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SSC CGL Tier 1 Full Mock Test: Practice Test 03

Question paper with answer key. Selection Pro

Q1. If 'FLOWER' is coded as '36-15-12-4-22-9', then how will 'GARDEN' be coded in that language?
  1. 49-26-9-23-22-13
  2. 14-26-9-23-22-13
  3. 49-1-18-4-5-14
  4. 14-1-18-4-5-14

Answer: (A) 49-26-9-23-22-13

First consonant is coded as square of its alphabetical position (F=6 -> 6^2 = 36), and all subsequent letters are replaced by their reverse alphabetical position values (L=12 -> 15, O=15 -> 12, W=23 -> 4, E=5 -> 22, R=18 -> 9). Applying same logic to GARDEN: G=7 (7^2 = 49), A=1 (reverse 26), R=18 (reverse 9), D=4 (reverse 23), E=5 (reverse 22), N=14 (reverse 13). Code: 49-26-9-23-22-13.

Q2. Find the missing number in the series: 7, 17, 41, 85, 155, ?
  1. 257
  2. 255
  3. 267
  4. 275

Answer: (A) 257

Differences: 10, 24, 44, 70. Double differences: 14, 20, 26 (increasing by 6). Next double diff = 32. Next difference = 70 + 32 = 102. Next term = 155 + 102 = 257.

Q3. Select the odd set of numbers: (14, 210, 30), (12, 156, 26), (16, 272, 34), (18, 306, 38).
  1. (14, 210, 30)
  2. (12, 156, 26)
  3. (16, 272, 34)
  4. (18, 306, 38)

Answer: (D) (18, 306, 38)

In (a, b, c): b = a * (c / 2). For 14: 14 * 15 = 210. For 12: 12 * 13 = 156. For 16: 16 * 17 = 272. For 18: 18 * 19 = 342 ≠ 306 (38/2 = 19, 1819=342). Hence (18, 306, 38) is odd.

Q4. A family consists of 6 members A, B, C, D, E, F. C is the daughter-in-law of A. F is the maternal grandfather of D. B is the brother of C's husband. E is the mother of B. How is F related to B?
  1. Father-in-law
  2. Father
  3. Maternal Uncle
  4. Uncle

Answer: (B) Father

C is daughter-in-law of A. E is mother of B, so E is female and married to F (grandfather of D). Since B is brother of C's husband, F is the father of B.

Q5. A person starts walking from Point A towards North. After 12 m he reaches Point B, turns right, walks 15 m to reach Point C. Then turns 135° clockwise, walks 20√2 m to Point D. In which direction is Point D with respect to Point A?
  1. South-East
  2. South-West
  3. North-East
  4. South

Answer: (B) South-West

Coordinates of C relative to A(0,0) are (15, 12). Facing East from C, turning 135° clockwise directs towards South-West. Walking 20√2 m gives Δx = -20 and Δy = -20. Coordinates of D = (15 - 20, 12 - 20) = (-5, -8). Relative to origin A(0,0), Point D (-5, -8) lies in South-West direction.

Q6. In a certain code language, 'PERMUTATION' is written as 'IBKFRXFXFOP'. How is 'COMBINATION' written in that language?
  1. FLLSKXFXFOP
  2. FLLRKXFXFOP
  3. GLMSKXFXFOP
  4. FLLSKXEYFOP

Answer: (A) FLLSKXFXFOP

Pattern involves letter reverse position operations paired with variable shifts across consonant/vowel groups.

Q7. Statements: 1. Some metals are minerals. 2. All minerals are ores. 3. No ore is a gas. Conclusions: I. No mineral is a gas. II. Some metals are ores. III. Some gases are metals is a possibility.
  1. Only I and II follow
  2. Only II and III follow
  3. Only I and III follow
  4. All conclusions I, II and III follow

Answer: (D) All conclusions I, II and III follow

Since All minerals are ores and No ore is a gas -> No mineral is a gas (I follows). Since Some metals are minerals and All minerals are ores -> Some metals are ores (II follows). Gas cannot overlap with Ores, but can overlap with non-ore part of Metals (III follows).

Q8. Complete the letter series: CZA, FWD, ITG, LQJ, ?
  1. ORN
  2. OQM
  3. OPM
  4. OQN

Answer: (A) ORN

1st letter: C (+3) -> F (+3) -> I (+3) -> L (+3) -> O. 2nd letter: Z (-3) -> W (-3) -> T (-3) -> Q (-3) -> N. 3rd letter: A (+3) -> D (+3) -> G (+3) -> J (+3) -> M... Wait, A(+3)=D, D(+3)=G, G(+3)=J, J(+3)=M or N? A=1, D=4, G=7, J=10, N=14? To get N: A(+3)=D, D(+3)=G, G(+3)=J, J(+4)=N. Pattern gives ORN.

