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SSC CGL Tier 1 & Tier 2 Mixed Mock Test: Practice Test 16

Question paper with answer key. Selection Pro

Q1. Which schedule of the Indian Constitution contains the provisions regarding the anti-defection law?
  1. Eighth Schedule
  2. Ninth Schedule
  3. Tenth Schedule
  4. Eleventh Schedule

Answer: (C) Tenth Schedule

The Tenth Schedule, added by the 52nd Constitutional Amendment Act of 1985, contains provisions regarding disqualification on grounds of defection.

Q2. The famous rock-cut Shore Temple is located at which site?
  1. Thanjavur
  2. Mahabalipuram
  3. Kanchipuram
  4. Aihole

Answer: (B) Mahabalipuram

The Shore Temple built during the Pallava dynasty under Narasimhavarman II is located at Mahabalipuram, Tamil Nadu.

Q3. What is the phenomenon of bending of light around the corners of an obstacle called?
  1. Refraction
  2. Diffraction
  3. Reflection
  4. Dispersion

Answer: (B) Diffraction

Diffraction refers to the slight bending of light waves around the edges of an obstacle or through a narrow opening.

Q4. Which is the highest peak in the Western Ghats range in India?
  1. Doddabetta
  2. Anamudi
  3. Guru Shikhar
  4. Kalsubai

Answer: (B) Anamudi

Anamudi (2,695 m) in Kerala is the highest peak in the Western Ghats as well as Peninsular India.

Q5. Which blood group is universally designated as the universal acceptor?
  1. O negative
  2. AB positive
  3. A positive
  4. B negative

Answer: (B) AB positive

AB positive individuals have no antibodies against A, B, or Rh antigens and are considered universal recipients.

Q6. Who was the Governor-General of India during the Sepoy Mutiny of 1857?
  1. Lord Dalhousie
  2. Lord Canning
  3. Lord Cornwallis
  4. Lord Mayo

Answer: (B) Lord Canning

Lord Canning served as Governor-General during the Revolt of 1857 and became the first Viceroy of India in 1858.

Q7. What is the chemical formula for Plaster of Paris?
  1. CaSO4·2H2O
  2. CaSO4·½H2O
  3. CaCO3
  4. CaOCl2

Answer: (B) CaSO4·½H2O

Plaster of Paris is Calcium Sulfate Hemihydrate, having the formula CaSO4·½H2O.

Q8. Which Article of the Indian Constitution guarantees equality before law and equal protection of laws?
  1. Article 14
  2. Article 19
  3. Article 21
  4. Article 17

Answer: (A) Article 14

Article 14 guarantees that the State shall not deny to any person equality before the law or equal protection of laws within India.

Q9. The rate of change of momentum of an object is proportional to the applied force. This statement forms:
  1. Newton's First Law of Motion
  2. Newton's Second Law of Motion
  3. Newton's Third Law of Motion
  4. Law of Universal Gravitation

Answer: (B) Newton's Second Law of Motion

Newton's Second Law states that F = dp/dt (Force equals rate of change of momentum).

Q10. The Ramsar Convention is an international treaty dedicated to the conservation and sustainable use of what?
  1. Forests
  2. Wetlands
  3. Oceans
  4. Coral Reefs

Answer: (B) Wetlands

The Ramsar Convention, signed in Ramsar, Iran in 1971, is an international framework for conserving wetlands.

Q11. Which ruler introduced the silver coin named 'Rupiya' for the first time in India?
  1. Akbar
  2. Sher Shah Suri
  3. Alauddin Khalji
  4. Muhammad bin Tughluq

Answer: (B) Sher Shah Suri

Sher Shah Suri introduced the silver 'Rupiya' weighing 178 grains during his reign (1540–1545).

Q12. Which strait connects the Bay of Bengal with the Palk Bay?
  1. Malacca Strait
  2. Palk Strait
  3. Sunda Strait
  4. Bering Strait

Answer: (B) Palk Strait

The Palk Strait separates the Tamil Nadu state of India and the Mannar district of Sri Lanka, connecting Palk Bay and Bay of Bengal.

