CSIR NET 2022 Question Paper Mathematical Sciences

CSIR MATHEMATICAL SCIENCES BIL
Topic:‐ 704_PARTA_CSIR_SEPT22_SET1_BIL

1) In a test with multiple choice questions, candidates get 4 marks for a correct answer and lose 1 mark for an incorrect
answer. Two candidates A and B attempting 18 and 13 questions, respectively, secure equal marks. How many more
INCORRECT answers does A have compared to B?
बह िवक प प वाले एक टे ट म, अ यिथय को प येक सही उ र के िलए 4 अंक पा होते ह और प येक गलत उ र के िलए 1 अंक कम िकया जाता है दो
अ यिथय , A और B ने कमशः 18 व 13 प को कर, एक समान अंक पा िकये A के, B क अपे ा िकतने अिधक गलत उ र ह?
[Question ID = 555][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q1]
1. 3 [Option ID = 2217]
2. 4 [Option ID = 2218]
3. 5 [Option ID = 2219]
4. 6 [Option ID = 2220]

2) A ranks 10th from both the top and the bottom in merit among the girls in her class. B ranks 6th from the top and 16th
from the bottom among boys in the same class. If A is immediately ahead of B in merit order, her rank in the entire class
would be
अपनी क ा म, लड़िकय के वरीयता कम म, A का थान दोन ऊपर से व नीचे से, 10 वां है उसी क ा म, लड़क के वरीयता कम म, B का थान ऊपर से 6
ठा और नीचे से 16 वां है वरीयता कम म, A यिद B के ठीक ऊपर है, अपनी पूरी क ा म उसका (A का) थान होगा
[Question ID = 556][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q2]
1. 16th from the top and 26th from the bottom
ऊपर से 16 वां और नीचे से 26 वां [Option ID = 2221]
2. 15th from the top and 26th from the bottom
ऊपर से 15 वां और नीचे से 26 वां [Option ID = 2222]
3. 15th from the top and 27th from the bottom
ऊपर से 15 वां और नीचे से 27 वां [Option ID = 2223]
4. 16th from the top and 27th from the bottom
ऊपर से 16 वां और नीचे से 27 वां [Option ID = 2224]

3) Given figure represents pH, partial pressure of CO2 (pCO2), and temperature (T) in an experiment conducted in a
water sample over 20 days. Which of the following statements can definitely be made based on this experiment?

[Question ID = 557][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q3]

1. High CO2 causes global warming.

अिधक CO2 से भूमड
ं लीय तापकम म वृि होती है

[Option ID = 2225]
2. High temperature causes acidification.

अिधक तापमान से अ लीयकरण होता है

[Option ID = 2226]
3. There is a decrease in pH and an increase in both T and pCO2 over 20 days.

20 िदन के अंतराल पर, pH घटता है और तापमान व, pCO2 दोन म वृि होती है

[Option ID = 2227]
4. pH and pCO2 are positively correlated while pH and T are inversely correlated.

pH व pCO2 धना मक सहसंबिं धत ह, जबिक pH व T पितलोमतः सहसंबिं धत ह

[Option ID = 2228]

4) A 360 ml aqueous solution contains 40% alcohol. How much will be the approximate percentage of alcohol if 3600 ml of
water is added to the solution?
एक 360 िमली जलीय घोल का 40% अ कोहल है. यिद इस घोल म 3600 िमली पानी िमलाया जाये तो लगभग िकतने पितशत अ कोहल होगा?

[Question ID = 558][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q4]
1. 2.6

[Option ID = 2229]
2. 3.6

[Option ID = 2230]
3. 4.0

[Option ID = 2231]
4. 1.0

[Option ID = 2232]

5) A set of 27 similar looking coins has 26 identical coins and one dummy coin having less weight. What is the minimum
number of weighings that will ensure identification of the dummy coin using a two‐pan balance?
एक जैसे िदखने वाले 27 िस क के सेट म 26 िस के अिभ न (एक प) ह और एक कम भार वाला पित पी िस का है दो पलड़ वाली एक तराजू से यूनतम
िकतनी बार तौल कर पित पी िस के क पहचान सुिनि त क जा सकेगी?
[Question ID = 559][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q5]
1. 3 [Option ID = 2233]
2. 4 [Option ID = 2234]
3. 5 [Option ID = 2235]
4. 6 [Option ID = 2236]

6) If 90 people are to be seated randomly in 15 rows of 6 seats each, what is the probability that a person gets a seat at
either end of a row?
यिद 90 लोग को या ि छक प से 15 पंि य म, 6 पित पंि म, बैठाया जाये तो िकसी यि क पंि के दोन छोर म से एक पर बैठने क पाियकता
िकतनी है?
[Question ID = 560][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q6]
1. 1/2 [Option ID = 2237]
2. 1/4 [Option ID = 2238]
3. 1/3 [Option ID = 2239]
4. 1/15 [Option ID = 2240]

7)

[Question ID = 561][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q7]
1. A [Option ID = 2241]
2. B [Option ID = 2242]
3. C [Option ID = 2243]
4. D [Option ID = 2244]

8) Consider the following four statements.

Statement 1: “Statement 3 is true.”
Statement 2: “Statement 1 is true”
Statement 3: “Statement 1 is true and Statement 2 is false”
Statement 4: “Statements 1, 2 and 3 are false”
Which of the above statements must be true for the four statements to be mutually consistent?
िन निलिखत चार कथन पर यान द

कथन 1: "कथन 3 स य है"
कथन 2: "कथन 1 स य है"
कथन 3: "कथन 1 स य है और कथन 2 अस य है"
कथन 4: "कथन 1, 2, और 3 अस य ह ”

इन चार कथन को अ यो य अिवरोधी होने के िलए उपयु कथन म से कौनसा स य होना आव यक है?
[Question ID = 562][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q8]
1. Statement 1
कथन 1 [Option ID = 2245]
2. Statement 2
कथन 2 [Option ID = 2246]
3. Statement 3
कथन 3 [Option ID = 2247]
4. Statement 4
कथन 4 [Option ID = 2248]

9) On a track of 200 m length, S runs from the starting point and R starts 20 m ahead of S at the same time. Both reach
the end of the track at the same time. S runs at a uniform speed of 10 m/s. If R also runs at a uniform speed, then how
much more time would R take to run the entire course?
एक 200 मी ल बे ट ैक पर, ट ैक के आरंिभक िबंदु से S, व उसके 20 मी आगे से R, एक ही समय दौड़ना आर भ करते ह ट ैक के अंत पर दोन एक ही समय पहच
ँ ते
ह S 10 मी/से क एकसामान गित से दौड़ता है यिद R भी एकसमान गित से दौड़ता है, तो R को पूरे ट ैक को दौड़ने म िकतना और अिधक समय लगेगा?

