A girl goes to school at a speed of 21 km/hr. She comes back with a speed of 42 km/hr. Find her average speed for the whole journey.
- ((a))
28 km/h
- ((b))
26 km/h
- ((c))
30 km/h
- ((d))
20 km/h
Show Answer
28 km/h
120 questions · 90 minutes · with answers · free
A girl goes to school at a speed of 21 km/hr. She comes back with a speed of 42 km/hr. Find her average speed for the whole journey.
28 km/h
26 km/h
30 km/h
20 km/h
28 km/h
A hollow spherical shell is made of a metal of density 36 g/cm3. Its internal and external radius are 1 cm and 2 cm, respectively. What is the weight (in kg) of the shell ?
1.056
2.38
1.944
2.57
1.056
65% of 240 + ?% of 150 = 201
40
30
25
35
40
The present cost of a house is ₹155120. After a year, its cost increased to ₹197932. The percentage increase (rounded off to the nearest integer) in the cost of the house is:
25
23
28
26
25
The sum of 10 numbers is 372. Find their average.
38.2
35.2
36.2
37.2
38.2
The digit in place of A that makes 25432A7 divisible by 9 is:
1
3
4
0
1
If a shopkeeper bears 25% loss, then which of the following statements is/are correct?
Statement A: The cost price of 15 articles is equal to the selling price of 20 articles.
Statement B: The cost price of 12 articles is equal to the selling price of 17 articles.
Neither Statement A nor B is correct.
Both Statements A and B are correct.
Only Statement A is correct.
Only Statement B is correct.
Neither Statement A nor B is correct.
A triangle has two equal sides of 13 cm each and third side of 10 cm. The area (in cm2) of the triangle is:
45
50
40
60
45
The average of first 123 odd natural numbers, is:
123.5
124
122.5
123
123.5
If the price of an item increased from ₹3,135 to ₹4,389, what is the percentage change?
20% increase
25% increase
40% increase
40% decrease
20% increase
A money lender borrows a sum of ₹7,000 from market at compound interest at a rate of 5% per annum, compounded annually. The amount paid after two year will be:
₹7,717.50
₹7,900
₹7,800
₹7,860.25
₹7,717.50
How many seconds will a boy take to run one complete round around a square field of side 20 metres, if he runs at a speed of 16 km/h?
13
21
17
18
13
The dimensions of a rectangular solid are 8 cm × 4 cm × 1 cm. What is the length (in cm) of its diagonal?
10
9
15
13
10
Find the value of 80-2 ÷ 8015 × 80-10
80-26
80-19
80-20
80-27
80-26
The sum of five numbers is 655. The average of the first two numbers is 75 and the third number is 130. Find the average of the remaining two numbers?
188.5
205
206
187.5
188.5
Which of the following ratio is smallest?
21 : 59
12 : 33
24 : 37
26 : 52
21 : 59
An Uber auto covers a distance of 525 km in 21 hours. What is its speed in km/h?
26
22
25
33
26
Aman offers a discount scheme, such that on buying 12 rough copies, get x rough copies for free. If the equivalent percentage discount is 25%, then what is the value of x?
4
6
3
5
4
Mohan bought an article for ₹1,520 and sold it for ₹1,870. Find his profit percentage
(correct to two places of decimals).
21.36%
23.03%
22.78%
20.15%
21.36%
In what ratio should sugar costing ₹40 per kg be mixed with sugar costing ₹81 per kg so that by selling the mixture at ₹57.5 per kg, there is a profit of 25%?
4 : 34
35 : 6
5 : 33
8 : 36
4 : 34
Amit can do a piece of work in 6 hours. Gopal can do it in 42 hours. With the assistance of Akshay, they completed the work in 3 hours. In how many hours can Akshay alone do it?
7
9
6
8
7
Anjani can do a certain piece of work in 30 days. Anjani and Khushbu can together do the same work in 24 days, and Anjani, Khushbu and Sushmita can do the same work together in 12 days. In how many days can Anjani and Sushmita do the same work?
Alice can complete a task in 18 days, and Bob can complete the same task in 24 days. If they work together, how long will it take for them to complete the task?
