Indian Institute of Technology Guwahati (IIT-G) 2007 JAM Geophysics - Question Paper

JAM Geophysics 2007
Full ques. Paper in attachment

Geophysics Paper 2007

IMPORTANT NOTE FOR CANDIDATES

   Geology Section : Q. Nos. 1-15 Objective Questions and Q. Nos. 46-52 Subjective Questions.

   Physics Section    Q. Nos. 16-30 Objective Questions and Q. Nos. 53-59 Subjective Questions.

   Mathematics Section : Q. Nos. 31-45 Objective Questions and Q. Nos. 60-66 Subjective questions.

   Select any TWO Sections.

   Attempt ALL objective and subjective questions of the selected TWO Sections.

   Questions 1-45 (objective questions) carry three marks each for correct answer and questions 46-66 (subjective questions) carry fifteen marks each. There will be negative marking for wrong answers to objective questions.

   Write the answers to the objective questions in the Answer Table for Objective Questions provided on page 9 only.

GEOLOGY SECTION

1.    Find the odd man out from the following :

(A)    Isogyres

(B)    Extinction

(C)    Melatope

(D)    Isochromes

2.    Match the sedimentary rocks in Group 1 with their category Group 2.

	Group 1		Group 2
P.	Shale	1.	Chemical
Q.	Chert	2.	Clastic
R.	Sandstone	3.	Biogenic
S.	Limestone

(A)    P-l, Q-3, R-l, S-2    (B) P-3, Q-2, R-2, S-l

(C)    P-2, Q-l, R-2, S-3    (D) P-2, Q-l, R-3, S-l

3. Indicate the correct order in terms of decreasing iron (wt. %) in the following iron minerals.

(A)    Magnetite - Hematite - Goethite - Siderite

(B)    Hematite - Magnetite - Goethite - Siderite

(C)    Goethite - Siderite - Hematite - Magnetite

(D)    Siderite - Goethite - Magnetite - Hematite

4.    Which one of the following twins does NOT belong to monoclinic system?

(A)    Manebach

(B)    Baveno

(C)    Carlsbad

(D)    Dauphine

5.    Indicate the correct order (oldest to youngest) of the following volcanic episodes :

(A)    Rajmahal - Malani - Panjal - Deccan

(B)    Malani - Rajmahal - Deccan - Panjal

(C)    Malani - Panjal - Rajmahal - Deccan

(D)    Panjal - Rajmahal - Deccan - Malani

6.    If in a fold the cleavage and bedding are parallel to each other on the limbs but crosses the bedding at high angles on the crest and trough, it is a / an

(A)    Cheveron fold

(B)    Isoclinal fold

(C)    Recumbent fold

(D)    Overturned fold

7.    In case of seismic waves, which one of the following is TRUE?

(A)    P (Primary) waves can not travel through the body of the earth

(B)    Rayleigh waves can travel through the body of the earth

(C)    S (Secondary) waves can not travel through the body of the earth

(D)    Love waves can not travel through the body of the earth

8.    Match the following metamorphic facies from Group 1 to its characteristic minerals from Group 2.

Group 1 P. Greenschist facies Q. Amphibolite facies R. Granulite facies

Group 2 1.    Pyroxene, Sillimanite 2.    Chlorite, Garnet, Pyroxene 3.    Hornblende, Garnet, Quartz 4.    Chlorite, Epidote, Quartz

---

Choose the correct answer from the following :

(A) P-4, Q-3, R-l

(C) P-3, Q-4, R-2

10.    Which one of the following statements, in relation to magmatic crystallization, is CORRECT?

(A)    Phase boundary is a line on a phase diagram where only one phase is stable

(B)    A sample that plots on liquidus will contain no crystals

(C)    A sample will contain no liquid at temperature below solidus

(D)    Latent head is released from a sample when it is converted from solid to liquid

11.    Find the odd man out from the following :

(A)    Barchan

(B)    Yardang

(C)    Seif

(D)    Fjord

12.    A coarse grained rock consisting of abundant ca-plagioclase, olivine and pyroxene is _Anr"*-t5a    -

(B)    Ecologite

(C)    Gabbro

(D)    Dunite

eric pressure is termed as (C) Isohyte    (D) Isotherm

13. A line joining points of equal atmosph (A) Isograd    (B) Isobar

---

16. Two metal wires A and B, having lengths I and 21 and radii R and 2R respectively are joined end to end along their axis. When one end of the system is fixed and other end is pulled with a constant force F, the elongation in both the wires is equal. The ratio of their Young's modulus Y_A : Y_B is

(A) 2 : 1    (B) 4 : 1    (C)l:2    (D) 1 : 4

A transformer has 100 turns in primary and 200 turns in the secondary. If primary is connected to 220 V DC supply, the voltage across the secondary coil is

(A) 440 V    (B) 220 V    (C) 110 V    (D) 0 V

Which of the following phenomenon does NOT produce completely polarized light from unpolarized light?

