Author name: Umar

This is a classic cube-cutting problem. A large cube is painted on all sides and then cut into 64 smaller, identical cubes. We need to find how many of these smaller cubes have no paint.

• Determine the dimensions: If a large cube is cut into 64 smaller cubes, then the number of smaller cubes along each edge of the large cube is the cube root of 64. The cube root of 64 is 4 (since 4 * 4 * 4 = 64). So, the large cube is a 4x4x4 arrangement of smaller cubes.
• Identify unpainted cubes: Cubes with no paint are those located entirely in the interior of the large cube, not touching any of its original outer surfaces.
• Calculate inner dimensions: To find the dimensions of this unpainted inner core, we subtract 2 from each dimension of the large cube (1 for the layer removed from the front and 1 for the layer removed from the back, similarly for top/bottom and left/right). So, the inner cube's dimensions are (4-2) x (4-2) x (4-2) = 2x2x2.
• Count unpainted cubes: The number of cubes in this inner core is 2 * 2 * 2 = 8.

Options B (27), C (36), and D (32) are incorrect. 27 would be the answer for a 5x5x5 cube (3x3x3 inner core).

The given sequence is 1, 4, 4, 16, 64. We need to identify the pattern to find the next term.

• Let's analyze the relationship between consecutive terms:
• The first term is 1.
• The second term is 4.
• The third term is 4. Notice that the third term is the product of the first and second terms (1 * 4 = 4).
• The fourth term is 16. This is the product of the second and third terms (4 * 4 = 16).
• The fifth term is 64. This is the product of the third and fourth terms (4 * 16 = 64).
• This pattern indicates that each term, starting from the third, is the product of the two preceding terms.
• To find the next term, we multiply the last two terms: 16 * 64 = 1024.

Therefore, the next number in the sequence is 1024. Options A (256), B (512), and D (2048) are incorrect as they do not follow this specific multiplicative pattern.

This question presents a number sequence and asks for the next term. The sequence is 1, 1, 2, 3, 5, 8, 13.

• Upon examining the sequence, we can observe a pattern where each number (after the first two) is the sum of the two preceding numbers. This is known as the Fibonacci sequence.
• Let's verify the pattern:
• 1 + 1 = 2
• 1 + 2 = 3
• 2 + 3 = 5
• 3 + 5 = 8
• 5 + 8 = 13
• To find the next number in the sequence, we apply the same rule to the last two terms: 8 + 13 = 21.

Therefore, the next number in the sequence is 21. Options A (19), C (23), and D (27) do not follow the established Fibonacci pattern and are incorrect distractors.

The square root of a number 'x' is a value 'y' that, when multiplied by itself, gives 'x' (i.e., y * y = x). We need to find the square root of 169.

• We are looking for a number that, when squared, equals 169.
• Let's test the given options:
• A: 11 * 11 = 121 (Incorrect)
• B: 13 * 13 = 169 (Correct)
• C: 17 * 17 = 289 (Incorrect)
• D: 289 is the square of 17, not the square root of 169. This is a common distractor, confusing the square of a number with its square root.

Therefore, the square root of 169 is 13. Knowing common perfect squares is helpful for these types of questions.

This question asks us to find a number when a certain percentage of it is known. We are given that 25% of a number is 20.

• Understanding Percentages: 25% can be expressed as a fraction (1/4) or a decimal (0.25).
• Setting up the equation: Let the unknown number be 'x'. The problem states that 25% of x is 20, which can be written as 0.25 * x = 20.
• Solving for x: To find x, divide 20 by 0.25: x = 20 / 0.25. Alternatively, since 25% is 1/4, if 1/4 of the number is 20, the whole number is 4 times 20.
• Calculation: 20 / 0.25 = 80, or 20 * 4 = 80.

Thus, the number is 80. Options A (60), B (70), and D (90) are incorrect because 25% of these numbers are 15, 17.5, and 22.5 respectively, not 20.