[Question ID = 563][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q9]
1. 0.5 second
0.5 सेकड
ं

[Option ID = 2249]
2. 1.0 second
1.0 सेकड
ं

[Option ID = 2250]
3. 1.5 second
1.5 सेकड
ं

[Option ID = 2251]
4. 2.2 seconds
2.2 सेकड
ं

[Option ID = 2252]

10) The arithmetic mean of five numbers is zero. The numbers may not be distinct. Which of the following must be true?
पांच सं याओं का अंकगिणतीय मा य शू य है सं याएं पृथक (िभ न) नह भी हो सकती ह िन निलिखत म से कौनसा स य होना आव यक है?
[Question ID = 564][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q10]
1. The product of the numbers is zero
सं याओं का गुणनफल शू य है [Option ID = 2253]
2. At most two of these numbers are positive
इन सं याओं म से अिधकतम दो सं याएं धना मक ह [Option ID = 2254]
3. There cannot be exactly one zero
मात एक सं या शू य नह हो सकती है [Option ID = 2255]
4. There cannot be exactly one non‐zero number
मात एक सं या शू येतर (गैर‐शू य) नह हो सकती है [Option ID = 2256]

11)

[Question ID = 565][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q11]
1. A [Option ID = 2257]
2. B [Option ID = 2258]
3. C [Option ID = 2259]
4. D [Option ID = 2260]

12) Of all the English magazines published in a country, magazine M is read by the highest number of readers. It
necessarily follows that
एक देश म पकािशत सभी अंगेजी पित काओं म से, पितका M क पाठक सं या सवािधक है यह अिनवाय प से अनुसरण करता है िक

[Question ID = 566][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q12]
1. M is the most popular English magazine published in the country.
M देश म पकािशत सवािधक लोकिपय अंगज
े ी पितका है

[Option ID = 2261]
2. M is the most popular English magazine in the country.
M देश म सवािधक लोकिपय अंगज
े ी पितका है

[Option ID = 2262]
3. M is the most popular magazine in the country.
M देश म सवािधक लोकिपय पितका है

[Option ID = 2263]
4. The study has not considered the readership of English magazines published outside the country.
इस अ ययन म देश से बाहर पकािशत अंगज
े ी पितकाओं के पाठकगण पर िवचार नह िकया गया है

[Option ID = 2264]

13) The number of three digit PINs, in which the third digit is the sum of the first two digits, is
तीन अंक वाले िपन क सं या, िजसम तीसरा अंक पहले दो अंको का योग है, है
[Question ID = 567][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q13]
1. 55 [Option ID = 2265]
2. 9 [Option ID = 2266]
3. 45 [Option ID = 2267]
4. 11 [Option ID = 2268]

14) Consider a right angled triangle BAC with medians CM and BL having the same length. The ratio of the length of BC to
that of ML is
एक समकोण ितभुज BAC का िवचार कर िजसक मि यकाओं CM व BL क ल बाई समान है BC और ML क ल बाई का अनुपात है

[Question ID = 568][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q14]
1. 2 [Option ID = 2269]
2. 3/4 [Option ID = 2270]
3. 4/3 [Option ID = 2271]
4. 1 [Option ID = 2272]

15) A battalion consists of elephants, horses and soldiers totaling to 3500. There are twice as many horses as elephants and
one‐fourth of the soldiers are riding these animals. In the stand still position, number of feet on ground is 7500. The number
of horses in the battalion is
हािथय , घोड़ और िसपािहय से बनी एक बटािलयन है िजनक कुल सं या 3500 है इसम घोड़ क सं या हािथय क सं या क दोगुनी है और एक‐चौथाई
िसपाही इन जानवर पर सवार है ठहरी हई अव था म, धरातल पर चरण क सं या 7500 है बटािलयन म घोड़ क सं या है
[Question ID = 569][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q15]
1. 525 [Option ID = 2273]
2. 625 [Option ID = 2274]
3. 550 [Option ID = 2275]
4. 600 [Option ID = 2276]

16) The graph shows number of employees, market share (as % by number of units sold), and sale (in Rs. crore) for five
companies A, B, C, D, E.

Select the CORRECT statement
पांच कंपिनय A, B, C, D, E के कािमक क सं या, बाजार िह सेदारी (बेची गयी इकाइय क सं या पितशत के प म), और िवकय िबकी (करोड़ . म) को
गाफ म िदखाया गया है

सही कथन को चुिनए
[Question ID = 570][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q16]
1. A has the highest market share per employee, C has the highest sale for its market share
A क बाजार िह सेदारी पित कािमक सवािधक है, C क िवकय िबकी बाजार िह सेदारी के िलए सवािधक है [Option ID = 2277]
2. C has the highest market share per employee, B has the highest sale for its market share
C क बाजार िह सेदारी पित कािमक सवािधक है, B क िवकय िबकी बाजार िह सेदारी के िलए सवािधक है [Option ID = 2278]
3. D has the highest market share per employee, E has the highest sale for its market share
D क बाजार िह सेदारी पित कािमक सवािधक है, E क िवकय िबकी बाजार िह सेदारी के िलए सवािधक है [Option ID = 2279]
4. A has the highest market share per employee, B has the highest sale for its market share
A क बाजार िह सेदारी पित कािमक सवािधक है, B क िवकय िबकी बाजार िह सेदारी के िलए सवािधक है [Option ID = 2280]

17) The wholesale price per unit of an item is C0 up to first 19 units. The unit price falls by 10% if 20 to 29 units are
purchased and by another 10 % if 30 or more units are purchased. If 120 units are bought, the total price paid is
approximately
िकसी व तु क पित इकाई थोक क मत, पथम 19 इकाइय तक C0 है यिद 20 से 29 इकाइय क खरीद क जाये तो, इकाई क मत 10% घट जाती है और 30 या
अिधक इकाइय क खरीद पर अित र 10% घट जाती है यिद 120 इकाइयां खरीदी जाएँ, चुकाई गयी कुल क मत लगभग है