(A) Absorption (B) Refraction    (C) Scattering (D) Reflection

The escape velocity from the earth is V(,. For a planet with radius three times and density twice that of the earth, the escape velocity will be

(A) V₀V2    (B) 3V₀V2    (C) 2V₀V2    (D) V₀S

In the P-V diagram shown in the figure, the work done by the system of gases along the path ACB is

(A)

(B)

(C)

(D)

Parallel light is incident from air on a surface of glass plate at Brewster angle. Which one of the following statements is CORRECT?

(A)    Incident and reflected rays are right angle to each other

(B)    Incident and refracted rays are parallel to each other

(C)    Refracted and reflected rays are at right angle to each other

(D)    There is no refracted ray in the glass medium

23.    In a simple cubic structure of lattice constant a, one plane among a set of parallel planes intercepts x, y and 2-axis 2a, a, and a respectively. The interplanar spacing is

(A) aV6    (B) a    (C) a/S    (D) a/3

24.    A simple pendulum, suspended from the ceiling of a stationary cart, has a time period 2 seconds. When the cart accelerates in the horizontal direction with an acceleration of 10 m/s², the time period of the pendulum is ( g = 10 ms ~²)

(A) 2^1/2 seconds (B) 2^3/2 seconds (C) 2^1/4 seconds (D) 2^3/4 seconds

25.    In a reverse biased ideal p-n junction diode, with increase in the bias voltage the current will

(A)    depend on temperature and saturate

(B)    depend on temperature and increase linearly

(C)    be independent of temperature and saturate

(D)    be independent of temperature and increase linearly

26.    Two long, parallel straight conducting wires carry the same current in the same direction. If the distance between them is halved and the current in both is doubled, the force per unit length between them will change by a factor of

(A) 1/8    (B) 8    (C) 4    (D) 1/4

27.    The radiation emitted by a radioactive source of half life 3 hrs is 32 times higher than the safety limit. Minimum time for the radiation to be under the safety limit is

(A) 9 hrs    (B) 12 hrs    (C) 15 hrs    (D) 18 hrs

28.    A uniform electric field E - E ₀e _z exists in a region of permittivity y. A homogeneous sphere of radius a with permittivity ₂(< ) is embedded in the region. At the centre of the sphere

(A)    VE=0,VD = 0

(B)

(C)    VE*0,VD = 0

(D)    V.*0,V.Z)*0

29.    Moment of inertia of a uniform circular disk of radius R and mass M about the tangential axis parallel to its diameter is

_(A) a*l (B) 51    (O net (D) 5l

30. In a diatomic gas system, molecules are free to translate, rotate and vibrate. The average kinetic energy per molecule is

(A) kT    (B) kT    (C) kT    (D) -kT

2 2 2 2

31. Let {* }, {a_n } and {b_n } be three sequences whose n.th terms are related by a_n =2

. If /*is a function generated by the sequence {x_n }, where x_n+1 = a_n +b_n,

then the number of real roots of the equation fix) = Ois equal to

(A) 0    (B) 1    (C) 2    (D) 3

32.    Consider the function f: R² > R defined by

fi^x,y) = \    _

[x + y, x<0.

