Indian Institute of Technology Guwahati %28IIT-G%29 2006 JAM Geophysics - Question Paper
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JAM 2006 Geophysics
Full ques. Paper in attachment
JAM 2006
GEOPHYSICS TEST PAPER
IMPORTANT NOTE FOR CANDIDATES
Select any Two Sections. Attempt ALL objective a nd subjective questions of the same Two Sections. Questions 1- 45 (objective questions) carry three marks each and questions 46 -66 (subjective questions) carry fifteen marks each.
Write the answers to the objective questions in the Answer Table for Objective Questions provided on page 17 only)
GEOLOGY SECTION
1. Plutonic equivalent of Trachyte is
(A) diorite
(B) gabbro
(C) granite
(D) syenite
2. The river meanders at the mature stage with gentle gradient. The formation of pointbar will be on:
(A) outer zone of the bend
(B) inner zone of the bend
(C) straight channel segment
(D) steep bank of the channel.
3. Match the features in Group 1 with the agents responsible for these features from Group 2
|
Group 1 Group 2 |
|
P. |
Arete |
1. |
River |
|
Q. |
Backswamp |
2. |
Ground Water |
|
R. |
Yardangs |
3. |
Glacier |
|
S. |
Stalactites and stalagmites |
4. |
Wind |
|
|
Choose the correct answer from the following: |
(A) P-4, Q-3, R-1, S-2
(b) P-2, Q-1, R-3, S-4
(c) P-3, Q-1, R-4, S-2
(D) P-1, Q-2, R-4, S-3
4. The area bounded by two fault planes dipping away from each other with hanging walls going downward is called as:
(A) dome
(B) grabben
(C) horst
(D) klippe
|
|
Group 1 |
Group 2 |
|
P. |
axial plane is horizontal 1. |
Isoclinal fold |
|
Q. |
hinges are sharp and angular 2. |
Parallel fold |
|
R. |
limbs are parallel 3. |
Recumbant fold |
|
S. |
thickness of bed remains constant 4. |
Cheveron fold |
|
Choose the correct answer from the following: |
|
|
(A) |
P-2, Q-4, R-2, S-1 |
|
|
(B) |
P-1, Q-3, R-2, S-4 |
|
|
(C) |
P-4, Q-2, R-1, S-3 |
|
|
(D) |
P-3, Q-4, R-1, S-2 |
|
6. Which of the following rock indicates initiation of metamorphism
(A) phyllite
(b) schist
(C) shale
(D) slate
7. Barrovian metamorphism of pelitic rocks is characterized by the first appearance of index minerals in a particular sequence. Which one of the following is the correct sequence.
(A) chlorite-garnet-biotite-kyanite-staurolite-sillimanite
(B) garnet-biotite-chlorite-staurolite-sillimanite-kyanite
(C) chlorite-biotite-garnet-staurolite-kyanite-sillimanite
(D) biotite-chlorite-garnet-kyanite-staurolite-sillimanite
8. A crystal has three crystallographic axes of 2 fold symmetry and mirror plane perpendicular to each of these crystallographic axes. The Herman-Manguin notation for crystal would be
(A) 2/m 2/m 2/m
(b) 2m
(C) 2mm
(D) 23
9. Indicate the correct order in terma of increasing Si : O ratio.
(A) phlogopite-beryl-plagioclase-epidote
(B) epidote-beryl-phlogopite-plagioclase
(C) beryl-phlogopite-plagioclase-epidote
(D) plagioclase-phlogopite-epidote-beryl
10. Sandstones and purple shales of Muree Series of Potwar region, equivalent to Dagshai and Kasauli beds of northwest Himalaya belongs to
(A) Upper Eocene
(B) Lower Eocene
(C) Middle Miocene
(D) Lower Miocene
11. A radiogenic isotope has half-life of 1 hour and we have 10000 atoms of that particular isotope in a particular system at a particular time. How much atoms of that isotope will be there after 6 hours?