[Question ID = 571][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q17]
1. 99 C0

[Option ID = 2281]
2. 97 C0

[Option ID = 2282]
3. 91 C0

[Option ID = 2283]
4. 81 C0

[Option ID = 2284]

18) Two digital clocks show times 09h 13m and 09h 17m, respectively, at one instant. Exactly 30 seconds later the clocks
show 09h14m and 09h17m, respectively. Which one of the following options is a possible difference between the times
maintained by the two clocks?
एक समय, दो िडिजटल घिड़याँ कमशः 09घं 13िम और 09घं 17िम समय दशाती ह ठीक 30 सेकंड प ात् घिड़याँ कमशः 09घं 14िम और 09घं 17िम दशाती ह
दो घिड़य ारा संधा रत समय के बीच का संभािवत अंतर ,नीचे िदए गए िवक प म से कौन सा है?
[Question ID = 572][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q18]
1. 3m 00s
3िम 00से [Option ID = 2285]
2. 30s
30से [Option ID = 2286]
3. 4m 00s
4िम 00से [Option ID = 2287]
4. 4m 30s
4िम 30से [Option ID = 2288]

19) There are two concentric circular tracks A and B of width 2 m each as shown in the figure. If r = 30m, what is the ratio
of the areas of Track A to Track B?
जै स ा िक िचत म िदखाया गया है, दो संके दी वृताकार ट ैक A और B ह, िजनक प येक क चौड़ाई 2 मी है यिद r = 30 मी है, ट ैक A और ट ैक B के ेतफल का
अनुपात िकतना है?

[Question ID = 573][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q19]
1. 28/13 [Option ID = 2289]
2. 2/1 [Option ID = 2290]
3. 29/14 [Option ID = 2291]
4. 5/3 [Option ID = 2292]

20) A 5 kg watermelon contains 99% water by weight. Some of the water evaporates and the melon now contains 98%
water by weight. What is the weight (in kg) of watermelon now?
एक 5 िकगा तरबूज़ म भार का 99% पानी है इसका कुछ पानी वाि पत हो जाता है और तरबूज म अब के भार का 98% पानी है तरबूज का भार (िकगा म) अब
िकतना है?
[Question ID = 574][Question Description = 101_704_PARTA_CSIR_SEPT22_SET1_BIL_Q20]
1. 4.5 [Option ID = 2293]
2. 2.5 [Option ID = 2294]
3. 4.8 [Option ID = 2295]
4. 4.9 [Option ID = 2296]

Topic:‐ S1 B UNIT –1

1) UNIT – 1

[Question ID = 289][Question Description = 121_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q21]
1. It does not converge.

यह अिभस रत नह होती

[Option ID = 1153]
2. It converges to e ‐1 ‐1.

यह e ‐ 1 ‐1 क ओर अिभस रत होती है

[Option ID = 1154]
3. It converges to e ‐1.

यह e ‐1 क ओर अिभस रत होती है

[Option ID = 1155]
4. It converges to e ‐1 +1.

यह e ‐1 +1 क ओर अिभस रत होती है

[Option ID = 1156]

2) UNIT – 1

[Question ID = 290][Question Description = 122_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q22]
1.

[Option ID = 1157]
2.

[Option ID = 1158]
3.

[Option ID = 1159]
4.

[Option ID = 1160]

3) UNIT – 1

[Question ID = 291][Question Description = 123_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q23]
1.

[Option ID = 1161]
2.

[Option ID = 1162]
3.

[Option ID = 1163]

4.

[Option ID = 1164]

4) UNIT – 1

[Question ID = 292][Question Description = 124_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q24]
1.

[Option ID = 1165]
2.

[Option ID = 1166]
3.

[Option ID = 1167]
4.

[Option ID = 1168]

5) UNIT – 1

[Question ID = 293][Question Description = 125_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q25]
1.

[Option ID = 1169]
2.

[Option ID = 1170]
3.

[Option ID = 1171]
4.

[Option ID = 1172]

6) UNIT – 1

[Question ID = 294][Question Description = 126_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q26]
1.

[Option ID = 1173]
2.

[Option ID = 1174]
3.

[Option ID = 1175]

4.

[Option ID = 1176]

7) UNIT – 1

[Question ID = 295][Question Description = 127_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q27]
1. 1

[Option ID = 1177]
2. 2

[Option ID = 1178]
3. infinite and countable

अनंत और गणनीय

[Option ID = 1179]
4. infinite and uncountable

अनंत और अगणनीय

[Option ID = 1180]

8) UNIT – 1

[Question ID = 301][Question Description = 128_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q28]
1.

[Option ID = 1201]
2.

[Option ID = 1202]
3.

[Option ID = 1203]
4.

[Option ID = 1204]

9) UNIT – 1

Suppose A and B are similar real matrices, that is, there exists an invertible matrix S such that A=SBA‐1.
Which of the following need not be true?

ु ्कमणीय आव्यहू S है िजसके िलए A=SBA‐1 है
मान िक A तथा B सम प वास्तिवक आव्यहू ह, अथात् ऐसा कोई व्यत
िनम्न म से कौन सा कथन सत्य होना आवश्यक नह है?

[Question ID = 297][Question Description = 129_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q29]
1. Transpose of A is similar to the transpose of B.

A का प रवत B के सम प है

[Option ID = 1185]
2. The minimal polynomial of A is same as the minimal polynomial of B.

A का अि पष्ठ बहपद B के अि पष्ठ बहपद के बराबर है

[Option ID = 1186]
3. trace(A)=trace(B).

[Option ID = 1187]
4. The range of A is same as the range of B.

A का परास और B का परास बराबर ह

[Option ID = 1188]

10) UNIT – 1

[Question ID = 302][Question Description = 130_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q30]
1.

[Option ID = 1205]
2.

[Option ID = 1206]
3.

[Option ID = 1207]
4.

[Option ID = 1208]

11) UNIT – 1

[Question ID = 299][Question Description = 131_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q31]

1.

[Option ID = 1193]

2.

[Option ID = 1194]

3.

[Option ID = 1195]

4.

[Option ID = 1196]

12) UNIT – 1

[Question ID = 300][Question Description = 132_ 704_PARTB_CSIR_SEPT22_SET1_BIL_Q32]
1.

