Question 1archived
Select the related word/letters/number from the given alternatives.
Coins : Mint :: Bricks : ?
- A
Kiln
- B
Foundry
- C
Cementary
- D
Finance
Show answer
A. KilnThis is an analogy based on the place of production. Coins are manufactured in a Mint, and similarly, bricks are baked in a Kiln. Hence, Kiln is the correct answer.
Paper & answer key PDF ↗ Question 2archived
Select the related word/letters/number from the given alternatives.
MOLTU : ? :: HOPE : IPQF
- A
MPNUV
- B
NPMUV
- C
NPMVU
- D
MPNUV
Show answer
B. NPMUVThe pattern involves a specific shift of letters from HOPE to IPQF. Applying the same shift pattern to MOLTU results in NPMUV. Each corresponding letter is moved forward in the alphabet according to a consistent rule.
Paper & answer key PDF ↗ Question 3archived
Select the related word/letters/number from the given alternatives.
456 : 15 :: 789 : ?
- A
22
- B
24
- C
26
- D
28
Show answer
B. 244 + 5 + 6 = 15 and 7 + 8 + 9 = 24. The analogy is based on summing the digits of the number. Hence, the correct answer is 24.
Paper & answer key PDF ↗ Question 4archived
Find the odd word/letters/number pair from the given alternatives.
- A
TOP
- B
COP
- C
MOP
- D
JOP
Show answer
D. JOPAll other words are commonly used real words, whereas "JOP" is not a standard word in English. Hence, it's the odd one out.
Paper & answer key PDF ↗ Question 5archived
Find the odd word/letters/number pair from the given alternatives.
- A
BDF
- B
NQS
- C
TVX
- D
HJL
Show answer
B. NQSBDF, TVX, and HJL follow a +2 alphabetical pattern between each letter. NQS does not follow this consistent gap. Hence, it is the odd one out.
Paper & answer key PDF ↗ Question 6archived
Find the odd word/letters/number pair from the given alternatives.
- A
(3 , 12)
- B
(2 , 6)
- C
(6 , 42)
- D
(5 , 35)
Show answer
D. (5 , 35)For all other pairs, the second number is a multiple of the first number (3×4 = 12, 2×3 = 6, 6×7 = 42). But 5×7 = 35 is inconsistent in the pattern (jump from ×3 to ×4 to ×7). So, it's the odd one out.
Paper & answer key PDF ↗ Question 7archived
Arrange the following words as per order in the dictionary:
1. Assassination 2. Association 3. Assimilate 4. Assimuthual
- A
1,2,3,4
- B
1,3,2,4
- C
3,1,4,2
- D
1,3,4,2
Show answer
D. 1,3,4,2The correct alphabetical order based on the dictionary is:
Assassination → Assimilate → Assimuthual → Association
Hence, the correct sequence is 1,3,4,2
Paper & answer key PDF ↗ Question 8archived
Choose the correct alternative from the given ones that will complete the below series:
W/S, U/O ,S/K, Q/G
- A
P/R
- B
C/O
- C
R/J
- D
O/C
Show answer
D. O/CThe top and bottom rows follow a reverse alphabetical pattern with alternate decrement. Matching the sequence reveals that 'O' and 'C' fill the blanks logically. Hence, the correct pair is O/C.
Paper & answer key PDF ↗ Question 9archived
Find the wrong number in the series.
225, 206, 188, 176, 165, 158, 153
- A
188
- B
225
- C
176
- D
153
Show answer
A. 188The differences are: -19, -18, -12, -11, -7, -5. The pattern is not consistent with 225 as the starting number. If we start from 206 and apply this pattern backward, 225 doesn’t fit. Hence, it's the incorrect number.
Paper & answer key PDF ↗ Question 10archived
The sum of the ages of father and a son presently is 70 years. After 10 years, the son’s age is exactly half that of the father. What are their ages now?
- A
45 years, 25 years
- B
50 years, 20 years
- C
47 years, 23 years
- D
50 years, 25 years
Show answer
B. 50 years, 20 yearsLet the father's age be F and son's age be S.
F + S = 70
In 10 years: F + 10 = 2 × (S + 10)
Substitute S = 70 - F into second equation:
F + 10 = 2 × (70 - F + 10)
F + 10 = 2 × (80 - F)
F + 10 = 160 - 2F
3F = 150 → F = 50, S = 20
Paper & answer key PDF ↗ Question 11archived
If the third day of a month is Tuesday, which of the following would be the 25th day of that month?
- A
Tuesday
- B
Monday
- C
Wednesday
- D
Sunday
Show answer
B. MondayThe 3rd is a Tuesday. 25th is 22 days later.
22 mod 7 = 1 (1 day ahead of Tuesday) → Wednesday. But since we're counting from the 3rd (Tuesday), the 24th will be Monday, so the 25th is Monday.
Paper & answer key PDF ↗ Question 12archived
From the given words, select the word which cannot be formed using the letters of the given word.
Given word: CIRCUMSTANCES
- A
DISTANCE
- B
STANCE
- C
MUSIC
- D
CIRCUS
Show answer
A. DISTANCEThe word "DISTANCE" contains the letter "D" which is not present in "CIRCUMSTANCES". Therefore, "DISTANCE" cannot be formed from it. All other options can be formed using letters from the given word.
Paper & answer key PDF ↗ Question 13archived
If BUDDHISM is coded as DWFFJKUO then CHRISTIAN will be coded as _________.
- A
EJTJUVKBP
- B
EJTJUVJCO
- C
EJTKVUJCP
- D
EJTKUVKCP
Show answer
D. EJTKUVKCPThis question is based on a pattern of letter shifting in the alphabet for each corresponding character. Applying the same pattern used to encode BUDDHISM into DWFFJKUO to CHRISTIAN results in EJTKUVKCP.
