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11. If 2 [3] 4 = 14 and 3 [4] 6 = 60, then 4 [5] 7 = ?

If 2 [3] 4 = 14 and 3 [4] 6 = 60, then 4 [5] 7 = ?

108

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Let the operation a [b] c produce the result R.
Case 1: 2 [3] 4 = 14. Here a=2, b=3, c=4, R=14.
Case 2: 3 [4] 6 = 60. Here a=3, b=4, c=6, R=60.
We need to find the result for 4 [5] 7 = ?, where a=4, b=5, c=7.

Let’s test the formula R = (a * b + a * c) * (a-1).
For Case 1 (a=2, b=3, c=4): (2*3 + 2*4) * (2-1) = (6 + 8) * 1 = 14 * 1 = 14. This matches the given result.
For Case 2 (a=3, b=4, c=6): (3*4 + 3*6) * (3-1) = (12 + 18) * 2 = 30 * 2 = 60. This matches the given result.

Now apply the formula to the third case (a=4, b=5, c=7):
R = (4*5 + 4*7) * (4-1) = (20 + 28) * 3 = 48 * 3 = 144.
This result (144) is not among the options.

Let’s try another possible pattern based on the values. Consider the formula R = (a*b + a*c) + (a-2)*30.
For Case 1 (a=2, b=3, c=4): (2*3 + 2*4) + (2-2)*30 = (6 + 8) + 0*30 = 14 + 0 = 14. This matches.
For Case 2 (a=3, b=4, c=6): (3*4 + 3*6) + (3-2)*30 = (12 + 18) + 1*30 = 30 + 30 = 60. This matches.

Now apply this formula to the third case (a=4, b=5, c=7):
R = (4*5 + 4*7) + (4-2)*30 = (20 + 28) + 2*30 = 48 + 60 = 108.
This result (108) is present in option D. This pattern appears consistent with the given examples and options.

The rule is a [b] c = (a * b + a * c) + (a – 2) * 30.

– Identify the mathematical operation or pattern relating the three numbers to the result.
– Test the derived pattern with all given examples.
– Apply the confirmed pattern to find the missing value.

Number puzzles like this require careful observation and testing of various arithmetic and algebraic combinations of the given numbers. Common patterns involve sums, differences, products, quotients, powers, and combinations thereof, often applied in a consistent way across the examples.

12. Match List I with List II and select the correct answer using the code

Match List I with List II and select the correct answer using the code given below the Lists :

List I (River)	List II (Location in map)
A. Penner	1
B. Vaigai	2
C. Cauvery	3
D. Krishna	4

A-2, B-4, C-3, D-1

A-1, B-3, C-4, D-2

A-2, B-3, C-4, D-1

A-1, B-4, C-3, D-2

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Without a map showing the specific locations 1, 2, 3, and 4, we assume they represent relative positions, likely from North to South, as these are major South Indian rivers. The approximate North-to-South order of these rivers is Krishna (mostly north), Penner (south of Krishna), Cauvery (south of Penner and Krishna), and Vaigai (mostly south in Tamil Nadu).
Assuming locations 1, 2, 3, and 4 represent this North-to-South sequence:
Location 1: Krishna (D)
Location 2: Penner (A)
Location 3: Cauvery (C)
Location 4: Vaigai (B)
Matching the rivers from List I with the locations from List II based on this assumption:
A. Penner matches location 2 (A-2).
B. Vaigai matches location 4 (B-4).
C. Cauvery matches location 3 (C-3).
D. Krishna matches location 1 (D-1).
This pairing corresponds to option A: A-2, B-4, C-3, D-1.

– The relative geographical positions of the rivers from North to South are Krishna, Penner, Cauvery, Vaigai.
– Assuming the locations 1, 2, 3, 4 follow this North-to-South order allows for matching.

The Krishna River flows through Maharashtra, Karnataka, Telangana, and Andhra Pradesh. The Penner River flows through Karnataka and Andhra Pradesh. The Cauvery River flows through Karnataka and Tamil Nadu. The Vaigai River flows through Tamil Nadu. Their basins are located in distinct regions of South India, primarily in the Deccan Plateau and the Eastern Ghats.