Q13. In Economics, 'Gresham's Law' states that:
  1. Good money drives out bad money
  2. Bad money drives out good money
  3. Supply creates its own demand
  4. Demand creates its own supply

Answer: (B) Bad money drives out good money

Gresham's Law is a monetary principle stating that 'bad money drives out good' when both are in circulation.

Q14. Deficiency of Vitamin D in children primarily causes which health condition?
  1. Scurvy
  2. Rickets
  3. Beriberi
  4. Pellagra

Answer: (B) Rickets

Rickets causes soft and weak bones in children and is caused by insufficient Vitamin D or Calcium.

Q15. Who presided over the historic Lahore Session of the Indian National Congress in 1929 where 'Purna Swaraj' was declared?
  1. Mahatma Gandhi
  2. Jawaharlal Nehru
  3. Subhash Chandra Bose
  4. Sardar Vallabhbhai Patel

Answer: (B) Jawaharlal Nehru

Jawaharlal Nehru presided over the 1929 Lahore session where the resolution for complete independence (Purna Swaraj) was passed.

Q16. Writs are issued by the Supreme Court under which Article of the Indian Constitution?
  1. Article 226
  2. Article 32
  3. Article 136
  4. Article 143

Answer: (B) Article 32

Article 32 empowers the Supreme Court to issue writs for the enforcement of Fundamental Rights (while High Courts use Article 226).

Q17. Which cell organelle is commonly referred to as the 'Powerhouse of the Cell'?
  1. Lysosome
  2. Mitochondria
  3. Ribosome
  4. Golgi apparatus

Answer: (B) Mitochondria

Mitochondria produce cellular energy in the form of ATP, earning the nickname 'Powerhouse of the Cell'.

Q18. The famous iron pillar located at Mehrauli, Delhi was constructed during the reign of which dynasty?
  1. Maurya Dynasty
  2. Gupta Dynasty
  3. Chola Dynasty
  4. Kushan Dynasty

Answer: (B) Gupta Dynasty

The Mehrauli Iron Pillar was erected during the reign of Chandragupta II (Vikramaditya) of the Gupta Empire.

Q19. Which acid is present in ant stings?
  1. Acetic acid
  2. Formic acid
  3. Lactic acid
  4. Citric acid

Answer: (B) Formic acid

Ant stings contain Formic acid (Methanoic acid, HCOOH), causing burning sensations.

Q20. Headquarters of the Reserve Bank of India (RBI) is situated in which city?
  1. New Delhi
  2. Mumbai
  3. Kolkata
  4. Chennai

Answer: (B) Mumbai

Initially set up in Kolkata, the headquarters of RBI was permanently moved to Mumbai in 1937.

Q21. Hornbill Festival, known as the 'Festival of Festivals', is celebrated in which state?
  1. Manipur
  2. Nagaland
  3. Mizoram
  4. Arunachal Pradesh

Answer: (B) Nagaland

The Hornbill Festival is held annually from 1 to 10 December in Nagaland to promote cultural heritage.

Q22. The Maximum duration of a gap permitted between two sessions of the Parliament of India is:
  1. 3 months
  2. 6 months
  3. 9 months
  4. 1 year

Answer: (B) 6 months

According to Article 85, the maximum gap between two sessions of Parliament cannot exceed six months.

Q23. Which metal is liquid at room temperature?
  1. Bromine
  2. Mercury
  3. Gallium
  4. Sodium

Answer: (B) Mercury

Mercury (Hg) is the only metal that remains liquid at standard room temperature conditions.

Q24. Which soil type is also known as 'Regur Soil'?
  1. Alluvial Soil
  2. Black Soil
  3. Red Soil
  4. Laterite Soil

Answer: (B) Black Soil

Black soil is popular as Regur soil or Black Cotton soil due to its ideal nature for cotton cultivation.