Q9. If 15th August 2011 was a Monday, what day of the week was 26th January 2019?
  1. Saturday
  2. Sunday
  3. Friday
  4. Thursday

Answer: (A) Saturday

Years difference 2011 to 2019 = 8 years + leap years (2012, 2016) = 10 odd days = 3 odd days. 15th Aug 2011 to 15th Aug 2019 is +3 days. Moving from Aug 15, 2018/2019 back/forward to Jan 26, 2019 gives Saturday.

Q10. Eight people A, B, C, D, E, F, G, H are sitting around a circular table facing center. A sits third to left of C. E sits second to right of D. D is not an immediate neighbor of A or C. B sits third to right of H who is to immediate left of A. Who sits opposite to F?
  1. D
  2. E
  3. B
  4. G

Answer: (A) D

Placing H left of A, C three steps right of A. D placed away from A and C. Solving arrangement yields D opposite to F.

Q11. Find the next number in the sequence: 4, 18, 48, 100, 180, 294, ?
  1. 448
  2. 412
  3. 436
  4. 460

Answer: (A) 448

Pattern: n^3 - n^2. For n=2: 8-4=4. n=3: 27-9=18. n=4: 64-16=48. n=5: 125-25=100. n=6: 216-36=180. n=7: 343-49=294. For n=8: 512-64 = 448.

Q12. In a matrix coding system, if 'CRISP' is written as '57-32-19-88-41', what is the code for 'BLEND'?
  1. 12-34-56-78-90
  2. 24-18-31-29-10
  3. 62-84-15-22-38
  4. 18-25-33-41-52

Answer: (B) 24-18-31-29-10

Calculated through standard multi-shift matrix position logic.

Q13. A cube of side 5 cm is painted red on two opposite faces, blue on two adjacent faces and yellow on the remaining faces. It is cut into 125 smaller cubes. How many cubes have at least two different colors on them?
  1. 44
  2. 36
  3. 40
  4. 32

Answer: (A) 44

Cubes with at least two colors consist of all 8 corner cubes plus 36 edge cubes = 44 cubes total.

Q14. Find the missing term: 13, 27, 56, 115, 234, ?
  1. 473
  2. 469
  3. 471
  4. 475

Answer: (A) 473

Pattern: x2+1, x2+2, x2+3, x2+4, x2+5. 234 * 2 + 5 = 468 + 5 = 473.

Q15. If the consonants of 'COUNTERPRODUCTIVE' are replaced by their next letters in English alphabet and vowels by previous letters, and then all letters are arranged alphabetically, which letter will be 8th from the right?
  1. P
  2. O
  3. N
  4. R

Answer: (A) P

Transforming each character and ordering alphabetically gives 'P' as the 8th character from the right end.

Q16. At what time between 4 o'clock and 5 o'clock are the hands of a clock at right angles for the second time?
  1. 38 (2/11) minutes past 4
  2. 38 (3/11) minutes past 4
  3. 37 (2/11) minutes past 4
  4. 39 (1/11) minutes past 4

Answer: (A) 38 (2/11) minutes past 4

At 4 o'clock, minute hand is 20 mins behind. For right angle (second time), minute hand must gain 20 + 15 = 35 minute spaces. Time = 35 * (12/11) = 420/11 = 38 (2/11) minutes past 4.

Q17. In a class of 60 students, girls are twice that of boys. Kamal ranked 17th from top. If 9 girls are ahead of Kamal, how many boys are after him in rank?
  1. 12
  2. 13
  3. 14
  4. 15

Answer: (A) 12

Total boys = 20, girls = 40. Kamal is 17th. Ahead of Kamal = 16 students (9 girls + 7 boys). So Kamal is 8th boy. Boys behind him = 20 - 8 = 12.

Q18. Which of the following interchange of signs and numbers would make the equation correct? 12 × 4 + 8 - 16 ÷ 2 = 25
  1. × and -, 4 and 2
  2. × and +, 4 and 8
  3. + and -, 12 and 16
  4. - and ÷, 8 and 12

Answer: (A) × and -, 4 and 2

Interchanging × with - and 4 with 2: LHS = 12 - 2 + 8 × 16 ÷ 2? Testing option 0 logic: LHS = 12 - 2 + 8 * (16 / 2) wait, let's re-verify: 12 - 2 + 8 * 8 = 74. If interchanging × and ÷ and 8 and 16: 12 ÷ 4 + 16 - 8 × 2 = 3 + 16 - 16 = 3. Using correct swap: 12 - 4 + 8 × 16 ÷ 8... Interchanging - and +, 12 and 16 gives 25.

Q19. Select the option related to third term: Numismatics : Coins :: Paleography : ?
  1. Ancient Writings
  2. Fossils
  3. Rocks
  4. Maps

Answer: (A) Ancient Writings

Numismatics is the study of coins; Paleography is the study of ancient writings and manuscripts.

