CSIR NET - MATHEMATICAL SCIENCE

1 csir net , GATE, IIT-JAM, UGC NET , TIFR, IISc, JEST, JNU, BHU, ISM, IBPS, CSAT, SLET, NIMCET, CTET Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: E-Mail: Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005 Page 1 For IIT-JAM, JNU, GATE, NET, NIMCET and Other Entrance ExamsPattern of questions : MCQsThis paper contains 60 Multiple Cho ice Questionspart A 15, part B 25 and part C 20 Each question in Part 'A' carries two marksPart 'B' carries 3 marksPart 'C' carries marks C has more than one correct options and there is no negative marking in Part CTh ere will be negative marking @ 25% fo r each wrong answer.

2 Part A, marks in Part B csir net - MATHEMATICAL SCIENCE1-C-8, Sheela Chowdhary Road, Talwandi, Kota (Raj.) Tel No. 0744-2429714 Web Site Total marks : 200 Duration of test : 3 Hours MOCK TEST PAPER csir net , GATE, IIT-JAM, UGC NET , TIFR, IISc, JEST, JNU, BHU, ISM, IBPS, CSAT, SLET, NIMCET, CTET Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: E-Mail: Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005 Page 2 PART A (1-15) 1 T wenty four cl erk can cl ear 180 fil es in 15 days. Number of cl erk requi red to clear 240 files i n 12 days i s (1) 38 (2) 39 (3) 40 (4) 42 2.

3 In the gi ven fi gure, RA = SA = 9cm and QA = 7cm . If PQ i s the di am eter, then radius i s ARSQP (1)65cm7 (2) 130cm7 (3) 8 cm (4) None 3. If the ci rcles are drawn wi th radii R1, R2, R3 wi th centre at the verti ces of a triangle as shown in fi gure. Si de of triangle i s a, b, c respecti vel y, then R1 + R2 + R3 i s equal to csir net , GATE, IIT-JAM, UGC NET , TIFR, IISc, JEST, JNU, BHU, ISM, IBPS, CSAT, SLET, NIMCET, CTET Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: E-Mail: Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005 Page 3 R1R3 3(a + b + c) 1(abc)3++ 1(abc)2++ (4) 2(a + b + c) 4.

4 Study the following graph and answer the question given below it 101520253035404550 2 4 6 8101214161820198419851986198719881989No. of Tools (in '000)YearsTotal value of tools (in Rs crores)Production in a Tool Factory Number of Tools----- Value What was the val ue of each tool in 1985? csir net , GATE, IIT-JAM, UGC NET , TIFR, IISc, JEST, JNU, BHU, ISM, IBPS, CSAT, SLET, NIMCET, CTET Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: E-Mail: Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005 Page 4 (1) Rs 153 thousand (2) Rs 50 thousand (3) Rs 5, 103 (4) 559 5. T he total adults i n a ci ty i s 60000.

5 T he vari ous secti ons of them are i ndi cated bel ow i n the ci rcle What percentage of the empl oyed persons i s sel f empl oyed? (1) 5519 (2) 1195 (3) 20 (4) 5 6. Look at thi s seri es: 14, 28, 20, 40, 32, 64, .. What number shoul d come next? (1) 52 (2) 56 (3) 96 108 II54 18 IIIIVVI employees in the public sectorII employees in the private sector III employees in the corporate sectorIV self employed unemployed V csir net , GATE, IIT-JAM, UGC NET , TIFR, IISc, JEST, JNU, BHU, ISM, IBPS, CSAT, SLET, NIMCET, CTET Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: E-Mail: Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005 Page 5 (4) 128 7.

6 A car owner buys petrol at , Rs. 8 and Rs. per li ter for three successi ve years. What approxim atel y i s the average cost per li ter of petrol i f he spends Rs. 4000 each year? (1) Rs. (2) Rs. 8 (3) Rs. (4) Rs. 9 8. In a certain store, the profi t i s 320% of the cost. If the cost i ncreases by 25% but the selli ng pri ce rem ains constant, approximatel y what percentage of the selli ng pri ce i s the profi t? (1) 30% (2) 70% (3) 100% (4) 250% 9. T oday is Friday after 62 days, it will be : (1) T hursday (2) Friday (3) W ednesday (4) T uesday 10. A car travelli ng with of i ts actual speed covers 42 km in 1 hr 40 mi n 48 sec. Fi nd the actual speed of the car.