8 days
10 days
8 days
The highest common factor of 363, 495, and 561 is N. The digit sum of N is:
4
6
7
5
4
A sum, when invested at 10% simple interest per annum, amounts to ₹4560 after 2 years. What is the simple interest (in ₹) on the same sum at the same rate of interest in 2 years?
3040
760
380
1520
3040
An amount of ₹440 is divided among three persons in the ratio of 7 : 17 : 16. The difference between the largest and the smallest shares (in ₹) in the distribution is:
114
84
110
127
114
How many times 0.25 is 2.5?
5 times
12 times
10 times
1 time
5 times
Evaluate: 41 - [36 - {48 ÷ 2 - (6 - 12 ÷ 2) ÷ 3}]
29
28
30
31
29
The LCM of two prime numbers K and P (where K > P) is 667. Find the value of 3P + K.
108
128
88
98
108
In covering a distance of 192 km, Anmol takes 9 hours more than Nikhil. If Anmol doubles his speed, then he would take 7 hour less than Nikhil. Anmol's speed is:
6 km/h
14 km/h
3 km/h
15 km/h
6 km/h
If 25% of a number is added to 78, then the result is the same number. 80% of the same number is:
83.2
103.2
113.2
53.2
83.2
The sum of five numbers is 655. The average of the first two numbers is 78 and the third number is 121. Find the average of the remaining two numbers?
189
190
200
199
189
A store marks a washing machine at ₹25,000 and offers a series of two discounts: 10% and then 20% on the reduced price. What is the final price after both discounts?
₹22,500
₹17,500
₹18,000
₹18,500
₹22,500
Find the compound interest (in ₹, rounded off to the nearest integer) on ₹2,55,000 in 1.5 years at 8% per annum, the interest being compounded half-yearly.
34,180
31,480
31,840
32,480
34,180
What will be the value of the following expression, if the ‘−‘ and the ‘×’ signs are interchanged?
18 × 2 + 5 − 9 ÷ 3 × 2 − 6 = ?
19
12
8
23
19
Based on the English alphabetical order, three of the following four letter-clusters are alike in a certain way and thus form a group. Which letter-cluster DOES NOT belong to that group? (Note: The odd one out is not based on the number of consonants/vowels or their position in the letter-cluster.)
LQV
INS
VAF
DJN
LQV
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(13, 27, 41)
(44, 31, 18)
(18 ,16, 14)
(19, 24, 21)
(21, 25, 28)
(15, 13, 14)
(18 ,16, 14)
Select the correct mirror image of the given figure when the mirror is placed at MN as shown below.












What should come in place of the question mark (?) in the given series?
6 10 18 30 46 ?
65
66
63
64
65
This question is based on the five, three-digit numbers given below.
(Left) 372 196 388 198 329 (Right)
(Example- 697 – First digit = 6, second digit = 9 and third digit = 7)
(NOTE: All operations to be done from left to right.)
What will be the resultant if the second digit of the highest number is added to the second digit of the lowest number?
16
15
17
18
16
In a certain code language, ‘WITH’ is coded as ‘7894’ and ‘THIN’ is coded as ‘8745’. What is the code for ‘W’ in the given code language?
9
8
7
4
9
Which of the following letter-number clusters will replace the question mark (?) in the given series to make it logically complete?
VRL 21, BXR 32, HDX 43, NJD 54, TPJ 65, ?
ZXP 76
IVP 76
ZVP 76
ZVP 75
ZXP 76
Read the given statement(s) and conclusions carefully. Assuming that the information given in the statement(s) is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statement(s).
Statements:
All vans are utilities.
All trucks are utilities.
Conclusions:
(I) Some vans are trucks.
(II) Some utilities are trucks.
Only conclusion (I) follows.
Neither conclusion (I) nor (II) follows.
Only conclusion (II) follows.
Both conclusions (I) and (II) follow.
Only conclusion (I) follows.
Based on the English alphabetical order, three of the following four letter-clusters are alike in a certain way and thus form a group. Which letter-cluster DOES NOT belong to that group?
(Note: The odd one out is not based on the number of consonants/vowels or their position in the letter-cluster.)