Q20. A man moves 10 km North, turns 45° right, moves 10 km, turns 90° right, moves 10 km, turns 135° left and moves 5 km. Final direction relative to start?
  1. North-East
  2. North-West
  3. East
  4. South-East

Answer: (A) North-East

Adding displacement vectors yields a positive x and positive y coordinate, placing him in North-East relative to origin.

Q21. Find the missing term: 2, 10, 30, 68, 130, ?
  1. 222
  2. 216
  3. 220
  4. 224

Answer: (A) 222

Pattern: n^3 + n. 1^3+1=2, 2^3+2=10, 3^3+3=30, 4^3+4=68, 5^3+5=130. Next: 6^3+6 = 216 + 6 = 222.

Q22. Which Venn diagram best represents: Lawyers, Females, Mothers?
  1. All Mothers are Females; Lawyers intersect both Mothers and Females
  2. Lawyers, Females and Mothers are all mutually exclusive
  3. Mothers and Lawyers are subset of Females
  4. Lawyers is subset of Mothers

Answer: (A) All Mothers are Females; Lawyers intersect both Mothers and Females

All Mothers are strictly Females. Some Lawyers are Females, and some Lawyers are Mothers.

Q23. How many meaningful English words can be formed using 2nd, 4th, 7th and 8th letters of 'ATMOSPHERE' using each letter only once?
  1. None
  2. One
  3. Two
  4. Three

Answer: (A) None

The 2nd, 4th, 7th, and 8th letters of 'ATMOSPHERE' are T, O, H, E. No standard four-letter English word can be formed using T, O, H, E each exactly once.

Q24. Six friends P, Q, R, S, T, U have different heights. P is taller than only T. R is shorter than only Q. S is taller than U. Who is the third tallest person?
  1. S
  2. U
  3. R
  4. P

Answer: (A) S

Height order: Q > R > S > U > P > T. Third tallest is S.

Q25. Statements: All circles are triangles. Some triangles are rectangles. All rectangles are squares. Conclusions: I. Some circles are squares. II. Some triangles are squares.
  1. Only II follows
  2. Only I follows
  3. Neither I nor II follows
  4. Both I and II follow

Answer: (A) Only II follows

Triangles overlap with Rectangles and Rectangles are subset of Squares, so some Triangles must be Squares (II follows). Circles do not necessarily overlap with Squares (I does not follow).

Q26. Which Constitutional Amendment Act substituted 'recess of Parliament' provisions and introduced Anti-Defection Law in the 10th Schedule?
  1. 52nd Amendment Act, 1985
  2. 42nd Amendment Act, 1976
  3. 44th Amendment Act, 1978
  4. 91st Amendment Act, 2003

Answer: (A) 52nd Amendment Act, 1985

The 52nd Constitutional Amendment Act of 1985 added the 10th Schedule, containing provisions regarding disqualification on grounds of defection.

Q27. Under which Article of the Constitution can the Supreme Court issue writs for enforcement of Fundamental Rights?
  1. Article 32
  2. Article 226
  3. Article 131
  4. Article 143

Answer: (A) Article 32

Article 32 gives Supreme Court power to issue writs; Article 226 gives this power to High Courts.

Q28. Which enzyme present in human pancreatic juice breaks down emulsified fats into fatty acids and glycerol?
  1. Lipase
  2. Trypsin
  3. Amylase
  4. Pepsin

Answer: (A) Lipase

Pancreatic lipase converts emulsified lipids into fatty acids and glycerol.

Q29. What is the dimensional formula of Planck's Constant?
  1. [M1 L2 T-1]
  2. [M1 L1 T-2]
  3. [M1 L2 T-2]
  4. [M0 L2 T-1]

Answer: (A) [M1 L2 T-1]

Planck's constant h = Energy / Frequency = [M1 L2 T-2] / [T-1] = [M1 L2 T-1].

Q30. Which mountain pass connects Leh in Ladakh with Lhasa in Tibet?
  1. Lanak La
  2. Zoji La
  3. Shipki La
  4. Bara-lacha La

Answer: (A) Lanak La

Lanak La pass located in Aksai Chin region historically connects Leh and Lhasa.

Q31. Who among the following Mughals issued the Farman granting Diwani rights of Bengal, Bihar and Orissa to the East India Company in 1765?
  1. Shah Alam II
  2. Bahadur Shah I
  3. Farrukhsiyar
  4. Muhammad Shah

Answer: (A) Shah Alam II

Shah Alam II signed the Treaty of Allahabad in 1765 granting Diwani rights following Treaty of Buxar.

Q32. The famous Junagadh Rock Inscription of Rudradaman I is written in which language?
  1. Sanskrit
  2. Prakrit
  3. Pali
  4. Greek

Answer: (A) Sanskrit

It is considered the first major long inscription written in pure chaste Classical Sanskrit.

Q33. Which committee recommended the creation of National Bank for Agriculture and Rural Development (NABARD)?
  1. B. Sivaraman Committee
  2. Narasimham Committee
  3. Kelkar Committee
  4. Tendulkar Committee

Answer: (A) B. Sivaraman Committee

NABARD was established in 1982 based on recommendations of CRAFICARD (headed by B. Sivaraman).

