Series!!

**1. Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ….., x _{n}.**

**Solution:**

Given sequence: 5, 10, 15, 20, 25, ……, x_{n}.

Therefore, the arithmetic series for the given sequence is 5 + 10 + 15 + 20 + 25 + …… + x_{n.}

**2. Write the formula for arithmetic and geometric series.**

**Solution:**

As we know, the arithmetic sequence is of the form: a, a + d, a + 2d, a + 3d, …

Hence, the formula for arithmetic series is a + (a + d) + (a + 2d) + (a + 3d) + …

Similarly, the geometric sequence is of the form: a, ar, ar^{2},…., ar^{(n-1)},…

Hence, the formula for geometric series is a + ar + ar^{2} + …+ ar^{(n-1)}+ …

**3. Find the missing number in the given series 13, 24, 46, 90, 178, ?.**

**Solution:**

Given series: 13, 24, 46, 90, 178, ?.

24 – 13 = 11

46 – 24 = 22

90 – 46 = 44

178 – 90 = 88

The logic used here is that the difference between two successive numbers is doubled consecutively.

So, if 88 is doubled, we get 176.

Hence, 178 + 176 = 354.

Thus, the missing term in the sequence is 354.

Therefore, the complete series is 13, 24, 46, 90, 178, 354.

**4. Find the missing number in the given series 4, 18, ___, 100, 180, 294, 448.**

**Solution:**

The given sequence is obtained as follows:

2^{3} – 2^{2} = 8 – 4 = 4

3^{3} – 3^{2} = 27 – 9 = 18

4^{3} – 4^{2} = 64 – 16 = 48

5^{3} – 5^{2} = 125 – 25 = 100

6^{3} – 6^{2} = 216 – 36 = 180

7^{3} – 7^{2} = 343 – 49 = 294

8^{3} – 8^{2} = 512 – 64 = 448

Hence, the missing number in the series is 48.

Therefore, the complete series is 4, 18, 48, 100, 180, 294, 448.

**5. Determine the missing numbers in the series 5, 6, 9, 14, 21, ?.**

**Solution:**

Given the number series: 5, 6, 9, 14, 21, ?.

5 + 1 = 6

6 + 3 = 9

9 + 5 = 14

14 + 7 = 21

21 + 9 = 30.

Hence, the missing number here is 30.

Here, the series follows a pattern of the sum of consecutive odd numbers.

So, the complete number series is 5, 6, 9, 14, 21, **30**.

**6. Complete the series 1, 2, 10, 37, 101, __.**

**Solution:**

Given series: 1, 2, 10, 37, 101, ___.

1 + 1^{3} = 1 + 1 = 2

2 + 2^{3} = 2 + 8 = 10

10 + 3^{3} = 10 + 27 = 37

37 + 4^{3} = 37 + 64 = 101

101 + 5^{3} = 101+ 125 = 226

Thus, the given series follows a pattern of the sum of cubes of the consecutive natural numbers.

So, the complete series 1, 2, 10, 37, 101, **226**.

**7. Find out the wrong term in the given series: 2, 3, 12, 37, 86, 166, 288.**

**Solution:**

Given series: 2, 3, 12, 37, 86, 166, 288.

2 + 1^{2} = 2 + 1 = 3

3 + 3^{2} = 3 + 9 = 12

12 + 5^{2} = 12 + 25 = 37

37 + 7^{2} = 37 + 49 = 86

86 + 9^{2} = 86 + 81 = **167**

167 + 11^{2} = 167 + 121 = 288.

Here, the series follows a pattern of addition of the square of the consecutive odd numbers.

So, from the given number series 2, 3, 12, 37, 86, 166, 288, the wrong term is 166, because it should be 167.

**8. Find the missing number 25: 37:: 49:?**

**Solution:**

Here, 5^{2} = 25 and (5+1)^{2} + 1 = 37

Similarly, 7^{2} = 49 and (7+1)^{2} + 1 = 65.

Hence, the missing number is 65.

**9. 11 : 121 :: 13 : ____. Find the missing value.**

**Solution:**

Here, 11^{2} = 121

So, 13^{2}= 169

So, the missing number is 169.

I.e., 11: 121 :: 13 : **169**.

**10. Find out the missing term in the given series: 11, 17, 39, 85, ?.**

**Solution:**

Given series: 11, 17, 39, 85, ?.

11 + (3^{2} – 3) = 11 + 6 = 17

17 + (5^{2} – 3) = 17 + 22 = 39

39 + (7^{2} – 3) = 39 + 46 = 85

85 + (9^{2} – 3) = 85 + 78 = 163

Therefore, the missing number in the given series is 163.

I.e., 11, 17, 39, 85, **163**.

Coding – Decoding

**Q 1.** In a certain code language “CONSTRUCTION” is written as “EMPQVPWAVGQL”. What will be the code for “DESTRUCTION” in the same language?

- FCURTSERKMP
- EFTVSVDVJPO
- FCURTSFSLOQ
- None of the above
- Cannot be determined

**Q 2.** In a certain code language, “YEARLY” is written as “BVZIOB”. What will be the code for “ANNUAL” in the same language?

- ZFMOMM
- ZNNFZA
- ZMMFZO
- XCADGF
- ZXAMMO

**Q 3.** In a certain code language “EASY” is written as “5117”. In the same code language, how will “BEAM” be written as?