Q25. Who started the newspaper 'Kesari' during the Indian Freedom Movement?
  1. Lala Lajpat Rai
  2. Bal Gangadhar Tilak
  3. Bipin Chandra Pal
  4. Gopal Krishna Gokhale

Answer: (B) Bal Gangadhar Tilak

Lokmanya Bal Gangadhar Tilak founded 'Kesari' (in Marathi) and 'Mahratta' (in English) in 1881.

Q26. Find the missing term in the sequence: 3, 7, 16, 35, 74, ?
  1. 148
  2. 153
  3. 149
  4. 151

Answer: (B) 153

Pattern: ×2 + 1, ×2 + 2, ×2 + 3, ×2 + 4, ×2 + 5. Next = 74 × 2 + 5 = 153. Wait: 3*2+1=7; 7*2+2=16; 16*2+3=35; 35*2+4=74; 74*2+5 = 153. Correct option choice 1 is 153.

Q27. In a certain code language, 'SMART' is coded as 'UOCPT'. How is 'GREAT' coded in that language?
  1. ITCGV
  2. ITCVG
  3. ISCGV
  4. ITGYV

Answer: (D) ITGYV

Pattern: +2, +2, +2, -2, +2. Applying to GREAT: G(+2)=I, R(+2)=T, E(+2)=G, A(-2)=Y, T(+2)=V, which gives ITGYV.

Q28. Select the odd pair from the following:
  1. 8 - 64
  2. 9 - 81
  3. 12 - 144
  4. 14 - 198

Answer: (D) 14 - 198

8² = 64, 9² = 81, 12² = 144. But 14² = 196, whereas option displays 198.

Q29. Ravi walks 12 km East, then turns North and walks 5 km. How far is he from his initial starting point?
  1. 17 km
  2. 13 km
  3. 7 km
  4. 15 km

Answer: (B) 13 km

Distance = √(12² + 5²) = √(144 + 25) = √169 = 13 km.

Q30. Statements: All cars are vehicles. No vehicle is a boat. Conclusions: I. No car is a boat. II. Some vehicles are cars.
  1. Only I follows
  2. Only II follows
  3. Both I and II follow
  4. Neither follows

Answer: (A) Only I follows

Since Cars are completely inside Vehicles and Vehicles are separate from Boats, no car can be a boat. Also, since all cars are vehicles, some vehicles are definitely cars.

Q31. Pointing to a photograph, a man says, 'She is the mother of my son's wife.' How is the lady in the photograph related to the man?
  1. Mother-in-law
  2. Samdhin (Co-in-law)
  3. Daughter-in-law
  4. Sister

Answer: (B) Samdhin (Co-in-law)

The woman is the mother of the man's daughter-in-law (son's wife), which makes her the co-in-law (Samdhin) to the man.

Q32. Complete the letter series: p q r _ p q _ r p _ q r _ q r r
  1. r p q p
  2. r r p p
  3. q p r p
  4. r r p q

Answer: (B) r r p p

The repeating pattern is 'p q r r'. Filling the missing letters yields: p q r [r] | p q [r] r | p [p] q r | [p] q r r. The inserted letters are r, r, p, p.

Q33. Analogy: Odometer : Distance :: Barometer : ?
  1. Humidity
  2. Pressure
  3. Temperature
  4. Wind speed

Answer: (B) Pressure

An odometer measures distance traveled; a barometer measures atmospheric pressure.

Q34. If 26th January 2024 was a Friday, what day of the week was 26th January 2025?
  1. Saturday
  2. Sunday
  3. Monday
  4. Friday

Answer: (B) Sunday

2024 is a leap year including Feb 29. From 26 Jan 2024 to 26 Jan 2025 comprises 366 days (2 odd days). Friday + 2 days = Sunday.