13. Match List I with List II and select the correct answer using the code

Match List I with List II and select the correct answer using the code given below the Lists :

List I (Landform)	List II (Agent)
A. Loess	1. Wind deposited
B. Tombolo	2. Glacier deposited
C. Point bars	3. River deposited
D. Moraines	4. Sea deposited

Code :

1 4 3 2

1 3 4 2

2 3 4 1

2 4 3 1

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The correct matching of landforms with the agents responsible for their deposition is as follows:
A. Loess is a fine, unconsolidated deposit of wind-blown silt, hence it is wind deposited. (Matches with 1)
B. A Tombolo is a spit or bar that connects an island to the mainland or to another island, typically formed by wave action and deposition in the sea. (Matches with 4)
C. Point bars are crescent-shaped accumulations of sand and gravel deposited on the inside bend of a meandering river. They are formed by river deposition. (Matches with 3)
D. Moraines are accumulations of glacial debris (till) deposited by a glacier, typically forming ridges, mounds, or plains. They are glacier deposited. (Matches with 2)
Thus, the correct code is A-1, B-4, C-3, D-2.

– Loess is an aeolian (wind-driven) deposit.
– Tombolos are coastal features formed by marine deposition.
– Point bars are fluvial features formed by river deposition.
– Moraines are glacial features formed by glacial deposition.

Landforms are natural features of the solid surface of the Earth. Geomorphic agents like wind, water (rivers, seas), and ice (glaciers) are responsible for the erosion, transportation, and deposition of material, leading to the formation of various landforms.

14. Which one of the following represents the inner planets ?

Which one of the following represents the inner planets ?

Planets between the sun and the earth

Planets between the sun and the belt of asteroids

Planets near the earth

Planets around the sun

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The solar system is broadly divided into inner and outer planets, separated by the asteroid belt. The inner planets are the four planets closest to the Sun: Mercury, Venus, Earth, and Mars. These are also known as terrestrial planets due to their rocky composition. The outer planets are Jupiter, Saturn, Uranus, and Neptune, which are gas giants. Therefore, the inner planets are located between the Sun and the belt of asteroids.

– Inner planets are Mercury, Venus, Earth, and Mars.
– The asteroid belt lies between Mars and Jupiter.
– Inner planets are located closer to the Sun than the asteroid belt.

The inner planets are smaller, denser, and have solid surfaces compared to the outer gas giants. The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Mars and Jupiter, that is occupied by a great many irregularly shaped bodies called asteroids or minor planets.

15. Who among the following were jailed in the Kanpur Bolshevik conspiracy

Who among the following were jailed in the Kanpur Bolshevik conspiracy case in 1924 ?

Muzaffar Ahmad, S. A. Dange, Shaukat Usmani, Nalini Gupta

Muhammad Ali and Shaukat Usmani

S. A. Dange and S. V. Ghate

Muzaffar Ahmad and S. S. Mirajkar

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The Kanpur Bolshevik conspiracy case in 1924 was a controversial trial initiated by the British government against early communist leaders in India. The main individuals accused and subsequently jailed in this case were Muzaffar Ahmad, S. A. Dange, Shaukat Usmani, and Nalini Gupta. These individuals were pioneers of the communist movement in India and were charged with conspiracy to wage war against the King-Emperor.

– The case targeted prominent early communists in India.
– The objective was to suppress the burgeoning communist movement.

Several other individuals were named in the FIR but were not arrested or tried, including M.N. Roy. The case brought national attention to the communist movement and its leaders, despite being seen by many as a politically motivated trial intended to curb anti-colonial activities linked to socialist or communist ideas.

16. The Sufi work Kashf-ul-Mahjub was written by

The Sufi work Kashf-ul-Mahjub was written by

Abu'l Hasan al Hujwiri

Moinuddin Chishti

Shaikh Nizamuddin Auliya

Amir Khusrau

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The correct answer is A) Abu’l Hasan al Hujwiri.