- 4512
- 4567
- 2513
- 2514
- 2563

**Q 4.** “SPECIAL” is written as “65” in a certain code language what will “CONNECT” be coded as?

- 70
- 64
- 32
- 78
- 74

**Q 5.** In a certain code language, “ISSUE” is written as “341145”, in the same code language what will be the code for “DATES”?

- 4567
- 340045
- 4120519
- 7600
- 604

**Related logical reasoning links:**

I. Water : : II : Thermometer

I. (A) Humidity (B) Rain (C) Pitcher (D) Evaporation

II. (P) Temperature (Q) Mercury (R) Doctor (S) Fever

(A) DP

(B) AS

(C) BR

(D) CQ

Ans: D

First contains the second.

Question: 2

I : Garland : : II : Star

I. (A) Perfume (B) Hero (C) Flower (D) Honour

II. (P) Galaxy (Q) Shine (R) Sun (S) Night

(A) CP

(B) CR

(C) BS

(D) DQ

Ans: A

First is a part of the second.

Question: 3

I. Ship : : II : Platform

I. (A) Captain (B) Quay (C) Port (D) Shore

II. (P) Coolie (Q) Station (R) Train (S) Bench

(A) AP

(B) BR

(C) CQ

(D) DS

Ans: B

First is the place where the second stops temporarily.

Question: 4

I : Modern : : II : Old

I. (A) Ancient (B) Death (C) Famous (D) Civilisation

II. (P) Industrialisation (Q) Young (R) Fashion (S) Western

(A) AS

(B) AQ

(C) BR

(D) CR

Ans: B

The words in each pair are antonyms of each other.

Question: 5

I. Increase : : II : Descend

I. (A) Grow (B) Decrease (C) Rise (D) Price

II. (P) Reduce (Q) Down (R) Ascend (S) Mountain

(A) AQ

(B) AR

(C) BR

(D) CP

Ans: C

The words in each pair are antonyms of each other.

**Directions (Q6 – Q10):** Study the data given below and answer the following questions:

‘Royal Monarch Regal’ is written as @ # *,

‘Regal legacy Gold’ is written as * % ?,

‘Hope Gold Life’ is written as % & $,

‘Regal Monarch Morals’ is written as # * ∀

**Q 6.** What will be the code for Regal?

- %
- *
- $
- #
- ?

**Q 7.** What will be the code for “Gold Legacy”?

- # &
- % #
- ? %
- * ∀
- & $

**Q 8.** Which word is coded as #?

- Moral
- Life
- Regal
- Monarch
- Legacy

**Q 9.** In the given coded language, which of the following words has been coded as &?

- Gold
- Life
- Hope
- Either ‘2’ or ‘3’
- None of the above

**Q 10. **What is the code for royal?

- %
- @
- ?
- *
- ∀

**Q 1. **In a certain code language “CONSTRUCTION” is written as “EMPQVPWAVGQL”. What will be the code for “DESTRUCTION” in the same language?

- FCURTSERKMP
- EFTVSVDVJPO
- FCURTSFSLOQ
- None of the above
- Cannot be determined

**Question 1. If MENTAL = 390, ABILITY = 546, REASONING = 918, then COMPETENCY = ?**

- a. 782
- b. 842
- c. 1190
- d. 1340

Solution:

- Answer: (c)MENTAL = 39013+5+14+20+1+12= 65 (Sum of alphabets codes)6 (Number of alphabets)⇒ 6 × 65 = 390ABILITY = 5461+2+9+12+9+20+25 = 78 (Sum of alphabets codes)7 (Number of alphabets)⇒ 7×78 = 546COMPETENCY = ?3+15+13+16+5+20+5+14+3+25 = 119 (Sum of Alphabets codes)10 (Number of Alphabets)⇒ 119 × 10 = 1190

**Question 2. Which number replaces the question mark in the given figure?**

- a. 4
- b. 5
- c. 7
- d. 9

Solution:

- Answer: (c)

**Question 3. How many small cubes will have no faces coloured?**

- a. 8
- b. 12
- c. 36
- d. 18

Solution:

- Answer: (a)
_{}After dividing into small cubes of 1**8**cubes.

**Question 4. How many small cubes will have at least two faces coloured, one with red and another with yellow?**

- a. 4
- b. 8
- c. 12
- d. 24

Solution:

- Answer: (c)At Least two faces coloured one with red and another with yellow =
**12**

**Question 5. In a certain code 34 means ‘project work’. What is the meaning of 4 and 3 in that code?**

**Based on the following statements, select the correct option:**

**Statement I : ‘173’ means ‘completed project on time.**

**Statement II : ‘640’ means ‘received an award for the hard work’.**

- a. The data in statement I alone are sufficient to answer the question
- b. The data in statement II alone are sufficient to answer the question
- c. The data in both the statements together are sufficient to answer the question
- d. The data even in both the statements together are not sufficient to answer the question

Solution:

- Answer: (a, b)Given Coding3→ Project4 → Work34 → Project work173 → Completed project on time640 → Received award for hard workHence, any one statement from I and II alone are sufficient to answer the question

**Question 6.**

**Fact 1: All tortoises like to jump.**

**Fact 2: Some tortoises like to fly.**

**Fact 3: Some tortoises look like their followers.**

**If the first there statements are facts, which of the following statements must also be a fact?**

**I. All tortoises who like to fly look like their followers.**

**II. Tortoises who like to fly also like to jump.**

**III. Tortoises who like to jump do not look like their followers.**

- a. I only
- b. II only
- c. I and III only
- d. II and III only

Solution:

- Answer: (b)(i) Not true for all(ii) True for all(iii) Not true for all

**Question 7. At what time between 3 PM and 4 PM the angle between the minute and hour hands be nine degrees, the minute hand being ahead of the hour hand?**

- a. 3 h 15 m 45 s
- b. 3 h 16 m
- c. 3 h 16 m 30 s
- d. 3 h 18 m

Solution:

- Answer: (d)3 PM to 4 PM11/2M – 30H = 9⇒ 11/2M – 30 × 3 = 9⇒ 11/2M = 9 + 90M = 99 × 2/11 = 18⇒ 3 h 18 minute

**Question 8. Which expression will replace the question mark?**

- a. E 7
- b. D 10
- c. D 7
- d. E 10

Solution:

- Answer: (d)

**Question 9. The digits/numbers from 1 to 12 of the clock dial are replaced by the letters of the English alphabet. The replacement starts with the letter ‘C’ but vowels and immediate next consonants of vowel are not included in the replacement. The classes in the school start at N : T and last till a time when the minute hand is at K and the hour hand between S and T, very slightly ahead of S. Five periods of equal duration are held during this interval. The break of 7 minutes is given to students after 1 ^{st} period and duration of break increases by 2 minutes after each period. The exact duration of a period in minutes is:**

- a.32
- b.33
- c. 34
- d. 35

Solution:

- Answer: (b)N : T = 8.00 AM to 11.25 AM= 3Hours 25 Minutes.= 180 + 25 = 205 MinutesTotal Break time = 7+9+11+13 = 40 Min.So, 205 – 40 = 165Duration of period in min. 165/5 = 33 Minutes

**Question 10. In TEACHER is coded as KBADFBM, MATURE is coded as ALONEG, then the code of BOARD will be __________.**

- a. AMDJC
- b. MADKC
- c. MACKD
- d. AMCJD

Solution:

- Answer: (a)
_{}Sum or difference of place values should be 7._{}Sum or difference of place values should be 6._{}Sum or difference of place values should be 5.

**Question 11. In a performing arts competition, there are six participants M, P, B, K, L and V. It is given that M and P are good at dancing and acting. B and K are good at tabla but not good at singing. P and V are good at playing the guitar an also good at singing. Who among them is/are good at dancing, singing, playing Guitar and acting?**

- a. M and P
- b. Only P
- c. Only V
- d. Only B

Solution:

- Answer: (b)Only P is there common in all

**Question 12. What is the total number of squares in the given figure?**

- a. 62
- b. 72
- c. 82
- d. 92

Solution:

- Answer: (b)
**72**Squares.

**Question 13. In a certain coding system if**

**25 + 10 × 4 = 19**

**10 ÷ 3 – 3 = 10**

**Then the value of**

**16 × 5 + 40 – 10 ÷ 2 =**

- a. 10
- b. 11
- c. 12
- d. 13

Solution:

- Answer: (d)So, the 16 × 5 + 40 – 10 ÷ 2 = ?16 + 5 – 40 ÷ 10 × 2= 21 – 4 × 2 =
**13**Therefore, option (d) is correct.

**Question 14. In the given sequence, which symbol comes five symbols before the symbol which comes nine symbols after the second appearance of the symbol which occur four times in the sequence?**

**1 >9 ∈< L * M 2 N > Q A ÷ S 8 > 4 U $ V @ A > X 2 Q B = D < Z**

- a. A
- b. S
- c. @
- d. 8

Solution:

- Answer: (b)Four time occurring → >Nine symbol after second appearance of > → $Five symbol before $ →
**S**

**Question 15. Find the values of W, X, Y and Z in the given figure.**

- a. 2, 9, 6, 7
- b. 3, 5, 1, 5
- c. 4, 1, 8, 7
- d. 8, 1, 2, 5

Solution:

- Answer: (a)Sum of numbers vertically, horizontally and diagonally is equal and by observation wesee it is 45.

**Question 16. Statement: T % R, R $ M, M @ D, D © H**

- a. Only I
- b. I and III
- c. I and IV
- d. III and IV

Solution:

- Answer: (a)T≤ R → T ≤ RR ≤ M → R ≥ MM @D → M = DD © H → D < Hi.e. T ≤ R, M = D ≤ R, M = D < H(i)
**D % R → D ≤ R**(ii) H # R → H > R(iii)T ©M → T < D(iv)T % D → T ≤ DOnly D % R → D ≤ R satisfies

**Question 17. Statement: M @ B, B # N, N $ R, R © K**

- a. I and III
- b. I, II and III
- c. II, III and IV
- d. I, III and IV

Solution:

- Answer: (c)M @ B → M = BB # N → B > NN $ R → N ≥ RR © K → R < Ki.e M = B > N ≥ R and K > R(i) K © R → K < R(ii) R © B → R < B(iii) M $ R → M ≥ B(iv) N ©M → N < M(ii),(iii) and (iv) are correct

**Question 18. Identify the region which represents philosophers who are musicians and writers.**

- a. h + i + j + k
- b. h + i
- c. k + j
- d. j

Solution:

- Answer: (a)

**Question 19. How many actors are magicians?**

- a. g
- b. g + h
- c. f +g + h
- d. f + g – h

Solution:

- Answer: (c)

**Question 20. How many actors are also philosophers but not historians or**

- a. l + k
- b. g + h + k
- c. m + f + l + k
- d. m + f + s

Solution:

- Answer: (d)

**Question 21. Bhupen’s birthday is on the 13 ^{th} of June and Mainu’s birthday is on 23^{rd} of April. If in a particular year, Mainu’s birthday was on Monday, what will be the day on Bhupen’s birthday in the same year?**

- a. Tuesday
- b. Wednesday
- c. Thursday
- d. Friday

Solution:

- Answer: (b)Mainu’s Birthday → 23
^{rd}April MondayBhupen’s Birthday → 13^{th}JuneOdd days from April 23^{th}to 13^{th}JuneApril + May + June7+31+13 = 51 days⇒ 51/7 = 7 week = 2 odd days.So Bhupen’s birthday is on Monday +2 =**Wednesday**.

