Title K-2518 (Physical Science) (Paper-II).pdf ✅

Test Paper : II Test Subject : Physical Sciences Test Subject Code : K-2518 Roll No. OMR Sheet No. : ____________________ Name & Signature of Invigilator/s Signature : _________________________________ Name : _________________________________ Time : 2 Hours Maximum Marks : 200 Number of Pages in this Booklet : 16 Number of Questions in this Booklet : 100 K-2518 1 ±Üâ.£.®æãà./P.T.O. Instructions for the Candidates 1. Write your roll number in the space provided on the top of this page. 2. This paper consists of Hundred multiple-choice type of questions. 3. At the commencement of examination, the question booklet will be given to you. In the first 5 minutes, you are requested to open the booklet and compulsorily examine it as below : (i) To have access to the Question Booklet, tear off the paper seal on the edge of the cover page. Do not accept a booklet without sticker seal or open booklet. (ii) Tally the number of pages and number of questions in the booklet with the information printed on the cover page. Faulty booklets due to pages/questions missing or duplicate or not in serial order or any other discrepancy should be got replaced immediately by a correct booklet from the invigilator within the period of 5 minutes. Afterwards, neither the Question Booklet will be replaced nor any extra time will be given. 4. Each item has four alternative responses marked (A), (B), (C) and (D). You have to darken the circle as indicated below on the correct response against each item. Example : A B C D where (C) is the correct response. 5. Your responses to the questions are to be indicated in the OMR Sheet kept inside this Booklet. If you mark at any place other than in the circles in the OMR Sheet, it will not be evaluated. 6. Read the instructions given in OMR carefully. 7. Rough Work is to be done in the end of this booklet. 8. If you write your name or put any mark on any part of the OMR Answer Sheet, except for the space allotted for the relevant entries, which may disclose your identity, you will render yourself liable to disqualification. 9. You have to return the test OMR Answer Sheet to the invigilators at the end of the examination compulsorily and must not carry it with you outside the Examination Hall. 10. You can take away question booklet and carbon copy of OMR Answer Sheet after the examination. 11. Use only Blue/Black Ball point pen. 12. Use of any calculator, electronic gadgets or log table etc., is prohibited. 13. There is no negative marks for incorrect answers. 14. In case of any discrepancy found in the Kannada translation of a question booklet the question in English version shall be taken as final. A»Ü¦ìWÜÚWæ ÓÜãaÜ®æWÜÙÜá 1. D ±Üâo ̈Ü ÊæáàÆᤩ¿áÈÉ J ̈ÜXÔ ̈Ü ÓܧÙÜ ̈ÜÈÉ ̄ÊÜá3⁄4 ÃæãàÇ... ®ÜíŸÃÜ®Üá° ŸÃæÀáÄ. 2. 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Paper II 2 K-2518 *K2518* Total Number of Pages : 16 1. The eigenvalues of a 5×5 matrix B are 2, 1, 0, –1, –2. The determinant of eB is (A) e (B) 1 e (C) 1 (D) 0 2. Given d x A exp 2 , A(e ) ˆ ˆ dx   − = π     is (A) –ex (B) ex (C) –e–x (D) e–x 3. The value of sinx (x)dx ∞ − ∞ δ′ ∫ is (A) 1 (B) –1 (C) 0 (D) ∞ 4. A solution of the differential equation 3 4 dy y dx x = − is (A) y2 x3 = const. (B) 3 2 2 y const x = . (C) 3 2 2 3 y x − = const . (D) 3 2 2 3 y x + = const . Physical Sciences Paper – II Note : This paper contains hundred (100) objective type questions. Each question carries two (2) marks. All questions are compulsory. 5. If Ak ij is a third rank mixed tensor, it transforms under the coordinate change { } x x{ } i j → as (A) A x x x x x x k A ij i m j n k l l mn = ∂ ∂ ∂ ∂ ∂ ∂ (B) A x x x x x x k A ij i m j n l k l mn = ∂ ∂ ∂ ∂ ∂ ∂ (C) A x x x x x x k A ij m i n j l k l mn = ∂ ∂ ∂ ∂ ∂ ∂ (D) A x x x x x x k A ij m i n j k l l mn = ∂ ∂ ∂ ∂ ∂ ∂ 6. Which of the following is not an su(2) matrix ? (A) e e i i φ φ 0 0 −       (B) 0 0 e e i i θ θ −       − (C) 1 1 1 1       (D) 0 0 i i       7. Which of the following matrices are Hermitian ? a. 0 1 −1 0       b. 1 1 1 1−       c. 0 0 i −i       d. i i 1 1 −       (A) a, b, c (B) b, c (C) b, c, d (D) a, d, c