To find the average (or arithmetic mean) of a set of numbers, you sum all the numbers and then divide by the count of the numbers. In this question, we need to find the average of 10 and 20.

• First, sum the numbers: 10 + 20 = 30.
• Next, count how many numbers there are: There are 2 numbers (10 and 20).
• Finally, divide the sum by the count: 30 / 2 = 15.

Therefore, the average of 10 and 20 is 15. Options A (12), C (18), and D (20) are incorrect because they do not represent the correct midpoint or average value between 10 and 20. 12 and 18 are arbitrary values, while 20 is simply one of the numbers, not their average.

This question involves solving a basic linear algebraic equation, 3x = 12. The goal is to find the value of the unknown variable 'x'. In this equation, '3x' means '3 multiplied by x'.

To isolate 'x' and solve the equation, we need to perform the inverse operation of multiplication, which is division. We must divide both sides of the equation by 3 to maintain equality:

• 3x / 3 = 12 / 3
• x = 4

Therefore, option C is the correct answer. If we substitute x=4 back into the original equation, 3 * 4 = 12, which is true. Options A (2), B (3), and D (6) are incorrect because substituting these values into the equation would result in false statements (e.g., 3 * 2 = 6, not 12; 3 * 3 = 9, not 12; 3 * 6 = 18, not 12).

This question asks to identify the 'odd one out' from a list of items, which means finding the item that does not share a common characteristic or category with the others. The items are Gold, Silver, Diamond, and Plastic.

Gold and Silver are precious metals, naturally occurring elements known for their value, luster, and use in jewelry and currency. Diamond is a precious gemstone, a naturally occurring mineral known for its hardness and brilliance. All three (Gold, Silver, Diamond) are valuable natural resources.

Plastic, however, is a synthetic material, an artificial polymer manufactured by humans, not a naturally occurring precious element or mineral. Therefore, Plastic is the odd one out because it belongs to a fundamentally different category of materials compared to the other three natural, precious substances.

This analogy question requires us to identify the relationship between the first pair of words and apply it to the second. The pair Hand: Glove establishes a relationship where a glove is an item of clothing worn directly on the hand, often as a close-fitting covering or first layer for protection or warmth.

Applying this same relationship to Foot: ?, we need to find an item of clothing that is worn directly on the foot in a similar close-fitting manner. A Sock perfectly fits this description, serving as a direct, form-fitting covering for the foot, analogous to how a glove covers a hand. Options B (Shoe), C (Slipper), and D (Sandal) are incorrect because while they are all types of footwear, they are typically worn over a sock or are outer coverings, not the direct, form-fitting layer that a glove or sock represents.

This question asks us to complete an analogy, which requires identifying the relationship between the first pair of words and applying that same relationship to the second pair. The first pair is Book: Reading. The relationship here is that a book is an object whose primary purpose or function is reading.

Following this logic, we need to find the primary purpose or function of a Fork. A fork is a utensil primarily designed and used for the act of eating. Therefore, Eating is the correct answer, as it directly corresponds to the primary function of a fork. Options A (Drawing), B (Writing), and D (Cooking) are incorrect because while a fork might be tangentially involved in cooking, or one could theoretically draw with it, none represent its fundamental and primary purpose in the same way reading is to a book.

To solve this sequence, we need to identify the mathematical rule connecting each number to the next. Let's examine the progression: from 4 to 9, from 9 to 19, and from 19 to 39. The pattern is consistently 'multiply the previous number by 2, then add 1'.

• 4 x 2 + 1 = 9
• 9 x 2 + 1 = 19
• 19 x 2 + 1 = 39

Applying this rule to the last number in the sequence, 39, we perform the calculation: 39 x 2 + 1 = 78 + 1 = 79. Therefore, option B is the correct answer. Options A (59), C (61), and D (81) are incorrect because they do not adhere to the established 'multiply by 2 and add 1' pattern of the sequence.