**Question 22. At what time duration of a week are all the doctors available at the clinic?**

- a. Sunday for 3 hrs.
- b. Thursday for hr.
- c. Thursday for 1 hr.
- d. Sunday for 1 hr.

Solution:

- Answer: (b)All doctor’s time schedule.Dr. Ashutosh → 12 – 4 PM (Tuesday, Thursday and Sunday)Dr. Dhan wantri → 10AM – 2PM (Monday, Thursday, Friday. Sunday)Dr. Shehnaz → 9AM – 12:30 PM (Monday, Wednesday and Thursday)2PM – 4PM (Friday, Saturday, Sunday)Thursday is common all doctors and all doctors available at the clinic time is=
**Thursday**12:00 to 12:30 = 1/2 hr

**Question 23. On how many days and hours, Dr. Ashutosh and Dr. Shehnaz are available at the same time?**

- a. 1,212
- b. 1, 2
- c. 2,212
- d. 2, 2

Solution:

- Answer: (c)Dr. Ashutosh & Dr. Shehnaz are available on Sunday & Thursday.Sunday → 2PM – 4PM → 2 hourThursday → 12PM to 12.30PM → 1/2 hourTherefore
**2 day.**2212hour.

**Question 24. For how many hours in a week, Dr. Dhanwantri and Dr. Shehnaz are together available at the same time ?**

- a.512
- b. 6
- c. 5
- d.212

Solution:

- Answer: (c)Dr. Dhanwantri & Dr. Shehnaz are available same day and time.⇒ Thursday and Monday.Per day 10 AM to 12.30 PM =212hour2 day =
**5**hour

**Question 25. In a certain school, 62% of candidates qualified all the three subjects, namely English, Mathematics and Social Science. The following diagram gives the number of candidates who are not qualified in different subjects. What is the percentage of candidates who are not qualified in at least two subjects?**

- a. 2.63
- b. 6.00
- c. 7.00
- d. 18.42

Solution:

- Answer: (c)Let total students = A62% qualified and 38% not qualified38% of A = 30+12+50+10+5+8+75 = 19038/100 × A = 190A = (190×100)/38 = 500At Least two = (12+10+8+5) = 35 (not qualified)= 35/500 × 100 = 7

**Question 26. Samungou’s mother is the only daughter of Juhi’s father. How is Juhi’s husband related to Samungou ?**

- a. Brother
- b. Father
- c. Son
- d. Uncle

Solution:

- Answer: (b)Juhi is the only daughter so she is samungou’s mother.Juhi’s husband is Samungou’s
**father**.

**Question 27. A matrix of certain characters is given in the following. These characters follow a certain trend, row-wise or column-wise. Find out this pattern and choose the missing character.**

- a. 12
- b. 42
- c. 46
- d. 50

Solution:

- Answer: (c)X = 87–41 =
**46**

**Question 28. **Find the value of # in the figure below :

- a. 10
- b. 15
- c. 19
- d. 21

Solution:

- Answer: (c)

**Direction: (Question 29)**

**The yearly percentage expenditure of a school student on various items is shown in table given below:**

**Question 29. Which of the following figures represent the above data ?**

Solution:

- Answer: (b)Total angle of the circle is 360°.So according to given data calculatedBook = 30/100 × 360° = 108°Notebook = 10/100 × 360° = 36°Mess charge = 5/100 × 360° = 18°School fee = 20/100 × 360° = 72°Travel and accommodation = 35/100 × 360° = 126°
_{}

**Question 30. In an examination students are graded with four grades namely A, B, C and D and 72 students of the school secured A grade. The ratio of students who secured A grade to students with D grade is 2 : 5. Out of the total students, 30% secured B grade and 40% secured C grade. What is the total number of students in the school?**

- a. 840
- b. 600
- c. 420
- d. 360

Solution:

- Answer: (a)Student secured A grad = 72Ratio = 2/5 = 36/180So, students with D grade = 5 × 36 = 180A and D grade student = 72 + 180 = 25230% of total = 252Total Number of students in school = 252/30 × 100=
**840**

**Question 31. Given below are three statements followed by four alternatives. Select the alternative which follows logically, from the given statements.**

I. Only boys can register for a competition.

II. Many of the competitors are toppers.

III. All the names of toppers are marked with green colour.

- a. All toppers are competitors.
- b. Some of the competitors are boys.
- c. Some of the competitors are marked with green colour.
- d. Only the names of boys are marked with green colour.

Solution:

- Answer: (c)

**Question 32. Find the missing number in the given sequence. 1, 2, 2, 4, _____ 4, 2.**

- a. 1
- b. 2
- c. 3
- d. 4

Solution:

- Answer: BonusNo pattern can be deduced.

**Question 33. Which figure among the given options will appropriately replace the question mark?**

Solution:

- Answer: (b)By observation2x = y2y = z2x + y = zSo, 4x = zTherefore, option (b) is correct.