[Option ID = 1197]

2.

[Option ID = 1198]
3.

[Option ID = 1199]
4.

[Option ID = 1200]

Topic:‐ S1 B UNIT –2

1) UNIT – 2

[Question ID = 311][Question Description = 133_704_PARTB_CSIR_SEPT22_SET1_BIL_Q33]
1.

[Option ID = 1241]
2.

[Option ID = 1242]
3.

[Option ID = 1243]
4.

[Option ID = 1244]

2) UNIT – 2

[Question ID = 312][Question Description = 134_704_PARTB_CSIR_SEPT22_SET1_BIL_Q34]
1.

[Option ID = 1245]
2.

[Option ID = 1246]
3.

[Option ID = 1247]
4.

[Option ID = 1248]

3) UNIT – 2

[Question ID = 313][Question Description = 135_704_PARTB_CSIR_SEPT22_SET1_BIL_Q35]
1.

[Option ID = 1249]
2.

[Option ID = 1250]
3.

[Option ID = 1251]
4.

[Option ID = 1252]

4) UNIT – 2

[Question ID = 314][Question Description = 136_704_PARTB_CSIR_SEPT22_SET1_BIL_Q36]
1.

[Option ID = 1253]
2.

[Option ID = 1254]
3.

[Option ID = 1255]
4.

[Option ID = 1256]

5) Let G be a simple group of order 168. How many elements of order 7 does it have?

कोिट (order) 168 का एक सरल समूह G लीजीए इसम कोिट (order) 7 के िकतने अवयव ह ?

[Question ID = 315][Question Description = 137_704_PARTB_CSIR_SEPT22_SET1_BIL_Q37]
1. 6

[Option ID = 1257]
2. 7

[Option ID = 1258]
3. 48

[Option ID = 1259]
4. 56

[Option ID = 1260]

6) UNIT – 2

[Question ID = 316][Question Description = 138_704_PARTB_CSIR_SEPT22_SET1_BIL_Q38]
1. N is an ideal in R.

जो N है, वह R म गुणजावली है

[Option ID = 1261]
2. N is never an ideal in R.

जो N है, वह R म कभी गुणजावली नह है

[Option ID = 1262]
3. If R is non‐commutative, N is not an ideal.

यिद R कम‐िविनमेय िवहीन है तो N गुणजावली नह है

[Option ID = 1263]
4. If R is commutative, N is an ideal.

यिद R कम‐िविनमेय है तो N गुणजावली है

[Option ID = 1264]

7) UNIT – 2

[Question ID = 317][Question Description = 139_704_PARTB_CSIR_SEPT22_SET1_BIL_Q39]
1. I is a maximal ideal.

I उि चष्ठ गुणजावली है

[Option ID = 1265]
2. I is a prime ideal.
I अभाज्य गुणजावली है

[Option ID = 1266]
3. I = (1).

[Option ID = 1267]
4. I = (0).

[Option ID = 1268]

8) Let X be a connected metric space with at least two points. Which of the following is necessarily true?
मान िक X ऐसी संबं दूरीक समि है िजसम कम से कम दो िबंदु ह िनम्न म से कौन सा अिनवायत: सत्य है?
[Question ID = 318][Question Description = 140_704_PARTB_CSIR_SEPT22_SET1_BIL_Q40]
1. X has finitely many points.
X म िबंदुओं क संखय ् ा प रिमत है [Option ID = 1269]
2. X has countably many points but is not finite.
X गणनीय है परंतु प रिमत नह [Option ID = 1270]
3. X has uncountably many points.
X अगणनीय है [Option ID = 1271]
4. No such X exists.
ऐसे िकसी X का अि तत्व नह है [Option ID = 1272]

Topic:‐ S1 B UNIT –3

1) UNIT – 3

[Question ID = 327][Question Description = 141_704_PARTB_CSIR_SEPT22_SET1_BIL_Q41]
1. There exists a unique local solution.

इसका कोई अि तीय स्थानीय हल है

[Option ID = 1305]
2. There exists a local solution but may not be unique.

इसका कोई स्थानीय हल है िकंतु हो सकता है अि तीय न हो

[Option ID = 1306]
3. There may not exist any solution.

हो सकता है इसका कोई हल न हो

[Option ID = 1307]
4. If local solution exists then it is unique.

यह स्थानीय हल हो तो वह अि तीय ही होगा

[Option ID = 1308]

2) UNIT – 3

[Question ID = 328][Question Description = 142_704_PARTB_CSIR_SEPT22_SET1_BIL_Q42]
1.

[Option ID = 1309]
2.

[Option ID = 1310]
3.

[Option ID = 1311]
4.

[Option ID = 1312]

3) UNIT – 3

[Question ID = 329][Question Description = 143_704_PARTB_CSIR_SEPT22_SET1_BIL_Q43]
1.

[Option ID = 1313]

2.

[Option ID = 1314]
3.

[Option ID = 1315]
4.

[Option ID = 1316]

4) UNIT – 3

[Question ID = 330][Question Description = 144_704_PARTB_CSIR_SEPT22_SET1_BIL_Q44]
1.

[Option ID = 1317]
2.

[Option ID = 1318]
3.

[Option ID = 1319]

4.

[Option ID = 1320]

5) UNIT – 3

[Question ID = 331][Question Description = 145_704_PARTB_CSIR_SEPT22_SET1_BIL_Q45]
1. 0 and 4/ 3

0 तथा 4/ 3

[Option ID = 1321]
2. 0 and ‐4/3

0 तथा ‐4/ 3

[Option ID = 1322]
3. 0 and 16/9

0 तथा 16/ 9

[Option ID = 1323]
4. 4/3 and ‐4/3

4/ 3 तथा ‐4/ 3

[Option ID = 1324]

6) UNIT – 3

[Question ID = 332][Question Description = 146_704_PARTB_CSIR_SEPT22_SET1_BIL_Q46]
1.

[Option ID = 1325]
2.

[Option ID = 1326]
3.

[Option ID = 1327]
4.

[Option ID = 1328]

7) UNIT – 3

[Question ID = 333][Question Description = 147_704_PARTB_CSIR_SEPT22_SET1_BIL_Q47]
1.

[Option ID = 1329]

2.

[Option ID = 1330]

3.

[Option ID = 1331]
4.