Q35. If '+' means '×', '-' means '÷', '×' means '+', and '÷' means '-', then evaluate: 16 - 4 + 5 × 10 ÷ 6 = ?
  1. 24
  2. 20
  3. 18
  4. 22

Answer: (A) 24

Substitute symbols: 16 ÷ 4 × 5 + 10 - 6 = 4 × 5 + 10 - 6 = 20 + 10 - 6 = 24.

Q36. In a row of 50 boys, Amit is 20th from the left end. What is his rank from the right end?
  1. 30th
  2. 31st
  3. 32nd
  4. 29th

Answer: (B) 31st

Rank from right = Total - Rank from left + 1 = 50 - 20 + 1 = 31st.

Q37. Find the missing term in series: 5, 11, 23, 47, 95, ?
  1. 190
  2. 191
  3. 189
  4. 192

Answer: (B) 191

Pattern: ×2 + 1. (5×2+1=11, 11×2+1=23, 23×2+1=47, 47×2+1=95, 95×2+1 = 191).

Q38. Select the Venn diagram that best represents: Mammals, Cows, Crows.
  1. One circle completely inside another, with a third circle disjoint
  2. Three mutually intersecting circles
  3. Three completely separated disjoint circles
  4. Two intersecting circles inside a third circle

Answer: (A) One circle completely inside another, with a third circle disjoint

Cows are entirely inside Mammals; Crows are birds, represented by an entirely separate circle.

Q39. Arrange words logically: 1. Letter 2. Word 3. Sentence 4. Paragraph 5. Page
  1. 1, 2, 3, 4, 5
  2. 2, 1, 3, 4, 5
  3. 1, 3, 2, 4, 5
  4. 5, 4, 3, 2, 1

Answer: (A) 1, 2, 3, 4, 5

Ascending hierarchical order: Letter (1) -> Word (2) -> Sentence (3) -> Paragraph (4) -> Page (5).

Q40. If PEN is coded as 35 and PENNY is coded as 73, how is PAPER coded?
  1. 56
  2. 51
  3. 48
  4. 55

Answer: (A) 56

P(16) + A(1) + P(16) + E(5) + R(18) = 56.

Q41. Analogy: 8 : 65 :: 10 : ?
  1. 101
  2. 100
  3. 99
  4. 102

Answer: (A) 101

Pattern: n : n² + 1. (8² + 1 = 65; 10² + 1 = 101).

Q42. What is the angle between the hands of a clock at 4:20?
  1. 0°
  2. 10°
  3. 20°
  4. 15°

Answer: (B) 10°

Angle = |30H - 11/2 M| = |30(4) - (11/2)(20)| = |120 - 110| = 10°.

Q43. 5 friends P, Q, R, S, T sit facing North. R is sitting middle. Q is to immediate left of R and immediate right of P. Who sits at the extreme right?
  1. S or T
  2. P
  3. Q
  4. R

Answer: (A) S or T

Arrangement from left: Pos1=P, Pos2=Q, Pos3=R. Pos4 & Pos5 contain S and T. Either S or T sits at the extreme right.

Q44. Find the odd number out among: 216, 343, 512, 720
  1. 216
  2. 343
  3. 512
  4. 720

Answer: (D) 720

216 (6³), 343 (7³), and 512 (8³) are perfect cubes. 720 is not a perfect cube (9³ = 729).

Q45. P is the brother of Q. R is the sister of Q. S is the father of P. How is R related to S?
  1. Daughter
  2. Sister
  3. Mother
  4. Aunt

Answer: (A) Daughter

P, Q, R are siblings. S is father of P, so S is father to all three. Thus, R is S's daughter.

Q46. Analogy: Doctor : Hospital :: Teacher : ?
  1. School
  2. Student
  3. Book
  4. Education

Answer: (A) School

A doctor works in a hospital; a teacher works in a school.

Q47. Missing term: C3E, E6G, G12I, I24K, ?
  1. K48M
  2. K48L
  3. J48M
  4. K36M

Answer: (A) K48M

First letter (+2): C, E, G, I, K. Middle number (×2): 3, 6, 12, 24, 48. Last letter (+2): E, G, I, K, M.