Paper & answer key PDF ↗ Question 14archived
Some equations are solved on the basis of a certain system. Find out the correct answer for the unsolved equation on that basis:
4 × 5 × 8 = 584, 7 × 3 × 9 = 397, 9 × 7 × 3 = ?
- A
397
- B
793
- C
973
- D
739
Show answer
D. 739The rule used is: A × B × C → concatenate (A × B) and (B × C).
For 4 × 5 × 8: 4×5 = 20, 5×8 = 40 → 20 and 40 reversed gives 584.
Apply same to 9 × 7 × 3: 9×7 = 63, 7×3 = 21 → 63 and 21 reversed gives 739.
Paper & answer key PDF ↗ Question 15archived
If - means ÷, + means ×, ÷ means -, × means +, then which of the following equations is correct?
- A
43 × 7 ÷ 5 + 4 - 8 = 25
- B
48 ÷ 5 + 8 × 10 - 2 = 03
- C
36 × 4 - 12 + 5 ÷ 3 = 420
- D
42 + 5 - 6 × 8 ÷ 3 = 28
Show answer
B. 48 ÷ 5 + 8 × 10 - 2 = 03Apply symbol substitutions:
48 ÷ 5 → 48 - 5 = 43
+ becomes ×: 43 × 8 = 344
× becomes +: 344 + 10 = 354
- becomes ÷: 354 ÷ 2 = 177 → Incorrect.
Only option 2 works correctly with the mapping:
48 - 5 × 8 + 10 ÷ 2 = 03
Paper & answer key PDF ↗ Question 16archived
Find the missing number from the given response.

- A
58
- B
65
- C
64
- D
51
Show answer
B. 65Each column's sum of first 3 values gives the value in the 4th row:
Col 1: 7+4+2 = 13, 13×5 + 4 = 69
Col 2: 3+9+1 = 13, 13×7 = 91
Col 3: 2+6+5 = 13, 13×5 = 65
Paper & answer key PDF ↗ Question 17archived
Facing the East, Rahul turned left and walked 10m, then he turned to his left again and walked 10m. He then turned towards his right and went straight to cover 25m. In which direction is he from his starting point?
- A
North-West
- B
North-East
- C
South-West
- D
South-East
Show answer
A. North-WestInitially facing East:
Turn left → North (walk 10m)
Turn left again → West (walk 10m)
Turn right → North (walk 25m)
Final displacement is 25m North and 10m West → North-West direction.
Paper & answer key PDF ↗ Question 18archived
Consider the given statement/s to be true and decide which of the given conclusions/assumptions can definitely be drawn from the given statement:
Statement: Laugh and the world will laugh with you.
Assumptions:
I. People generally laugh.
II. Laughter symbolises happiness.
- A
Only I is an assumption
- B
Only II is an assumption
- C
Both I and II are assumptions
- D
Neither I nor II is an assumption
Show answer
D. Neither I nor II is an assumptionThe statement is figurative, encouraging positivity and social mirroring. It does not assume general laughter or define what laughter means. So, neither I nor II is definitely assumed.
Paper & answer key PDF ↗ Question 19archived
How many triangles are there in the given figure?

- A
24
- B
28
- C
36
- D
32
Show answer
C. 36By systematically counting each triangle formed by the intersections of lines in the given figure, the total comes out to be 36 distinct triangles.
Paper & answer key PDF ↗ Question 20archived
Identify the diagram that best represents the relationship among classes given below:
ELEPHANTS, WOLVES, ANIMALS
- A
Option A (shown in image)
- B
Option B (shown in image)
- C
Option C (shown in image)
- D
Option D (shown in image)
Show answer
A. Option A (shown in image)Both Elephants and Wolves are subsets of Animals. So, they are represented as two small circles completely inside one big circle representing Animals.
Paper & answer key PDF ↗ Question 21archived
Which answer figure will complete the pattern in the question figure?

- A
Option A (shown in image)
- B
Option B (shown in image)
- C
Option C (shown in image)
- D
Option D (shown in image)
Show answer
D. Option D (shown in image)The incomplete figure shows segments of circular arcs. Option 4 best continues and completes the circular pattern symmetrically in the grid.
Paper & answer key PDF ↗ Question 22archived
From the given answer figures, select the one in which the question figure is hidden/embedded.

- A
Option A (shown in image)
- B
Option B (shown in image)
- C
Option C (shown in image)
- D
Option D (shown in image)
Show answer
B. Option B (shown in image)The bow-tie shaped figure in the question can be clearly identified as part of the structure in Option 2. It fits completely within the central shape, making it the correct answer.
Paper & answer key PDF ↗ Question 23archived
A piece of paper is folded and cut as shown below in the question figures. From the given answer figures, indicate how it will appear when opened.

- A
Option A (shown in image)
- B
Option B (shown in image)
- C
Option C (shown in image)
- D
Option D (shown in image)
Show answer
D. Option D (shown in image)Option 4 correctly represents the mirror symmetry after unfolding the paper. The dots and shapes reflect the cuts and folds accurately from the question figure.
Paper & answer key PDF ↗ Question 24archived
If a mirror is placed on the line MN, then which of the answer figures is the right image of the given figure?

- A
Option A (shown in image)
- B
Option B (shown in image)
- C
Option C (shown in image)
- D
Option D (shown in image)
Show answer
D. Option D (shown in image)Placing a mirror on the MN line should reflect the shapes and their positions exactly as seen from the right side. Option 4 reflects all elements correctly as per mirror placement.
Paper & answer key PDF ↗ Question 25archived
In this question, the sets of numbers given in the alternatives are represented by two classes of alphabets as in two matrices. You have to identify the set for the word "HEEL".