(A) 78
(B) 156
(C) 313
(D) 625
12. Find the odd man out from the following
(A) stockwork
(B) ladder vein
(C) saddle reef
(D) banding
13. Sulfide chimneys are observed at
(A) vents of seafloor hotsprings around ridges
(B) inland hotspring vents in volcanic terrains
(C) sulfide mineral coatings on the chimneys of smelters
(D) mouths of explosive volcanoes
14. Within the mantle sudden density change produce seismic-wave discontinuities due to polymorphic transition or compositional change or a combination of both occur at a depth of
(A) 470 kms
(b) 570 kms
(c) 670 kms
(d) 760 kms
15. The estimated thickness of the moons lithosphere is about
|
(A) |
35 km |
|
(B) |
65 km |
|
(C) |
100 km |
|
(D) |
1000 km |
PHYSICS SECTION
16. In case of an inelastic collision which one of the following is true
(A) Total energy is not conserved
(B) Momentum is not conserved
(C) Kinetic energy is conserved
(D) Kinetic energy is not conserved
17. The root mean square speed of an ideal gas, made up of molecules of molecular weight
0 0831 kg/mol, at temperature 300 K is (Take universal gas constant R = 8 31 J/mol K)
|
(A) |
100 |
m/s |
|
(B) |
200 |
m/s |
|
(C) |
300 |
m/s |
|
(D) |
400 |
m/s |
engines A and B are the same. If the ratio of the respective efficiencies,
to 2 then the ratio of the hot reservoir temperatures
(A) 0 25
(B) 0 5
(C) 1 0
(D) 2 0
19. Which one of the following phenomenon cannot be described by the particle nature of electromagnetic radiations.
(A) Blackbody radiations
(B) Compton scattering
(C) Photoelectric effect
(D) X-ray diffraction
20. If a semiconductor is doped with donor atoms then the impurity levels created in the semiconductor are close to the
(A) bottom of the conduction band
(B) top of the valence band
(C) bottom of the valence band
(D) top of the conduction band
21. Binding energy per nucleon for the nuclei 4He, 56Fe, 197Au and 235U are given by B1; B2, B3 and B4, respectively. These binding energies satisfy the order
(A) B1< B2 < B3 < B4
(B) B1> B2 > B3 > B4
(C) B2 < B3 < B4< B1
(D) B2 > B3 > B4> B1
22. When a thin transparent sheet is introduced along the path of one of the slits in Youngs double slit experiment, then the fringe width
(A) decreases
(B) increases
(C) does not change
(D) does not change but intensity becomes half
23. An infinite wire, lying along the z -axis, carries a current I in the positive z direction denoted by k. The magnetic field at a point d i is M01
(A)
(B)
(C)
(D)
J
The radius of curvature of curved surface of a plano-convex thin lens of glass (refractive index n = 1 5) of focal length 0 4 m is
(A) 0 1 m
(B) 0 2 m
(C) 0 4 m
(D) 0 8 m
The engine of a train, emitting the sound of frequency v0 approaches an observer with constant speed. If the observer measures the frequencies as v1 when it is approaching and v2 while it is going away, the relation between the frequencies is given by
(A) V1 = V2 = V0
(B)
(C)
V1 < V0 < V2 V1 = V2 * V0
(D)
In a dielectric sphere the polarization P is given by P = kr3r . The corresponding bound volume charge density is equal to
(A) - 20 k
(B) -10 k
(C) 10k
(D) 20k
An ideal fluid is flowing through a tube of cylindrical cross section with smoothly varying radius. The velocity of fluid particles at the point where tubes cross sectional area is 1x 10-4 m2 is given by 0.01 m/s. The velocity at a point where cross sectional area is
2 x 10-4 m2 is given by
(A) 0 0025 m/s
(B) 0 005 m/s
(C) 0 02 m/s
(D) 0 04 m/s
28. The solution of Maxwells equation for electric field in free space is given by E = E0sin(t - x / c), where E0 is a constant, a> is the angular frequency and c is the speed of light. The corresponding solution for the magnetic field B is
(A) B = cE0sin(t - x / c)
E
(B) B =-sin(t - x / c)
c
E
(C) B =2-sina(t - x / c)
c
E
(D) B = 0sin(t - x / c)
c
The frequency of electron in n = 1 Bohr orbit is given by frequency of electron in the n -th orbit for n >1 is
(C) fj n3
(D) nf1
A signal of 1 mV is input to an amplifier circuit consisting of a transistor in common-emitter mode. What is the voltage gain if the collector current changes by 1 mA and the load resistance is equal to 1 kQ?
