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LIC AAO Preliminary Reasoning Ability

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LIC AAO Preliminary Reasoning Ability

shape Introduction

Scheme of Preliminary Examination for recruitment to the post of Assistant Administrative Officers (AAOs) in LIC is as follows:
  • Preliminary Examination consisting of objective test will be conducted online.

  • The test will have three sections (with separate timings for each section).

shape Pattern

Name of the tests Number of Questions Maximum Marks Medium of Exam Minimum Qualifying Marks Duration
SC/ST Others
Reasoning Ability 35 35 English & Hindi 16 18 20 minutes
Quantitative Aptitude 35 35 English & Hindi 16 18 20 minutes
English Language with special emphasis on grammar, vocabulary and comprehension 30 30 English 9 10 20 minutes
Total 100 70 1 hour

  • English Language test will be of qualifying nature and the marks in English Language will not be counted for ranking.

  • Candidates equal to 20 times of number of vacancies in each category, subject to availability, will be shortlisted for Main examination.


shape Samples

Number Series
1. In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces. 2, 3, 5, 7, 11, x, 17
    A. 12 B. 13 C. 14 D. 15

Answer: Option (B)
Explanation: Clearly, the given series consists of prime numbers starting from 2. The prime number after 11 is 13. So, 13 is the missing number.
2. In the following question, a number series is given with one term missing. Choose the correct alternative that will the same pattern and fills in the blank spaces. 1, 9, 17, 33, 49, 73,
    A. 97 B. 98 C. 99 D. 100

Answer: Option (A)
Explanation: The pattern is + 8, + 8, + 16, + 24,.... .'. Missing number = 73 + 24 = 97
3. In the following question, a number series is given with one term missing. Choose the correct alternative that will the same pattern and fills in the blank spaces. 3, 7, 15, 31, 63,
    A. 92 B. 115 C. 127 D. 131

Answer: Option (C)
Explanation: Each number in the series is the preceding number multiplied by 2 and then increased by 1. Thus, (3 * 2) + 1 = 7, (7 * 2) + 1 = 15, (15 * 2) + 1 = 31 ans so on. .'. Missing number = (63 * 2) + 1 =127.
4. In the following question, a number series is given with one term missing. Choose the correct alternative that will the same pattern and fills in the blank spaces. 1, 2, 3, 5, 8,
    A. 9 B. 11 C. 13 D. 15

Answer: Option (C)
Explanation: Each term in the series is the sum of the preceding two terms. Thus, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8 and so on. .'. Missing number = 5 + 8 = 13.
5. In the following question, a number series is given with one term missing. Choose the correct alternative that will the same pattern and fills in the blank spaces. 19, 2, 38, 3, 114, 4,
    A. 228 B. 256 C. 352 D. 456

Answer: Option (D)
Explanation: The sequence is a combination of two series : I. 19, 38, 114, (....) and II. 2, 3, 4 The pattern followed in I is * 2, * 3,... .'. Missing number = 114 * 4 = 456.
Coding-Decoding
1. In a certain code 'MISSIONS' is written as 'MSIISNOS'. How is 'ONLINE' written in that code?
    A. OLNNIE B. ONILEN C. NOILEN D. LNOENI E. ONNLIE

Answer: Option (A)
Explanation: First and last letter remain the same. The others interchange their positions in pair of two. So, NL become LN IN become NI so the code of ONLINE will be OLNNIE
2. In a certain code 'ROAR' is written as 'URDU'. How is 'URDU' written in that code?
    A. V X D Q B. XUGX C. ROAR D. VSOV E. V Z C P

Answer: Option (B)
Explanation: Each letter moves +3. Add 3 to each letter of URDU, so the code of URDU will be XUGX
3. In a certain code 'LIMCA' is written as 'HJLDZ'. Which of the following words is written as 'IFWJBP'?
    A. M E X I C O B. MERCURY C. JAPAN D. MIDNIGHT E. H O N D U S

Answer: Option (A)
Explanation: Each letter moves +1, -1, ....alternately except for L, which is –4. We have to find the word for the code IFWJBP. Add 4 to I then -1, +1 alternately to the remaining letters. The word will be MEXICO.
4. In a certain code 'HILTON' is written as 'I H T L N O'. How is 'BILLION' written in that code?
    A. IBLLION B. IBOILLN C. IBLLOIN D. IBLOILN 5. IBOLLIN

