28. Which of the following nuclear reactions will generate an isotope?
a. neutron particle emission b. positron emission c.
particle emission
d.
particle emission
Sol: In a nuclear reaction, an isotope cannot be generated by the emission of positron , particle or particle because it will change the atomic number of the parent nuclei. An isotope can be generated when the nuclei of an element are bombarded with slow neutrons e.g., particle emission is a hypothetical process. Correct choice: (1)
. Formation of isotope by neutron
Q. 29. The equivalent conductances of two strong electrolytes at infinite dilution in H2O (where ions move freely through a solution) at 250C are given below: What additional information/quantity one needs to calculate of an aqueous solution of acetic acid?
a. b. c. (C) The limiting equivalent conducted of d. Sol:
Correct choice: (1) Q. 30. Which one of the following is the strongest base in aqueous solution?
a. b. c. d.
Trimethylamine Aniline Dimethylamine Methylamine
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Sol: Aliphatic amines are more basic than aromatic amines and among aliphatic amines, the order of basicity in aqueous solution is
Correct choice: (3)
Q. 31. The compound formed as a result of oxidation of ethyl benzene by KMnO4 is
a. b. c. d.
benzophenone acetophenone benzoic acid benzyl alcohol
Sol:
Correct choice: (3)
Q. 32. The IUPAC name of
a. b. c. d.
is
1,1–diethyl–2,2–dimethylpentane 4,4–dimethyl–5,5–diethylpentane 5,5–diethyl–4,4–dimethylpentane 3–ethyl–4,4–dimethylheptane
Sol: IUPAC name of the given compound is: 3–ethyl–4,4–dimethyl heptane. Correct choice: (4) Q. 33. Which of the following species exhibits the diamagnetic behaviour?
a. b. c. d. NO Sol: , and NO are paramagnetic due to the presence of 2, 1 and 1 unpaired electrons respectively. have no unpaired electron and is diamagnetic in nature. Correct choice: (1) Q. 34. The stability of dihalides of Si, Ge, Sn and Pb increases steadily in the sequence
a. GeX2 << SiX2 << SnX2 << PbX2 b. SiX2 << GeX2 << PbX2 << SnX2 c. SiX2 << GeX2 << SnX2 << PbX2 www.cbseguess.com
will
d. PbX2 << SnX2 << GeX2 << SiX2 Sol: The stability of the lower oxidation state increases down the group in group 14. SiX2 << GeX2 << SnX2 << PbX2 Correct choice: (3) Q. 35. Identify the incorrect statement among the following:
a. b. c. d.
Ozone reacts with SO2 to give SO3. Silicon reacts with NaOH(aq) in the presence of air to give Na2SiO3 and H2O. Cl2 reacts with excess of NH3 to give N2 and HCl. Br2 reacts with hot and strong NaOH solution to give NaBr, NaBrO4 and H2O.
Sol: O3 + SO2
SO3 + O2
Si + 2NaOH + O2 3Cl2 + 2NH3
Na2SiO3 + H2O
N2 + 6HCl
3Br2 + 6NaOH
5NaBr + NaBrO3 + 3H2O Correct choice: (4)
Q. 36. The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizing power of the cationic species, K+, Ca2+, Mg2+, Be2+?
a. b. c. d. e. Sol: Greater the charge/size ratio of a cation, size but charge of all those ions is same. Thus, polarising power of these ions is in the order: K+ has a 1 unit charge less than that of Ca2+ and its size 2+ + is larger than that of Ca , thus polarising power of K is less than that of Ca2+. So, the correct order is Correct choice: (3) Q. 37. The density (in g mL–1) of a 3.60 M sulphuric acid solution that is 29% H2SO4 (Molar mass = 98 g mol–1) by mass will be
a. b. c. d.
.64 1.88 1.22 1.45
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Sol: Let the mass of solution be x g.
Correct choice: (3) Q. 38. The first and second dissociation constants of an acid H2A are 1.0 × 10–5 and 5.0 × 10–10respectively. The overall dissociation constant of the acid will be
a. b. c. d.
5.0 × 10–5 5.0 × 1015 5.0 × 10–15 0.2 × 105
Sol: Correct choice: (3) Q. 39. A mixture of ethyl alcohol and propyl alcohol as vapour pressure of 290 mm at 300 K. The vapour pressure of propyl alcohol is 200 mm. If the mole fraction of ethyl alcohol is 0.6, its vapour pressure (in mm) at the same temperature will be
a. b. c. d.
350 300 700 360
Sol:
Correct choice: (1) Q. 40. In conversion of lime–stone to lime, The values of that and be spontaneous is
and
are +179.1 kJ mol–1 and 160.2 J/K respectively at 298 K and 1 bar. Assuming
do not change with temperature, temperature above which conversion of limestone to lime will
a. 1008 K b. 1200 K www.cbseguess.com
c. 845 K d. 1118 K Sol: when
The decomposition of CaCO3 to CaO and CO2 would become spontaneous would be –ve. But limiting condition can be arrived at when
zero. Correct choice: (4)
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would become
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