AHO
GNY
TAH
ELS
AHO
Seven friends, Q, R, S, T, W, X and Y, are sitting around a circular table facing the centre of the table. Only one person sits between Q and W. Q sits immediately to the right of X. Y sits immediately to the left of W. Only R sits between Q and T. How many people sit between Q and Y when counted from the right of Y?
Two
One
Three
Four
Two
Which of the following letter-number clusters will replace the question mark (?) in the given series to make it logically complete?
UUU4, QQQ4, MMM4, III4, ?
EEE4
FFF4
HHH4
GGG4
EEE4
H, A, T, B, O, R, and D are sitting around a circular table facing the centre. D sits to the immediate right of A. T sits second to the left of A. O sits third to the left of T. Only one person sits between O and B. Who sits to the immediate left of T?
O
H
R
B
O
In a certain code language,
A + B means 'A is the mother of B'
A − B means 'A is the father of B'
A X B means 'A is the sister of B'
A / B means 'A is the brother of B'
A > B means 'A is the husband of B'
A * B means 'A is the wife of B'
How is M related to B if M − N + T X B > K ?
Mother
Mother's father
Father's sister
Sister
Mother
This question is based on the five, three-digit numbers given below.
(Left) 241 341 735 672 457 (Right)
(Example- 697 – First digit = 6, second digit = 9 and third digit = 7) (NOTE: All operations to be done from left to right.)
If all the numbers are arranged in ascending order, the position(s) of how many numbers will remain unchanged?
1
4
2
3
1
Select the pair that follows the same pattern as that followed by the two pairs given below. Both pairs follow the same pattern.
BNM - CMN
EFT - FEU
UIO - VJP
SWE - TVF
LIN - MNO
WER - XFT
UIO - VJP
5P is related to 4O in a certain way. In the same way, 3N is related to 2M. To which of the following is 1L related, following the same logic?
0K
2K
1K
0J
0K
Ronak starts from Point A and drives 5 km towards the north. He then takes a right turn, drives 6 km, turns right and drives 9 km. He then takes a right turn and drives 11 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90° turns only unless specified.)
5 km to the east
4 km to the west
5 km to the west
4 km to the east
5 km to the east
Rohit starts from Point A and drives 9 km towards East. He then takes a right turn, drives 6 km, turns left and drives 7 km. He then takes a right turn and drives 3 km. He takes a final right turn, drives 16 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90-degree turns only unless specified.)
8 km towards East
8 km towards West
9 km towards North
9 km towards South
8 km towards East
In a certain code language,
A + B means ‘A is the wife of B’
A < B means ‘A is the sister of B’
A ! B means ‘A is the son of B’
A : B means ‘A is the father of B’
Based on the above, how is S related to E if 'S : M < I + L ! E’?
Son's wife's sister
Son's wife's brother
Son's wife's father
Son's wife's mother
Son's wife's sister
Which of the following letter-number clusters will replace the question mark (?) in the given series to make it logically complete?
ASG37, OEU78, CQI119, QCW160, ?
EOK200
FOK201
EOK201
ECK201
EOK200
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statements.
Statements:
All tables are beds.
Some tables are pillows.
All pillows are curtains.
Conclusions:
(I) Some curtains are tables.
(II) Some pillows are beds.
Neither conclusion (I) nor (II) follows.
Both conclusions (I) and (II) follow.
Only conclusion (II) follows.
Only conclusion (I) follows.
Neither conclusion (I) nor (II) follows.
In the following expression, what will be the final value calculated after interchanging all the ‘1’s and ‘2’s?
4 + 2 − 1 + 1 − 2 − 1 + 3 − 4 + 2 + 1 − 6
1
-4
7
-2
1
What should come in place of the question mark (?) in the given series?
13 138 263 327 391 418 ?
427
434
445
463
427
Identify the option that when put in place of the question mark (?) will logically complete the series.












In a row of 17 students facing north, Giyanshi is 9th from the left end. If Uri is 5th to the right of Giyanshi, what is Uri's position from the right end of the line?
1
4
2
3
1
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statements.