Answer: Option (C)
Explanation: Letters are interchanged in each pair. So code of BI become IB, IO become OI. So code BILLION will be IBLLOIN
5. If in the English alphabet, every alternate letter from B onwards is written in small letters while others are written in capitals, then how will the 3rd day from Tuesday be coded?
    A. W e D N e S d A Y B. W E d n E S d A Y C. T H U R S d A Y D. T h U r S d A Y E. f r I d A Y

Answer: Option (E)
Explanation: The small letters are b, d, f, h, j, l, n, p, r, t, v, x, z. The third day from tuesday will be friday and code will be frIdAY.
Non-Verbal Series
1. Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures.

    A. 1 B. 2 C. 3 D. 4 E. 5

Answer: Option (A)
Explanation: One, two, three, one, two, three.....arcs get inverted sequentially. This inversion takes place in an ACW direction.
2. Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures.

    A. 1 B. 2 C. 3 D. 4 E. 5

Answer: Option (A)
Explanation: Both the larger and the smaller squares move to the adjacent corner ACW in each turn. Also, the shading in the smaller square moves 1, 2, 3, 4, 5, ... steps ACW sequentially and the shading in the larger square moves 1, 2, 3, 4, 5,.... steps CW sequentially.
3. Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures.

    A. 1 B. 2 C. 3 D. 4 E. 5

Answer: Option (A)
Explanation: One step, the middle element rotates through 180o and in the next step, the other two elements rotate through 180[latex]^{0}[/latex]. The two steps are repeated alternately.
4. Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures.

    A. 1 B. 2 C. 3 D. 4 E. 5

Answer: Option (D)
Explanation: In one step, the existing element enlarges and a new element appears inside this element. In the next step, the outer element is lost.
5. Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures.

    A. 1 B. 2 C. 3 D. 4 E. 5

Answer: Option (E)
Explanation: The number of parts increases by one along with the number of sides in the figure.
Number Ranking
1. In a row of trees, one tree is fifth from either end of the row. How many trees are there in the row?
    A. 8 B. 9 C. 10 D. 11

Answer: Option (B)
Explanation: Clearly, number of trees in the row = (4 + 1 + 4) = 9.
2. In a queue, Amrita is 10th from the front while Mukul is 25th from behind and Mamta is just in the middle of the two. If there were 50 persons in the queue, what position does Mamta occupy from the front?
    A. 20th B. 19th C. 18th D. 17th

Answer: Option (C)
Explanation: Number of persons between Amrita and Mukul = 50 -(10 + 25) = 15. Since Mamta lies in middle of these 15 persons,so Mamta's position is 8th from Amrita i.e. 18th from the front.
3. Manisha ranked sixteenth from the top and twenty-ninth from the bottom among those who passed an examination. Six boys did not participate in the competition and five failed in it. How many boys were there in the class?
    A. 40 B. 44 C. 50 D. 55 E. 58

Answer: Option (D)
Explanation: Number of boys who passed = (15 + 1 + 28) = 44. Total number of boys in the class = 44 + 6 + 5 = 55.
4. Manoj and Sachin are ranked seventh and eleventh respectively from the top in a class of 31 students. What will be their respective ranks from the bottom in the class?
    A. 20th and 24th B. 24th and 20th C. 25th and 21st D. 26th and 22nd E. None of these

Answer: Option (C)
Explanation: Number of students behind Manoj in rank = (31 - 7) = 24. So, Manoj is 25th from the bottom. Number of students behind Sachin in rank = (31 - 11) = 20. So, Sachin is 21st from the bottom.
5. In a row of ten boys, when Rohit was shifted by two places towards the left, he became seventh from the left end. What was his earlier position from the right end of the row?
    A. First B. Second C. Fourth D. Sixth

Answer: Option (B)
Explanation: A number of boys in the row = 10. Rohit's new position is 7th from the left or 4th from the right. His earlier position was two places to the right of his new position i.e. his earlier position was second from the right.
Alphabet Series
1. APZLT, CQYNR, ERXPP, GSWRN, ?
    A. KVIJUJ B. JUUVK C. ITVTL D. KUUVJ

