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# 1st and 2and Semester Physics Streem (2013-December) Question Papers

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### 1st and 2and Semester Physics Streem (2013-December) Question Papers

1. 1. - ^, (r lOMATl1 USN First Semester B.E. Degree Examination, Dec.2013lJan.2Ul4 Engineering Mathematics -I Time: 3 hrs. Max. Marks:100 Note: l. Answer any FIW full questions, choosing at leust twofrom each part. 2. Answer all objective type questions only in OMR sheet page 5 of the answer booklel 3. Answer to objective tlpe questions on sheets other than OMR will not be valued. PART _ A o o o 1 u.,,. ,Choose : L for the following the a . ii) o 3e If iii) -!. > ;n bo' troo .= .a -l a= o() (g0 ooi >d B) (-l)nnl iv) y: C) (-.rt*i (x + l)n*1 () o> oZ t, (-l)n (n + 1)! A) ioo YJO oC FO I x+l E : 3o;;ect.answels If (ax +b)- with (-1)'n! D) (x + l)n 1-1)n-rn! (". m: n, then y, is fli A) n! an B)0 C) n! bn D)n! The geometriCal interpretation of Lagrange's mean value theorem is f(b)-f(a) B) f,r.t_f(b)+f(a)C; l''lc)_ f(b)-f(a) A)f'(c)=g,(c) g(b)-g(a) b-a b-a D)noneof these The Maclaurin's series expansion of e-' is 2! 3! ,,:3! C) *- x- * x3 (04 Marks) D) * *4*d* 2t3!.213! b. Ify:sinlog (x2 +2x+ l),provethat(x+ l)'yr,+ r+(2n+ 1)(x+ 1)yn+1n2+4)yn:0. (04 Marks) c. d. 2 a. 3.) oi= If x ispositive, showthatx> log (1 +x) (06 Marks) Using Maclourin's series, expand log (1 + e*) upto the terms containing x Choose the correct answers for the following . i) (06 Marks) : .--.. /,|;J3!I equalto -+l lis " -( f;-x ) lim =:: o-X A) o: 6: r"-L*. 2 B)-2 C) 1 D)-1 ii) If \$ be the angle between the tangent and radius vector at any point on the curve alE r = (e), then sin \$ is equal to !o A) 5.e boo -50 o= iii) 9O tr> iv) o L.)< o o z = L o b. c. C) ,do 'dr l'-tY ,2*rl-rr2 s1 ''*,lY' 'rl*x'-rr, ct ? *,,'Y '11 t + z -rt2 ,t : a' cosm0. Find the radius of curvature for the curve v2=d9:*), x - D) dsl : Find the Pedal equation of the curve x d. gt.do 'ds The rate at which the curve is bending called A) radius of curvature B) curvature C) circle of curvature D) The radius of curvature for polar curve r (e) is given by A) ' ,i 6i drlds axis. lim (ax + t )x. Evaluate*--*(.ax-l) (04 Marks) where the curve meets the (06 Marks) (06 Marks)
2. 2. 1OMAT11 3 a. Choose the correct answers for the following i) If u: log (x2 + f + r'1,then I 2v ts .,-+ x'+y'+z' If ,, 0z 2x ii) : u:(x, x'+v'+7,- y) and y is a function x, then . du au ^'d* Cd, fu aury ndu -r 'dx ,l I l ax q - 2z D) *2 +y2 +12 *2 +y2 -12 -au du audv ax dx dy dx ^.au du dufo ut dudy A 2z c) ) ax dx ar ax dx - ,' ^2. iii) If r={*.s=- a2f a2f , then the condition for the shddle point is &t=3 oxo i','"'' dx' dy' :,,, A) rr-s2?O g)rt-s2:o iv) Ifu:x*yr z,y=,!+z,z:z,then / J[ b. a r1r* s'> D)rt-s2+0 O ''u'l ]ir.qrulto x'Y'zl c)0 B) -1 A)1 C) mirror is given by the formula of these .none (04 Marks) D) I -I u= Z . If .qual errors. 'e' are made (t + r) in the determination of u and v. Show that the rosulting error in f is el - - I. ^ u: f(2x-3y.3y -42.42-2x).prove +"^*1tu;^ ,ur-)'v) that 1;.i n*i;=0. d. If x: u(1 - v), y: uY, Ftove that JJ' :1. c. 4 a. ' If Choose the correct answers for the following : Direotional derivative is maximum along A) tangent to the surface C) any unit vector (04 Marks) (06 Marks) (06 Marks) i) ,ii) Ifr: iii) If f : iv) B) normal to the Suiftce D) coordinate axes lx;+y1 + 2rl, then Vrn is 3x2 - lf C) V.Vr' + 4z2,thencurl (grad f) is A) 4x - 6y + 8z B) 4x1-6y; + 8z k C) b' If the base vectors er and azzta orthogonal then I e1 x A)0 D) none of these B)-1 c)+1 D)3 e2 | is D) none of these (04 Marks) -+ b. If F =(x+y+l)i+ j-(x+y)k, c. Find constants,a, and,b, such that showthat F.crulF =0. i Also find a scalar function \$such that d. = (axy + r31i+ (3x2 i - V0. Prove that a spherical coordinate system is orthogonal. 1^{A (04 Marks) - z)j+ (brr2 - y)k is irrotational. (06 Marks) (06 Marks)