(A) 10
(B)
102
103
104
MATHEMATICS SECTION
31. Let an, an > 0 be a convergent series. Now, consider the following statements:
n>1
P: The series is always convergent.
a + a2 +-----+ a
1 2 n
Q: The series
}
Then,
(A) both P and Q are true
(B) P is true and Q is false
(C) both P and Q are false
(D) P is false and Q is true
+| x - | , if x is rational
2 I 2 J
if x is irrational.
Then,
(A) f is continuous and differentiable only at x=
(B) f is continuous only at x = 2 but not differentiable at x
(C) f is neither continuous nor differentiable at x =
(D) f is continuous and differentiable for every x = [0,1]
33. The value of the integral j)
1 x y
34. The integral US f (x, y, z) dzdydx is equal to
0 0 0
i x x
(A)
(B)
(C)
(D)
0 0 z
1 x z
SSS f(x, y, z) dy dz dx
0xz
1 1 z
SSS f(x, y, z) dy dz dx
0 x 0
35. Consider the initial value problem (IVP): xy' -y = 0, y (0) = 0. Now, consider the following statements:
P: Picards theorem is applicable to the above IVP.
Q: The above IVP has exactly one solution.
Then,
(A) both P and Q are true
(B) P is false but Q is true
(C) both P and Q are false
(D) P is true but Q is false
36. Let Q be the set of rational numbers in . Then
(A) Q is closed in
(B) Q is open in
(C) Q is both open and closed in
(D) Q is neither open nor closed in
37. The radius of convergence of the power series
38. Consider the differential equation y" + 6 y' + 25 y = 0 with initial condition y (0) = 0. Then, the general solution of the IVP is
(A) e - 3 x (A cos 4 x+B sin 4 x )
Be x sin 4 x A e-4x sin3x
(B)
(C)
(D) e 4x (A cos3x + B sin3x)
Let F (x, y, z) = x2 yi+ y j + z2 k. If p = curlF and q = divF, then ( p, q ) is
(A) (- x2 k, 1 + 2xy + 2z)
(B) (2xyi + j + 2z k, 1 + 2xy + 2z)
(C) ( - x2 k, x2 y + y + z2)
(D) (2xyi+ j + 2z k, x2 y + y + z2)
40. Let V = { (x, y, z, w) : x + y + z - 3 w = 0, x - y + z -w = 0, x- 7 y + z + 5 w = 0} be a vector subspace of 4. Then dim (V) is
(A) 1
(B) 2
(C) 3
(D) 4
Let T : 3 3 be a linear transformation defined by
T (x, y, z ) = ( x + y + z, y + z, z ). Then Tn ( x, y, z ), for n >1, is
( n + n x + ny +--2 z, y + nz, z
(x + ny + (n2 -n +1)z, y + nz, z )
42. Suppose that the moment generating function of a random variable X is
1 e-1 +1 e~21 +1 e21. Then Var (X) is 244
43. Perform Newtons method to the equation x3 -x-2 = 0 starting with x0 =1. In this operation, the value of x2 (the second iterate) is
0, if x<-1 1/8, if -1<x< 0
1/4, if 0<x< 1
1/2, if 1<x< 2
1, if x > 2.