Answer: Option (C)
Explanation: The first letter in every group is ascending in the order of ACEGI. The second letter in every group is also ascending in the order of PQRST, the third letter in every group is descending in the order of ZYXWV, the fourth letter in every group is ascending in the order of LNPRT and the last letter in every group is descending with a gap of one letter, i.e., TRPNL
2. RAP, MAP, HOT FUN,?
    A. HNE B. PGI C. STN D. CAT

Answer: Option (D)
Explanation: a, e, i, o, u are vowels and there is a vowel consonant relationship in every group of the series.
3. CWE, FQH, RDI,?
    A. XBZ B. TGU C. MCO D. FUT

Answer: Option (C)
Explanation: Add the alphabetic numerical value of each letter in the group and then sum up the unit and tens which is equal to four everywhere, i.e., CWE = 3 + 23 + 5 = 31 which is equal to 3 + 1= 4, FQH = 6 + 17 + 8 = 31 (3 + 1) = 4 and so on
4. J, F, M, A, M,?
    A. M B. J C. D D. S

Answer: Option (B)
Explanation: The series contains the first letter of the months of the year in continuity.
5. prt ......... bdf, hjl, npr
    A. uwy B. vya C. vxz D. axy

Answer: Option (C)
Explanation: There is a gap between one letter in every letter of the group. Moreover, every second group of the series starts after a gap of one letter, i.e., after prt, we see vxz.
Directions
1. Rasik walked 20 m towards the north. Then he turned right and walks 30 m. Then he turns right and walks 35 m. Then he turns left and walks 15 m. Finally he turns left and walks 15 m. In which direction and how many meters is he from the starting position?
    A. 15 m West B. 30 m East C. 30 m West D. 45 m East

Answer: Option (D)
Explanation:

2. If South-East becomes North, North-East becomes West and so on. What will the West become?
    A. North-East B. North-West C. South-East D. South-West

Answer: Option (C)
Explanation:

3. One morning after sunrise, Suresh was standing facing a pole. The shadow of the pole fell exactly to his right. To which direction was he facing?
    A. East B. West C. South D. Data is inadequate

Answer: Option (C)
Explanation: Sun rises in the east in the morning. Since the shadow of Suresh falls to his right. So he is facing South.
4. A man walks 5 km toward the south and then turns to the right. After walking 3 km he turns to the left and walks 4 km. And then he goes back 10 km straight. Now in which direction is he from the starting place?
    A. South-East B. North-West C. South D. West

Answer: Option (B)
Explanation: From the given directions, now he is 1km in the North-West direction.
5. Iam facing south. I turn right and walk 20 m. Then I turn right again and walk 10m. Then I turn left and walk 10m and then turning right walk 20m. Then I turn right again and walk 60m. In which direction am I from the starting point?
    A. North B. North-West C. North-East D. East

Answer: Option (C)
Explanation: The movements of the person are from A to F, as shown in Fig. Clearly, the final position is F which is to the North-east of the starting point A.
Analogy
1. Odometer is to mileage as compass is to
    A. speed B. hiking C. needle D. direction

Answer: Option (D)
Explanation: An odometer is an instrument used to measure mileage. A compass is an instrument used to determine direction. Choices a, b, and c are incorrect because none is an instrument.
2. Marathon is to race as hibernation is to
    A. winter B. bear C. dream D. sleep

Answer: Option (D)
Explanation: A marathon is a long race and hibernation is a lengthy period of sleep. The answer is not choice a or b because even though a bear and winter are related to hibernation, neither completes the analogy. (Choice c) is incorrect because sleep and dream are not synonymous.
3. Cup is to coffee as the bowl is to
    A. dish B. soup C. spoon D. food

Answer: Option (B)
Explanation: Coffee goes into a cup and soup goes into a bowl. Choices a and c are incorrect because they are other utensils. The answer is not choice d because the word food is too general.
4. Elated is too despondent as enlightened is to
    A. aware B. ignorant C. miserable D. tolerant

Answer: Option (B)
Explanation: Elated is the opposite of despondent; enlightened is the opposite of ignorant.
5. An optimist is too cheerful as a pessimist is to
    A. gloomy B. means C. petty D. helpful

Answer: Option (A)
Explanation: An optimist is a person whose outlook is cheerful. A pessimist is a person whose outlook is gloomy. The answer is not (choice b) because a pessimist does not have to be mean. (Choices c) and d is incorrect because neither adjective describes the outlook of a pessimist.
Arithmetical Reasoning
1. If you write down all the numbers from 1 to 100, then how many times do you write 3?
    A. 11 B. 18 C. 20 D. 21