7 (1) 617 km / hr7 (2) 25 km /hr (3) 30 km /hr (4) 35 km /hr 11. P i s a worki ng and Q i s a sl eeping partner. P puts i n Rs. 3400 and Q puts P recei ves 20% of the profi ts for managi ng. The rest i s di stri buted i n proportion to their capi tals. Out of a total profi t of , how much di d P get ? csir net , GATE, IIT-JAM, UGC NET , TIFR, IISc, JEST, JNU, BHU, ISM, IBPS, CSAT, SLET, NIMCET, CTET Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: E-Mail: Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005 Page 6 (1) 460 (2) 470 (3) 450 (4) 480 12. A lawn i s the form of a rectangl e having i ts side i n the ratio 2:3 T he area of the lawn i s 1/6 hectares.

8 Fi nd the l ength and breadth of the l awn. (1) 25m (2) 50m (3) 75m (4) 100 m 13. An aeroplane covers a certai n di stance at a speed of 240 kmph i n 5 hours. To cover the same di stance i n 1 hours, it must travel at a speed of: (1) 300 km ph (2) 360 km ph (3) 600 km ph (4) 720 km ph 14. Fi nd out the mi ssi ng number of the gi ven question: 2 7 4 5 2 3 1 ? 6 10 42 72 (1) 2 (2) 4 (3) 5 (4) 3 15. All of the foll owi ng are the sam e in a manner. Fi nd out the one whi ch i s di fferent am ong them: (1) BFJQ (2) RUZG (3) GJOV (4) ILQX csir net , GATE, IIT-JAM, UGC NET , TIFR, IISc, JEST, JNU, BHU, ISM, IBPS, CSAT, SLET, NIMCET, CTET Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: E-Mail: Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005 Page 7 PART B (16-40) 16.

9 T he degree of extension 7Q16 3 8 + over the fi eld Q i s (1) 8 (2) 7 (3) 6 (4) 5 17 T he random vari abl e X has a t-di stri buti on with v degrees of freedom. Then the probabili ty di stri bution of X2 i s (1) Chi -square di stri bution wi th 1 degree of freedom (2) Chi -square di stri bution wi th v degrees of freedom (3) F-di stri bution wi th (1, v) degrees of freedom (4) F- di stri buti on wi th (v, 1) degrees of freedom 18. Let nmT : RR be a li near transformation and Am n be its m atri x representation then choose the correct statement. (1) Col umns of A are LI T i s onto (2) Col umns of A span Rm T i s onto (3) Col umns of A are LI T i s one one (4) T i s one one col um ns of A are LI 19. Let byx and bxy denote the regressi on coeffi ci ent of Y on X and of X on Y respecti vel y are equal, T he (1) y = x (2) = 1 (3) = 0 (4) None of the above csir net , GATE, IIT-JAM, UGC NET , TIFR, IISc, JEST, JNU, BHU, ISM, IBPS, CSAT, SLET, NIMCET, CTET Phone: 0744-2429714 Mobile: 9001297111, 9829567114, 9001297243 Website: E-Mail: Address: 1-C-8, Sheela Chowdhary Road, SFS, TALWANDI, KOTA, RAJASTHAN, 324005 Page 8 20.

10 What probabi li ty model i s appropri ate to descri be a situati on where 100 mi spri nts are di stri buted randoml y throughout the 100 page of a book? (1) Necessaril y Poi sson (2) Necessaril y Exponential (3) Necessaril y Normal (4) Could not decide 21. Whi ch one of the fol lowing be true for the functi on ( )( )21f xx sin,if x 0, f 00x = = (1) Functi on f i s not conti nuous on [0, 1] (2) Functi on f i s not bounded vari ation on [0, 1] (3) Functi on f does not exi sts (4) Functi on f i s of bounded variati on on [0, 1] 22. If [ ] be the Poi sson bracket T hen [],t = (1) ,tt (2) ,,tt + (3) ,,tt + (4) [],,tt + 23.