ind B = P ( 0 < X < 2
|
a |
|
r_ |
1 |
|
I |
2 |
|
3 |
3 |
|
8, |
8 |
|
1 |
3 |
|
8, |
8 |
|
3 |
7 |
|
8, |
8 |
|
1 |
1 |
|
8, |
4 |
|
45. Let Xj,X2,X3,, Xn be a random sample from a normal population N(ju,a ),
1 n
where u and a2 are unknowns. Suppose that S2 =-V (Xi -X)2, where X is
n -11=1
the sample mean. It is known that cS2 follows a %2 -distribution with (n -1) degrees of freedom. Then c is equal to
n
a
n
a2
n -1
a
n -1
2
a
GEOLOGY SECTION
46. (a) What is the relationship between an earthquake focus and the corresponding
epicenter? (6)
(b) What are the three kinds of Plate margins and associated magmatism? (9)
47. (a) What is dip slip fault? In an area a bed is dipping towards west at 42. The area
had been affected by fault dipping toward east at 45. With the help of neat diagrams show the relative movements of the blocks resulting in repetition of bed and and omission of bed (9)
(b) How you define monocline? A N-S trending bed is exposed on an easterly
sloping ground with the bed-dipping west. Find the thickness of the bed, if the slope of the ground is 15 E; width of the bed measured perpendicular to strike is 100 m; dip of the bed is 30W.
(6)
48. (a) Why startovolcano like Mount Fuji in Japan has steep sides and shield volcano
like Mauna Loa in Hawaii have gentle surface slopes? (6)
(b) How you define conformable and unconformable sequence? What geological events are indicated by angular unconformity? (9)
49. (a) Where do back-arc basins form and what is the necessary conditions for the
formation of back-arc basins? How is the nature of magmatism different from that of a forearc? (9)
(b) Compare Airys and Pratts hypothesis on isostasy with the help of a neat diagram.
(6)
50. (a) Distinguish between perthitic and rapakivi texture with the help of neat
sketch. (6)
(b) Give the idealized Bouma sequence. Where do you find such a sequence of deposition of sediments? (9)
51. (a) Mention the broad tectonic regime and mode of occurrence of porphyry-copper
deposits. (6)
(b) Mention 3 locality of each of occurrences of Iron, Manganese and Copper deposits in India. (9)
52. (a) A grain of undeformed quartz is in contact with an untwined plagioclase, both
showing first order gray interference color. How do you distinguish the two?
(6)
(b) What is an optical indicatrix? Draw a positive biaxial indicatrix indicating the optic axes, the optic axial angle and circular sections. (9)
PHYSICS SECTION
An ideal diatomic gas at pressure pi and volume Vi doubles its volume adiabatically. Find
(a) the final pressure and (6)
(b) the work done by the gas. (9)
A charge of magnitude 9.8 x 10-10C and mass 2 0 x 10-6 kg is suspended through a silk thread along the line passing through the center and parallel to the length of two parallel plates with a spacing of 0 1m. The plates are connected to a voltage source of 2000 V. (Take g = 9.8ms-2). Find
(a) the electric field experienced by the charge and (6)
(b) the angle that the thread makes with the vertical when charge is in equilibrium.
(9)
55. A cylinder of 1 kg mass and 0 02 m diameter left at the top of an inclined plane of height 1 m rolls down without slipping. (Take g =9 8 ms-2)
(a) What is the kinetic energy of the cylinder when it reaches at the bottom of inclined plane? (6)
(b) Find the velocity of center of mass of cylinder on reaching the bottom of inclined plane. (9)
56. Two waves described by y1 = A sin(a t + kx) and y2 = A sin(a t - kx) are traveling along a string. Let A = 0 001 m, k = 3 142 m-1 and a =157 l s-1 (Take n = 3.142 )
(a) Find the magnitude and direction of velocity of these waves. (6)
(b) What shall be the amplitude of resultant wave on the string at x = 0 5 m.