Answer: Option (C)
Explanation: Clearly, From 1 to 100, there are ten numbers with 3 as the unit's digit - 3, 13, 23, 33, 43, 53, 63, 73, 83, 93 and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
2. Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today?
    A. 20 years B. 22 years C. 25 years D. 27 years

Answer: Option (C)
Explanation: Let Varun's age today = x years. Then, Varun's age after 1 year = (x + 1) years. Therefore x + 1 = 2 (x - 12) => x + 1 = 2x - 24 => x = 25. So, required number = 10 + 10 = 20.
3. In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box?
    A. 18 B. 36 C. 45 D. None of these

Answer: Option (D)
Explanation: Let R, G and B represent the number of balls in red, green and blue boxes respectively. Then, R + G + B = 108 ...(i), G + R = 2B ...(ii) B = 2R ...(iii) From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R. Putting G = 3R and B = 2R in (i), we get: R + 3R + 2R = 108 => 6R = 108 => R = 18. Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.
4. Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married?
    A. 23 years B. 25 years C. 33 years D. 35 years

Answer: Option (A)
Explanation: Ayush's present age = 10 years. His mother's present age = (10 + 20) years = 30 years. Ayush's father's present age = (30 + 5) years = 35 years. Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years. Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.
5. In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3: 2 respectively. The number of girls not participating in sports is 5 more than the number of boys not participating in sports. If the number of boys participating in sports is 15, then how many girls are there in the class?
    A. 20 B. 25 C. 30 D. Data inadequate

Answer: Option (C)
Explanation: Let the number of boys and girls participating in sports be 3x and 2x respectively. Then, 3x = 15 or x = 5. So, number of girls participating in sports = 2x = 10. Number of students not participating in sports = 60 - (15 + 10) = 35. Let a number of boys not participating in sports be y. Then, a number of girls not participating in sports = (35 -y). Therefore (35 - y) = y + 5 2y 30 y = 15. So, number of girls not participating in sports = (35 - 15) = 20. Hence, total number of girls in the class = (10 + 20) = 30.
Blood Relations
1. If A is the brother of B; B is the sister of C; and C is the father of D, how D is related to A?
    A. Brother B. Sister C. Nephew D. Cannot be determined

Answer: Option (D)
Explanation: If D is Male, the answer is Nephew. If D is Female, the answer is Niece. As the sex of D is not known, hence, the relation between D and A cannot be determined. Niece - A daughter of one's brother or sister, or of one's brother-in-law or sister-in-law. Nephew - A son of one's brother or sister, or of one's brother-in-law or sister-in-law.
2. Pointing to a photograph Lata says, "He is the son of the only son of my grandfather." How is the man in the photograph related to Lata?
    A. Brother B. Uncle C. Cousin D. Data is inadequate

Answer: Option (A)
Explanation: The man in the photograph is the son of the only son of Lata's grandfather i.e., the man is the son of Lata's father. Hence, the man is the brother of Lata.
3. Deepak said to Nitin, "That boy playing with the football is the younger of the two brothers of the daughter of my father's wife." How is the boy playing football related to Deepak?
    A. Son B. Brother C. Cousin D. Brother-in-law

Answer: Option (B)
Explanation: Father's wife → mother. Hence, the daughter of the mother means sister and sister's younger brother means brother. Therefore, the boy is the brother of Deepak.
4. Veena who is the sister-in-law of Ashok is the daughter-in-law of Kalyani. Dheeraj is the father of Sudeep who is the only brother of Ashok. How Kalyani is related to Ashok?
    A. Mother-in-law B. Aunt C. Wife D. None of these

Answer: Option (D)
Explanation: Ashok is the only brother of Sudeep and Veena is the sister-in-law of Ashok. Hence Veena is the wife of Sudeep. Kalyani is the mother-in-law of Veena. Kalyani is the mother of Ashok.
5. Pointing to Varman, Madhav said, "I am the only son of one of the sons of his father." How is Varman related to Madhav?
    A. Nephew B. Uncle C. Father or Uncle D. Father

