Mathematics Paper I 2018 PDF

DO }iOT OPEN THE SEAL UNTII, ${STRUCTED TO NO SO Question Booklet No. 101 482 In...

DO }iOT OPEN THE SEAL UNTII, ${STRUCTED TO NO SO Question Booklet No. 101 482 Invigilatar's signature 201 I TGT * PAPEIT.-I : MATHEMATICS Tinie : 2 Hours Maximum Marks : 100 l ROLL NO. INSTRUCTIONS FOR CANDIDATES 1. This Question Booklet contains 50 optional questions. Each question comprises four responses (answers). You will selsct ONLY ONE response which you consider the best and darken the bubble on the OMR RESPONSE SHEET. 2- DO NOT write your Narne or anlthing else except Roll No. and the actual answers to the U, question, anywhere on the OMR RESPONSE SlmET. m 3' 4. DO NOT handle your OIvIR RESPONSE SHEET in such a manner as to mutilateo fold, etc. No candidate shall be admitted to the Examination Hall 20 nninutes after commencement r distribution of the T'est Booklet. The invigilator of the Examination Hall rvill be the tirne-ireepm and his decision in this regard is final. No candidate shall have in his/her possession inside the Examination t{ali any book, notehook or loose paper, calculator, mobile phcne. etc., except. hislher admit card and other things paper pcrnritted by the Commission. 6. Imr:irediately after tlre final beil indicating the closure of the examination, stop bubbling. Be seated iitl the OMR RESPONSE SHEET is collected by the invigilator, thereafter vor may leave the Examination FIall- 7 Volation of an-v of the atrove rules will render the candidate liable to expulsion fiom the exami- I nation and disqualifieation fi'om the e.xamination, and according to the nature and gravity of hisl her offence, helshe rnay be detrarred from f-uture exarninations aad interviews to tre conducted bv the comrnission and other suclr organization (i.e., LIPS{], ssc and spscsi. T{B CANDTNATES ARE ALLOWED TO IAKE TIIIS QUf,STI$N SOOKLBT ONLY ATTER. COMPLETION OF 2 {TWO) }IOURS OT EXAMINATI*N TIil{I. DO NOT OPEII*' THE SEAL UNT'II, I}{STR.UCTED TO CIO SO SEAL I One of the fbctors of the polynomial 5 The sum of all the elements of, a 2>:f Zx3 _ 3x2 _ t7x _t_ 30 is matrix cut tiom a calendar month is (A) x-3 found to be 48. The srnallest element cf the rnatrix is (B) 5x -? (C) x*Z (A) 7 (D) x12 (B) I 2. The difference and the products of two numbers are 3 and 10 respectively. The (c) e difference of the cubes of the numbers can be (D) r0 (A) 30 7 The sum of loC, and locu is (B) ee (A) ,,CU (B) ,,C, (c) Ta7 (D) tr7 (c) t,c* * (D) a The rth root of n * n * n.". up to rdh 'oC* 8. nct+ncz+nCz*... 4 nCp-t equals term is (A) n (A) ztr (B) nntL a) 2n*1 (c) (C) 2n*1 * L nn (D) zft*2 (D) n2/n 4. If + 23 + 33 +... + n3:225, then 13 g. If i : ,f1, then ltot1;1021...a 1t5o 1 +2 + 3 +... +rz is equal to equals (A) rzs (A) *1 +i (B) 7s (B) r-i (c) 25 (c) I (D) 15 (D) 0 5 A verlical cone of height ft and base area 10. The material of a cylinder of base ar.ea a and height ft is melted to make solid a is cut horizontally at half the height. cones of the same base atea s and height The volrrrnes of the cut portions are at h/2. The total number of cones that can the ratio be made is (A) 1 :8 (A) 6 (B) | :7 (B) I (C) 7 :8 (c) lo (D) t :2 (D) t2 I 01iYY8-20 1 8/N{AIH*I (2) r 11. A moderately symrnetric distribution of 1+sin20 data possesses a mean of 10 and median 16. equals cos 20 12. The mode of the given distribution is estimated as (A) tan 0 (A) 16 (B) 1+tan0 (B) 14 I (c) 13 (c) 1+tan0 (D) 11 1+ tan0 t2. Evaluation of the integral Jlagxdx, (D) 1* tan0 apart &om the constant of integration, yields 17. Ir sino- = 1 [t.l) then tan 20 is given s[-.2)' (A) log x by (B) Tagx - x (C) r log x 9 (A) (D) xlogx-x zs 13. The derivative ofxu with respect to log r 22 is (B) ? (A) I log x 7 (B) luil (c) 40 (C) #tn (D) xnd 24 {D) 14. If 1, o, o? arc the eube roots of udty, 18. 'fhe rules fbr arvarding marks in an then I 1 equals MCQ type test lvith S0 questions are as tl) tblioll,s : (A) (i,2 All questions must be atten:pted; 2 marks {B) *az fcreach correct answer, and 0.5 mark (C) (D3 deducted for each wrotlg answer. (D) -603 If a candidate scores 0 in the test, the number of questions correcttry answered 15. The number of odd integers of three is digits that can be formed with digits 1, 2, 3, 4 without repetition is (A) t2 (A) t2 (B) 14 (B) 16 (c) 16 tc) 2* (D) (D) 24 i8 t 01 IYYS-2 0 1 81tui1\1'H-I (3)  23. A rnatrix,{ is termed as singular matrix if 19. Evaluation of the limit lim x*+0 l+l L; ) (A) all the elernents of rnatrix I are 0 yields (B) the determinant of the matrix,4 is 0 (A) 0 (C) the inverse of matrix -4 is the {B) 1 rnatrix ,4 itself (c) 5 (D) 2s (D) the product of the rnatrix. and its transpose is a aull rnatrix 20. The inequality " !:2rs is correctlY 2x+4 satisfied by the values of x when Io 0 1l (A) 0