3. 3. 1OMAT11 PART _ B 5 a. Choose the correct answers for the following : 1l il 7 Jsin x dx is equal to 0 A) ii) The asymptote of (2 A) iii) x:2 .2 JfiA iv) c. d. 6 a. : C) x - axis Evaluate + acosx)dx -)z a(1 - cos0) is B) 3a Iar,t 0' D) none of these =:"'" a^ *3 is axis ) n c){ '2 2 6a D) 35 B)I 2 1(tr C): The entire length f the asteroid x2l3 + A) b' - x)l : B) y - The ar€a of the cordioid r A)_ ?) 32n Bt '35 zero f : '3 )/7 a-," JA D) '2 . rS D) Cy,za uy:airrrr.*iating a. (04 Marks) under the integral si 2a Evaluate I"'.lZu- *2dr. using reduction formula. Find the volume of generated by the revolution of the curve line. Choose the D ii) corrbct'u.rr*.r, for the following : (06 Marks) . The general solution of the differential equation dyldx : (y/x,) + tan (y/x) is B) sin (y/x) : cx sin (y/x) : c C) cos(y/x) : ci , ,: cos (y/x) : c ,,D) .A) ''.'the family of straight lines passing through the origin is represented by the differential equation: A) ydx+xdy:0 B)xdy-ydx:0 xdx+ydy:0 D)ydy-xdx:0 iii) The homogeneous differential equation Mdx + Ndy : 0 can be reduced to a C) differential equation, in which the variables are separated by the substitution A) v: vx B)x*y:v c) xy: v D)x-y:v ir) The equationy A) b. c. d. y: ae-" Solve 1, + fl9dx - 2x: c represents the orthogonal trajectories of the family B) x2 + 2f :u c) xy:.a y = e3*1x + l)2. D) x + 2y: a (04 Marks) (04 Marks) Solve (1 + xy) ydx+ (1 -xy) xdy:0. Find the orthogonal trajectory of the cordioids r: 3 of 4 (06 Marks) a(l - cos 0). (06 Marks)
4. 4. 1OMATl1 7 a. Choose the correct answers for the following i) : If every minor of order 'r' of a matrix A i, ,..o, then rank of A is A) greater than r B) equal r C) less than or -r----- -" . D) less rvo' / than r. "q*l,o -: The trivial solution for the given system of equations x + ly * 3z:0, 3x + 4y+ 42* 0, J 7x+ 10 y + l2z:0 is ii) A) (1, 1, t) B) (1,0,0) c) (0, 1,0) iii) Matrix has a value. This statement / "> -' "'' . . , 11) is always true B) depends upon the matrices C) is false iv){.ai1singularandp(A):p(A:B)thenthesystemhas D) (0,0,0) D; none of these solution B) infinitely many solution c) trivial sorution D) no solution. Using elementary transformations, find the rank of the matrix '; ' ,.' A) unique b. ,' tt l:41 I ^ 3 l-2 2 _l 21. (04Marks) s_l c. Showthat the system* d. Apply Gauss 8a. 2x+ 5y t 7z i y'* z:4;2x+ y - z: l; x- y *22:2 :- 52 ; 2x-r y - z: Jordan method to sorve the system of equation 0; + S, + i ;': ;.- Choose the correct answers lor the following A square matrix A is called orthosonai i) A)A:AL ii) B)A':A-I The eigen vatues ofrhe ,nu,ri* ii0 iv) ' A)lrJ6' is consistent, solve the (06 Marks) : (06 Marks) : Iif ,,,gy AA-r:I D) none of these | | fl ^r, 142 2) B)ltJ5 c)Js D)l form xf +2xf-3xj are respecrively T11e^iTex;d A) 2,.t B) C) 1, -: njrron. of these Two square matrices A and B are similar. if ::. A) A: B B) B : p-rAI, C) Ar : Br D) A-r : B-r. signature of the quadratic " 1,2 1 * 322 - 12yz + 4zx_gxy to tt . .urronfuii Orljo Marks) Reduce the quadratic c. Determine the characteristic roots and eigen vectors 21 s I-6 -6 A=l 7 l, -4 . .:. b. d' :,' -41 3j Reduce the quadratic form gx2 + 7y2 of . form (04 Marks) (06 Marks) xl + 2xl - 7"1 ***rF* - 4xp2+ 8x2x3 into sum of squares. (06 Marks)