**Question 34. Given below are 9 pictures, A, B, C, D, E, F, H and I. On the basis of a similar relationship, classify the pictures into three groups. Which among the given options represents the suitable group combination?**

- a. (A, D, F); (B, C, H); (E, G, I)
- b. (A, D, H); (B, C, F); (E, G, I)
- c. (A, D, F); (B, C, H); (E, G, I)
- d. (B, C, H); (D, E, F); (A, G, I)

Solution:

- Answer: (a) and (c)a. Options (A, D, F); (B, C, H); (E, G, I)Options (A, D, F) are equal sequence(B, C, H) are equal sequence(E, G, I) are equal sequenceTherefore, option (a, c) is correct.

**Question 35. If – means ÷, _+ means ×, ÷ means –, × means +, then which of the following is correct?**

**(A) 36 – 12 × 6 ÷ 3 + 4 = 60**

**(B) 52 ÷ 4 + 5 × 15 – 3 = 37**

**(C) 36 × 4 – 12 + 5 ÷ 3 = 420**

**(D) 43 × 7 + 5 + 4 – 8 = 25**

- a. A
- b. B
- c. C
- d. D

Solution:

- Answer: (b)– → ÷+ → ×÷ → –× → +So, 52 ÷ 4 + 5 × 15 – 3 = 37⇒52 – 4 × 5 + 15 ÷ 3 = 37⇒ 52 – 20 + 5 = 37⇒ 37 = 37Therefore, option (b) is correct.

**Question 36. The following figure represents the number of students in each of the clubs in a school.**

**Find the number of students representing at least two clubs of the school.**

- a. 90
- b. 134
- c. 146
- d. 183

Solution:

- Answer: (c)Diagram showing all the bubbles showing the number of students at least of two clubs.16 + 10 + 15 + 12 +24 + 36 + 11 + 8 + 14 =
**146**Therefore, option (c) is correct.

**Question 37. The ratio of boys and girls in a school for the last five academic years are given in the following graph. If the number of girls in 2016-17 is half of that in 2017-18, what is the ratio of boys in 2017-18 to boys in 2016-17?**

- a. 1 : 1
- b. 3 : 2
- c. 14 : 5
- d. 7 : 3

Solution:

- Answer: (c)Let B
_{1}& G_{1}, represents the number of boys and girls represented in year 2016–2017.And, B2 & G2 represent the number of boys and girls represented in year 2017–2018.B_{1}/G_{1}= 1, B_{2}/G_{2}= 1.40, G_{1}/G_{2}= 1/2⇒B_{2}/B_{1}=(1.4G_{2})/G_{1}=(1.4 G_{2})/(G_{2}/2)=2.8/1=28/10=14/5Ratio =**14:5**Therefore, option (c) is correct.

**Question 38. A manufacturer of tennis balls is claimed that their balls are the best as it (a ball) would rise constantly 10% of the height from which it was dropped.**

**If the ball is dropped from 27 feet, how much approximately in feet the ball travels (in feet) before coming to rest?**

- a. 32.4
- b. 33
- c. 34.6
- d. 36

Solution:

- Answer: (b)

**Question 39. Find the values of X and Y.**

- a. 289, 3
- b. 289, 5
- c. 121, 7
- d. 121, 4

Solution:

- Answer: (a)√64=8√25+√9=8√9=3(√25×√9)=15√25=5√25–√9=2√x=√100+√49x = 289y = √100-√49 = 10 – 7 = 3

**Question 40. Which is the missing term of the following sequence?**

**002 B, 009 I, 028 J, _____, 126 I**

- a. 048 L
- b. 065 K
- c. 172 G
- d. 186 N

Solution:

- Answer: (b)

**Question 41. How many triangles are there in the given figure?**

- a. 21
- b. 22
- c. 23
- d. 24

Solution:

- Answer: (b)Total 22 triangle

**Question 42. In a class of 60 students, where girls and boys are in the ratio 2 : 3, the boy ‘Kartik’ is ranked 17 ^{th} from the top. If there are 9 girls ahead of Kartik, what is the ratio of the number of girls and boys after the rank position of Kartik?**

- a. 9 : 27
- b. 15 : 28
- c. 16 : 27
- d. 16 : 28

Solution:

- Answer: (b)Total students 60Girls = 24Boys = 36Rank of Kartik from top = 17Ahead → 9 girls7 boysKartik (17)After that there are36 – 8 = 28 boys24 – 9 =15 girlsRatio of girls and boys ⇒
**15 : 28**

**Question 43. Select the pair that has the same analogy as given pair 9876 : 12234567**

- a. 34562 : 89776
- b. 1234 : 122345
- c. 654321 : 922346
- d. 9993 : 8886

Solution:

- Answer: (d)Therefore, option (d) is correct.

**Question 44. A square piece of paper is folded as shown, punched and unfloded. Which of the alternative figures resembles the unfolded paper?**

Solution:

- Answer: (d)By observation

**Question 45.**

**Then, 23 is given by**

Solution:

- Answer: (d)Therefore, option (d) is correct.

