Tiêu đề K-2520 (Physical Sciences) (Paper-II).pdf ✅

Paper : II Subject : physical science Subject Code : 25 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 – 2520 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 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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Total Number of Pages : 16 Paper II 2 K – 2520 1. Identify the vector that is perpendicular to both ˆ ˆ ˆˆ ˆ ˆ (i 2 j 3k) and ( i j 2k) + − −+ − from the following. (A) ˆ ˆ ˆ i 3j 2k + + (B) ˆ ˆ ˆ 2i 3j k + + (C) ˆ ˆ ˆ −+ + i 5j 3k (D) ˆ ˆ ˆ i jk + + 2. If ˆ ˆ 2 2 A 2yi x yj and 2x y = − φ=  , then ∇φ   A. at (1, 1) is (A) 1 2 (B) –2 (C) 6 (D) 12 3. The value of the integral d dx x e dx ikx ( ( δ )) −∞ ∞ ∫ where k is a constant and δ(x) is the Dirac delta function is given by (A) zero (B) sin k (C) cos k (D) – ik 4. The two independent solutions of the following differential equation d y dx dy dx y 2 2 + + 3 2 = 0 are (A) e–x, e–2x (B) ex , e3x (C) e2x, e3x (D) ex , e–2x 5. The number of independent components of a real antisymmetric tensor of rank two in 4 dimensions is (A) 4 (B) 6 (C) 8 (D) 10 physical science Paper – II Note : This paper contains hundred (100) objective type questions. Each question carries two (2) marks. All questions are compulsory. 6. If v(x, y) = 2xy + 3, f(z) = u(x, y) + iv(x, y) is analytic and further f(z = 0) = 2 + 3i, then the function u(x, y) is (A) x2 – y2 + 2xy (B) x2 – y2 + y (C) x2 – y2 + 2 (D) x2 – y2 + 2x 7. The value of O dz z c ∫ where c is a unit circle with origin as its center and the integration is done in a clockwise path is (A) 2πi (B) – 2πi (C) zero (D) i/ 2π 8. The number of independent parameters of the group O(3) and SU(2) are respectively (A) 3, 3 (B) 3, 2 (C) 2, 3 (D) 2, 2 9. Any Hermitian 2 × 2 matrix H can be expressed in terms of the 2 × 2 identity matrix I and three Pauli sigma matrices σx , σ y , σz as H = a0 I + a j j j x y z σ = ∑, , where (A) a0 is real and ax , ay , az are pure imaginary (B) a0 , ax , ay , az are all pure imaginary (C) a0 is pure imaginary and ax , ay , az are all real (D) a0 , ax , ay , az are all real