[Option ID = 1332]

8) UNIT – 3

[Question ID = 334][Question Description = 148_704_PARTB_CSIR_SEPT22_SET1_BIL_Q48]

1.

[Option ID = 1333]

2.

[Option ID = 1334]
3.

[Option ID = 1335]
4.

[Option ID = 1336]

Topic:‐ S1 B UNIT –4

1) UNIT – 4

[Question ID = 335][Question Description

= 149_704_PARTB_CSIR_SEPT22_SET1_BIL_Q49]
1. [Option ID = 1337]

2. [Option ID = 1338]

3. [Option ID = 1339]

4. [Option ID = 1340]

2) UNIT – 4

[Question ID = 336][Question Description =

150_704_PARTB_CSIR_SEPT22_SET1_BIL_Q50]
1. [Option ID = 1341]

2. [Option ID = 1342]

3. [Option ID = 1343]

4. [Option ID = 1344]

3) UNIT – 4

[Question ID = 337][Question Description =

151_704_PARTB_CSIR_SEPT22_SET1_BIL_Q51]
1. 0.95 [Option ID = 1345]
2. 0.9 [Option ID = 1346]
3. 0.975 [Option ID = 1347]
4. 0.92 [Option ID = 1348]

4) UNIT – 4

[Question ID = 338][Question Description =

152_704_PARTB_CSIR_SEPT22_SET1_BIL_Q52]
1.

[Option ID = 1349]

2.

[Option ID = 1350]

3.

[Option ID = 1351]

4.

[Option ID = 1352]

5) UNIT – 4

[Question ID = 339][Question Description =

153_704_PARTB_CSIR_SEPT22_SET1_BIL_Q53]
1. (5+Y, X‐3). [Option ID = 1353]
2. (‐5‐Y, X‐3). [Option ID = 1354]
3. (5+Y, X‐3). [Option ID = 1355]
4. (‐5‐Y, X‐3). [Option ID = 1356]

6) UNIT – 4

[Question ID = 340][Question Description = 154_704_PARTB_CSIR_SEPT22_SET1_BIL_Q54]

1.

[Option ID = 1357]

2.

[Option ID = 1358]
3.

[Option ID = 1359]

4.

[Option ID = 1360]

7) UNIT – 4

[Question ID = 341][Question Description =

155_704_PARTB_CSIR_SEPT22_SET1_BIL_Q55]
1. [Option ID = 1361]

2. [Option ID = 1362]

3. [Option ID = 1363]

4. [Option ID = 1364]

8) UNIT – 4

[Question ID = 342][Question Description =

156_704_PARTB_CSIR_SEPT22_SET1_BIL_Q56]
1. 0.81 [Option ID = 1365]
2. 0.89 [Option ID = 1366]
3. 0.64 [Option ID = 1367]
4. 0.36 [Option ID = 1368]

9) UNIT – 4

[Question ID = 343][Question Description =

157_704_PARTB_CSIR_SEPT22_SET1_BIL_Q57]
1. (‐0.5, 2.5) [Option ID = 1369]
2. (0.5, 2.5) [Option ID = 1370]
3. (‐2.0, 0.4) [Option ID = 1371]
4. (‐2.0, ‐0.4) [Option ID = 1372]

10) UNIT – 4

[Question ID = 344][Question Description = 158_704_PARTB_CSIR_SEPT22_SET1_BIL_Q58]
1. central chi‐square with 8 degrees of freedom

8 स्वातं य कोिट वाला कदीय काई वग

[Option ID = 1373]
2. not chi‐square

काई‐वग नह

[Option ID = 1374]
3. central chi‐square with 9 degrees of freedom

9 स्वातं य कोिट वाला कदीय काई – वग

[Option ID = 1375]
4. non‐central chi‐square

अकदीय काई‐वग

[Option ID = 1376]

11) UNIT – 4

[Question ID = 345][Question Description =

159_704_PARTB_CSIR_SEPT22_SET1_BIL_Q59]
1. Connected but not orthogonal
संब लेिकन लांिबक नह [Option ID = 1377]
2. Orthogonal but not connected
लांिबक लेिकन संब नह [Option ID = 1378]
3. Neither connected nor orthogonal
न संब , न लांिबक [Option ID = 1379]
4. Both connected and orthogonal
संब तथा लांिबक दोन [Option ID = 1380]

12) UNIT – 4

[Question ID = 346][Question Description =

160_704_PARTB_CSIR_SEPT22_SET1_BIL_Q60]

1.

[Option ID = 1381]

2.

[Option ID = 1382]

3.

[Option ID = 1383]

4.

[Option ID = 1384]

Topic:‐ S1 C UNIT –1

1) UNIT – 1

[Question ID = 365][Question Description = 161_SET 1

MATHS_Q61]
1.

[Option ID = 1457]

2.

[Option ID = 1458]

3.

[Option ID = 1459]

4.

[Option ID = 1460]

2) UNIT – 1

[Question ID = 366][Question Description = 162_SET 1 MATHS_Q62]

1.

[Option ID = 1461]
2.

[Option ID = 1462]
3.

[Option ID = 1463]
4.

[Option ID = 1464]

3) UNIT – 1

[Question ID = 367][Question Description = 163_SET 1 MATHS_Q63]
1.

[Option ID = 1465]

2.

[Option ID = 1466]
3.

[Option ID = 1467]

4.

[Option ID = 1468]

4) UNIT – 1

[Question ID = 368][Question Description = 164_SET 1 MATHS_Q64]
1. Only S1.
केवल S1.

[Option ID = 1469]
2. Only S3.
केवल S3.

[Option ID = 1470]
3. Only S1 and S2.
केवल S1 तथा S2.

[Option ID = 1471]
4. Only S2 and S3.
केवल S2 तथा S3.

[Option ID = 1472]

5) UNIT – 1

[Question ID = 369][Question Description = 165_SET 1 MATHS_Q65]

1.

[Option ID = 1473]

2.

[Option ID = 1474]
3.

[Option ID = 1475]

4.

[Option ID = 1476]

6) UNIT – 1

[Question ID = 370][Question Description = 166_SET 1 MATHS_Q66]
1. The limit does not exist.

इस सीमा का अि तत्व नह है
[Option ID = 1477]
2.

[Option ID = 1478]
3.

[Option ID = 1479]
4.

[Option ID = 1480]

7) UNIT – 1

[Question ID = 371][Question Description = 167_SET 1 MATHS_Q67]
1.