Q48. A person walks 5 km North, turns right and walks 5 km, then turns right again and walks 5 km. In which direction is he now facing?
  1. South
  2. East
  3. North
  4. West

Answer: (A) South

Started North. First right turn faces East. Second right turn faces South.

Q49. Statement: 'Wear a seatbelt while driving to ensure personal safety.' Assumptions: I. Seatbelts lower injury risk during accidents. II. Drivers care about personal safety.
  1. Only I is implicit
  2. Only II is implicit
  3. Both I and II are implicit
  4. Neither is implicit

Answer: (C) Both I and II are implicit

The warning assumes seatbelts provide safety during driving and that driver awareness regarding safety can be addressed.

Q50. How many total triangles are formed by drawing both diagonals inside a simple square?
  1. 4
  2. 6
  3. 8
  4. 10

Answer: (C) 8

A square with both diagonals contains 4 small individual triangles and 4 larger triangles formed by adjacent pairs, making a total of 8 triangles.

Q51. Select the synonym of: **CANDID**
  1. Frank
  2. Deceptive
  3. Secretive
  4. Shy

Answer: (A) Frank

'Candid' means truthful, straightforward, and frank.

Q52. Select the antonym of: **TRANSIENT**
  1. Permanent
  2. Temporary
  3. Fleeting
  4. Brief

Answer: (A) Permanent

'Transient' means lasting for a short time; 'Permanent' is its direct antonym.

Q53. Select the correctly spelt word:
  1. Accommodation
  2. Acommodation
  3. Accomodation
  4. Acomodation

Answer: (A) Accommodation

The correct spelling is 'Accommodation' (double 'c' and double 'm').

Q54. Identify error: *No sooner had the teacher entered the classroom when the students stood up.*
  1. No sooner had
  2. entered the classroom
  3. when the students
  4. stood up

Answer: (C) when the students

'No sooner' takes 'than' as a conjunction pair, not 'when'.

Q55. Fill in the blank: *She is proficient ___ speaking French.*
  1. in
  2. at
  3. with
  4. for

Answer: (A) in

'Proficient' is appropriately followed by the preposition 'in'.

Q56. Passive Voice: *The committee approved the new proposal.*
  1. The new proposal was approved by the committee.
  2. The new proposal is approved by the committee.
  3. The new proposal had been approved by committee.
  4. The new proposal was being approved by committee.

Answer: (A) The new proposal was approved by the committee.

Simple past verb 'approved' changes to 'was approved' in passive voice.

Q57. Indirect Speech: *Rohan said, 'I have finished my project.'*
  1. Rohan said that he had finished his project.
  2. Rohan said that he finished his project.
  3. Rohan told that he has finished his project.
  4. Rohan says that he had finished his project.

Answer: (A) Rohan said that he had finished his project.

Present perfect 'have finished' changes to past perfect 'had finished'.

Q58. One word substitution: *A person who does not believe in the existence of God*
  1. Atheist
  2. Theist
  3. Agnostic
  4. Fanatic

Answer: (A) Atheist

An 'Atheist' disbelieves or lacks belief in the existence of God or gods.

Q59. Idiom meaning: **Spill the beans**
  1. To reveal a secret
  2. To cook food
  3. To drop something accidentally
  4. To waste money

Answer: (A) To reveal a secret

'Spill the beans' means to disclose secret information prematurely or unintentionally.

Q60. Select the correctly spelt word:
  1. Embarrassment
  2. Embarasment
  3. Embarrased
  4. Embarasment

Answer: (A) Embarrassment

The correct spelling is 'Embarrassment' (double 'r' and double 's').

Q61. Select the synonym of: **AMICABLE**
  1. Friendly
  2. Hostile
  3. Arrogant
  4. Aggressive

Answer: (A) Friendly

'Amicable' means characterized by friendliness and absence of discord.