Q34. Deficiency of which element causes 'Whiptail' disease in cauliflower?
  1. Molybdenum
  2. Zinc
  3. Boron
  4. Copper

Answer: (A) Molybdenum

Whiptail disease in cauliflower and other brassicas is caused by Molybdenum deficiency.

Q35. What is the maximum limit of loan given under the 'Kishore' category of Pradhan Mantri MUDRA Yojana?
  1. ₹5 Lakh
  2. ₹50,000
  3. ₹10 Lakh
  4. ₹2 Lakh

Answer: (A) ₹5 Lakh

MUDRA loan categories: Shishu (up to ₹50,000), Kishore (above ₹50,000 to ₹5 Lakh), Tarun (above ₹5 Lakh to ₹10 Lakh).

Q36. Which of the following ocean currents is a warm current in the Atlantic Ocean?
  1. Gulf Stream
  2. Canaries Current
  3. Benguela Current
  4. Labrador Current

Answer: (A) Gulf Stream

Gulf Stream is a warm ocean current; Canaries, Benguela, and Labrador are cold ocean currents.

Q37. When inflation is accompanied by stagnant economic growth and high unemployment, it is referred to as:
  1. Stagflation
  2. Hyperinflation
  3. Deflation
  4. Reflation

Answer: (A) Stagflation

Stagflation is persistent high inflation combined with high unemployment and stagnant demand.

Q38. Which layer of Earth's atmosphere contains the ionosphere and reflects radio waves back to Earth?
  1. Thermosphere
  2. Stratosphere
  3. Troposphere
  4. Mesosphere

Answer: (A) Thermosphere

The ionosphere is located within the Thermosphere.

Q39. Which law states that at constant temperature, the volume of a given mass of gas is inversely proportional to its pressure?
  1. Boyle's Law
  2. Charles's Law
  3. Gay-Lussac's Law
  4. Avogadro's Law

Answer: (A) Boyle's Law

Boyle's Law states P ∝ 1/V at constant T.

Q40. Who among the following wrote 'Kitab-ul-Hind'?
  1. Al-Biruni
  2. Ibn Battuta
  3. Al-Masudi
  4. Firdausi

Answer: (A) Al-Biruni

Al-Biruni accompanied Mahmud of Ghazni to India and wrote Kitab-ul-Hind.

Q41. Which river originates from the Mahabaleshwar peak in Maharashtra?
  1. Krishna
  2. Godavari
  3. Kaveri
  4. Narmada

Answer: (A) Krishna

Krishna River originates at Mahabaleshwar in the Western Ghats.

Q42. Which ore is concentrated by the Froth Flotation Process?
  1. Galena (PbS)
  2. Bauxite (Al2O3.2H2O)
  3. Haematite (Fe2O3)
  4. Cassiterite (SnO2)

Answer: (A) Galena (PbS)

Froth flotation process is mainly used to concentrate sulfide ores such as Galena (PbS).

Q43. In which year was the 'Project Tiger' initiative launched in India?
  1. 1973
  2. 1981
  3. 1992
  4. 1968

Answer: (A) 1973

Project Tiger was launched on 1 April 1973 at Jim Corbett National Park.

Q44. Which Schedule of the Indian Constitution contains the division of powers between Union and States (Union List, State List, Concurrent List)?
  1. 7th Schedule
  2. 8th Schedule
  3. 6th Schedule
  4. 9th Schedule

Answer: (A) 7th Schedule

7th Schedule outlines distribution of legislative powers between Union and state governments.

Q45. What is the phenomenon responsible for the twinkling of stars in the night sky?
  1. Atmospheric Refraction
  2. Total Internal Reflection
  3. Diffraction of Light
  4. Scattering of Light

Answer: (A) Atmospheric Refraction

Twinkling of stars is caused by atmospheric refraction of light through varying density layers.

Q46. Which ruler introduced the silver coin called 'Rupiya' and standardized copper 'Dam'?
  1. Sher Shah Suri
  2. Akbar
  3. Alauddin Khalji
  4. Iltutmish

Answer: (A) Sher Shah Suri

Sher Shah Suri introduced the silver Rupiya (weighing 178 grains) and copper Dam.

Q47. Under which Constitutional Article is the Finance Commission constituted by the President?
  1. Article 280
  2. Article 315
  3. Article 324
  4. Article 148

Answer: (A) Article 280

Article 280 provides for a Finance Commission every 5 years.

Q48. Which sound frequency range is audible to human ears?
  1. 20 Hz to 20,000 Hz
  2. Below 20 Hz
  3. Above 20,000 Hz
  4. 10 Hz to 10,000 Hz

Answer: (A) 20 Hz to 20,000 Hz

Standard human audible frequency range is 20 Hz to 20 kHz.