[Option ID = 1481]
2.

[Option ID = 1482]
3.

[Option ID = 1483]
4.

[Option ID = 1484]

8) UNIT – 1

[Question ID = 372][Question Description = 168_SET 1 MATHS_Q68]
1.

[Option ID = 1485]
2.

[Option ID = 1486]
3.

[Option ID = 1487]
4.

[Option ID = 1488]

9) UNIT – 1

[Question ID = 373][Question Description = 169_SET 1 MATHS_Q69]
1.

[Option ID = 1489]
2.

[Option ID = 1490]
3.

[Option ID = 1491]
4.

[Option ID = 1492]

10) UNIT – 1

Let (X, d) be a finite non‐singleton metric space. Which of the following statements are true?

मान िक (X, d) कोई प रिमत एकलेतर (non‐singleton) दूरीक समि है िनम्न म से कौन से वक्तव्य सच है?

[Question ID = 374][Question Description = 170_SET 1 MATHS_Q70]
1.

[Option ID = 1493]
2.

[Option ID = 1494]
3.

[Option ID = 1495]
4.

[Option ID = 1496]

11) UNIT – 1

[Question ID = 375][Question Description = 171_SET 1 MATHS_Q71]
1.

[Option ID = 1497]
2.

[Option ID = 1498]
3.

[Option ID = 1499]

4.

[Option ID = 1500]

12) UNIT – 1

[Question ID = 376][Question Description = 172_SET 1 MATHS_Q72]

1.

[Option ID = 1501]

2.

[Option ID = 1502]

3.

[Option ID = 1503]

4.

[Option ID = 1504]

13) UNIT – 1

[Question ID = 377][Question Description = 173_SET 1 MATHS_Q73]

1.

[Option ID = 1505]
2.

[Option ID = 1506]
3.

[Option ID = 1507]
4.

[Option ID = 1508]

14) UNIT – 1

[Question ID = 378][Question Description = 174_SET 1 MATHS_Q74]

1.

[Option ID = 1509]

2.

[Option ID = 1510]

3.

[Option ID = 1511]

4.

[Option ID = 1512]

15) UNIT – 1

[Question ID = 379][Question Description = 175_SET 1 MATHS_Q75]
1. The nullity of T is at least 3.
T क शूनय् ता कम से कम 3 है

[Option ID = 1513]
2. The rank of T is at least 4.
T क कोिट (rank) कम से कम 4 है

[Option ID = 1514]
3. The rank of T is at least 3.
T क कोिट (rank) कम से कम 3 है

[Option ID = 1515]
4. T is invertible.
T व्यत
ु क
् मणीय है

[Option ID = 1516]

16) UNIT – 1

[Question ID = 380][Question Description = 176_SET 1 MATHS_Q76]
1.

[Option ID = 1517]
2.

[Option ID = 1518]
3.

[Option ID = 1519]
4.

[Option ID = 1520]

17) UNIT – 1

[Question ID = 381][Question Description = 177_SET 1 MATHS_Q77]

1.

[Option ID = 1521]
2.

[Option ID = 1522]

3.

[Option ID = 1523]

4.

[Option ID = 1524]

18) UNIT – 1

[Question ID = 382][Question Description = 178_SET 1 MATHS_Q78]
1.

[Option ID = 1525]
2.

[Option ID = 1526]

3.

[Option ID = 1527]

4.

[Option ID = 1528]

Topic:‐ S1 C UNIT –2

1) UNIT – 2

[Question ID = 383][Question Description = 179_704_PARTC_CSIR_SEPT22_SET1_BIL_Q79]
1.

[Option ID = 1529]

2.

[Option ID = 1530]

3.

[Option ID = 1531]
4.

[Option ID = 1532]

2) UNIT – 2

[Question ID = 384][Question Description = 180_704_PARTC_CSIR_SEPT22_SET1_BIL_Q80]
1.

[Option ID = 1533]
2.

[Option ID = 1534]
3.

[Option ID = 1535]
4.

[Option ID = 1536]

3) UNIT – 2

[Question ID = 385][Question Description = 181_704_PARTC_CSIR_SEPT22_SET1_BIL_Q81]
1.

[Option ID = 1537]

2.

[Option ID = 1538]
3.

[Option ID = 1539]
4.

[Option ID = 1540]

4) UNIT – 2

[Question ID = 386][Question Description = 182_704_PARTC_CSIR_SEPT22_SET1_BIL_Q82]
1.

[Option ID = 1541]
2.

[Option ID = 1542]
3.

[Option ID = 1543]
4.

[Option ID = 1544]

5) UNIT – 2

[Question ID = 387][Question Description = 183_704_PARTC_CSIR_SEPT22_SET1_BIL_Q83]
1.

[Option ID = 1545]
2.

[Option ID = 1546]
3.

[Option ID = 1547]
4.

[Option ID = 1548]

6) UNIT – 2

[Question ID = 388][Question Description = 184_704_PARTC_CSIR_SEPT22_SET1_BIL_Q84]

1.

[Option ID = 1549]
2.

[Option ID = 1550]
3.

[Option ID = 1551]

4.

[Option ID = 1552]

7) UNIT – 2

Which of the following are class equations for a finite group?

िनम्न म कौन सी प रिमत समूह के िलए वग समीकरण (class equations) ह?

[Question ID = 389][Question Description = 185_704_PARTC_CSIR_SEPT22_SET1_BIL_Q85]
1. 1+3+3+3+3+13+13=39

[Option ID = 1553]
2. 1+1+2+2+2+2+2+2=14

[Option ID = 1554]
3. 1+3+3+7+7=21

[Option ID = 1555]
4. 1+1+1+2+5+5=15

[Option ID = 1556]

8) UNIT – 2

Which of the following statements are necessarily true regarding a group G of order 2022?

िनम्न वक्तव्य म से कौन से कोिट (order) 2022 के समूह G के िलए अिनवायत: सत्य ह?

[Question ID = 395][Question Description = 186_704_PARTC_CSIR_SEPT22_SET1_BIL_Q86]

1.

[Option ID = 1577]
2.

[Option ID = 1578]
3.

[Option ID = 1579]
4.