Then f is

(A)    continuous on R²

(B)    discontinuous only at one point on the non-negative j-axis

(C)    continuous only at one point on the y-axis

(D)    continuous only on the set {(jc,y)e R² : x * 0 }

33.    Volume of the solid generated by revolving the region bounded by the lines x = 0 , y = 1 and the curve y = 4x about the line y -1 is equal to

(A) n!Q    (B) n! 2    (C) 5/2    (D) Zn/2

34. Let T : R² > R³ be a linear transformation such that

is equal to

' 1 1 f"1! y ' 1 ' 1 1 (B) 1 (C) i -1 (D) i 1 3 3 3 , 1 , V 1 ; v-1,

X 1 2 3 4 5 fix) -3 0 15 k 105

Then the value of k is equal to (A) 81    (B) 51    (C) 48    (D) 40

a.t)

37. The value of the integral J [(3x²+4xy+y² )dbe + (2x^a +2y)ciy | along the path

<0.0 s

x* +y* = 2xy is equal to

(A) 0    (B) 1

38,    The directions along which there is no change in the value of the function f ix,y) = e ⁽**⁺ *^y) at the point (3, - 2) are equal to

(A) - 0.61 - 0.8 j 0.6 + 0.8 j    CB) 0.6 - 0.8 j, - 0.6 I + 0.8 ] (C) - 0.61 -0.8 ), 0.6 i - 0.8 j    (D) 0.6i + 0.8 j, - 0.6 i + 0,8 ]

39.    If v(x,y) = 0xy(x² -y²) is a conjugate harmonic function of u(x,y)=x* -ax²y² +y⁴ then the value of (a, 0) is equal to

(A) (6,4)    (B) (6,2)    (C) (4,6)    CD) (4,4)

. The value of the integral j> [e*^%n fz³ jdz , where C = {z : j z | = 1}, is equal

41.    If the volume of the parallelopiped generated by the three vectors ik-2ai + 2j + ak_f b = 2i +4j+l and c = 0i+0j -k is equal to 4 then a and 0 are related as

(A) a = 0/4    (B) a = 0/2    (C) a = 20    CD) a = 40

42.    Let R be the set of real numbers. Which one of the following statements CAN NOT hold?

(A)    Arbitrary union of open sets in R is an open set in R

(B)    Arbitrary intersection of open sets in. R is an open set in R

(C)    Finite union of closed sets in R is a closed set in R

(D)    Finite intersection of open sets in B m n nrwm ea* ir.

be the probability distribution function of a random variable X. If Z

P{Z < a } = , then the value of a is equal to 8

44. Let {x_k } be a sequence obtained by using the iterative scheme

= 0.45+ (0.1+ 0.2 c) x_k -0.8 cxl.

The value of c for which {x_k } converges quadratically to 0.5 is equal to

(A) -1/8    (B) -1/2    (C) 1/6    (D) 1/4

46. (a) Briefly describe how seismic waves can be used to infer that the outer core of the Earth is liquid while the inner core is solid.    (9)

(b) Why is the composition of the core of the Earth thought to be largely metallic iron? (6)

47. (a) Define Isomorphism and Polymorphism.    (6)

(b) What are polymorphs? Give names of two minerals each of the polymorphs of any two - CaCC>3, C, AlSiOs and FeS2.    (9)

48. (a) Define, giving figures, (i) dendritic, (ii) rectangular and (iii) radial drainage pattern and how does each form?    (9)

(b) Define cirque, valley and piedmont glacier.    (6)

49. (a) Define briefly (i) an overturned fold (ii) a recumbent fold (iii) a nappe.    (9)

(b) What is a transform fault? What are triple junctions and how are they classified? (6)

50. (a) Briefly describe the main features of seafloor spreading.    (6)

(b) Briefly explain what critical test proved the seafloor does move?    (9)

(iii) What is the Mohs scale of hardness? How does one determine the hardness of a mineral?    (9)

(b) Plagioclase Feldspar contains variable amounts of Na and Ca in addition to Al, Si, and O. The Na end-member has the formula NaAlSisOs. Because the size of Na⁺¹ and Ca⁺² ions are similar Ca⁺² can substitute for Na⁺¹. Would the formula of Ca end-member be CaAlSigOg? Explain.    (6)

In the figure above, a diagrammatic cross-section showing relationship of variousl sedimentary and igneous rock units is given. Note the given ages of the two igneous! intrusive rocks. Cg-conglomerate, Sd-sandstone, Sh-shale and Lst-limestone.| With reference to this figure answer the following questions :

(i)    Arrange the formations 1 to7 from oldest to youngest.

(ii)    What can be inferred about the ages of the sedimentary formations 1-7 based on thej ages of the two intrusive igneous rocks?

(iii)    When did the folding occur in the area?