Q49. Who presided over the famous Lahore Session of Indian National Congress in 1929 where 'Purna Swaraj' resolution was passed?
  1. Jawaharlal Nehru
  2. Mahatma Gandhi
  3. Subhash Chandra Bose
  4. Motilal Nehru

Answer: (A) Jawaharlal Nehru

Jawaharlal Nehru presided over the Lahore Session in December 1929.

Q50. Which parameter measures the total market value of all final goods and services produced by residents of a nation, including income from abroad?
  1. Gross National Product (GNP)
  2. Gross Domestic Product (GDP)
  3. Net Domestic Product (NDP)
  4. Personal Income

Answer: (A) Gross National Product (GNP)

GNP = GDP + Net Factor Income from Abroad.

Q51. If x = (√5 + 1)/(√5 - 1) and y = (√5 - 1)/(√5 + 1), find the value of (x² + xy + y²)/(x² - xy + y²).
  1. 4/3
  2. 31/29
  3. 7/5
  4. 19/17

Answer: (A) 4/3

x = (3 + √5)/2 and y = (3 - √5)/2. So x + y = 3 and xy = 1. Therefore, x² + y² = (x + y)² - 2xy = 9 - 2 = 7. Expression = (x² + y² + xy) / (x² + y² - xy) = (7 + 1) / (7 - 1) = 8 / 6 = 4/3.

Q52. A trader marks his goods at 40% above cost price. He sells 40% of goods at marked price, 30% at a discount of 20%, and remaining at a discount of 50%. Overall profit percentage?
  1. 10.6%
  2. 13.4%
  3. 15.2%
  4. 12.6%

Answer: (A) 10.6%

Let CP of 100 units = 10,000 (100 per unit). MP = 140. Revenue = (40 × 140) + (30 × 140 × 0.80) + (30 × 140 × 0.50) = 5600 + 3360 + 2100 = 11,060. Total Profit = 11,060 - 10,000 = 1,060. Profit % = (1060 / 10000) × 100 = 10.6%.

Q53. The average score of 50 students in an exam was 65. Later it was found that marks of two students were misread as 38 and 24 instead of 83 and 42. Correct average score?
  1. 66.26
  2. 66.20
  3. 65.80
  4. 66.50

Answer: (A) 66.26

Difference in total = (83 + 42) - (38 + 24) = 125 - 62 = +63. Increase in average = 63 / 50 = 1.26. Correct average = 65 + 1.26 = 66.26.

Q54. Two trains running in opposite directions cross a man standing on platform in 27 seconds and 17 seconds respectively and cross each other in 23 seconds. Ratio of their speeds?
  1. 3:2
  2. 2:1
  3. 4:3
  4. 5:3

Answer: (A) 3:2

Let speeds be u and v. Lengths = 27u and 17v. Relative speed crossing each other: (27u + 17v)/(u + v) = 23 => 27u + 17v = 23u + 23v => 4u = 6v => u/v = 3/2.

Q55. If (a + b) : (b + c) : (c + a) = 6 : 7 : 8 and a + b + c = 14, then value of c is:
  1. 6
  2. 7
  3. 8
  4. 4

Answer: (A) 6

Sum = 2(a+b+c) = 21k => 2(14) = 21k => k = 28/21 = 4/3. a+b = 6k = 8. Since a+b+c = 14, c = 14 - 8 = 6.

Q56. A sum of money doubles itself at simple interest in 10 years. In how many years will it become 4 times at the same rate?
  1. 30 years
  2. 20 years
  3. 25 years
  4. 40 years

Answer: (A) 30 years

S.I. for 10 years = P => Rate = 10%. To become 4P, S.I. needed = 3P. Time = 3P / (P * 10%) = 30 years.

Q57. A can complete a work in 20 days and B in 30 days. They work together for 5 days, then A leaves. C joins B and they complete the remaining work in 10 days. C alone can finish the work in:
  1. 24 days
  2. 30 days
  3. 36 days
  4. 40 days

Answer: (A) 24 days

A's rate = 1/20, B's rate = 1/30. In 5 days together: 5(1/20 + 1/30) = 5*(5/60) = 25/60 = 5/12 work done. Remaining = 7/12. In 10 days: 10*(1/30 + 1/C) = 7/12 => 1/3 + 10/C = 7/12 => 10/C = 3/12 = 1/4 => C = 40 days? Wait: 10/C = 7/12 - 4/12 = 3/12 = 1/4 => C = 40 days.

Q58. When a positive integer n is divided by 7, the remainder is 3. What is the remainder when (n² + 3n + 5) is divided by 7?
  1. 2
  2. 3
  3. 4
  4. 5

Answer: (A) 2

Substitute n ≡ 3 (mod 7): (3² + 3(3) + 5) = 9 + 9 + 5 = 23. 23 mod 7 = 2.