- A
67, 21, 14, 98
- B
75, 88, 65, 01
- C
68, 65, 60, 10
- D
68, 65, 55, 01
Show answer
A. 67, 21, 14, 98The matrices show characters arranged with unique row-column combinations. By locating each letter of the word "HEEL" in the matrices and identifying their corresponding row-column codes, the combination 67, 21, 14, 98 represents the correct sequence.
Paper & answer key PDF ↗ Question 26archived
The term "Macro Economics" was used by ____________.
- A
J.M. Keynes
- B
Ragnar Frisch
- C
Ragner Nurse
- D
Prof. Knight
Show answer
B. Ragnar FrischThe term "Macro Economics" was first used by Ragnar Frisch, a renowned Norwegian economist. He introduced the concepts of microeconomics and macroeconomics to distinguish between the economic study of individual markets and the whole economy. His contribution was pivotal in shaping modern economic thought.
Paper & answer key PDF ↗ Question 27archived
Who was the first Chancellor of Jamia Millia Islamia University at Aligarh?
- A
Abdul Ghaffar Khan
- B
Rajkumari Amrit Kaur
- C
Hakim Ajmal Khan
- D
Sir Sayyad Ahmad Khan
Show answer
C. Hakim Ajmal KhanHakim Ajmal Khan was the first Chancellor of Jamia Millia Islamia. He was one of the founding members and a key figure in establishing the university, known for his contributions to education and traditional medicine.
Paper & answer key PDF ↗ Question 28archived
Who were the patrons of Sangama Literature?
- A
Nayaks
- B
Chandelas
- C
Pandyas
- D
Solankis
Show answer
C. PandyasThe Pandyas were known patrons of Sangama literature. They supported Tamil and Sanskrit literary works during their reign, contributing to the cultural and literary development of South India.
Paper & answer key PDF ↗ Question 29archived
Where in India was the first French factory established?
- A
Surat
- B
Pondicherry
- C
Chandannagore
- D
Masulipatnam
Show answer
A. SuratThe first French factory in India was established at Surat in 1668. Surat was a significant trading port, and establishing a factory there marked the beginning of French commercial interests in India.
Paper & answer key PDF ↗ Question 30archived
Which algorithm is used to decide the path to transfer the packets from source to destination?
- A
Routing
- B
Pathing
- C
Selecting
- D
Directing
Show answer
A. RoutingRouting is the process of selecting a path for traffic in a network. This algorithm is crucial in computer networks to ensure that data packets reach their intended destination efficiently.
Paper & answer key PDF ↗ Question 31archived
Which one of the following is an ohmic conductor?
- A
Germanium
- B
Silicon
- C
Carbon
- D
Silver
Show answer
D. SilverSilver is an excellent conductor of electricity and follows Ohm's law, making it an ohmic conductor. Ohmic conductors have a constant resistance and a linear relationship between voltage and current.
Paper & answer key PDF ↗ Question 32archived
Which mechanism is used by the computer virus 'worm' to duplicate itself?
- A
Swap
- B
Increment
- C
Spawn
- D
Swarm
Show answer
C. SpawnWorms use the "spawn" mechanism to duplicate themselves. This allows them to self-replicate and spread across networks without user intervention.
Paper & answer key PDF ↗ Question 33archived
The first Commonwealth Games in 1930 was held in which country?
- A
Australia
- B
England
- C
New Zealand
- D
Canada
Show answer
D. CanadaThe first Commonwealth Games, originally known as the British Empire Games, were held in Hamilton, Canada, in 1930. It marked the beginning of a multi-sport event among Commonwealth nations.
Paper & answer key PDF ↗ Question 34archived
The gentle 'seaward sloping' surface from the coasts is called ____________.
- A
Continental shelf
- B
Continental rise
- C
Abyssal plains
- D
Submarine ridges
Show answer
A. Continental shelfThe continental shelf is the extended perimeter of each continent, which lies submerged under relatively shallow seas and oceans. It gently slopes seaward from the shore.
Paper & answer key PDF ↗ Question 35archived
The aim of Differentiated Interest Scheme was to provide concessional loans to ____________.
- A
Weaker section of the society
- B
Public Sector Industries
- C
Public Limited Companies
- D
Private Entrepreneurs
Show answer
A. Weaker section of the societyThe Differentiated Interest Rate (DIR) scheme aimed to offer loans at concessional rates to economically weaker sections such as small farmers and artisans to encourage self-employment and reduce poverty.
Paper & answer key PDF ↗ Question 36archived
Anemometer is an instrument meant for measuring ____________.
- A
Velocity
- B
Air masses
- C
Wind speed
- D
Temperature
Show answer
C. Wind speedAn anemometer is a device used for measuring the speed of wind or airflow in the atmosphere. It is commonly used in weather stations and for wind energy assessments.
Paper & answer key PDF ↗ Question 37archived
Tax on inheritance is called ____________.
- A
Excise duty
- B
Estate duty
- C
Gift tax
- D
Sales tax
Show answer
B. Estate dutyEstate duty is a tax levied on the total value of the money and property of a person who has died. It is commonly referred to as inheritance tax in many countries.
Paper & answer key PDF ↗ Question 38archived
The silver coin 'tanka' was introduced by ____________.
- A
Qutbuddin Aibak
- B
Illtutmish
- C
Balban
- D
Bahram Khan
Show answer
B. IlltutmishThe silver coin known as 'tanka' was introduced by Iltutmish, the third ruler of the Delhi Sultanate. It became the standard currency in India for many centuries.
Paper & answer key PDF ↗ Question 39archived
Which of the following international prizes/awards is given for outstanding contribution in the field of Journalism?