Statements:
All hats are roses.
Some drinks are hats.
Conclusions:
(I) All drinks are roses.
(II) Some roses are drinks.
Neither conclusion (I) nor (II) follows.
Only conclusion (II) follows.
Only conclusion (I) follows.
Both conclusions (I) and (II) follow.
Neither conclusion (I) nor (II) follows.
What should come in place of the question mark (?) in the given series?
9 15 23 33 45 ?
57
59
60
58
57
In a certain code language, ‘ROSE’ is coded as ‘2673’ and ‘HERO’ is coded as ‘7136’.
What is the code for ‘H’ in the given code language?
6
7
3
1
6
All 43 people are standing in a row facing North. Munir is 11th from the right end while Dilip is 24th from the left end. How many people are there between Munir and Dilip?
6
7
5
8
6
AYOL is related to ONEC in a certain way based on the English alphabetical order. In the same way, EGAB is related to SVQS. To which of the given options is UZWA related, following the same logic?
IOMR
MORI
MIOR
IORM
IOMR
L, M, N, O, P, Q, and R are sitting around a circular table facing the centre. Only one person sits between P and O when counted from the right of P. Only one person sits between O and N. Only one person sits between P and Q. Only two people sit between R and N. Only one person sits between L and Q. Who sits third to the right of M?
R
L
N
O
R
In a certain code language, ‘MINE’ is coded as ‘3591’ and ‘IRKS’ is coded as ‘2436’. What is the code for ‘I’ in the given code language?
2
5
6
3
2
This question is based on the five, three-digit numbers given below.
(Left) 430 284 491 231 487 (Right)
(Example- 697 – First digit = 6, second digit = 9 and third digit = 7)
NOTE - All operations to be done from left to right. What will be the resultant if the second digit of the highest number is added to the second digit of the lowest number?
7
9
12
6
7
What will come in place of the question mark (?) in the following equation if ‘+’ and ‘–‘ are interchanged and ‘×’ and ‘÷′ are interchanged?
200 × 5 ÷ 14 − 41 + 18 = ?
583
612
590
609
583
What is the percentage of urban population of India according to the 2011 Census?
35.16%
41.16%
25.16%
31.16%
35.16%
Who was the king of Jagdishpur during the Revolt of 1857?
Tatya Tope
Kunwar Singh
Bahadur Shah Zafar
Hukum Singh
Tatya Tope
Which of the following is a government scheme for rural employment in India?
Skill India
Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA)
Swachh Bharat Mission
Ayushman Bharat
Skill India
During winter months, dry continental winds from Central Asia primarily come in contact with trade winds over which of the following regions of India?
Northeastern India
Eastern India
Northwestern India
Southern India
Northeastern India
To which of the following countries did Nana Saheb flee after being defeated in the Revolt of 1857?
Burma
China
Sri Lanka
Nepal
Burma
Which of the following is the primary objective of the Boiler Act, 2024?
Promote renewable energy use in industries
Provide subsidies for boiler manufacturing
Increase the export of boilers
Establish stricter safety standards for boiler operations
Promote renewable energy use in industries
During whose tenure as the Viceroy of India was the first session of the Indian National Congress held?
Lord Ripon
Lord Dufferin
Lord Curzon
Lord Lytton
Lord Ripon
What is the composition of a Lok Adalat?
A Lok Adalat consists of a judicial officer and two lawyers.
A Lok Adalat consists of a judicial officer, a lawyer and a social worker.
A Lok Adalat consists of only the judicial officer.
A Lok Adalat consists of a judge and a group of legal experts.
A Lok Adalat consists of a judicial officer and two lawyers.
Which of the following countries won the maximum number of medals at Paris 2024 Olympics?
Great Britain
USA
France
People's Republic of China
Great Britain
The Vichitra Veena has about how many sympathetic strings of varying lengths which run parallel to and under the main strings?
12
16
14
10
12
Which economist's ideas had a strong influence on the agricultural and industrial focus of the Second Five Year Plan?
PC Mahalanobis
Manmohan Singh
Amartya Sen
Jagdish Bhagwati
PC Mahalanobis
Which body has the constitutional mandate to investigate all matters relating to the safeguards provided for Scheduled Castes under the Constitution?