The given sequence 121, 144, 169, 196 follows a clear mathematical pattern involving perfect squares of consecutive integers. A foundational understanding of squares reveals that 121 is 11 squared (11 x 11), 144 is 12 squared (12 x 12), 169 is 13 squared (13 x 13), and 196 is 14 squared (14 x 14).

To find the next number, we must continue this progression by squaring the next consecutive integer, which is 15. Calculating 15 x 15 yields 225, making option A the accurate answer. Options B (256, which is 16 squared), C (289, which is 17 squared), and D (324, which is 18 squared) are incorrect because while they are perfect squares, they do not maintain the sequential order of the base numbers (11, 12, 13, 14, 15) established in the given series.

Photosynthesis is a vital biochemical process that sustains most life on Earth. Plants, algae, and some bacteria use this process to convert light energy into chemical energy, producing food for themselves and oxygen for other organisms. Understanding the inputs and outputs of photosynthesis is crucial for comprehending basic biology and ecology.

• Carbon dioxide is the correct answer. Plants absorb carbon dioxide from the atmosphere through tiny pores called stomata on their leaves. This gas, along with water absorbed from the soil and energy from sunlight, is used in the chloroplasts to produce glucose (a sugar for energy) and oxygen as a byproduct.
• Helium is an inert gas and plays no role in the biological process of photosynthesis.
• Oxygen is a product of photosynthesis, released by plants into the atmosphere, not taken in for the process itself.
• Hydrogen is a component of water (H2O), which is absorbed by plants, but gaseous hydrogen is not directly taken in for photosynthesis.

Our solar system is home to eight planets, each with unique characteristics, including varying sizes. Understanding the relative sizes of these celestial bodies is a fundamental concept in astronomy. The question asks to identify the largest planet among the given options, which requires basic knowledge of planetary facts.

• Jupiter is the correct answer. It is a gas giant and by far the largest planet in our solar system, both in terms of diameter and mass. Its diameter is approximately 140,000 kilometers (87,000 miles), making it more than twice as massive as all the other planets combined.
• Mercury is the smallest planet in our solar system, significantly smaller than Jupiter.
• Venus is often called Earth's 'sister planet' due to its similar size, but it is still much smaller than Jupiter.
• Earth, our home planet, is the fifth-largest planet but is dwarfed by the immense size of Jupiter.

Plateaus are elevated flatlands, and some of the world's most spectacular examples are found in high-altitude regions. Pakistan's diverse geography includes several impressive plateaus. The question specifically asks for the highest plateau within Pakistan, which is a key geographical feature of the country.

• Deosai Plains is the correct answer. Located in the Gilgit-Baltistan region of Pakistan, the Deosai Plains are one of the highest plateaus in the world, with an average elevation of over 4,000 meters (13,000 feet). It is also a national park, famous for its unique ecosystem and wildlife.
• Fairy Meadows is a beautiful grassland near Nanga Parbat, known for its stunning views, but it is not a plateau and not the highest.
• Tibet refers to the Tibetan Plateau, which is indeed the world's highest and largest plateau, but it is primarily located in China, not Pakistan. While parts of the greater Himalayan region extend into Pakistan, the Deosai Plains are the highest plateau specifically within Pakistan.
• None of the above is incorrect as Deosai Plains is the accurate answer.

Mount Everest, the world's highest peak, presents an immense challenge to mountaineers. Achieving such a feat requires extraordinary skill, endurance, and determination. The question asks about the first Pakistani woman to conquer this formidable mountain, a significant milestone in the country's history of adventure sports.

• Samina Baig is the correct answer. She made history on May 19, 2013, by becoming the first Pakistani woman to successfully summit Mount Everest. Her achievement inspired many and highlighted the potential of women in extreme sports.
• Naila Kiyani is also a notable Pakistani female mountaineer who summited Mount Everest, but she did so in 2023, making her a more recent achiever, not the first.
• Rashida Khan is not widely recognized as a prominent Pakistani female Everest climber.
• None of the above is incorrect because Samina Baig holds the distinction of being the first.