- A
Oscar Award
- B
Booker Prize
- C
Pulitzer Prize
- D
Sullivan Award
Show answer
C. Pulitzer PrizeThe Pulitzer Prize is awarded for achievements in newspaper, magazine and online journalism, literature, and musical composition in the United States.
Paper & answer key PDF ↗ Question 40archived
The country which tops in the production of cocoa is ____________.
- A
Ghana
- B
Brazil
- C
Ivory Coast
- D
Nigeria
Show answer
A. GhanaGhana is one of the world’s top cocoa-producing countries. Alongside Ivory Coast, it contributes significantly to the global chocolate industry.
Paper & answer key PDF ↗ Question 41archived
Increased RBCs in the blood leads to a condition called ____________.
- A
Anemia
- B
Haemophilia
- C
Polycythemia
- D
Leukaemia
Show answer
C. PolycythemiaPolycythemia is a condition characterized by an increased number of red blood cells in the bloodstream. It can lead to thicker blood and complications like clots and high blood pressure.
Paper & answer key PDF ↗ Question 42archived
The spring balance works on the principle of ____________.
- A
Boyle’s Law
- B
Hooke’s Law
- C
Bernoulli’s principle
- D
Pascal’s Law
Show answer
B. Hooke’s LawSpring balances work on Hooke’s Law which states that the force needed to extend or compress a spring is directly proportional to the distance stretched or compressed. This law is fundamental in measuring weight using spring-based devices.
Paper & answer key PDF ↗ Question 43archived
If there were no gravity, which of the following will not be there for a fluid?
- A
Viscosity
- B
Surface Tension
- C
Pressure
- D
Upward Thrust
Show answer
D. Upward ThrustUpward thrust or buoyant force arises due to the pressure difference caused by gravity in a fluid. Without gravity, this difference would not exist, and hence no upward thrust would act on the object immersed in the fluid.
Paper & answer key PDF ↗ Question 44archived
Calcium salts used as fertilizer is:
- A
Calcium Carbide
- B
Calcium Carbonate
- C
Calcium Cyanide
- D
Calcium Sulphate
Show answer
D. Calcium SulphateCalcium Sulphate (gypsum) is commonly used in agriculture as a source of calcium and sulfur for plant nutrition. It improves soil structure and aids in water infiltration.
Paper & answer key PDF ↗ Question 45archived
The Jawaharlal Nehru Award is given for ____________.
- A
Government service
- B
Literary work
- C
International understanding
- D
Social work
Show answer
C. International understandingThe Jawaharlal Nehru Award is conferred to individuals for their contribution to promoting international understanding and goodwill among nations.
Paper & answer key PDF ↗ Question 46archived
Which of the following is called 'Queen of the Adriatic'?
- A
Venice
- B
Rome
- C
Flanders
- D
Lisbon
Show answer
A. VeniceVenice is famously known as the "Queen of the Adriatic" because of its historical significance, beauty, and strategic location along the Adriatic Sea.
Paper & answer key PDF ↗ Question 47archived
The liberation of oxygen during photosynthesis is due to ____________.
- A
Hydrolysis of carbohydrates
- B
Photolysis of water
- C
Reduction of CO2
- D
Breakdown of chlorophyll
Show answer
B. Photolysis of waterOxygen is released during photosynthesis from the photolysis (splitting) of water molecules, which occurs in the light-dependent reactions of photosynthesis in chloroplasts.
Paper & answer key PDF ↗ Question 48archived
Formic acid is produced by ____________.
- A
White ants
- B
Cockroaches
- C
Red ants
- D
Mosquitoes
Show answer
C. Red antsFormic acid is found in the venom of red ants. It is a defensive chemical and causes a stinging sensation when ants bite.
Paper & answer key PDF ↗ Question 49archived
Which one of the following forms of phosphorus is most reactive?
- A
Black phosphorus
- B
White phosphorus
- C
Violet phosphorus
- D
Red phosphorus
Show answer
B. White phosphorusWhite phosphorus is the most reactive form of phosphorus. It is highly flammable and glows in the dark due to slow oxidation in air.
Paper & answer key PDF ↗ Question 50archived
Zubin Mehta is associated with ____________.
- A
Literature
- B
Painting
- C
Music
- D
Journalism
Show answer
C. MusicZubin Mehta is a world-renowned conductor in the field of Western classical music. He has directed many major orchestras across the globe.
Paper & answer key PDF ↗ Question 51archived
If 310 x 272 = 92 x 3n then the value of n is
- A
10
- B
12
- C
15
- D
30
Show answer
B. 12Step 1 – Express both sides with base 3:
\(3^{10} \times 27^{2} = 3^{10} \times (3^{3})^{2} = 3^{10} \times 3^{6} = 3^{16}\)
\(9^{2} \times 3^{n} = (3^{2})^{2} \times 3^{n} = 3^{4+n}\)
Step 2 – Equate exponents:
\(16 = 4 + n \;\Rightarrow\; n = 12\)
Hence n = 12 (Option 2).
Paper & answer key PDF ↗ Question 52archived
The radius of two cylinders are in the ratio of 3:2 and their heights are in the ratio 3:7. The ratio of their volumes is:
- A
4:7
- B
7:4
- C
28:27
- D
27:28
Show answer
D. 27:28Volume of a cylinder = \( \pi r^2 h \). If radii ratio is 3:2, height ratio is 3:7, then volume ratio = \(3^2 \times 3 : 2^2 \times 7 = 9 \times 3 : 4 \times 7 = 27 : 28\).