Election Commission of India
National Commission for Minorities
National Commission for Scheduled Castes
National Human Rights Commission
Election Commission of India
The political landscape in India fundamentally changed as a result of the fourth general election held in the year _____.
1961
1977
1967
1972
1961
The coastal strip between Daman and Goa is called the:
Coromandel Coast
Karnataka Coast
Konkan Coast
Malabar Coast
Coromandel Coast
Efficiency of Carnot engine can be increased by:
decreasing the amount of working substance
increasing the amount of working substance
decreasing the sink temperature
increasing the sink temperature
decreasing the amount of working substance
Where was the IBSF World Billiards Championship 2024 held?
Doha, Qatar
Amman, Jordan
Abu Dhabi, United Arab Emirates
Damascus, Syria
Doha, Qatar
Tuzuk-i-Baburi was written in which language?
Turkish
Urdu
Hindi
Sanskrit
Turkish
Which Indian sand artist won the Golden Sand Master Award at the International Sand Sculpture Championship held at St. Petersburg city of Russia in July 2024?
Manas Kumar Sahoo
Sudarsan Pattnaik
Manisha Swarnkar
Rajat Kumar
Manas Kumar Sahoo
In June 2024, the Indian Army opened the Khalubar War Memorial for tourists located in which State or Union Territory?
Jammu and Kashmir
Goa
Ladakh
Uttarakhand
Jammu and Kashmir
Provision for the Administration and Control of Scheduled Areas and Scheduled Tribes is mentioned under which of the following schedules?
Sixth Schedule, Part A
Sixth Schedule, Part B
Fifth Schedule, Part B
Fifth Schedule, Part A
Sixth Schedule, Part A
Union Finance Minister, while presenting Union Budget for 2022-23, announced the National Ropeways Development Programme, which is known as ______________.
Vishwamala
Parikrammala
Parvatmala
Darshanmala
Vishwamala
In India, dryland farming is primarily practiced in regions with which of the following annual rainfall levels?
Between 75 and 90 cm
More than 120 cm
Between 90 and 120 cm
Less than 75 cm
Between 75 and 90 cm
In October 2024, the Union Cabinet approved giving the status of 'classical language' to how many languages?
3
9
5
7
3
Which of the following changes was proposed in the 2024 Budget to benefit employees’ social security through the National Pension Scheme (NPS) as per Budget 2024?
Decrease employer contribution from 14% to 10%
Decrease employee contribution from 14% to 10%
Increase employer contribution from 10% to 14%
Increase employee contribution from 10% to 14%
Decrease employer contribution from 14% to 10%
Which sector is primarily involved in agriculture and natural resource extraction?
Primary
Secondary
Quaternary
Tertiary
Primary
The British response after the Indian Rebellion of 1857 was to:
all the princely states were annexed under British rule
immediately grant India self-rule
provide economic aid to Indian farmers
community, caste, tribal and provincial loyalties were promoted in the army
all the princely states were annexed under British rule
Which of the following is correct about Specific heat capacity of water?
The specific heat of water remains constant in the temperature range 0°C to 100°C.
The specific heat of water varies slightly with temperature.
With rise in temperature from 0°C, it increases.
With rise in temperature from 0°C, it decreases.
The specific heat of water remains constant in the temperature range 0°C to 100°C.
The charge of two H+ ions is ________.
−1.6 × 10-19 C
+3.2 × 10-10 C
+3.2 × 10-19 C
−1.6 × 10-19 C
What is the maximum limit for a contactless payment transaction using a debit or credit card in India as of 2024?
₹1,000
₹500
₹5,000
₹10,000
₹1,000
Consider an ideal gas system. For an exothermic reaction occurring at constant pressure, how does the enthalpy change?
Path dependent
Zero
Positive
Negative
Path dependent
The Deccan Plateau is mostly composed of:
alluvial soil
limestone and sandstone
granite and basalt
pumice and red soil
alluvial soil
Which Five Year Plan is often associated with a 'Rolling Plan' concept due to political changes?
