Title 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
Total Number of Pages : 16 K – 2520 3 Paper II 10. One of the eigen values of the matrix eA is ea, where A i i = −           a a a 0 0 0 0 0 0 , the product of the other two eigen values is (A) 1 (B) ea (C) e2a (D) e–a 11. Three fair coins are tossed together. Find the probability of getting one head and two tails. (A) 1 4 (B) 1 3 (C) 3 8 (D) 1 2 12. Given the matrix A =           1 3 111 111 111 what is the value of Det (eA) ? (A) e 1 3 (B) e (C) e2 (D) e3 13. A particle thrown upwards from earth’s surface reaches a height of 100 m and returns back. The acceleration of the particle at its highest point of reach has the value (A) zero (B) g 4 (C) g 2 (D) g 14. Suppose the radius of the earth were to shrink by 1%, its mass remaining the same, the acceleration due to gravity would (A) increase by 4% (B) decrease by 1% (C) not change at all (D) increase by 2% 15. If the differential cross-section in scattering is equal to a2 , where a is a constant, then the total cross-section will be (A) a2 2 (B) πa2 (C) 2πa2 (D) 4πa2 16. The center of mass of an L-shaped uniform wire as shown in the figure, with OA = OB = l, is at O (A) l l 2 2 ,       (B) l l 4 4 ,       (C) l l 3 3 ,       (D) 2 3 2 3 l l ,       • •
Total Number of Pages : 16 Paper II 4 K – 2520 17. If the Lagrangian of a mass m is given by L = 1 2 2 mx + xf, f being a constant, then x(t) can be obtained in terms of the constants c1 , c2 as (A) c1 + c2 t (B) c f m t 1 2 + (C) c c t f m t 1 2 2 2 + + (D) c1 + c2 t + ft2 18. A body of mass m moves in a circular orbit of radius R in a potential : V(r) = − K r , where K is a constant, then its orbital angular momentum about the centre of the circle is (A) 2Rkm (B) 2RKm (C) RKm (D) Rkm 19. Identify the correct Hamilton’s equations of motion from the following. (A) q  H p and p H q i i i i = ∂ ∂ = ∂ ∂ (B) q  H p and p H q i i i i = − ∂ ∂ = ∂ ∂ (C) q  H p and p H q i i i i = ∂ ∂ = − ∂ ∂ (D) q  H p and p H q i i i i = − ∂ ∂ = − ∂ ∂ 20. If the potential energy of a body is V(x) = (x2 – 4x + 4), the point of stable equilibrium is given by (A) x = 4 (B) x = 2 (C) x = –2 (D) x = 0 21. A rigid body consisting of three particles A, B, C is constrained such that A, B are rigidly fixed to be at rest. Which of the following statements correctly describes the behaviour of C ? (A) C can move on the surface of a sphere of constant radius (B) C can move on the circumference of a circle of constant radius with line joining A, B passing normally through the centre of the circle (C) C can move along the line joining A, B (D) C can move parallel to the line joining A, B 22. If the motion of planet (of mass m) around sun (of mass m) is treated as a two body problem, T the period of revolution, a, the semimajor axis and G, the gravitational constant, then the exact form of the third law of Kepler is (A) T a GM 2 3 4 = π (B) T a GMm 2 3 2 4 = π (C) T a G M m 2 3 2 4 = + π ( ) (D) T a M m GMm 2 3 2 4 = π ( ) +