(iv)    What are the surfaces between formations 3-4 and 5-6 called?    (15)1

PHYSICS SECTION

Consider a solid sphere of mass M and radius R with uniform mass distribution. Find out the gravitational field strength at a distance r away from the centre of the sphere for

(a) 0 < r < R and r > R    (9)

(b) Sketch the gravitational field strength as a function of r.

54. A water supply tower of cross sectional area A with a load of m on the water surface is drained out by a narrow pipe of a cross sectional area a ( A) through a valve, a distance h below the water level. Calculate pressure and velocity at point P when

55. X-rays of 4 A wavelength falls on electron cloud and gets scattered. Determine maximum change in

(a)    kinetic energy of electron

(b)    velocity of electron. h

use = 0.024 A, h =6.6xl0^-34 Joule - sec, and c = 3 x 10 m/sec

m c

A thin rectangular polarizer P_t with x -axis as pass axis is kept at the origin. Another identical polarizer P₂ with z -axis as the pass axis is kept parallel to P_x at y=d. A Half Wave Plate (HWP) is introduced between P₁ and P₂ with its optic-axis making 45 with the pass axis of P₁. An unpolarized light propagating along y -axis is incident normally on Pj from left hand side. What would be the state of polarization after P₁, half wave plate, and P₂ ?    (15)

Consider two isolated vessels A and B. Each contains N molecules of a perfect monatomic gas at pressure P and temperature T_A and T_B respectively. The vessels are brought into thermal contact, keeping the pressure of the gas constant at P. Find the change in the entropy of the system at the equilibrium and show that the change in the entropy is positive.    (15)

58. A n -type silicon rod of length 0.7 cm has a cross sectional area of 0.1 cm². A DC bias voltage ol 35 V across the rod results in a 5.6 ampere DC current. Under this DC bias, an electric pulse applied at one end takes 10 // s to traverse the length of silicon rod.

Determine

(a) mobility of the charge carriers    (6)

(b) carrier concentration.

A long, straight, cylindrical conductor of radius a carries a uniform current I. This conductor has a cylindrical hole along its length at a distance d from the centre with its axis parallel to the axis of the conductor. Calculate the magnetic field inside the hole. (15)

MATHEMATICS SECTION

60. (a) Solve : 4 -j- - 5 (x2 -1) = .    (9)

y dx    y

(b) Discuss the convergence of the series

Inn J l+2+---+n

y .    (6)

1 J_ 9 J-----L n

61. (a) Perform two iterations of Newton-Raphson method to estimate the point on the parabola y=x² closest to the point (2, 1), taking the initial approximation x₀ =1. (9)

(b) Find the eigenvalues of A⁴, where A =

'I 0 -1 9 4 1

(6)

3 1

/

F = -x²yi+xy² j+(y³ -x³)k

around the curve C , where C is the intersection of the sphere x² +y² +z² -25 and the plane z =3 . The orientation of the curve C is counterclockwise when viewed from above.    (9)

(b) For n=l,2, -- and xe [0,1 ], let g_n (x) = x / (l + n x² ). Given that x=l/y[n is a point of maxima of the function g_n {x) on [0, 1 ], discuss the uniform convergence of the series

* on [0,1].    (6)

"Ti n(l + nx )

Consider the following system of linear equations

3x+y+2z =-1 x+2y-z= a x+z=-1 2x+by-z = c.

Determine the values of a, b and c for which the above system has (i) no solution,

(ii) infinitely many solutions, and (iii) a unique solution.    (15)

Number on die	1	2	3	4	5	6
Frequency	k	20	20	20	20	Si 1 o

Determine the values of k for which the hypothesis that the die is unbiased be rejected at the 0.025 significance level.    (9)

[Given: xl (0.975)=12.83, xl (0.025)=0.83, xl (0.975)=14.45 and *|(0.025)=1.24.]

Let X and Y be the continuous random variables with joint probability density function

(b)

x+y

0<jc<1, ley <3 otherwise.

f{x,y) =

5 0 ,

Find P{(X+F)>3}.

(6)

65. Apply the Residue theorem for complex variable to evaluate the integral

7 xsinx ,

r ₂--17n\    <¹⁵)

I (x²+16)(x+2)

Find the mass of a metallic block of varying density p{x,y,z)=p₀+xyz, bounded by the planes x=0, ;y=0, z= 0 and the sphere x²+y²+z²=a² lying in the octant x>0, y>0 and z> 0. Here p₀ is the constant density of the metallic block at (0,0,0).    (15)

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