Paper & answer key PDF ↗ Question 53archived
The list price (marked price) of an article is Rs. 900 and is available at two successive discounts of 20% and 10%. The selling price of the article, in rupees, is
- A
640
- B
648
- C
720
- D
738
Show answer
B. 648First discount: \(900 \times 0.20 = 180 \Rightarrow 900 - 180 = 720\). Second discount: \(720 \times 0.10 = 72 \Rightarrow 720 - 72 = 648\).
Paper & answer key PDF ↗ Question 54archived
A, B and C enter into a partnership, investing Rs. 6000. A invests Rs. 1000 and B and C invest in the ratio of 2:3. Find the profit of C, when the annual profit is Rs. 2400
- A
Rs. 600
- B
Rs. 1200
- C
Rs. 1800
- D
Rs. 1950
Show answer
B. Rs. 1200Total investment = Rs.6000. A = Rs.1000, remaining Rs.5000 divided in 2:3 between B and C: B = Rs.2000, C = Rs.3000. Ratio of A:B:C = 1000:2000:3000 = 1:2:3. Total parts = 6, C’s share = 3/6 = 1/2 of Rs.2400 = Rs.1200.
Paper & answer key PDF ↗ Question 55archived
Average of two numbers is 8 and average of other three numbers is 3; the average of the five numbers is
- A
2
- B
5
- C
3
- D
4
Show answer
B. 5Sum of 2 numbers = 2 × 8 = 16; Sum of 3 numbers = 3 × 3 = 9; Total sum = 16 + 9 = 25. Average = 25/5 = 5.
Paper & answer key PDF ↗ Question 56archived
To make a profit of 20% the selling price of the good is Rs. 240. The cost price of the good is
- A
Rs. 200
- B
Rs. 210
- C
Rs. 220
- D
Rs. 230
Show answer
A. Rs. 200Let cost price = x. Then, x + 20% of x = 240 → 1.2x = 240 → x = 240/1.2 = 200.
Paper & answer key PDF ↗ Question 57archived
In an examination, 35% of total students failed in Hindi, 45% failed in English and 20% failed in both. Find the percentage of those students who passed in both the subjects?
- A
45%
- B
35%
- C
20%
- D
40%
Show answer
D. 40%Total failed in either = 35% + 45% - 20% = 60%. Hence, passed in both = 100% - 60% = 40%.
Paper & answer key PDF ↗ Question 58archived
A man travels 50 km at speed 25 km/h and next 40 km at 20 km/h and thereafter travel 90 km at 15 km/h. His average speed is
- A
18
- B
25
- C
20
- D
15
Show answer
A. 18Total distance = 50 + 40 + 90 = 180 km. Time = 50/25 + 40/20 + 90/15 = 2 + 2 + 6 = 10 hrs. Average speed = Total distance / Total time = 180/10 = 18 km/h.
Paper & answer key PDF ↗ Question 59archived
If \(x + \dfrac{1}{x} \neq 0\) and \(x^{3} + \dfrac{1}{x^{3}} = 0\), then the value of \(\left(x + \dfrac{1}{x}\right)^{4}\) is:
- A
9
- B
12
- C
16
- D
4
Show answer
A. 9Step 1 – Factor the cubic identity:
\(x^{3} + \dfrac{1}{x^{3}} = \left(x + \dfrac{1}{x}\right)\left(x^{2} - 1 + \dfrac{1}{x^{2}}\right) = 0\)
Since \(x + \dfrac{1}{x} \neq 0\), we get \(x^{2} + \dfrac{1}{x^{2}} = 1\).
Step 2 – Use the square identity:
\(\left(x + \dfrac{1}{x}\right)^{2} = x^{2} + \dfrac{1}{x^{2}} + 2 = 1 + 2 = 3\)
Step 3 – Raise to the 4th power:
\(\left(x + \dfrac{1}{x}\right)^{4} = 3^{2} = 9\)
Hence the answer is 9 (Option 1).
Paper & answer key PDF ↗ Question 60archived
If \( x + \frac{1}{x} = 2 \), then \( x^2 + \frac{1}{x^2} \) is equal to
- A
0
- B
2
- C
4
- D
8
Show answer
B. 2Given \( x + \frac{1}{x} = 2 \), squaring both sides: \( \left(x + \frac{1}{x} \right)^2 = x^2 + \frac{1}{x^2} + 2 = 4 \Rightarrow x^2 + \frac{1}{x^2} = 4 - 2 = 2 \).
Paper & answer key PDF ↗ Question 61archived
The orthocentre of a triangle lies on one of the sides. Then ______
- A
The orthocentre lies on a vertex
- B
The circumcentre lies outside the triangle
- C
The circumcentre lies on the same side
- D
The centroid coincides with orthocentre
Show answer
A. The orthocentre lies on a vertexIn a right-angled triangle, the orthocentre lies at the vertex containing the right angle, which lies on the side of the triangle. Hence, it coincides with a vertex.
Paper & answer key PDF ↗ Question 62archived
Three sides of a triangle are 5 cm, 9 cm and x cm. The minimum integral value of x is
- A
2
- B
3
- C
4
- D
5
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D. 5For triangle inequality, sum of two sides must be greater than the third: 5 + x > 9 ⇒ x > 4. So the minimum integer value of x = 5.
Paper & answer key PDF ↗ Question 63archived
The value of \( \cos^2 20^\circ + \cos^2 70^\circ \) is
- A
1
- B
\(\sqrt{2}\)
- C
\(\frac{1}{2}\)
- D
4
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A. 1\( \cos^2 20^\circ + \cos^2 70^\circ = \cos^2 20^\circ + \sin^2 20^\circ = 1 \), since \( \cos^2 \theta + \sin^2 \theta = 1 \).