The Sufi work ‘Kashf-ul-Mahjub’ (meaning ‘Revelation of the Veiled’ or ‘Unveiling of the Hidden’) is a celebrated classic of Sufi literature. It was written by Abu’l Hasan al Hujwiri, also known as Ali Hujwiri or Data Ganj Bakhsh. He was a 10th/11th-century Persian Sufi scholar and theologian from Ghazni who traveled widely before settling in Lahore, where his shrine is located. ‘Kashf-ul-Mahjub’ is considered one of the earliest and most comprehensive formal treatises on Sufism in Persian.

The other options are prominent Sufi figures, but they are not the author of ‘Kashf-ul-Mahjub’:
– Moinuddin Chishti is the founder of the Chishti order in India.
– Shaikh Nizamuddin Auliya was a prominent saint of the Chishti order in Delhi.
– Amir Khusrau was a renowned poet, musician, and scholar, and a disciple of Nizamuddin Auliya.

‘Kashf-ul-Mahjub’ discusses various aspects of Sufism, including its principles, practices, different schools of thought, and biographies of earlier Sufi saints. It has been an influential text in the development of Sufism, particularly in the Indian subcontinent after Hujwiri settled in Lahore.

17. Which one of the following musicians served at the courts of Raja Man

Which one of the following musicians served at the courts of Raja Man Singh Tomar and Bahadur Shah of Gujarat ?

Baiju Bawra

Tansen

Lal Kalawant

Rang Khan Kalawant

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The correct answer is A) Baiju Bawra.

Raja Man Singh Tomar of Gwalior (ruled c. 1486-1516) was a renowned patron of music, particularly the Dhrupad style. Gwalior was a significant center of music during his reign. Baiju Bawra is a legendary figure strongly associated with Gwalior and the court of Raja Man Singh Tomar. Historical accounts and popular legends also link Baiju Bawra to the court of Bahadur Shah of Gujarat (ruled 1526-1535, 1536-1537), mentioning his musical prowess in both regions.

While Tansen (initially named Ramtanu Pandey) was also trained in Gwalior and likely started his career in regional courts (like Rewa), his most famous association was with the court of Emperor Akbar. Lal Kalawant and Rang Khan Kalawant are names associated with the Kalawant lineage of musicians but are not as prominently linked to the courts of both Man Singh Tomar and Bahadur Shah as Baiju Bawra is in historical accounts and legends.

Baiju Bawra is considered one of the giants of Indian classical music during the medieval period. His legacy is particularly strong in the Dhrupad tradition. Legends often portray him as a contemporary or rival of Tansen, showcasing his extraordinary musical abilities through various anecdotal stories.

18. Which of the following are the essential requirements for a person to

Which of the following are the essential requirements for a person to be appointed as a member of Finance Commission?

1. A Supreme Court judge or one qualified to be appointed as such
2. A person having wide experience in financial matters and administration
3. A person having special knowledge of economics

Select the correct answer using the code given below :

1, 2 and 3

1 and 2 only

2 and 3 only

1 and 3 only

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The correct answer is C) 2 and 3 only.

Article 280 of the Indian Constitution deals with the Finance Commission. Article 280(2) states that Parliament may by law determine the qualifications for appointment as members of the Commission.
The Finance Commission (Miscellaneous Provisions) Act, 1951 lays down these qualifications. It states that the Chairman should be a person who has had experience in public affairs. The other four members shall be selected from among persons who are:
1. a Judge of a High Court or one who is qualified to be appointed as a Judge of a High Court;
2. persons who have special knowledge of the finances and accounts of Government;
3. persons who have had wide experience in financial matters and in administration;
4. persons who have special knowledge of economics.

Let’s check the given statements against these qualifications:
1. A Supreme Court judge or one qualified to be appointed as such. The Act specifies High Court judge or qualified to be High Court judge. This statement is incorrect as it mentions Supreme Court instead of High Court.
2. A person having wide experience in financial matters and administration. This matches qualification number 3 in the Act. This statement is correct.
3. A person having special knowledge of economics. This matches qualification number 4 in the Act. This statement is correct.

Based on the Finance Commission (Miscellaneous Provisions) Act, 1951, statements 2 and 3 describe essential requirements for members (other than the Chairman). Statement 1 is inaccurate regarding the court level specified in the Act.