**Question 46. Complete the following figural series by choosing the correct answer from the given alternatives.**

Solution:

- Answer: (a)Inner square = +1, +2, +3, +4: anticlockwiseBlack circle = +1, +3, +5, +7: clockwiseWhite circle = +1, +4, +9, +16: anticlockwise

**Question 47. A problem figure is given below. When it is rotated, it fits into one of the option figures. Identify the option figure.**

Solution:

- Answer: (d)
_{}

**Question 48. The problem figure given below is a figure matrix. Complete the matrix with suitable option figure.**

Solution:

- Answer: (d)

**Question 49. Nine figures are given below. Identify the correct group of classification.**

- a. a, b, m; b, e, n; c, f, p
- b. a, b, m; c, d, n; e, f, p
- c. a, d, f; b, e, p; c, m, n
- d. a, c, n; b, e, m; d, f, p

Solution:

- Answer: (d)
**a, c, n**→ plane figure (polygon)**b, e, m**→ Solid figure**d, f, p**→ Closed curveTherefore, option (d) is correct.

**Question 50. An identity is given below through some symbols. In the options these symbols are decoded. Identify the correct option of which the signs satisfy the given identity.**

Solution:

- Answer: (a)⇒ 156 + 3 = 159159 =
**159**

**Question 51. Complete the following figural series by choosing the correct answer from the given alternatives.**

Solution:

- Answer: (d)By observation

**Question 52. A pentagonal figure is given below. Identify which two of the pieces among A, B, C, D and E given below will NOT be required to complete the pentagonal figure.**

- a. Both A and C
- b. Both B and D
- c. Both A and D
- d. Both B and E

Solution:

- Answer: (d)Therefore, option (d) is correct.

**Question 53. A problem figure is given below. When it is folded into a cube. Which one of the cubes will be formed from the given cubes will be formed from the given alternatives?**

Solution:

- Answer: (d)The figures which are in the opposite face can’t come on the adjacent face.Therefore, the correct option is (d).

**Question 54. A problem figure is given of which the mirror image is X and the water image of X is Y. Identify the appearance of Y from the given alternative figures:**

Solution:

- Answer: (b)Therefore, the correct option is b).

**Question 55. A hexagonal figure is given below. Identify which among the pieces A, B, C, D, E and F given below will NOT be required to complete the hexagonal figure.**

- a. B
- b. D
- c. E
- d. F

Solution:

- Answer: (b)D is not required

**Question 56. Which one of the given rules the number 70 follows?**

- a. n
^{3}+ 4n - b. 2n
^{3}+ 2n - c. n
^{3}+ 3n/2 - d. n
^{2}+ 5n

Solution:

- Answer: (c)By using option (c)
**n**When we usen = 4 it gives 70^{3}+ 3n/2

**Question 57. What are the values of x and y in the given matrix?**

- a. 25, 136
- b. 30, 148
- c. 35, 128
- d. 40, 156

Solution:

- Answer: (d)In C
_{1}16 + 9 – 12 = 1313 = 13Similarly to C_{2}63 + x – 53 = 50x = 103 – 63x = 40Similarly to C_{3}y + 102 – 140 = 118y = 258 – 102 = 156**x = 40****y = 156**

**Question 58. The numbers are arranged in a certain pattern. The values of a, b and c respectively in the pattern are:**

- a. 4, 16, 5
- b. 3, 16, 7
- c. 3, 15, 5
- d. 2, 18, 7

Solution:

- Answer: (b)Value of a((7+a+14+10+5+9))/2= 24⇒(a + 45)/2 = 24⇒a = 48 – 45 = 3Value of b((1+6+8+18+6+9+7+3))/2 = 34b + 52 = 68b = 16Similarly, value of C((5+16+12+C))/2 = 20C + 33 = 40C = 7a, b, c =
**3, 16, 7**

**Question 59. Direction: Take the given statements as true though in reality they may not be so and decide which of the conclusions logically follow from the statements?**

**Statements:**

**1. All the cucumbers are carrots.**

**2. Some carrots are brinjals.**

**3. All the brinjals are tomatoes.**

**Conclusions:**

**I. Some tomatoes are carrots.**

**II. All the carrots are tomatoes.**

**III. Some brinjals are cucumbers.**

**IV. All the brinjals are cucumbers.**

- a. Both the conclusion II and IV follows
- b. Both the conclusion II and III follows
- c. Both the conclusion III and IV follows
- d. Both the conclusion I and III follows

Solution:

- Answer: BonusOnly conclusion I follow.

**Question 60. Aman, Ayaz and Ashwinder are members of a joint family. Among them Aman is the eldest of all.**

**Aman is six years elder than Ayaz.**

**Ayaz is eight years elder than Ashwinder.**

**The sum of the present ages of Aman and Ayaz is five times the age of Ashwinder four years ago.**

**Then the present age of Aman is :**

- a. 20 years
- b. 24 years
- c. 28 years
- d. 32 years

Solution:

- Answer: (c)Let say ages of Aman is AAyaz is BAshwinder is CGivenA = B + 6 …(1)B = C + 8 …(2)A + B = (C–4) …(3)So, A + B = 5C – 20Put the value of eqn. (2) in eqn. (1)We getA = (C + 8) + 6A = C + 14 …(4)Now put the value of A and B in eqn.⇒ C + 14 + C + 8 = 5C – 20⇒ 2C + 22 = 5C – 20⇒ 3C = 42C = 42/3= 14So, B = 22, A = 28So, Aman’s age is
**28.**

**Question 61. Direction: Complete the given analogy by choosing the correct group from the given alternatives**

**B F I D L : N R U P X :: A J E K C : ?**

- a. G M F I K
- b. I G D K F
- c. M V Q W O
- d. K I F M G

Solution:

- Answer: (c)Therefore, option (c) is correct

**Question 62. What is the difference between the female population of above 60 years and the adult female population below 60 years in the extension?**

- a. 850
- b. 710
- c. 630
- d. 420

Solution:

- Answer: (c)Now total population = A+A+1010+930+240+2203000 = 2A + 2400 ⇒ A = 300Adult female are above 18 = 930Now required difference930 –300 =
**630**Therefore, option (c) is correct.