Fourth Plan
Fifth Plan
Sixth Plan
Eighth Plan
Fourth Plan
Which of the following parts of the Indian Constitution contains Articles 239 to 241 that deals with union territories?
Part X
Part VII
Part IX
Part VIII
Part X
Jamshedpur is an ideal location for which of the following types of industries?
Cotton Textile Industry
Dairy Industry
Iron and Steel Industry
Paper and Pulp Industry
Cotton Textile Industry
Ajanta, which is located in Aurangabad district of Maharashtra, is famous for which of the following monuments of Buddhist architecture?
Stambhas
Caves
Viharas
Stupas
Stambhas
Which company launched Topaz BankingSLM and Topaz ITOpsSLM in October 2024, using the NVIDIA AI Stack for enterprise AI?
Wipro
Mphasis Limited
Infosys
Tech Mahindra
Wipro
Which Schedule of the Indian Constitution contains the list of recognised languages in India?
Eighth Schedule
Ninth Schedule
Tenth Schedule
Eleventh Schedule
Eighth Schedule
‘Providing early childhood care and education to all children until they complete the age of 6 years’ belongs to which Section of the Indian Constitution?
Fundamental Rights
Fundamental Duties
Legal responsibilities
Directive Principles of State Policy
Fundamental Rights
Read the following statements carefully and select the correct option regarding their correctness.
Statement I: ‘Project Tiger’ is a Centrally Sponsored Scheme (CSS) of the Ministry of Environment, Forests and Climate Change.
Statement II: The National Tiger Conservation Authority (NTCA) has been fulfilling its mandate of strengthening tiger conservation in the country within the ambit of the Wildlife (Protection) Act 1972.
Statement I is incorrect, while Statement II is correct.
Statement I is correct, while Statement II is incorrect.
Both Statement I and Statement II are correct.
Both Statement I and Statement II are incorrect.
Statement I is incorrect, while Statement II is correct.
The kinetic energy of a particle depends on which of the following?
Both mass and velocity of the particle
Both mass and acceleration of the particle
Only velocity of the particle
Only mass of the particle
Both mass and velocity of the particle
As of October 2024, the highest GST collection of ₹2.10 lakh crore was recorded in ______________.
October 2024
July 2024
August 2024
April 2024
October 2024
Who was the ruler of Delhi when Babur invaded?
Mahmud Lodi
Ibrahim Lodi
Sikandar Lodi
Daulat Khan Lodi
Mahmud Lodi
As per the 'State of Economy' report in the RBI bulletin, in H1 FY25, what fraction of the gross FDI inflows was sourced from Singapore, Mauritius, the UAE, the Netherlands and the US?
Three-fourths
One-third
Half
Two-thirds
Three-fourths
Vijay Kumar N was honoured with the Sangeet Natak Akademi Yuva Puraskar (2008) for his contribution to _________ dance.
Bharatanatyam
Odissi
Kathakali
Kathak
Bharatanatyam
By how much percentage did HDFC Bank's net profit grow year-on-year (Y-o-Y) in Q2 FY25?
10%
5.3%
4%
15%
10%
Within which dates of December every year, Konark experiences a surge of tourists and art enthusiasts alike, to envision the biggest and the grandest of dance festivals in the state of Odisha?
6th to 10th
1st to 5th
15th to 20th
10th to 15th
6th to 10th
The establishment of how many Artificial Intelligence Centres of Excellence (AI-COEs) (focused on health, agriculture, and sustainable cities) were announced by Union Education Minister Dharmendra Pradhan in October 2024?
Five
Two
Seven
Three
Five
__________ has the power to amend the Constitution of India.
The Election Commission of India
The Prime Minister of India
The President of India
The Parliament of India
The Election Commission of India
Who is the director of the Kannada film ‘Kantara’, which won the award for Best Popular Film Providing Wholesome Entertainment at the 70th National Film Award 2024?
Rohit Shetty
Raj B Shetty
Rishab Shetty
Rakshit Shetty
Rohit Shetty
Which of the following are the types of Rural Development Strategies?
Only 2 and 3
Only 1 and 3
1, 2 and 3
Only 1 and 2
Only 2 and 3
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