6. 6. 06PHYt2t22 2 b. c. d. rr'3|' r' Obtain an expression for energy eigen value of a particle in a potential well of infinite height. (07 Marks) Explain the most probable state of the particle by drawing probability curves. (05 Marks) The position and momentum of 2 kev electrons are simultaneously determined and if its position is located within 0.12 nn, what is the percentage of uncertainty in its momentum= (04 Marks) 3. Choose the correct answers for the following i) A) ii) iii) c. 4 a. u,+ ., + " D) independent of T If Fermi energy of a metal is 3 eV, its Fermi temperature is A) 3'"5 r 104 K B) 1.6 x 102 K c) 3.5 , 103 K, '', " D) 10-12 K Current,of 3A is flowing through a cylindrical copper wire ofradius 3 mm. the current density is nearly A) 105 B) 1or c) 106 A/# D) 10-6 A/m2 Drift velocity of electrons in a metal depends on A) mass of eterman B) applied electric field C) mean collision time D) all of these Define mean tree path. mean collision time and relaxation time. Derive an expression for conductivity in metals. (10 Marks) Explain the merits of quantum free eleOtron theory. (06 Marks) Nrl .:.,, iv) b. 12 gl|IiT.? : At very high temperatures, the mean collision time or an electron t, A/m2 Choose the correct answers for tfre,fof6wing (04 Marks) i) The dipolemendent between the pair iD separated by a distance of l0 prm is A) 10 x 10-12 B) 10-12 C) 10 x 1012 D) 10-12 cm The distance between plates of a parallel plate capacitor is doubled. The capacitance iii) cm ' of cm opposite charges each of magnitude 1 pC cm A) doubled B) halved C) increases,by 4 times D) decreases by 4 times Relation,between magnetic flux density, permeability and magnetic (with uiual notations) is given by '' field intensity A)p:BH B) B: pH C) H: Bpr il; No relation exist iv) " ;Barium titanate is an example of " A) ferromagnetic material B) superconducting mateiial C) ferroelectric material D) none of these Explain various electrical polarization mechanisms in dielectrics. (06 Marks) What are ferroelectrics? Explain ferloelectric hysterisis. (05 Marks) Briefly explain the paramagnetism phenomenon using Langevin's theory. (05 Marks) ,,,,,... b. "c. d. 5 a. PART _ B Choose the correct answers for the following : Pumping process in diode LASER is by i) optical means B) forward bias C) electrical discharge D) thermal means Semiconductor LASER is not preferred in LASER drilling since A) beam is less powerful B) beam is highly powerful C) beam has large wavelength D) none of these A) i, (04 Marks)
7. 7. 06P}IYl2l22 5 a. iii) Holograms can give a clear 3D image if they are observed under A) white light B) green light C) blue light D) same wavelength of light used for recording the hologram. ir) LASER beam is highly powerful due to A) high intensity B) less broadening C) constructive interference D) all of these With the necessary diagram, explain the construction and working of He-Ne c. d. 6 a. d. Marks) Wlf LASER is preferred for environmental pollution monitoring? Explain the principle and relative merits of LIDAR system (05 Marks) Find the ratio between Einstein coefficients for stimulated and spontaneous transmissions in a LASER system emitting light of wavelength 5000 A. (04 Marks) ., ,:"'.,,. Choose the correct answers for the following If the critical temperature lor specimen is above 0 K. i) A) semiconductor B) conductor .. a. (04 Marks) it must be C) insulator D) super conductor SQUID is used ro measure A) high magnetic field ,: B) low magnetic field ,:. D) high resistance C) high potential dilference iii) Propagation of light ray in graded index fiber is by eg\$TFi.e.L B) diffiaction , ggi:1,t",;l'ri" C) reflective confinement D) none of these iv) Shorter wavelength radiations are not preferred in optical fibers due to A) high absorption loss B) high scattering loss C) not easily available D) none of these Explain type I and type II super conductors with necessary graph and example. (06 Marks) Obtain an expression for angle of acceptance and numerical aperture of an optical fiber. Also explain the condition for light propagation in a optical fiber. (06 Marks) An optical fiber has core index of 1.6 and cladding index of 1.4 with core diameter of 40 pm. Calculate 'V' number ratio when the fiber is in air and;ih water of