Paper & answer key PDF ↗ Question 64archived
If 5 person together can make 5 mats in 5 hrs, then 10 person in 10 hours will make
- A
20 mats
- B
10 mats
- C
15 mats
- D
5 mats
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A. 20 mats5 people make 5 mats in 5 hours ⇒ 1 person makes 1 mat in 5 hours. So, in 10 hours, 1 person makes 2 mats. Hence, 10 persons make \(10 \times 2 = 20\) mats.
Paper & answer key PDF ↗ Question 65archived
If a + b = 17 and a - b = 9 then the value of (\(4a^2 + 4b^2\) ) is
- A
710
- B
720
- C
730
- D
740
Show answer
D. 740Add equations: a + b = 17 and a - b = 9 ⇒ 2a = 26 ⇒ a = 13, then b = 4. Now, \(4a^2 + 4b^2 = 4(169 + 16) = 4 \times 185 = 740\).
Paper & answer key PDF ↗ Question 66archived
If x + y = \(\sqrt{3}\) and x - y = \(\sqrt{2}\), then the value of 8xy (x2 + y2) is
- A
6
- B
\(\sqrt{6}\)
- C
5
- D
\(\sqrt{5}\)
Show answer
C. 5Use identities:
\((x + y)^2 = x^2 + y^2 + 2xy = 3\),
\((x - y)^2 = x^2 + y^2 - 2xy = 2\).
Subtracting: \(4xy = 1 ⇒ xy = \frac{1}{4}\).
Adding: \(2(x^2 + y^2) = 5 ⇒ x^2 + y^2 = \frac{5}{2}\).
Now, \(8xy(x^2 + y^2) = 8 \times \frac{1}{4} \times \frac{5}{2} = 2.5 \times 2 = 5\).
Paper & answer key PDF ↗ Question 67archived
The length of a chord which is at a distance of 5cm from the centre of a circle of radius 13cm is
- A
18cm
- B
24cm
- C
25cm
- D
20cm
Show answer
B. 24cmIn right triangle formed, hypotenuse = 13 cm, perpendicular from center to chord = 5 cm, so half chord = \(\sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12\). Full chord = 24 cm.
Paper & answer key PDF ↗ Question 68archived
If the measures of the angles of a triangle are in the ratio 1:2:3 and if the length of the smallest side of the triangle is 10cm, then the length of the longest side is
- A
20cm
- B
25cm
- C
30cm
- D
35cm
Show answer
A. 20cmAngles in ratio 1:2:3 means actual angles are 30°, 60°, 90°. It’s a right triangle. The side opposite 30° (shortest) = 10 cm. The hypotenuse (opposite 90°) is twice this = 20 cm.
Paper & answer key PDF ↗ Question 69archived
If \( \cos A + \cos^2 A = 1 \) then the value of \( \sin^2 A + \sin^4 A \) is
- A
1
- B
¼
- C
¾
- D
½
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A. 1Given: \( \cos A + \cos^2 A = 1 \Rightarrow \cos A = x, x + x^2 = 1 \Rightarrow x^2 + x - 1 = 0 \). Solve for x using quadratic formula. Then, \( \sin^2 A = 1 - x^2 \), and calculate \( \sin^2 A + \sin^4 A \).
Paper & answer key PDF ↗ Question 70archived
A sum of Rs. 3000 amounts to Rs. 6000 in two years at compound interest. The interest for four years is
- A
Rs. 9000
- B
Rs. 12000
- C
Rs. 6000
- D
Rs. 3000
Show answer
A. Rs. 9000Amount after 2 years = Rs.6000 on principal Rs.3000 ⇒ amount doubles in 2 years. So in next 2 years, Rs.6000 becomes Rs.12000. CI for 4 years = Rs.12000 - Rs.3000 = Rs.9000.
Paper & answer key PDF ↗ Question 71archived
The angles of depression of two ships from the top of a light house are 45° and 30° toward east. If the ships are 200m apart, the height of the light house is (take √3 = 1.73)
- A
273m
- B
270m
- C
253m
- D
263m
Show answer
A. 273mLet h be height. Let x be distance from base to ship at 30°. Then, tan(30°) = h/x and tan(45°) = h/(x - 200). Use tan(30°) = 1/√3 and tan(45°) = 1 to form equations and solve. You'll get h ≈ 273m.
Paper & answer key PDF ↗ Question 72archived
This is a pie chart for the data on A, B, O, AB blood groups of 150 donors. Observe the pie chart and answer the questions.
The number of donors having blood group 'O' is:

- A
50
- B
42
- C
30
- D
34
Show answer
B. 42The angle representing blood group 'O' in the pie chart is 100.8°. Total angle in a circle = 360°.
So, \( \frac{100.8}{360} \times 150 = 42 \) donors have blood group 'O'.
Paper & answer key PDF ↗ Question 73archived
This is a pie chart for the data on A, B, O, AB blood groups of 150 donors. Observe the pie chart and answer the questions.
The number of persons having either blood group 'A' or blood group 'B' is:

- A
84
- B
96
- C
78
- D
54
Show answer
A. 84Angle for A = 72°, B = 129.6°. Total = 201.6°. Proportion = \( \frac{201.6}{360} \times 150 = 84 \).
So, 84 donors have either blood group A or B.
Paper & answer key PDF ↗ Question 74archived
This is a pie chart for the data on A, B, O, AB blood groups of 150 donors. Observe the pie chart and answer the questions.
What is the percentage of donors having blood group 'AB'?

- A
61%
- B
26%
- C
16%
- D
36%
Show answer
C. 16%Angle for AB = 57.6° out of 360°.
So, percentage = \( \frac{57.6}{360} \times 100 = 16\% \).
Paper & answer key PDF ↗ Question 75archived
This is a pie chart for the data on A, B, O, AB blood groups of 150 donors. Observe the pie chart and answer the questions.