**Question 63. A set of three number is given 484, 529, 961, Choose the set which is similar to the given set from the given alternatives.**

- a. 841, 625, 196
- b. 729, 576, 324
- c. 784, 676, 289
- d. 441, 361, 225

Solution:

- Answer: (a) and (c)4 + 8 + 4 → 165 + 2 + 9 → 169 + 6 + 1 → 16Sum of digits in all numbers is sameSimilarly,7 + 8 + 4 = 196 + 7 + 6 = 192 + 8 + 9 = 19option (c) is correct.Also,484, 529, 961 are the squares of 2 odd numbers and 1 even number.Similarly, 841, 625, 196 are the squares of 2 odd numbers and 1 even number.Option (a) is correct.

**Question 64. What is the missing number in the third figure?**

- a. 2, 53
- b. 4, 101
- c. 5, 166
- d. 6, 223

Solution:

- Answer: (b)So, the missing numbers are
**4**and**101**.Therefore, option (b) is correct.

**Question 65. In the alternatives, which one does NOT show the correct position of faces?**

Solution:

- Answer: BonusFolding this we get,F opposite to EB opposite to DA opposite to CAll the options are possible as in none of the option opposite faces are placedadjacent.

**Question 66. Direction: The different faces of a cube are shown through three folded cube shape. Identify which one of the figures given in the alternatives represents the unfolded cube.**

Solution:

- Answer: (d)observing the cube we getOn unfolding cubes given we will get option (d) correct.

**Question 67. Which house is the first to perform?**

- a. Violet
- b. Indigo
- c. Green
- d. Red

Solution:

- Answer: (a)First to perform is →
**Violet.**

**Question 68. Which house performed on ‘Thursday’?**

- a. Red
- b. Green
- c. Indigo
- d. Yellow

Solution:

- Answer: (a)

**Question 69. What are the values of # and @ in the figure given below?**

a. M, 15

- a. M, 15
- b. M, 60
- c. N, 30
- d. N, 50

Solution:

- Answer: (a)

**Question 70. Which one of the following does NOT turn out to be meaningful by substitution of the set of signs (x, –, =, ÷), sequentially in the given alternatives?**

- a. 24 * 3 * 10* 120* 2
- b. 12 * 4 * 8* 160*4
- c. 10 * 8 * 16 * 192 * 3
- d. 16 * 4 * 14 *200 * 4

Solution:

- Answer: (a)24×3–10 = 120 ÷ 272–10 = 6062 ≠ 60Option (a) does not satisfy.

**Question 71. Statements:**

- a. M * T # 4 @ Z @ R = P
- b. M * P # Y @ T @ Z = R
- c. M = T @ Y @ Z # Z $ R
- d. M @ T # Y = Z @ R * P

Solution:

- Answer: (b)M*P≠ Y & T@ Z = RTherefore, option (b) is correct.

**Question 72. Which of the following pair is different?**

- a. 16, 18
- b. 96, 108
- c. 56, 63
- d. 86, 99

Solution:

- Answer: (d)16 = 2 x 818 = 2 x 956 = 7 x 863 = 7 x 996 = 12 x 8108 = 12 x 9
**88 = 11 x 8**99 = 11 x 9(86, 99) is not satisfying the pattern, it should be (88, 99)

**Question 73. If you have to make the right side ball arrangement look like left side, how many minimum number of circles you would require to move?**

- a. 3
- b. 4
- c. 5
- d. 6

Solution:

- Answer: (a)We have to move only 3

**Question 74. Which figure comes in place of ‘?’ in the figure given below?**

Solution:

- Answer: (d)Difference between the first and third picture is equal to the middle.

**Question 75. Based on the above statements, find who is the second eldest amongst the five cousins?**

Solution:

- Answer: (b)

**Question 76. Who all are younger to O?**

Solution:

- Answer: (a)

**Question 77. Which numbers will replace the question marks if the numbers in the circles have linkages with:**

- a. 5, 15; 8, 5
- b. 5, 0; 8, 20
- c. 6, 15; 9, 5
- d. 6, 20; 9, 35

Solution:

- Answer: (c)There are two sets of clocks placed with a time difference of 45min and 35min respectively.

**Question 78. Find out the figure that does not match with the other figure.**

- a. A
- b. B
- c. C
- d. D

Solution:

- Answer: (c)No. of lines in the figure is equal to the number of the square box made inside, which is not trueonly for figure c

**Question 79. What are the numbers of blocks to be crossed for covering the shortest path from ‘A’ to ‘B’? One cannot move diagonally and on a block with the number ‘2’.**

- a. 15
- b. 19
- c. 27
- d. 37

Solution:

- Answer: (d)

**Question 80. One a staircase, Yaima is further up than Aloka but is lower than Srinivas. Ranjan is in the middle. Jeet is between Yaima and Ranjan. Aloka is between Ranjan and Danial. There is none below Barisha. Who is in the fifth position?**

- a. Aloka
- b. Danial
- c. Jeet
- d. Yaima

Solution:

- Answer: (c)7 -Srinivas6 -yaima5 -Jeet4 -Ranjan3 -Aloka2 -Daniel1 -BarishaJeet is at the fifth stair

**Question 81. What is the difference between the number of females and males in the generation to which Samson belongs?**

- a. 1
- b. 2
- c. 3
- d. 0

Solution:

- Answer: (a)
^{}Samson Generation 2 male and 3 females so the difference is 1.