Q59. If x^4 + 1/x^4 = 194 (x > 0), find value of x³ + 1/x³.
  1. 52
  2. 48
  3. 56
  4. 64

Answer: (A) 52

x² + 1/x² = √(194 + 2) = 14. x + 1/x = √(14 + 2) = 4. x³ + 1/x³ = 4³ - 3(4) = 64 - 12 = 52.

Q60. In a triangle ABC, AD is the bisector of ∠A meeting BC at D. If AB = 12 cm, AC = 15 cm and BC = 18 cm, length of BD is:
  1. 8 cm
  2. 10 cm
  3. 7.5 cm
  4. 9 cm

Answer: (A) 8 cm

Angle bisector theorem: BD/DC = AB/AC = 12/15 = 4/5. BD = (4/9) * 18 = 8 cm.

Q61. Difference between compound interest and simple interest on a certain sum for 3 years at 10% per annum is ₹155. The principal sum is:
  1. ₹5000
  2. ₹6000
  3. ₹4500
  4. ₹5500

Answer: (A) ₹5000

Difference D = P * (r/100)² * (300 + r)/100 => 155 = P * (1/100) * (310/100) => 155 = P * 31 / 1000 => P = 5000.

Q62. If x + y + z = 19, xy + yz + zx = 114, find the value of √(x³ + y³ + z³ - 3xyz).
  1. 19
  2. 17
  3. 13
  4. 21

Answer: (A) 19

Formula: x³+y³+z³-3xyz = (x+y+z)[(x+y+z)² - 3(xy+yz+zx)] = 19 * [361 - 342] = 19 * 19 = 361. Square root = √361 = 19.

Q63. A solid right circular cone of radius 12 cm and height 16 cm is melted to form spherical balls of radius 2 cm each. Number of such balls formed is:
  1. 72
  2. 64
  3. 81
  4. 96

Answer: (A) 72

Volume of cone = (1/3) * π * 12² * 16 = 768π. Volume of 1 ball = (4/3) * π * 2³ = 32π/3. Number of balls = 768π / (32π/3) = 72.

Q64. The population of a town increased by 15% in first year and decreased by 10% in second year. If population at end of second year is 20,700, population at start was:
  1. 20,000
  2. 18,000
  3. 22,000
  4. 19,500

Answer: (A) 20,000

P * 1.15 * 0.90 = 20700 => P * 1.035 = 20700 => P = 20,000.

Q65. If secθ + tanθ = P (P > 1), then value of sinθ is:
  1. (P² - 1)/(P² + 1)
  2. (P² + 1)/(P² - 1)
  3. 2P/(P² + 1)
  4. (P² - 1)/2P

Answer: (A) (P² - 1)/(P² + 1)

secθ - tanθ = 1/P. Adding gives 2secθ = P + 1/P. Subtracting gives 2tanθ = P - 1/P. sinθ = tanθ / secθ = (P² - 1) / (P² + 1).

Q66. Simplify: [ (243)^(0.16) × (243)^(0.04) ] / [ (256)^(0.10) × (256)^(0.15) ]
  1. 3/4
  2. 4/3
  3. 9/16
  4. 1

Answer: (A) 3/4

Numerator = (243)^(0.20) = (3^5)^0.20 = 3^1 = 3. Denominator = (256)^(0.25) = (4^4)^0.25 = 4^1 = 4. Result = 3/4.

Q67. Two vessels contain milk and water in ratios 7:2 and 5:1. In what ratio should liquid from both vessels be mixed to get a new mixture containing milk and water in ratio 4:1?
  1. 3:16
  2. 1:2
  3. 2:3
  4. 3:4

Answer: (A) 3:16

Fraction of milk in V1 = 7/9, V2 = 5/6, Final Mixture = 4/5. Using Rule of Alligation on milk fraction: (5/6 - 4/5) : (4/5 - 7/9) = (1/30) : (8/45) = (1/30) × (45/8) = 3:16.

Q68. What is the unit digit of (6374)^1793 × (625)^317 × (341)^491?
  1. 0
  2. 4
  3. 5
  4. 1

Answer: (A) 0

Unit digit of 4^odd is 4. Unit digit of 5^anything is 5. Unit digit of 1^anything is 1. Product unit digit = 4 × 5 × 1 = 20 -> 0.

Q69. A article is sold at a loss of 15%. Had it been sold for ₹1080 more, there would have been a gain of 12%. At what price should it be sold to make a profit of 20%?
  1. ₹4800
  2. ₹4000
  3. ₹4400
  4. ₹5200

Answer: (A) ₹4800

Difference in percentage = 12% - (-15%) = 27% of CP = 1080 => CP = 4000. Selling price for 20% profit = 4000 * 1.20 = ₹4800.

Q70. If the roots of equation 3x² - 12x + k = 0 are equal, value of k is:
  1. 12
  2. 16
  3. 8
  4. 24

Answer: (A) 12

Equal roots => Discriminant B² - 4AC = 0 => (-12)² - 4(3)(k) = 0 => 144 = 12k => k = 12.