Answer: Option (C)
Explanation: Madhav is the only son of one of the sons of Varman's father → Either Varman is the father or uncle of Madhav.
Decision Making
Directions (1 - 5): Study the given information & answer the following questions: Following are the criteria to recruit a Professor in an organization: The Applicant must a. be graduate in any discipline with min. 67% marks. b. have his/her age in between 28 to 33 years as on 26-09-2017. c. have a PG degree/ 3 years diploma or must have completed B.Ed. with more than 55% marks. d. have a minimum of 3 years experience in Teaching. e. be ready to join 1-year probation.
If a candidate satisfies all the criteria except
i. at (c) above, but is an Arts with Maths graduate with minimum 72% marks and has an experience of more than 4 years and more her/his case is to be referred to the Principal. ii. at (d) above, but master degree’s with minimum 60% marks, her/his is to be referred to the Vice Principal.
Details of applicants are given below in the questions. On the basis of the following course of action which is based on the data given above, mark the answer. All cases are given to you as on the date 26-09-2017.
1. Manika is a B.Sc. Graduate with 70% marks and has completed PG in M.Sc. She completed 27 years of age in 2015 and has 3 year's experience as a Maths Faculty. She is ready to join the probation period of one year.
    A. if the case is to be referred to the Principal. B. if the case is to be referred to Vice Principal. C. if the candidate is to be selected. D. if the information is inadequate to take a decision. E. if the candidate is not to be selected.

Answer: Option (C)
Explanation: Clearly Manika will be selected as she meets all the requirements.
2. Mamta is a graduate in B.A. and B.Ed. with 75% and 70% respectively. She has been working as a professor in Math for 5 years and has freelancing experience of 2 years. Mamta’s age is 30 years and she is ready to join 2-year probation.
    A. if the case is to be referred to the Principal. B. if the case is to be referred to Vice Principal. C. if the candidate is to be selected. D. if the information is inadequate to take a decision. E. if the candidate is not to be selected.

Answer: Option (C)
Explanation: Mamta will be selected for the post as she meets all the requirements.
3. Abhishek is a graduate in B.Sc. and postgraduate in M.Sc. with 78% marks and has been working for the past 7 years during which he worked as a teacher in coaching institute for two years. He was born on 07.11.1986 and is ready to join the probation period of 1year.
    A. if the case is to be referred to the Principal. B. if the case is to be referred to Vice Principal. C. if the candidate is to be selected. D. if the information is inadequate to take a decision. E. if the candidate is not to be selected.

Answer: Option (D)
Explanation: Since we do not know his B.Sc marks, so information is inadequate to take the decision.
4. Shobha, a 29-year-old science graduate with 70% marks in her graduation has 53% marks in her B.Ed. and she also has an Arts with Maths graduation securing 80% marks.She also worked with Satyam for a span of 5 years and she is willing to join the probation period for 1 year.
    A. if the case is to be referred to the Principal. B. if the case is to be referred to Vice Principal. C. if the candidate is to be selected. D. if the information is inadequate to take a decision. E. if the candidate is not to be selected.

Answer: Option (A)
Explanation: Since she has 53% marks in B.Ed but did Arts with Maths graduation securing 80% marks, so her case must be referred to the Principal.
5. Aman has been working as Assistant Professor for the past 5 years. She has completed MA and graduation with 73% marks each and is ready to join one-year probation. She was born on 22 Aug 1987.
    A. if the case is to be referred to Executive Head. B. if the case is to be referred to Vice President. C. if the candidate is to be selected. D. if the information is inadequate to take a decision. E. if the candidate is not to be selected.

Answer: Option (C)
Explanation: Clearly the candidate will be selected.
Mirror Images
1. Choose the alternative which is closely resembles the mirror image of the given combination.

    A. 1 B. 2 C. 3 D. 4

Answer: Option (B)
2. Choose the alternative which closely resembles the mirror image of the given combination.

    A. 1 B. 2 C. 3 D. 4

Answer: Option (B)
3. Choose the alternative which closely resembles the mirror image of the given combination.

    A. 1 B. 2 C. 3 D. 4

Answer: Option (A)
4. Choose the alternative which closely resembles the mirror image of the given combination.

    A. 1 B. 2 C. 3 D. 4

Answer: Option (D)
5. Choose the alternative which is closely resembles the mirror image of the given combination.

