Nội dung text 26 Mathematical Science * Paper-II.pdf
Test Paper : II Test Subject : MATHEMATICAL SCIENCE Test Subject Code : K-2614 Test Booklet Serial No. : _______________________ OMR Sheet No. : _________________________________ Roll No. (Figures as per admission card) Name & Signature of Invigilator/s Signature: ____________________________________ Signature: ___________________________________ Name : ____________________________________ Name : ___________________________________ Paper : II Subject : MATHEMATICAL SCIENCE Time : 1 Hour 15 Minutes Maximum Marks : 100 Number of Pages in this Booklet : 8 Number of Questions in this Booklet : 50 K-2614 1 /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 fifty 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 this cover page. Do not accept a booklet without sticker-seal and do not accept an 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 oval 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 the Paper I Booklet only. If you mark at any place other than in the ovals in the Answer 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 soon after the examination. 11. Use only Blue/Black Ball point pen. 12. Use of any calculator or log table etc., is prohibited. 13. There is no negative marks for incorrect answers. 1. ! ! " # $% 2. &'( !) *+ ,-./ 0 '1 "2 "2 3 % 3. $ ( 4 5' 6 7 '1 " ( " 2 8 52 % 5- 92 ( 0" 0 ( 0 ( 85 5 : $ ;4 ( 5 % (i) '1 " ( 2 ' 15 (51 8 7) ( < = )" $# $% (>, ? '1 " ( @ ( $ A 3%0 ( @ ( " $ A 3% (ii) ! "#$ ! "%$&" ' "(&")*+ (#, -.$/,0)&1 2",(3 2", "",45& 2",6#7)"& " #, & & 89.# :'5;<8& "=>1 < ?. &. 67"@&',A BC D@ @&',A',"(51)"& EF"" :',"(5 4. '&+ '1 2" (A)7(B)7(C) 0 (D)B 2 & 5 , CD E02F % '1 " B $CE0 7( 2 (5G 0 < 85(H& (" 5 I A ( % G&,E70H A BC D (C)$CE0 55J2% 5. '1 "&'( I ( K> OMR E0)5 7 I"# II767";"IG#7 J#K&L%OMR E0 )5 < 85(H& A C E0 "2 & 7 < LM N C C852 % 6. OMR E0)5 ( >O 2 "P52(0 # Q$. 7. B5(8 ( "( ( C80(, J% 8. 2 0 "!R 23!) 5 )
Total Number of Pages : 8 Paper II 4 K-2614 17. Determinant of the matrix 34 5 67 8 9 10 11 ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ is (A) Zero over the field F2 I with two elements (B) Zero over the field (C) Nonzero over the field F2 I with two elements (D) Nonzero over the field F3 I with two elements 18. Let T : V → W be a linear mapping where V and W are vector spaces over of dimensions 5 and 6 respectively. Which one of the following need not be true ? (A) Nullity of T ≤ 5 (B) Rank of T ≤ 6 (C) Rank of T ≤ 5 (D) Rank of T ≤ Nullity of T 19. Let {xn} be a sequence defined by n 1 n1 n 3 2x x 1, x , n 1 2 x + + == ≥ + then { }nx (A) Converges to 2 (B) Converges to 3 2 (C) Converges to 3 (D) Diverges 20. Let a, b, c, d be real numbers with ad – bc = 1. Define the meromorphic function f by az b f(z) cz d + = + . Then f maps the (A) Upper half plane to itself (B) Upper half plane to lower half plane (C) Lower half plane to right half plane (D) Upper half plane to right half plane 21. Suppose f(z) is analytic in the entire complex plane and bounded. Then f(z) must be (A) sin z (B) cos z (C) a polynomial of degree greater than one (D) a constant 22. The locus of the curve given by | z + 2 | = | z – 2 |, z ∈ (A) is an ellipse (B) is a circle (C) consists of only the origin o (D) is the y-axis 23. Suppose f(z) = u(x, y) + i v(x, y) is a nonconstant analytic function on . Consider the families of curves defined by u(x, y) = constant and v(x, y) = constant. Then these families (A) never intersect (B) are always parallel (C) are asymptotic to the line y = x (D) are always orthogonal 24. Let f(x, y) = y2 + 4xy + 3x2 + x3. Then (A) (0, 0) is a minimum point of f (B) (0, 0) is a saddle point of f (C) (0, 0) is a maximum point of f (D) 2 4 , 3 3 ⎛ ⎞ − ⎜ ⎟ ⎝ ⎠ is a maximum point of f 25. Let f, g : [0, 1] → [ 0, + ∞ ) be continuous functions satisfying sup f(x) = sup g(x) 0 ≤ x ≤ 10 ≤ x ≤ 1 Then (A) f(t) < g(t) for all t ∈ [0, 1] (B) f(t) > g(t) for all t ∈ [0, 1] (C) f(t) = g(t) for some t ∈ [0, 1] (D) f(t) ≠ g(t) for all t ∈ [0, 1]