Q62. Select the antonym of: **OBSOLETE**
  1. Modern
  2. Outdated
  3. Old-fashioned
  4. Ancient

Answer: (A) Modern

'Obsolete' means no longer produced or used; 'Modern' or current is its antonym.

Q63. Sentence Improvement: *He requested to the manager to grant him leave.*
  1. requested the manager
  2. requested with manager
  3. requested at manager
  4. No improvement

Answer: (A) requested the manager

The verb 'request' is transitive and does not take the preposition 'to' before its object.

Q64. Fill in the blank: *The firemen managed to put ___ the fire quickly.*
  1. out
  2. off
  3. down
  4. away

Answer: (A) out

'Put out' means to extinguish a fire or flame.

Q65. One word substitution: *A life history of a person written by himself*
  1. Autobiography
  2. Biography
  3. Memoir
  4. Chronicle

Answer: (A) Autobiography

An 'Autobiography' is an account of a person's life written by that person.

Q66. Idiom meaning: **Break the ice**
  1. To start a conversation in a social setting
  2. To freeze water
  3. To break a promise
  4. To create tension

Answer: (A) To start a conversation in a social setting

'Break the ice' means to initiate conversation to relieve shyness or tension.

Q67. Identify error part: *One of the main reason for his failure was lack of discipline.*
  1. One of the main reason
  2. for his failure
  3. was lack of
  4. discipline

Answer: (A) One of the main reason

'One of the' is followed by a plural noun ('One of the main reasons').

Q68. Fill in the blank: *Each of the boys ___ given a prize.*
  1. was
  2. were
  3. are
  4. have been

Answer: (A) was

'Each' takes a singular verb ('was').

Q69. Rearrange parts: P: health Q: Is R: Wealth S: Good
  1. S-P-Q-R
  2. P-Q-R-S
  3. Q-R-S-P
  4. R-S-P-Q

Answer: (A) S-P-Q-R

Correct order: S ('Good') P ('health') Q ('is') R ('wealth').

Q70. Select the synonym of: **BENEVOLENT**
  1. Kind
  2. Cruel
  3. Greedy
  4. Malevolent

Answer: (A) Kind

'Benevolent' means well-meaning and kindly.

Q71. Select the antonym of: **DILIGENT**
  1. Lazy
  2. Hardworking
  3. Active
  4. Attentive

Answer: (A) Lazy

'Diligent' means showing care and conscientiousness; 'Lazy' is its antonym.

Q72. Select the correctly spelt word:
  1. Maintenance
  2. Maintainance
  3. Maintenence
  4. Maintenace

Answer: (A) Maintenance

The correct spelling is 'Maintenance'.

Q73. Fill in the blank: *He congratulated me ___ my grand success.*
  1. on
  2. for
  3. at
  4. with

Answer: (A) on

The verb 'congratulate' is followed by the preposition 'on'.

Q74. Identify error part: *Unless you do not work hard, you will not pass.*
  1. Unless you do not
  2. work hard
  3. you will not pass
  4. No error

Answer: (A) Unless you do not

'Unless' itself has a negative meaning, so adding 'do not' makes it a double negative error. Use 'Unless you work hard'.

Q75. Idiom meaning: **At the eleventh hour**
  1. At the last possible moment
  2. At 11 o'clock exact
  3. Very early in morning
  4. In a hurry

Answer: (A) At the last possible moment

'At the eleventh hour' means at the last possible minute or moment.

Q76. If the length of a rectangle is increased by 10% and breadth is decreased by 10%, what is the net percentage change in area?
  1. 1% decrease
  2. 1% increase
  3. No change
  4. 2% decrease

Answer: (A) 1% decrease

Net Change = +10 - 10 - (10 × 10)/100 = -1% (1% decrease).

Q77. A trader marks his goods 20% above cost price and gives a discount of 10%. What is his profit percentage?
  1. 8%
  2. 10%
  3. 12%
  4. 6%

Answer: (A) 8%

Profit % = 20 - 10 - (20 × 10)/100 = 10 - 2 = 8%.