refractive index 1.33. Given wavelength of light is 500 nm. (04 Marks) ii) b. c. LAS% .' Choose the correct answers for the following i) ii) iii) iv) : (04 Marks) The atomic packing factor of NaCl crystal A) s2% B) r00% c) 74% D) 68% Four types of Bravasis lattices are observed in A) Rhombohedral structure B) Monoclinic system C) Triclinic system D) Orlhorhombic system Acrystalhas unit cellproperties a* b * c and cr: p:90o + B, is : ;]: A) orthorhombic B) ..,1;; C) tetragonal D) triclinic The Miller index of the plane parallel to Y-axis is monoclinic A)(101) B)(01 1) C)(1co1) D)(co 1 1) b. Obtain an expression for interplanar spacing in a crystal in terms of lattice parameters. c. What is coordination number? Explain this with reference to SC, BCC and fcc structures. (06 Marks) (06 Marks) d' X-ray of wavelength 5 A interacts with a crystal. If the second order reflection was observed at a glancing angle of 30o, calculate the lattice constant. (04 Marks)
8. 8. 10crv13/23 USN First/Second Semester B.E. Degree Examination, Dec.2013 /Jan.2Dl4 Elements of Givil Engineering and Engineering Mechanics Time: 3 hrs. Max. Marks:100 Note: l. Answer any FIW full questions, choosing at least two from each part. 2. Answer all objective lype questions only in OMR sheet page 5 of the onswer booklel ' ,, , 3. Answer to objective ltpe questions on sheets other than OMR will not be valaed. (J (.) PART _ A o I a I a. () 3e --^l -O ?a bridge b. c. 2 a. o -l' a= AE !o 5.v > (F ooo EOO ()= *o tr> o lr< * a'l minimum translation rotation these ' B) rotation D) none of these B) D) none of Z.CFry,:I lF/ "-Y: l*i *rre{.ut*" i:'; "*-*3'::': l;l ,.i* trb ,/"ril if,]ffi7 6ff*,") rotation Moment,+f a force will produce A) translation C) porn translatlon and rotatron L,). bottr translation ancl rotation A bloc'k'weighing w : 10 kN is resting on an inclined plane as shown in'>8ry,6. and Determine its components normal to and parallel to the inclined plane. The plane makes an angle of 20o with the horizontal. . (04 Marks) c, . A body is subjected to the tkee forces as shown in Fig.Q2(c). If possible determine the direction of the force "F" so that the resultant is in 'x' direction, when (i) F : 5000 N, ( ii) F : 3000 N. (12 Marks) 3a. Choose the correct answers for the following i) o o q (10 Marks) (06 Marks) maximum C) both translation (.) Z D) reservoir water maximum A) b. dam Choose the correct answers for the fullowing : (04 Marks) The component of a force perpendicular to its line of action is A) B) C) zero D) none of these The moment of a force about a moment centre lying on its line of action is A) B) minimum C) zero D) Two equal and opposite forces separated by a distance will produce ii) ?() so- D) camber What are infrastructure related projects? o() 63O 'ia On margin dam D) lift bridge B) soil Cl air D) none of these With the help of neat sketches, briefly explain the cross-section of road and gravity dam. A) a= a6 (04 Marks) bridge median dams i) bQi (! (! bridge Kerb iii) Jh ET (,) c i) ii) () goo .= c-.I Choose the correct answers for the following : A bridge constructed at some angle to river flow is A) -kpw B) square C) steel The stttlature that separates roads into separate lanes is called A) B) C) road The upstream side of a dam A) arch B) gravity C) earth ii) iii) ir) (04 Marks) : In case ofcoplanar concurrent force the resultant force passes through A) point of concurrence B) away from point of concurrence C) different plane D) none of these If two concurrent forces each of 'P' act at right angles to each other, their resultant is A) 2P B)P JiP D 2JP : 0 and IU: 0 for a coplanar nonconcurrent force system, then it is in If IV A) equilibrium B) translation C) rotation D) none of these Conditions of equilibrium for a coplanar concurrent force system is A) one B) two C) three D) four Q