Understanding the capitals of countries is a fundamental aspect of geography. Ukraine is a large country in Eastern Europe, and its capital city holds significant political, economic, and cultural importance. The capital of Ukraine is Kyiv, a historic city located on the Dnieper River.

• Kyiv is the correct answer. It is the largest city in Ukraine, serving as its administrative, cultural, and scientific center for centuries. It is also one of the oldest cities in Eastern Europe, known for its rich history and numerous architectural landmarks.
• Lviv is a major city in western Ukraine, renowned for its well-preserved historic center and cultural heritage, but it is not the capital.
• Odesa is a significant port city on the Black Sea coast, famous for its beaches and 19th-century architecture, but it is not the capital.
• Kharkiv is the second-largest city in Ukraine, located in the northeast, and was the capital of Soviet Ukraine from 1919 to 1934, but it is not the current capital.

The Right to Information (RTI) is a fundamental right in many democratic nations, empowering citizens to access information held by public authorities. In the context of the Indian Constitution, the Right to Information is implicitly derived from Article 19(1)(a), which guarantees the fundamental right to freedom of speech and expression. The Supreme Court of India has consistently interpreted this article to include the right to know and receive information, recognizing that informed citizens are essential for a healthy democracy.

• Article 19th is correct because it encompasses the freedom of speech and expression, from which the right to information is derived.
• Article 12th defines the term 'State' for the purpose of Part III of the Constitution, which deals with Fundamental Rights, but does not directly grant RTI.
• Article 15th prohibits discrimination on grounds of religion, race, caste, sex, or place of birth, unrelated to information access.
• Article 13th deals with laws inconsistent with or in derogation of fundamental rights, not the right to information itself.

FATA (Federally Administered Tribal Areas) merged with Khyber Pakhtunkhwa (KPK) under the 25th Constitutional Amendment. This landmark amendment was passed by the Parliament of Pakistan in May 2018. Its primary objective was to integrate the semi-autonomous tribal region into the mainstream administrative and political structure of Pakistan, extending the jurisdiction of the Supreme Court and High Courts to FATA, and abolishing the colonial-era Frontier Crimes Regulation (FCR). This historic legislative change aimed to bring FATA's population under the regular laws and judicial system, ensuring their fundamental rights and promoting development.

• The 21st Amendment (2015) established military courts for terrorism cases.
• The 22nd Amendment (2016) concerned the appointment of the Chief Election Commissioner.
• The 23rd Amendment (2017) extended the tenure of military courts. None of these relate to FATA's merger.

Pakistan officially became a nuclear state in 1998. On May 28, 1998, Pakistan conducted five simultaneous underground nuclear tests at Ras Koh Hills in the Chagai District of Balochistan. This event, known as "Chagai-I," was a direct response to India's nuclear tests earlier that month. These tests demonstrated Pakistan's nuclear deterrence capability, establishing it as the seventh country in the world to publicly declare and demonstrate its nuclear weapons status, fundamentally altering the strategic landscape of South Asia.

• 1996 and 1997 predate Pakistan's public nuclear tests and declaration of nuclear status.
• 1995 is also incorrect as Pakistan had not yet conducted its nuclear tests in that year. The decision and execution of the tests occurred later in response to regional developments.

The Islamic month called the "month of migration" is Rabi-ul-Awwal. The pivotal event of the Hijra, the migration of Prophet Muhammad (PBUH) and his companions from Mecca to Medina, commenced in the month of Safar, but their arrival in Medina occurred in Rabi-ul-Awwal. This arrival was a momentous occasion, marking the establishment of the first Islamic state and the beginning of the Islamic calendar, making Rabi-ul-Awwal profoundly significant for the consolidation of the Muslim community and the spread of Islam.