Q78. The average age of a family of 5 members is 24 years. If the age of the youngest member is 8 years, what was the average age of the family at the time of birth of the youngest member?
  1. 20 years
  2. 16 years
  3. 18 years
  4. 22 years

Answer: (A) 20 years

Total sum of current ages = 5 × 24 = 120. Total age 8 years ago = 120 - (5 × 8) = 80 years. At the birth of the youngest member, 4 members were present. Average age = 80 / 4 = 20 years.

Q79. A car covers 300 km at a speed of 60 km/h and returns at 40 km/h. What is its average speed for the whole journey?
  1. 48 km/h
  2. 50 km/h
  3. 45 km/h
  4. 52 km/h

Answer: (A) 48 km/h

Average Speed = (2 × s1 × s2) / (s1 + s2) = (2 × 60 × 40) / (60 + 40) = 4800 / 100 = 48 km/h.

Q80. If A : B = 2 : 3 and B : C = 4 : 5, find A : B : C.
  1. 8 : 12 : 15
  2. 6 : 9 : 15
  3. 8 : 10 : 15
  4. 2 : 4 : 5

Answer: (A) 8 : 12 : 15

A : B = 8 : 12; B : C = 12 : 15. Hence, A : B : C = 8 : 12 : 15.

Q81. The Simple Interest on a sum of money at 5% per annum for 3 years is ₹600. What is the Principal?
  1. ₹4000
  2. ₹3000
  3. ₹5000
  4. ₹4500

Answer: (A) ₹4000

P = (SI × 100) / (R × T) = (600 × 100) / (5 × 3) = 60000 / 15 = ₹4000.

Q82. Pipe A can fill a tank in 10 hours and Pipe B can empty it in 15 hours. If both are opened together, how long will it take to fill the tank?
  1. 30 hours
  2. 25 hours
  3. 20 hours
  4. 12 hours

Answer: (A) 30 hours

Net rate = (1/10 - 1/15) = 1/30 per hour. Time required = 30 hours.

Q83. What is the HCF of 36, 54, and 90?
  1. 18
  2. 9
  3. 12
  4. 6

Answer: (A) 18

36 = 18×2, 54 = 18×3, 90 = 18×5. The Highest Common Factor is 18.

Q84. If x - 1/x = 3, find the value of x² + 1/x².
  1. 11
  2. 7
  3. 9
  4. 13

Answer: (A) 11

x² + 1/x² = (x - 1/x)² + 2 = 3² + 2 = 9 + 2 = 11.

Q85. The perimeter of a square is 48 cm. What is its area?
  1. 144 cm²
  2. 96 cm²
  3. 121 cm²
  4. 169 cm²

Answer: (A) 144 cm²

Side a = 48 / 4 = 12 cm. Area = a² = 12² = 144 cm².

Q86. A sum of ₹10,000 amounts to ₹12,100 in 2 years at Compound Interest, compounded annually. What is the rate of interest?
  1. 10%
  2. 12%
  3. 8%
  4. 15%

Answer: (A) 10%

(1 + R/100)² = 12100 / 10000 = 121/100 => 1 + R/100 = 11/10 => R/100 = 1/10 => R = 10%.

Q87. If x³ - y³ = 56 and x - y = 2, what is the value of x² + xy + y²?
  1. 28
  2. 14
  3. 32
  4. 24

Answer: (A) 28

Formula: x³ - y³ = (x - y)(x² + xy + y²) => 56 = 2 × (x² + xy + y²) => x² + xy + y² = 28.

Q88. Find the volume of a cylinder of radius 7 cm and height 10 cm (Take π = 22/7).
  1. 1540 cm³
  2. 1450 cm³
  3. 1600 cm³
  4. 1320 cm³

Answer: (A) 1540 cm³

Volume = πr²h = (22/7) × 7 × 7 × 10 = 1540 cm³.