Paper II 3 K-2518 *K2518* Total Number of Pages : 16 8. The work done by the force F xi yj = +ˆ ˆ  along a circular path from (1, 0) to (0, 1) is (A) 0 (B) 1 (C) –2 (D) 2 9. The volume of the parallelopiped with edges A i j, B j k and C k i =+ =+ = + ˆˆ ˆ ˆ ˆ ˆ    is (A) 8 (B) 6 (C) 4 (D) 2 10. f(z) is a function of complex variable z given by 2 z 1 f(z) . (z 1) − = + (A) z = –1 is a simple pole (B) z = –1 is a branch point (C) z = 1 is a branch point (D) z = 1 is analytic in the region 1 z 1. 2 − = 11. Which differential equation has singularities at x = 1, –1, ∞ ? (A) Legendre differential equation (B) Bessel differential equation (C) Hermite differential equation (D) Laguerre differential equation 12. If F = ax + bv, where F, x, v are the magnitudes of force, position and velocity respectively, then a b has the dimensions (A) T–2 (B) T–1 (C) T (D) T2 13. The physical quantity that has the same dimension as the action S in Hamilton’s principle is (A) Linear momentum (B) Energy (C) Orbital angular momentum (D) Torque 14. qk is said to be a cyclic coordinate if (A) k L 0 q ∂ = ∂ (B) k L 0 q ∂ = ∂  (C) k L 2 n q ∂ = π ∂ (D) L(q ) L(q 2 ) k k = +π 15. If F = ∑qi Qi is the generating function of a set of canonical transformations then (A) pi = Qi , Pi = –qi (B) pi = qi , Pi = –Qi (C) pi = –Qi , Pi = qi (D) pi = –Qi , Pi = –qi 16. Lagrangian equations of motion : i i dL L 0 dt q q ∂ ∂ − = ∂ ∂  are applicable to (A) conservative, holonomic systems (B) non-conservative, holonomic systems (C) conservative, non-holonomic systems (D) non-conservative, non-holonomic systems 17. Phase space trajectory of a one-dimensional simple harmonic oscillator is (A) Hyperbola (B) Parabola (C) Ellipse (D) Cycloid 18. The Lagrangian equations of motion will remain unchanged, if the Lagrangian L is replaced by L + L′ where L′ is a total time derivative of a function of (A) Generalised coordinates and velocities (B) Generalised velocities and time (C) Generalised velocities (D) Generalised coordinates and time
Paper II 4 K-2518 *K2518* Total Number of Pages : 16 19. A planet moves in an orbit l r( ) 1 cos θ = +∈ θ where l and ∈ are constants, under the influence of a force 2 krˆ F(r) (k 0). r =− >   The orbital speed of the planet is minimum when (A) θ = 0 (B) 3 θ = π (C) 2 θ = π (D) θ = π 20. A particle of mass m moves in a central potential V(r) = kmr3 (k > 0). The angular momentum for which the orbit will be a circle of radius a about the origin is (A) ma k a (B) 2 ma 3ka (C) 2 ma ka (D) ma ka 21. If the Lagrangian of a system is 1 22 4 L(q, q,t) q (q) q 2   = − the equation of motion is (A) 2 2 qq (q) 4q 0   ++= (B) 2 3   q (q) 4q 0 ++= (C) 2 3   q (q) 4q 0 +−= (D) 2 2   q (q) 4q 0 +−= 22. If the orbit of the equation in r – θ plane is r = ekθ , then the central force varies as (A) 3 1 r (B) 2 1 r (C) 1 r (D) r 23. For which values of α and β is the following transformations Q = qα cos β q P = qα sin β q is a canonical transformation ? (A) 1, 2 2 α= β= (B) 1 2, 2 α= β= (C) 1 , 2 2 α=− β= (D) 1, 4 4 α= β= 24. If the spatial and temporal coordinates of two events in an inertial frame are : (x1 , y1 , z1 , t1 ) and (x2 , y2 , z2 , t2 ) then the following expression remains unchanged under Lorentz transformations (A) (x1 – x2 )2 + (y1 – y2 )2 + (z1 – z2 )2 (B) (x1 – x2 )2 + (y1 – y2 )2 + (z1 – z2 )2 – c2 (t1 – t2 )2 (C) (x1 – x2 )2 + (y1 – y2 )2 + (z1 – z2 )2 + c2 (t1 – t2 )2 (D) (x1 + x2 )2 + (y1 + y2 )2 + (z1 + z2 )2 – c2 (t1 + t2 )2