(9)
57. Consider a monatomic FCC solid with lattice constant V3 A .
(a) Find the interplanar spacing of a set of parallel (111) planes. (6)
(b) For what incident angle 9 the first order Bragg peak would be observed if a
0
monochromatic x-ray of wavelength 1 A is incident on these planes? (9)
58. Consider an LR circuit with an inductor L, a resistor R, a battery of emf E and a switch
S , all connected in series.
(a) Find an expression for current I in the circuit as a function of time after the switch S is closed. (9)
(b) What is value of I after a time that equals the time constant of this circuit?
(6)
59. Take radius of hydrogen atom H to be 5 3 x 10_11 m. (Take h = 1.054 x 10-34J s and me = 9 1 x 10-31 kg) Assuming momentum of electron to be same as order of uncertainty in momentum,
(a) Find the order of kinetic energy that an electron in the hydrogen atom is expected to have based on the uncertainty principle. (9)
(b) If de Broglie wavelength of electron matches with the circumference of orbit, what is the velocity of electron? (6)
Mathematics Section
60. (a) Suppose that f : [ a, b ] , a > 0 is continuous on the closed interval [a, b ],
that f is differentiable on the open interval (a, b ), and that b f (a) = a f (b) .
Then prove that there exists c e (a, b ) such that f (c) = c f '(c) . (6)
2
x ~
(b) Let f : [0, 2] be defined by f (x) = 2 + (x -1)3. Compute the absolute maximum and minimum value of f on [0,2]. (9)
x e [0,1]. Does the above condition imply that f (x) = 0 on [0,1]? Explain.
(6)
Let f :[0,1] be defined by f (x) = x3. Find the area of the surface generated by revolving the curve y = f (x) about the x-axis. (9)
Let f (x) = 1 + 3x2 + 5x4 + 7x6 +
for | x | < 1, be a power series. Determine
(6)
Let V be a vector subspace of 4 spanned by the vectors (1,1,1, -1) and (1, -1,0,1). Let W be another vector subspace of 4 spanned by the vectors (1,1, -1,1) and (1,3,4,- 5). Determine a basis for V n W. (9)
Consider the system of linear equations
x + y + z = 3
x + 2 y + 3 z = a x + 3 y + bz = 5.
Determine the values for a and b for which the above system has a unique solution, infinite number of solutions, and no solution. (9)
Solve: (4 x2 y + 5 x3 y2) dx + (2 x3 + 3 x4 y ) dy = 0. (6)
Let C be the boundary of the triangle with vertices (0,1,0), (1,0,0) and
/v /y
(2,1,0). If F(x,y,z) = -yi + y2 z j + zxk, then use Stokes theorem to
c
evaluate JF dr when C is traversed counter-clockwise when viewed from
C
above. (9)
Let u(x,y) = x3 -3xy2 + x + 3 be the real part of an analytic function f (x,y) on the entire complex plane. Determine the harmonic conjugate of u( x, y) .
(6)
65. (a) Let X1,X2,X3,---, X20 be a random sample of size 20 from a normal population N(0,ct2). Find the best critical region of size a = 0.05 for testing H0 :a2 = 1 against H1 :a2 = 2. (9)
[Given: (0.95) = 31.4, *19(0.95) = 30.1, (0.05) = 10.9 , and 9(0.05) = 10.1 ]
(b) Let X1,X2,X3,l, Xn be a random sample of size n from a normal population N (,16). Compute the minimum integral value of n such that P (X - 2 << X + 2) > 0.95, where X is the sample mean. (6)
[For Z ~N(0,1) and O(z) = P(-ro<Z<z), 0(1.645) = 0.95 and 0(1.96) = 0.975]
|
\c(x2 -y2), for (xy)GD
[ 0, otherwise,
where D is the triangle with vertices (0,0), (2,0) and (2,2), probability density function of the random variables X and Y. The table below gives the values of f (x) for 1< x < 9. |
|
X |
1 |
3 |
5 |
7 |
9 |
|
f ( X) |
1 |
0 |
1 |
0 |
1 |
|
|
Compute the forward difference table and determine f (2) up to four decimal places. (9) |
15
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