    A. 1 B. 2 C. 3 D. 4

Answer: Option (C)
Clocks & Calendars
1. It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
    A. Sunday B. Saturday C. Friday D. Wednesday

Answer: Option (C)
Explanation: On 31st December, 2005 it was Saturday. Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days. On 31st December 2009, it was Thursday. Thus, on 1st Jan 2010 it is Friday.
2. What will be the day of the week 15[latex]^{th}[/latex] August, 2010?
    A. Sunday B. Monday C. Tuesday D. Friday

Answer: Option (A)
Explanation: 15[latex]^{th}[/latex] August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010) Odd days in 1600 years = 0 Odd days in 400 years = 0 9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days 4 odd days. Jan. Feb. March April May June July Aug. (31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days 227 days = (32 weeks + 3 days) 3 odd days. Total number of odd days = (0 + 0 + 4 + 3) = 7 0 odd days. Given the day is Sunday.
3. Today is Monday. After 61 days, it will be:
    A. Wednesday B. Saturday C. Tuesday D. Thursday

Answer: Option (B)
Explanation: Each day of the week is repeated after 7 days. So, after 63 days, it will be on Monday. After 61 days, it will be on Saturday.
4. How many times are the hands of a clock at the right angle in a day?
    A. 22 B. 24 C. 44 D. 48

Answer: Option (C)
Explanation: In 12 hours, they are at right angles 22 times. In 24 hours, they are at right angles 44 times.
5. How many times in a day, are the hands of a clock in the straight line but opposite in direction?
    A. 20 B. 22 C. 24 D. 48

Answer: Option (B)
Explanation: The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only). So, in a day, the hands point in opposite directions 22 times.
Cubes and Dice
1. What will be the number at the bottom, if 5 is at the top; the two positions of the dice being as given below:

    A. 1 B. 2 C. 3 D. 6

Answer: Option (B)
Explanation: From figures (i) and (ii), it is clear that 4, 1, 3 and 6 he adjacent to 2. Therefore, 5 must lie opposite 2. Thus, if 5 is at the top, then 2 must be at the bottom.
2. If the total number of dots on opposite faces of a cubical block is always 7, find the figure which is correct.

    A. Fig.1 B. Fig.2 C. Fig.3 D. Fig.4

Answer: Option (B)
Explanation: Since the total number of dots on opposite faces is always 7, therefore, 1 dot appears opposite 6 dots, 2 dots appear opposite 5 dots and 3 dots appear opposite 4 dots.
3. Two positions of a block are given below. When 1 is at the top, which number will be at the bottom?

    A. 2 B. 3 C. 4 D. 6

Answer: Option (D)
Explanation: Number 2 is common to the two positions of the dice. We assume the dice in fig. (ii) to be rotated so that 2 remains on the top face (i.e. face V as per activity 1) and the numbers 3 and 6 move to the faces hidden behind 5 and 1 respectively [in fig. (i)]. Then, clearly, 5 lies opposite 3 and 6 lies opposite 1. Hence, when 1 is at the top, then 6 will be at the bottom.
4. What number is opposite 3 in the figure shown below? The given two positions are of the same dice whose each surface bears a number among 1, 2, 3, 4, 5 and 6.

    A. 2 B. 4 C. 5 D. 6

Answer: Option (C)
Explanation: From figures (i) and (ii), we conclude that 2, 6, 1 and 4 appear adjacent to 5. Therefore, 3 must appear opposite 5, Conversely, the number opposite 3 is 5.
5. Three different positions X, Y and Z of dice are shown in the figures given below. Which number lies at the bottom face in position X?

    A. 2 B. 3 C. 6 D. Cannot be determined

Answer: Option B
Explanation: From positions X and Y we conclude that 1, 5, 6 and 3 lie adjacent to 4. Therefore, 2 must lie opposite 4. From positions Y and Z we conclude that 4, 3, 2 and 5 lie adjacent to 6. Therefore, 1 must lie opposite 6. Thus, 2 lies opposite 4, 1 lies opposite 6 and consequently 5 lies opposite 3. As analyzed above, the number on the face opposite 5 is 3. In position X, since 5 lies on the top, therefore 3 must lie at the bottom face.
Embedded Figures etc 1. Fig. (X) is embedded in any of the four alternative figures. Find the alternative which contains fig. (X).

Answer: Option (d)
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