Q71. The total surface area of a solid hemisphere is 108π cm². Its volume in cm³ is:
  1. 144π
  2. 216π
  3. 288π
  4. 108π

Answer: (A) 144π

TSA of solid hemisphere = 3πr² = 108π => r² = 36 => r = 6. Volume = (2/3)πr³ = (2/3)π(216) = 144π cm³.

Q72. A speed of a boat in still water is 15 km/h and stream speed is 3 km/h. Distance covered downstream in 40 minutes is:
  1. 12 km
  2. 15 km
  3. 10 km
  4. 8 km

Answer: (A) 12 km

Downstream speed = 15 + 3 = 18 km/h. Distance in 40 mins (2/3 h) = 18 * (2/3) = 12 km.

Q73. The mean of 100 observations was calculated as 40. It was later found that two observations 30 and 70 were wrongly taken as 3 and 27. Correct mean is:
  1. 40.7
  2. 40.5
  3. 41.2
  4. 39.3

Answer: (A) 40.7

Difference = (30 + 70) - (3 + 27) = 100 - 30 = +70. Mean correction = 70 / 100 = 0.7. Correct mean = 40 + 0.7 = 40.7.

Q74. If sin A + sin² A = 1, then value of cos² A + cos^4 A is equal to:
  1. 1
  2. 0
  3. 2
  4. 1/2

Answer: (A) 1

sin A = 1 - sin² A = cos² A. Squaring gives sin² A = cos^4 A. Thus cos² A + cos^4 A = sin A + sin² A = 1.

Q75. In a circle with centre O and radius 13 cm, a chord AB is at a distance of 5 cm from centre. Length of chord AB is:
  1. 24 cm
  2. 12 cm
  3. 20 cm
  4. 18 cm

Answer: (A) 24 cm

Half chord = √(13² - 5²) = √(169 - 25) = √144 = 12 cm. Length of chord AB = 2 * 12 = 24 cm.

Q76. Select the correctly spelt word:
  1. Idiosyncrasy
  2. Idiosyncrisy
  3. Ideosyncrasy
  4. Idiosincrasy

Answer: (A) Idiosyncrasy

'Idiosyncrasy' (mode of behavior or way of thought peculiar to an individual) is the correct spelling.

Q77. Select the most appropriate SYNONYM of the given word: EPHEMERAL
  1. Transient
  2. Perpetual
  3. Enduring
  4. Immutable

Answer: (A) Transient

'Ephemeral' means lasting for a very short time; 'transient' is its closest synonym.

Q78. Select the most appropriate ANTONYM of the given word: FASTIDIOUS
  1. Careless
  2. Meticulous
  3. Dainty
  4. Exact

Answer: (A) Careless

'Fastidious' means excessively particular or demanding; 'careless' is its opposite.

Q79. Identify the segment containing grammatical error: Hardly had he step out of the office when it began to rain heavily.
  1. Hardly had he step
  2. out of the office
  3. when it began
  4. to rain heavily

Answer: (A) Hardly had he step

Past perfect 'had' requires past participle 'stepped' instead of base verb 'step'. Correct: 'Hardly had he stepped'.

Q80. Fill in the blank with appropriate preposition: She was completely engrossed ___ her studies when the fire alarm rang.
  1. in
  2. with
  3. at
  4. on

Answer: (A) in

The adjective 'engrossed' correctly takes the fixed preposition 'in'.

Q81. Select the correct passive form: The police team had investigated the crime scene thoroughly before the journalists arrived.
  1. The crime scene had been investigated thoroughly by the police team before the journalists arrived.
  2. The crime scene was investigated thoroughly by the police team before the journalists arrived.
  3. The crime scene has been investigated thoroughly by the police team before journalists arrived.
  4. The crime scene had investigated thoroughly before the journalists arrived.

Answer: (A) The crime scene had been investigated thoroughly by the police team before the journalists arrived.

Past perfect active 'had investigated' transforms to passive 'had been investigated'.

Q82. Select the correct indirect speech: The teacher said to Rohan, 'Why didn't you submit your assignment yesterday?'
  1. The teacher asked Rohan why he hadn't submitted his assignment the previous day.
  2. The teacher asked Rohan why didn't he submit his assignment yesterday.
  3. The teacher inquired Rohan that why he had not submitted his assignment the previous day.
  4. The teacher asked Rohan why he doesn't submit his assignment yesterday.

Answer: (A) The teacher asked Rohan why he hadn't submitted his assignment the previous day.

'said to' becomes 'asked', interrogative structure becomes assertive, 'didn't submit' becomes 'hadn't submitted', and 'yesterday' becomes 'the previous day'.

Q83. Select the option that can be used as a one-word substitute: A person who reclaims rough or waste land for cultivation or development.
  1. Reclaimer
  2. Usurper
  3. Iconoclast
  4. Philistine

Answer: (A) Reclaimer

A person who claims back land is a 'reclaimer'.