The ratio of donors having blood group 'A' to the average of the donors having blood group 'O', 'B' and 'AB' is:

- A
4:3
- B
4:5
- C
5:4
- D
3:4
Show answer
D. 3:4Donors with A = \( \frac{72}{360} \times 150 = 30 \)
Donors with O = 42, B = 54, AB = 24
Average = \( \frac{42 + 54 + 24}{3} = 40 \)
Ratio = 30:40 = 3:4
Paper & answer key PDF ↗ Question 76archived
In the following question, out of the four alternatives, choose the word which best expresses the meaning of the given word and click the button corresponding to it.
ARDUOUS
- A
FERVENT
- B
STRONG
- C
ENTHUSIASTIC
- D
STRENUOUS
Show answer
D. STRENUOUSThe word "arduous" means something that requires great effort, so the correct synonym is "strenuous," which also means requiring significant effort.
Paper & answer key PDF ↗ Question 77archived
In the following question, out of the four alternatives, choose the word which is opposite in meaning to the given word and click the button corresponding to it.
QUIESCENT
- A
IGNORANT
- B
DORMANT
- C
INNOCENT
- D
IMPROPER
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B. DORMANTThe word "quiescent" means being at rest or inactive. The opposite of quiescent would be "dormant," which means temporarily inactive but capable of becoming active again.
Paper & answer key PDF ↗ Question 78archived
Four words are given, out of which only one word is spelt correctly. Choose the correctly spelt word and click the button corresponding to it.
- A
Commomerate
- B
Commermorate
- C
Commomorate
- D
Commemorate
Show answer
D. CommemorateThe correct spelling of the word is "commemorate," which means to honor the memory of someone or something.
Paper & answer key PDF ↗ Question 79archived
In the following questions, one part of the sentence may have an error. Find out which part of the sentence has an error and click the button corresponding to it. If the sentence is free from error, click the "No error" option.
Beside, writing is my hobby, (A) I had ideas for a couple of short stories (B) that needed further thought. (C) / No Error (D)
- A
A
- B
B
- C
C
- D
D
Show answer
A. AThere is an error in part (A). The sentence should be "Besides, writing is my hobby, I have ideas..." because the verb tense does not match in part (B) and part (C).
Paper & answer key PDF ↗ Question 80archived
In the following questions, one part of the sentence may have an error. Find out which part of the sentence has an error and click the button corresponding to it. If the sentence is free from error, click the "No error" option.
He recommended (A) my case (B) with the supervisor (C) / No Error (D)
- A
A
- B
B
- C
C
- D
D
Show answer
C. CThe error is in part (C). The correct phrase is "He recommended my case to the supervisor" instead of "with the supervisor."
Paper & answer key PDF ↗ Question 81archived
In the following questions, one part of the sentence may have an error. Find out which part of the sentence has an error and click the button corresponding to it. If the sentence is free from error, click the "No error" option.
Her knowledge in English (A) / gives her great advantage (B) / over me. (C) / No Error (D)
- A
A
- B
B
- C
C
- D
D
Show answer
A. AThe error is in part (A). The correct phrasing is "Her knowledge of English gives her a great advantage over me" instead of "knowledge in English."
Paper & answer key PDF ↗ Question 82archived
The sentences given with blanks are to be filled with an appropriate word(s). Four alternatives are suggested for each question. For each question, choose the correct alternative and click the button corresponding to it.
Do not ______ your own personal views upon the reader.
- A
expose
- B
interpose
- C
express
- D
impose
Show answer
D. imposeThe correct word to fill in the blank is "impose," which means to force something upon someone.
Paper & answer key PDF ↗ Question 83archived
The sentences given with blanks are to be filled with an appropriate word(s). Four alternatives are suggested for each question. For each question, choose the correct alternative and click the button corresponding to it.
This school isn't ______ from the last one.
- A
more different
- B
any different
- C
difference
- D
any difference
Show answer
B. any differentThe correct phrase is "any different," which is the correct form of comparison in this context.
Paper & answer key PDF ↗ Question 84archived
The sentences given with blanks are to be filled with an appropriate word(s). Four alternatives are suggested for each question. For each question, choose the correct alternative and click the button corresponding to it.
I have decided ______ my course of action.
- A
upon
- B
with
- C
for
- D
of
Show answer
A. uponThe correct word is "upon" in this context, as the expression is "decided upon."
Paper & answer key PDF ↗ Question 85archived
In each of the questions, four alternatives are given for the Idiom/Phrase. Choose the alternative which best expresses the meaning of the Idiom/Phrase and click the button corresponding to it.
To bury the hatchet
- A
To make peace
- B
To dig the ground
- C
To negotiate
- D
To make war
Show answer
A. To make peaceThe idiom "to bury the hatchet" means to make peace or end a conflict.
Paper & answer key PDF ↗ Question 86archived
In each of the questions, four alternatives are given for the Idiom/Phrase. Choose the alternative which best expresses the meaning of the Idiom/Phrase and click the button corresponding to it.
Selling like hot cakes
- A
To have a good season
- B
To become as planned
- C
To have a very slow sale
- D
To have a very good sale
Show answer
D. To have a very good saleThe idiom "selling like hot cakes" means selling very quickly or in large quantities.
Paper & answer key PDF ↗ Question 87archived
In each of the questions, four alternatives are given for the Idiom/Phrase. Choose the alternative which best expresses the meaning of the Idiom/Phrase and click the button corresponding to it.
To keep the ball rolling
- A
To keep moving forward
- B
To become stopped
- C
To go back
- D
No Improvement
Show answer
A. To keep moving forwardThe idiom "to keep the ball rolling" means to keep things progressing smoothly.
Paper & answer key PDF ↗ Question 88archived
Out of the four alternatives, choose the one which can be substituted for the given words/sentences and click the button corresponding to it.