**Question 82. Which figure completes the statement?**

Solution:

- Answer: (b)According to the given figure, the middle figure goes inside the upper figure and the lower figure becomes upside down and goes at the top.Therefore, option (b) is correct

**Question 83. Identify the box that can be formed from the sheet of paper given below:**

- a. Only I
- b. Only II and III
- c. Only III
- d. Only IV

Solution:

- Answer: (a)When we fold the given unfolded figure it becomes the figure which is in option ITherefore, option (a) is correct.

**Question 84. Who is good in Chemistry, Biology and Physics but not in Social**

**Sciences?**

- a. A
- b. B
- c. C
- d. D

Solution:

- Answer: (c)C has all three Chemistry, Biology, Physics and but not social.

**Question 85. Who is good in Social Sciences, Biology and Fine Arts?**

- a. A
- b. B
- c. D
- d. E

Solution:

- Answer: (d)All three (Social Sciences, Biology, Fine Arts) are present in ETherefore, option (d) is correct.

**Question 86. Who is good in Chemistry, Fine Arts and Social Sciences?**

- a. A
- b. B
- c. D
- d. E

Solution:

- Answer: (b)All three (Chemistry, Fine Arts, Social Sciences) are present in B

**Question 87. Observing the pattern given in the following sequence, identify the missing number in the sequence.**

**3, 18, 219, ____, 100005**

- a. 1743
- b. 1746
- c. 4096
- d. 4100

Solution:

- Answer: (d)This sequence follows the pattern.2
^{1}+ 1 = 34^{2}+ 2=186^{3}+ 3 = 2198^{4}+ 4 =**4100**10^{5}+5 = 100,005

**Question 88. A solid cube of 4 cm side, painted on all its faces, is cut up into small cubes of 1 cm side. What is the ratio of the cubes without paint to the cubes with paint on exactly two faces?**

- a. 1 : 2
- b. 1 : 3
- c. 2 : 3
- d. 3 : 2

Solution:

- Answer: (b)In a 4×4×4 side cube. Number of cubes which is unpainted = (n–2)
^{3}Where n = 4Then (4–2)^{3 }= (2)^{3 }= 8Number of cubes two face painted = 12 (n–2) = 12 (4–2)= 12×2 = 24Required ration = 8:24 =**1 : 3**

**Question 89. A man walks 20m towards South, then after turning to his left, he walks 22m. Then he turns 90° in an anti-clockwise direction and walks 26m. Then again he turns to the left and walks up to 30m. How far (in metres) is the man from his initial position?**

- a. 16
- b. 14
- c. 10
- d. 9

Solution:

- Answer: (c)AC
^{2}= √((AB)^{ 2}+(BC)^{ 2})AC^{2}= √(36+64)AC = √100AC = 10

**Question 90. What comes in the place of the blanks?**

**XXIV, XXII, XXV, XXIII, XXVI, _____, ______, XXV**

- a. XXIV, XXVII
- b. XXVII, XXVIII
- c. XXV, XXVI
- d. XXIV, XXV

Solution:

- Answer: (a)By converting roman in numerals.24,22,25,23,26,
**_,_**,25The pattern is to -2 and +3 alternatively.24,22,25,23,26,**24,27**,25

**Question 91. In which of the ways given in the options would you place the number 1-7 side by side, so that:**

**• The sum of the numbers 2 and 7 and all the numbers between them total 28.**

**• The sum of the numbers 3 and 6 and all the numbers between them total 14.**

**• The sum of the number 1 and 7 and all the numbers between them total 23.**

**• The sum of the number 2 and 4 and all the numbers between them total 10.**

- a. 2 4 3 5 6 7 1
- b. 1 2 3 4 5 6 7
- c. 2 3 1 4 6 5 7
- d. 3 2 1 5 6 7 4

Solution:

- Answer: (c)2 + 3 + 1 + 4 + 6 + 5 + 7 =
**28**3 + 1 + 4 + 6 =**14**1 + 4 + 6 + 5 + 7 =**23**2 + 3 + 1 + 4 =**10**Therefore, option (c) is correct.

**Question 92. Read the information and then select the correct option:**

**Fact 1: Islands are surrounded by water.**

**Fact 2: Mani is an island.**

**Fact 3: Mani was formed by a volcano.**

**If the above three statements are facts, which of the following statements must also be a fact?**

**I. Mani is surrounded by water.**

**II. All islands are formed by volcanoes.**

**III. All volcanoes are on islands.**

- a. I only
- b. III only
- c. I and III only
- d. I and II only

Solution:

- Answer: (a)Only statement I is a fact according to given FactsTherefore, option (a) is correct.

**Question 93. The vowels of English are coded by their letter numbers appearing as two digited and then reversed. Thereafter these numbers are represented through a Pie diagram. What will be the central angle (nearest to degree) of the sector representing ‘U’?**

- a. 75
- b. 78
- c. 37
- d. 20

Solution:

- Answer: (d)A → 10E → 50I → 90O →51U → 12Central angle for U = 12/(10+50+90+51+12)× 360= 2/213 ×360 = 20.28 ≃ 20

**Question 94. For finding a numeric code of 3 digits, the following information is given:**

**The correct code is:**