• Muharram is the first month of the Islamic calendar, known for the Battle of Karbala, not the Hijra's arrival.
• Ramzan (Ramadan) is the ninth month, revered for fasting, and is not associated with the migration.
• Rajab is the seventh month, known for the Isra and Mi'raj (Night Journey and Ascension), but not the Hijra.

The Labour Party won the most recent United Kingdom general election, held on 4 July 2024. Under the leadership of Sir Keir Starmer, Labour secured a decisive parliamentary majority in the House of Commons, ending the Conservative Party's 14-year period in government. The election resulted in one of Labour's largest victories in modern British political history, enabling the party to form the new government with Keir Starmer becoming the Prime Minister of the United Kingdom.

The 2024 general election focused on key issues such as the economy, the cost-of-living crisis, healthcare, immigration, housing, and public services. Labour campaigned on promises of economic stability, strengthening the National Health Service (NHS), improving education, and promoting sustainable economic growth. The election outcome significantly reshaped the UK's political landscape and remains an important topic in current affairs and competitive examinations, particularly those covering international politics and global events.

Why the other options are incorrect:

• Conservative is incorrect because the Conservative Party lost the 2024 general election after governing the UK since 2010.
• Tories is incorrect because it is another name for the Conservative Party, which did not win the election.
• Whigs is incorrect because the Whig Party was a historical British political party that no longer contests modern UK general elections.

In the Constitution of Pakistan, the Fundamental Rights of citizens are enshrined in Article 8 to Article 28. This specific range falls under Chapter 1 of Part II, titled "Fundamental Rights and Principles of Policy." These articles guarantee essential liberties such as equality before the law, freedom of speech, assembly, association, movement, religion, and the right to property, ensuring that citizens are protected against state infringement and can exercise their basic human rights within the legal framework of the country.

• Article 32-45 primarily covers "Principles of Policy" and parts of "The Federation of Pakistan," which are directives for the state, not enforceable fundamental rights.
• Article 40-60 delves into the structure and powers of the Federation and Parliament, not fundamental rights.
• Article 90-120 pertains to parliamentary procedures and provincial governance, far removed from the section on fundamental rights.

The 18th Constitutional Amendment, passed in 2010, is widely recognized for restoring parliamentary democracy in Pakistan after the era of General Zia-ul-Haq's martial law. General Zia's 8th Amendment had significantly empowered the President, allowing unilateral dissolution of Parliament and weakening the Prime Minister's role. The 18th Amendment reversed these changes, notably by removing the President's power to dissolve the National Assembly (Article 58(2)(b)) and transferring substantial authority back to the Prime Minister, thereby strengthening the parliamentary system and restoring the original spirit of the 1973 Constitution.

• The 7th Amendment is unrelated to this restoration.
• The 8th Amendment, introduced by Zia, actually institutionalized presidential powers and weakened parliamentary democracy, making it the opposite of a restorative measure.
• The 13th Amendment (1997) was a step towards removing presidential powers but the 18th Amendment was the comprehensive overhaul that fully restored parliamentary supremacy.

The Kashmir dispute emerged immediately after the partition of British India in 1947, leading to the first Indo-Pakistani War. Both India and Pakistan claim the entire region of Jammu and Kashmir. India formally brought the Kashmir dispute to the United Nations Security Council on January 1, 1948, under Article 35 of the UN Charter. India accused Pakistan of aiding tribal invaders in Jammu and Kashmir, initiating the UN's involvement and leading to resolutions calling for a ceasefire and a plebiscite, making 1948 the correct answer.

• 1947 was when the dispute originated with partition and conflict, but the formal complaint to the UN occurred the following year.
• 1949 saw a UN-brokered ceasefire already in effect and resolutions passed, but not the initial formal presentation.
• 1950 involved continued UN mediation efforts and implementation of resolutions, but not the first formal submission of the dispute.