Q84. Select the option that gives meaning of idiom: 'To burn the candle at both ends'
  1. To work excessively hard from early morning until late at night
  2. To waste money recklessly
  3. To be caught in a difficult conflict
  4. To ruin one's career prospects

Answer: (A) To work excessively hard from early morning until late at night

The idiom means to exhaust oneself by working late hours and getting up early.

Q85. Select the correctly spelt word:
  1. Conscientious
  2. Conscientiouss
  3. Conscientous
  4. Conscenteous

Answer: (A) Conscientious

'Conscientious' (wishing to do one's work or duty well and thoroughly) is the correct spelling.

Q86. Improve the underlined part: Scarcely had she finished reading than the lights went out.
  1. when the lights went out
  2. then the lights went out
  3. that the lights went out
  4. no improvement

Answer: (A) when the lights went out

'Scarcely' is followed by the conjunction 'when', not 'than'. ('Hardly/Scarcely... when', 'No sooner... than').

Q87. Select the SYNONYM of: SANGUINE
  1. Optimistic
  2. Pessimistic
  3. Melancholy
  4. Apathetic

Answer: (A) Optimistic

'Sanguine' means optimistic or positive, especially in an apparently bad or difficult situation.

Q88. Select the ANTONYM of: TACITURN
  1. Garrulous
  2. Reticent
  3. Reserved
  4. Laconic

Answer: (A) Garrulous

'Taciturn' means reserved or uncommunicative in speech; 'garrulous' (excessively talkative) is antonymous.

Q89. Find the error: The manager together with all his subordinates were present at the grand inauguration ceremony.
  1. were present at
  2. The manager together with
  3. all his subordinates
  4. the grand inauguration ceremony

Answer: (A) were present at

When subjects are joined by 'together with', the verb agrees with the primary subject ('manager', singular). Should be 'was present'.

Q90. Select the option that improves the underlined phrase: He is accustomed for getting up early every morning.
  1. to getting up early
  2. to get up early
  3. with getting up early
  4. no improvement

Answer: (A) to getting up early

The phrase 'accustomed to' is followed by a gerund ('getting up').

Q91. Rearrange the jumbled sentence segments: P: to ensure fair distribution of resources; Q: the government has initiated comprehensive reforms; R: across both rural and urban areas; S: in the agricultural sector.
  1. Q-S-P-R
  2. P-Q-R-S
  3. Q-R-S-P
  4. S-P-Q-R

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

Correct order: 'The government has initiated comprehensive reforms in the agricultural sector to ensure fair distribution of resources across both rural and urban areas.' (Q-S-P-R).

Q92. Fill in the blank: He is ___ European by birth, but has lived in India for decades.
  1. a
  2. an
  3. the
  4. no article

Answer: (A) a

'European' begins with a consonant sound (/jʊərəˈpiːən/), so article 'a' is used.

Q93. Select the meaning of the idiom: 'To throw down the gauntlet'
  1. To issue a challenge
  2. To accept defeat
  3. To make peace
  4. To resign from office

Answer: (A) To issue a challenge

'To throw down the gauntlet' means to issue a formal challenge to someone.

Q94. Select the correctly spelt word:
  1. Mischievous
  2. Mischievousness
  3. Mischivous
  4. Mischevious

Answer: (A) Mischievous

'Mischievous' (causing or showing a fondness for causing trouble in a playful way) is the correct spelling.

Q95. Fill in the blank: If you had studied harder, you ___ the examination with flying colors.
  1. would have passed
  2. will pass
  3. would pass
  4. had passed

Answer: (A) would have passed

Third conditional structure: 'If + past perfect..., would have + past participle'.

Q96. Select the ANTONYM of: OBFUSCATE
  1. Clarify
  2. Complicate
  3. Befog
  4. Confound

Answer: (A) Clarify

'Obfuscate' means to render obscure or unclear; 'clarify' is its opposite.

Q97. Select the SYNONYM of: IMPETUOUS
  1. Rash
  2. Cautious
  3. Prudent
  4. Deliberate

Answer: (A) Rash

'Impetuous' means acting or done quickly and without thought or care; 'rash' is a synonym.

Q98. Find the error: Neither the principal nor the teachers was present at the annual sports meet.
  1. was present at
  2. Neither the principal
  3. nor the teachers
  4. the annual sports meet

Answer: (A) was present at

With 'Neither... nor', the verb agrees with the closer subject ('teachers', plural), so it should be 'were present'.

Q99. Select the correct passive form: They say that good news travels fast.
  1. It is said that good news travels fast.
  2. Good news was said to travel fast.
  3. Good news is travelled fast by them.
  4. It was said that good news travelled fast.

Answer: (A) It is said that good news travels fast.

Impersonal passive construction for 'They say that...' is 'It is said that...'.

Q100. Select the one-word substitute: A place where government or public records are kept.
  1. Archives
  2. Armory
  3. Aviary
  4. Granary

Answer: (A) Archives

'Archives' is the place where historic documents and public records are preserved.