[Option ID = 1580]

9) UNIT – 2

[Question ID = 396][Question Description = 187_704_PARTC_CSIR_SEPT22_SET1_BIL_Q87]
1. A is an integral domain.
A एक पूणाक य पांत है

[Option ID = 1581]
2. A is a finite ring.
A एक प रसीिमत वलय है

[Option ID = 1582]
3. A is a field.
A एक त े (field) है

[Option ID = 1583]
4. A is a product of two rings.
A दो वलय का गुणनफल है

[Option ID = 1584]

10) UNIT – 2

[Question ID = 397][Question Description = 188_704_PARTC_CSIR_SEPT22_SET1_BIL_Q88]
1.

[Option ID = 1585]
2.

[Option ID = 1586]

3.

[Option ID = 1587]
4.

[Option ID = 1588]

11) UNIT – 2

[Question ID = 398][Question Description = 189_704_PARTC_CSIR_SEPT22_SET1_BIL_Q89]
1.

[Option ID = 1589]
2.

[Option ID = 1590]
3.

[Option ID = 1591]

4.

[Option ID = 1592]

12) UNIT – 2

[Question ID = 399][Question Description = 190_704_PARTC_CSIR_SEPT22_SET1_BIL_Q90]

1.

[Option ID = 1593]
2.

[Option ID = 1594]
3.

[Option ID = 1595]
4.

[Option ID = 1596]

Topic:‐ S1 C UNIT –3

1) UNIT – 3

[Question ID = 412][Question Description = 191_SET 1 MATHS_Q91]
1.

[Option ID = 1645]
2.

[Option ID = 1646]
3.

[Option ID = 1647]
4.

[Option ID = 1648]

2) UNIT – 3

[Question ID = 413][Question Description = 192_SET 1 MATHS_Q92]

1.

[Option ID = 1649]

2.

[Option ID = 1650]

3.

[Option ID = 1651]

4.

[Option ID = 1652]

3) UNIT – 3

[Question ID = 414][Question Description = 193_SET 1 MATHS_Q93]
1. I is uniquely solvable.

I अि तीयत: साधनीय है

[Option ID = 1653]
2. II is uniquely solvable.

II अि तीयत: साधनीय है

[Option ID = 1654]
3. I has multiple solutions.

I के बहत से हल ह

[Option ID = 1655]
4. II has multiple solutions.

II के बहत से हल ह

[Option ID = 1656]

4) UNIT – 3

[Question ID = 415][Question Description = 194_SET 1 MATHS_Q94]
1.

[Option ID = 1657]
2.

[Option ID = 1658]
3.

[Option ID = 1659]
4.

[Option ID = 1660]

5) UNIT – 3

[Question ID = 416][Question Description = 195_SET

1 MATHS_Q95]
1. [Option ID = 1661]

2. [Option ID = 1662]

3. [Option ID = 1663]

4. [Option ID = 1664]

6) UNIT – 3

[Question ID = 417][Question Description = 196_SET 1 MATHS_Q96]
1.

[Option ID = 1665]
2.

[Option ID = 1666]
3.

[Option ID = 1667]
4.

[Option ID = 1668]

7) UNIT – 3

[Question ID = 418][Question

Description = 197_SET 1 MATHS_Q97]
1. [Option ID = 1669]

2. [Option ID = 1670]

3. [Option ID = 1671]

4. [Option ID = 1672]

8) UNIT – 3

[Question ID = 419][Question Description = 198_SET 1 MATHS_Q98]
1.

[Option ID = 1673]
2.

[Option ID = 1674]
3.

[Option ID = 1675]
4.

[Option ID = 1676]

9) UNIT – 3

[Question ID = 420][Question Description = 199_SET 1 MATHS_Q99]
1.

[Option ID = 1677]
2.

[Option ID = 1678]
3.

[Option ID = 1679]
4.

[Option ID = 1680]

10) UNIT – 3

[Question ID = 421][Question Description = 200_SET 1 MATHS_Q100]
1.

[Option ID = 1681]
2.

[Option ID = 1682]
3.

[Option ID = 1683]
4.

[Option ID = 1684]

11) UNIT – 3

[Question ID = 422][Question Description = 201_SET 1 MATHS_Q101]
1.

[Option ID = 1685]
2.

[Option ID = 1686]
3.

[Option ID = 1687]

4.

[Option ID = 1688]

12) UNIT – 3

[Question ID = 423][Question Description = 202_SET 1 MATHS_Q102]

1.

[Option ID = 1689]

2.

[Option ID = 1690]
3.

[Option ID = 1691]

4.

[Option ID = 1692]

Topic:‐ S1 C UNIT –4

1) UNIT – 4

[Question ID = 442][Question Description =

203_SET 1 MATHS_Q103]
1. All the states have same periods.
सभी अवस्थ ाओं के एक जैसे अविध काल ह [Option ID = 1765]
2. All the states are transient.
सभी अवस्थाय िणक ह [Option ID = 1766]
3. Some states are transient.
कुछ अवस्थाय िणक ह [Option ID = 1767]
4. All the states are recurrent.
सभी अवस्थाय पुनरावत ह [Option ID = 1768]

2) UNIT – 4

[Question ID = 443][Question Description = 204_SET 1 MATHS_Q104]
1. It is an irreducible Markov Chain.

यह एक अलघुकरणीय माक व शृंखला है

[Option ID = 1769]
2. All the states are recurrent.

सभी अवस्थाय पुरावत ह
[Option ID = 1770]
3.

[Option ID = 1771]
4. All the states have same period.

सभी अवस्थाओं के अविध काल समान ह
[Option ID = 1772]

3) UNIT – 4

[Question ID = 444][Question Description =

205_SET 1 MATHS_Q105]
1.

[Option ID = 1773]

2.

[Option ID = 1774]

3.

[Option ID = 1775]

4.

[Option ID = 1776]

4) UNIT – 4

[Question ID = 445][Question Description = 206_SET 1 MATHS_Q106]
1.

[Option ID = 1777]

2.

[Option ID = 1778]
3.

[Option ID = 1779]
4.

[Option ID = 1780]

5) UNIT – 4

[Question ID = 446][Question Description = 207_SET 1 MATHS_Q107]
1.

[Option ID = 1781]
2.

[Option ID = 1782]

3.

[Option ID = 1783]

4.