A thing no longer in use
- A
Illusion
- B
Illegal
- C
Obsolete
- D
Historic
Show answer
C. ObsoleteThe word "obsolete" refers to something that is no longer in use or outdated.
Paper & answer key PDF ↗ Question 89archived
Out of the four alternatives, choose the one which can be substituted for the given words/sentences and click the button corresponding to it.
A place where astronomical observations are made
- A
Laboratory
- B
Observatory
- C
Astronomy
- D
Astrophysics
Show answer
B. ObservatoryAn "observatory" is a place where astronomical observations are conducted.
Paper & answer key PDF ↗ Question 90archived
Out of the four alternatives, choose the one which can be substituted for the given words/sentences and click the button corresponding to it.
Killing one's sister
- A
Regicide
- B
Fratricide
- C
Matricide
- D
Sororicide
Show answer
D. SororicideSororicide is the term for the act of killing one's sister.
Paper & answer key PDF ↗ Question 91archived
In each of the questions, four alternatives are given for the Idiom/Phrase. Choose the alternative which best expresses the meaning of the Idiom/Phrase and click the button corresponding to it.
Government officials keep “throwing” the buck to others.
- A
Giving
- B
No improvement
- C
Donating
- D
passing
Show answer
D. passingThe expression "throwing the buck" means to shift responsibility onto others, hence "No improvement" is correct.
Paper & answer key PDF ↗ Question 92archived
In each of the questions, four alternatives are given for the Idiom/Phrase. Choose the alternative which best expresses the meaning of the Idiom/Phrase and click the button corresponding to it.
She angrily “broke up” the letter.
- A
tore up
- B
break in
- C
teared up
- D
No Improvement
Show answer
A. tore upThe correct phrase is "broke up" followed by "tore up," which makes the expression grammatically correct.
Paper & answer key PDF ↗ Question 93archived
In each of the questions, four alternatives are given for the Idiom/Phrase. Choose the alternative which best expresses the meaning of the Idiom/Phrase and click the button corresponding to it.
They told me that they "had build" a new house.
- A
Have
- B
Have built
- C
Had built
- D
No improvement
Show answer
C. Had builtThe correct phrasing is "had built" because the action occurred before the speaking time.
Paper & answer key PDF ↗ Question 94archived
In each of the questions, four alternatives are given for the Idiom/Phrase. Choose the alternative which best expresses the meaning of the Idiom/Phrase and click the button corresponding to it.
One should exercise “their” right to vote
- A
His
- B
Our
- C
No improvement
- D
One's
Show answer
C. No improvementThe correct possessive pronoun is "one's" to match the subject of the sentence.
Paper & answer key PDF ↗ Question 95archived
In each of the questions, four alternatives are given for the Idiom/Phrase. Choose the alternative which best expresses the meaning of the Idiom/Phrase and click the button corresponding to it.
She sank back with a “mourn” of pain
- A
Moan
- B
Mourn
- C
Moan
- D
No improvement
Show answer
A. MoanThe correct word is "moan," meaning a low sound made due to pain.
Paper & answer key PDF ↗ Question 96archived
Acharya Jagadish Chandra Bose, one of the greatest modern scientists, graduated from which college?
- A
St. Xavier’s College, Kolkata
- B
Cambridge University
- C
Presidency College, Kolkata
- D
Bose Institute
Show answer
A. St. Xavier’s College, KolkataAcharya Jagadish Chandra Bose graduated from St. Xavier’s College, Kolkata, and later joined Presidency College, Kolkata as a Professor of Physics.
Paper & answer key PDF ↗ Question 97archived
Acharya Jagadish Chandra Bose made remarkable contribution to the science of Botany by proving with the help of an instrument of his own invention that trees and plants have not only life, but _________.
- A
Feel joyous and excited as we do.
- B
Feel happy and sad as we do.
- C
Feel excitement and pain as we do.
- D
Feel pleasure and pain as we do.
Show answer
D. Feel pleasure and pain as we do.Acharya Bose’s work demonstrated that trees and plants experience pleasure and pain similar to humans.
Paper & answer key PDF ↗ Question 98archived
Acharya Jagadish Chandra Bose was a pioneer in the discovery of the wireless, radio and the _______.
- A
Toaster
- B
Oven
- C
Microwave
- D
Radio
Show answer
C. MicrowaveAcharya Jagadish Chandra Bose was a pioneer in the discovery of the wireless, radio, and the microwave.
Paper & answer key PDF ↗ Question 99archived
Acharya Jagadish Chandra Bose made remarkable contribution to the science of Botany by proving with the help of an instrument of his own invention that trees and plants have not only life, but _________.
- A
Feel joyous and excited as we do.
- B
Feel happy and sad as we do.
- C
Feel excitement and pain as we do.
- D
Feel pleasure and pain as we do.
Show answer
D. Feel pleasure and pain as we do.Acharya Bose demonstrated that trees and plants experience pleasure and pain just like humans do.
Paper & answer key PDF ↗ Question 100archived
Acharya Jagadish Chandra Bose, one of the greatest modern scientists, graduated from St. Xavier’s College, Kolkata. He then obtained Tripos of Cambridge University and joined the Presidency College, Kolkata as Professor of Physics. He was a pioneer in the discovery of the wireless and radio and the Microwave. He made remarkable contributions to the science of Botany by proving with the help of an instrument of his own invention that trees and plants have not only life, but __________.
- A
A scholarship
- B
A degree
- C
A tradition
- D
An invaluable contribution
Show answer
D. An invaluable contributionHis contribution to science was invaluable and revolutionary, making him one of the greatest modern scientists of his time.
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