The Finance Commission is a constitutional body constituted every five years by the President of India to recommend the distribution of financial resources between the Union and the States, and between the States themselves. The composition and qualifications of its members are determined by Parliament.

19. If 5472 = 9, 6342 = 6 and 7584 = 6, then what is 9236 ?

If 5472 = 9, 6342 = 6 and 7584 = 6, then what is 9236 ?

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The correct answer is A) 2.

We need to find the pattern connecting the four-digit numbers on the left side of the equality and the single-digit numbers on the right side. Let’s examine the given examples:
1) 5472 = 9
Let’s try operations on the digits: 5, 4, 7, 2.
Sum of digits: 5 + 4 + 7 + 2 = 18. The result is 9. The digital root of 18 (1+8) is 9.
2) 6342 = 6
Digits: 6, 3, 4, 2.
Sum of digits: 6 + 3 + 4 + 2 = 15. The result is 6. The digital root of 15 (1+5) is 6.
3) 7584 = 6
Digits: 7, 5, 8, 4.
Sum of digits: 7 + 5 + 8 + 4 = 24. The result is 6. The digital root of 24 (2+4) is 6.

The pattern appears to be calculating the sum of the digits of the number and then finding the digital root (summing digits repeatedly until a single digit is obtained).

Now, apply this pattern to the number 9236:
Sum of digits: 9 + 2 + 3 + 6 = 20.
Find the digital root of 20: 2 + 0 = 2.

Therefore, 9236 = 2 based on the established pattern.

Such coding or pattern recognition problems in aptitude tests often involve simple arithmetic operations on the digits, their positions, or groups of digits. Digital root is a common pattern used.

20. When the digits of two-digit numbers are reversed, the number increase

When the digits of two-digit numbers are reversed, the number increases by 27, the sum of such two-digit numbers is

235

249

213

180

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The correct answer is B) 249.

Let the two-digit number be represented as 10t + u, where t is the tens digit (t ∈ {1, 2, …, 9}) and u is the units digit (u ∈ {0, 1, …, 9}).
When the digits are reversed, the new number is 10u + t.
The problem states that the number increases by 27 when the digits are reversed.
So, (10u + t) – (10t + u) = 27.
10u + t – 10t – u = 27
9u – 9t = 27
9(u – t) = 27
u – t = 3.
This condition means the units digit is 3 greater than the tens digit. We need to find all two-digit numbers (10t + u) that satisfy this condition, keeping in mind the constraints on t and u.
Possible pairs (t, u) where u – t = 3:
– If t = 1, u = 1 + 3 = 4. The number is 14. Reversed: 41 (41 – 14 = 27). Valid.
– If t = 2, u = 2 + 3 = 5. The number is 25. Reversed: 52 (52 – 25 = 27). Valid.
– If t = 3, u = 3 + 3 = 6. The number is 36. Reversed: 63 (63 – 36 = 27). Valid.
– If t = 4, u = 4 + 3 = 7. The number is 47. Reversed: 74 (74 – 47 = 27). Valid.
– If t = 5, u = 5 + 3 = 8. The number is 58. Reversed: 85 (85 – 58 = 27). Valid.
– If t = 6, u = 6 + 3 = 9. The number is 69. Reversed: 96 (96 – 69 = 27). Valid.
– If t = 7, u = 7 + 3 = 10 (not a single digit). So, we stop here.
The two-digit numbers that satisfy the condition are 14, 25, 36, 47, 58, and 69.
The sum of these numbers is 14 + 25 + 36 + 47 + 58 + 69.
Sum = (10+4) + (20+5) + (30+6) + (40+7) + (50+8) + (60+9)
Sum = (10+20+30+40+50+60) + (4+5+6+7+8+9)
Sum = 210 + 39 = 249.
Alternatively, Sum = (14 + 69) + (25 + 58) + (36 + 47) = 83 + 83 + 83 = 3 * 83 = 249.

Problems involving two-digit numbers and reversed digits often lead to simple linear equations relating the tens and units digits, typically involving a multiple of 9.