[Option ID = 1784]

6) UNIT – 4

[Question ID = 447][Question

Description = 208_SET 1 MATHS_Q108]
1. [Option ID = 1785]

2. [Option ID = 1786]

3. [Option ID = 1787]

4. [Option ID = 1788]

7) UNIT – 4

[Question ID = 448][Question Description = 209_SET 1 MATHS_Q109]

1.

[Option ID = 1789]
2.

[Option ID = 1790]

3.

[Option ID = 1791]

4.

[Option ID = 1792]

8) UNIT – 4

[Question ID = 449][Question

Description = 210_SET 1 MATHS_Q110]
1.

[Option ID = 1793]

2.

[Option ID = 1794]

3.

[Option ID = 1795]

4.

[Option ID = 1796]

9) UNIT – 4

[Question ID = 450][Question Description = 211_SET 1 MATHS_Q111]
1.

[Option ID = 1797]
2.

[Option ID = 1798]

3.

[Option ID = 1799]

4.

[Option ID = 1800]

10) UNIT – 4

[Question ID = 451][Question

Description = 212_SET 1 MATHS_Q112]

1.

[Option ID = 1801]

2.

[Option ID = 1802]

3.

[Option ID = 1803]

4.

[Option ID = 1804]

11) UNIT‐ 4

[Question ID = 575][Question Description = 213_SET 1 MATHS_Q113]

1.

[Option ID = 2297]

2.

[Option ID = 2298]

3.

[Option ID = 2299]

4.

[Option ID = 2300]

12) UNIT – 4

[Question ID = 453][Question

Description = 214_SET 1 MATHS_Q114]
1. With respect to the squared error loss function, Bayes estimator is the mean of the posterior distribution.
विगत तिु ट हािन फलन के सापे , बेज़ आकलक, उत्तर पाियकता बंटन का माध्य है [Option ID = 1809]
2. With respect to the squared error loss function, Bayes estimator is the median of the posterior distribution.
विगत तिु ट हािन फलन के सापे , बेज़ आकलक, उत्तर पाियकता बंटन क माि यका है [Option ID = 1810]
3. With respect to the absolute error loss function, Bayes estimator is the median of the posterior distribution.

िनरपे तिु ट हािन फलन के सापे , बेज़ आकलक, उत्तर पाियकता बंटन क माि यका है [Option ID = 1811]
4. With respect to the absolute error loss function, Bayes estimator is the mean of the posterior distribution.
िनरपे तिु ट हािन फलन के सापे , बेज़ आकलक, उत्तर पाियकता बंटन का माध्य है [Option ID = 1812]

13) UNIT – 4

[Question ID = 454][Question Description = 215_SET 1 MATHS_Q115]
1.

[Option ID = 1813]
2.

[Option ID = 1814]
3.

[Option ID = 1815]
4.

[Option ID = 1816]

14) UNIT – 4

[Question ID = 455][Question Description = 216_SET 1 MATHS_Q116]
1.

[Option ID = 1817]
2.

[Option ID = 1818]
3.

[Option ID = 1819]
4.

[Option ID = 1820]

15) UNIT – 4

[Question ID = 456][Question Description = 217_SET 1 MATHS_Q117]
1.

[Option ID = 1821]

2.

[Option ID = 1822]
3. Survival function of the random variable X cannot be determined from the given information.

दी गई जानकारी से या ि छक चर X का अितजीिवता फलन िनि त करना संभव नह है

[Option ID = 1823]
4. The survival function, density function and distribution function can be determined from the given information.

दी गई जानकारी से अितजीिवता फलन, घनत्व फलन तथा बंटन फलन िनि त िकए जा सकते ह

[Option ID = 1824]

16) UNIT – 4

[Question ID = 457][Question Description = 218_SET 1 MATHS_Q118]
1. The Bayes estimator of µ under a proper prior is always biased.

उिचत पूव (proper prior) के अन्तगत µ का बेज़ आकलक भी सदा अिभनत है

[Option ID = 1825]
2. There is a proper prior for which the Bayes estimator of µ is unbiased.

ऐसा उिचत पूव (prior) है के अन्तगत µ का बेज़ आकलक अनिभनत है

[Option ID = 1826]
3. The Bayes estimator of µ under an improper prior is always biased.

अनुिचत पूव (improper prior) है के अन्तगत µ का वेज़ आकलक सदा अिभनत है

[Option ID = 1827]
4. There is an improper prior for which the Bayes estimator of µ is unbiased.

ऐसा कोई अनुिचत पूव (improper prior) है िजसके िलए µ का बेज़ आकलक अनिभनत है

[Option ID = 1828]

17) UNIT – 4

[Question ID = 458][Question Description

= 219_SET 1 MATHS_Q119]
1.

[Option ID = 1829]

2.

[Option ID = 1830]

3.

[Option ID = 1831]

4.

[Option ID = 1832]

18) Consider the hierarchical single linkage agglomerative clustering algorithm for three points X=(1,0), Y=(0,2), Z=(3,3),
and the squared Euclidean distance matrix. The clustering algorithm starts with three clusters. Then which of the following
statements are correct.
तीन िबंदुओं X=(1,0), Y=(0,2), Z=(3,3) तथा विगत यूि लडीय दूरी आव्यहू के िलए पदोच्चता‐िनभर, एकल‐बंध संचियक गुच्छन कलन िविध पर िवचार
गुच्छन कलन िविध तीन गुच्छ से आरंभ होती है तब िनम्न कथन म से कौन से सही ह [Question ID = 459][Question Description = 220_SET 1
MATHS_Q120]
1. At the first step, after combining two nearest clusters, the single linkage distance between the two newly formed clusters is 10.
पथम चरण म, दो समीपतम गुच्छ को िमलाने के बाद, नये बने दो गुच्छ के बीच एक‐बंध‐दूरी 10 है [Option ID = 1833]
2. At the first step, X and Y are merged to form a new cluster.
पथम चरण म, नया गुच्छ बनाने के िलए X तथा Y िमल जाते ह [Option ID = 1834]
3. At the first step, after combining two nearest clusters, the single linkage distance between the two newly formed clusters is 13.
पथम चरण म, दो समीपतम गुच्छ को िमलाने के बाद, नये बने दो गुच्छ के बीच एक‐बंध‐दूरी 13 है [Option ID = 1835]
4. At the first step, X and Z are merged to form a new cluster.
पथम चरण म नया गुच्छ बनाने के िलए, X तथा Z िमल जाते ह [Option ID = 1836]