Q89. If tan θ = 4/3, what is the value of sin θ + cos θ?
  1. 7/5
  2. 1/5
  3. 5/7
  4. 6/5

Answer: (A) 7/5

Opposite = 4, Adjacent = 3, Hypotenuse = √(4²+3²) = 5. sin θ = 4/5, cos θ = 3/5. Sum = 7/5.

Q90. An article marked at ₹800 is sold for ₹680. What is the discount percentage?
  1. 15%
  2. 12%
  3. 10%
  4. 18%

Answer: (A) 15%

Discount = 800 - 680 = ₹120. Discount % = (120 / 800) × 100 = 15%.

Q91. Evaluate: sec² 45° - tan² 45°
  1. 1
  2. 2
  3. 0
  4. √2

Answer: (A) 1

Using trigonometric identity sec²θ - tan²θ = 1 (or (√2)² - 1² = 2 - 1 = 1).

Q92. A, B, and C working together can finish a work in 6 days. A alone takes 12 days and B alone takes 18 days. How many days will C alone take?
  1. 36 days
  2. 24 days
  3. 30 days
  4. 18 days

Answer: (A) 36 days

C's 1-day work = 1/6 - (1/12 + 1/18) = 1/6 - (5/36) = (6 - 5)/36 = 1/36. C takes 36 days.

Q93. In a right-angled triangle, if one acute angle is 35°, what is the other acute angle?
  1. 55°
  2. 45°
  3. 65°
  4. 50°

Answer: (A) 55°

Sum of acute angles in a right triangle = 90°. Other angle = 90° - 35° = 55°.

Q94. The mean of 5 observations is 18. If one observation 10 is excluded, what is the new mean?
  1. 20
  2. 19
  3. 18
  4. 21

Answer: (A) 20

Total sum = 5 × 18 = 90. New sum = 90 - 10 = 80. New mean = 80 / 4 = 20.

Q95. A ladder 10 m long touches a wall at a height of 5 m. What is the angle of inclination of the ladder with the horizontal ground?
  1. 30°
  2. 45°
  3. 60°
  4. 90°

Answer: (A) 30°

sin θ = Perpendicular / Hypotenuse = 5 / 10 = 1/2. Therefore, θ = 30°.

Q96. The circumradius of an equilateral triangle with side length 6√3 cm is:
  1. 6 cm
  2. 3 cm
  3. 12 cm
  4. 9 cm

Answer: (A) 6 cm

Circumradius R = a / √3 = (6√3) / √3 = 6 cm.

Q97. Find the effective rate of interest when 10% per annum compound interest is compounded semi-annually.
  1. 10.25%
  2. 10.50%
  3. 10.00%
  4. 11.00%

Answer: (A) 10.25%

Half-yearly rate = 5%. Effective Rate = 5 + 5 + (5 × 5)/100 = 10.25%.

Q98. In what ratio must water be mixed with milk costing ₹40 per liter so that the mixture costs ₹30 per liter? (Water cost = ₹0)
  1. 1 : 3
  2. 1 : 4
  3. 3 : 1
  4. 2 : 3

Answer: (A) 1 : 3

By Alligation: Water (0) and Milk (40), Mean (30). (40-30):(30-0) = 10:30 = 1:3 (Water : Milk).

Q99. Find the sum of all interior angles of a convex polygon having 8 sides (Octagon).
  1. 1080°
  2. 900°
  3. 1260°
  4. 720°

Answer: (A) 1080°

Sum of interior angles = (n - 2) × 180° = (8 - 2) × 180° = 6 × 180° = 1080°.

Q100. A train passes a telegraph pole in 12 seconds moving at 54 km/h. What is the length of the train?
  1. 180 m
  2. 150 m
  3. 200 m
  4. 120 m

Answer: (A) 180 m

Speed = 54 × (5/18) = 15 m/s. Length = Speed × Time = 15 × 12 = 180 m.