The sum of the angles of a triangle is 180°. If the ratio of the angles is 1:2:3, then the angles are 180° * (1/6), (2/6), and (3/6). The smallest angle = 180° * (1/6) = 30°.

‘Operation Blue Star’ in 1984 was a controversial military action aimed at removing Sikh militants who had taken up residence in the Golden Temple in Amritsar, Punjab. The operation was ordered by then Prime Minister Indira Gandhi and resulted in heavy casualties. It led to widespread protests and had significant political repercussions, including the assassination of Indira Gandhi.

Volume of the tank = πr²h = π * 14² * 40 cm³. Convert this volume to liters (1 liter = 1000 cm³). The rate of flow = 2 liters/minute. Find the time to fill = Volume / Rate. Solving gives approximately 45 minutes.

‘Dogmatism’ is the correct answer. It refers to the tendency to lay down principles as incontrovertibly true, without consideration of evidence or the opinions of others. This term is often associated with a stubborn assertion of opinion over open-minded discussion. Unlike ‘Empiricism’ which relies on sensory experience, ‘Skepticism’ which doubts accepted beliefs, or ‘Pragmatism’ that focuses on practical results, dogmatism implies a rigid adherence to beliefs.

“The applications will be reviewed by the committee” is correct. It converts the future tense active voice into the future passive voice while keeping the original meaning.

The assumption is that global communication is dependent on the internet. The argument suggests that improving internet infrastructure will enhance global communication, implying that the internet is a key medium for such communication.

“New techniques are being developed by researchers” is correct. It uses the present continuous passive voice, reflecting the ongoing action in the active sentence.

“Groundbreaking” is the correct choice, meaning innovative and pioneering, especially in being the first of a kind. It fits the context of findings that contradict previous theories and introduce new perspectives. Example: “The groundbreaking research opened new avenues in neuroscience.”

Interest = ₹9200 – ₹8000 = ₹1200. Rate = (Interest / Principal) * (100 / Time) = (1200 / 8000) * (100 / 3) ≈ 5%.

Commission = 20% of ₹5000 = ₹1000. Basic salary + Commission = ₹5000 + ₹1000 = ₹6000. Bonus = 10% of ₹6000 = ₹600. Total salary = ₹6000 + ₹600 = ₹6600.

‘Celestial’ is the correct spelling for something related to the sky or heaven. The term is often used to describe heavenly bodies (like stars, planets, etc.) or the divine. The other options, ‘Celesstial’, ‘Selestial’, and ‘Celesstail’, are incorrect spellings.

“A new sculpture will be unveiled by the artist at the gallery” is the correct passive form. The future tense ‘will unveil’ becomes ‘will be unveiled’ in the passive voice. Example: “A new exhibit will be opened by the museum next month.”

The passage indicates that e-commerce offers consumers the ability to shop from anywhere and provides convenience and a wider range of options, making “Both B and C” the correct answer.

‘Byzantine’, when used to describe something other than the historical empire, often refers to a system or situation that is excessively complicated, and typically involves a great deal of administrative detail. The correct answer is ‘Complex and intricate’, implying a level of complexity and convolution often associated with bureaucracy. ‘Straightforward’, ‘Simple’, and ‘Clear’ are antonyms and would not describe something ‘Byzantine’.

According to the triangle inequality theorem, the third side must be less than the sum of the other two sides and greater than their difference. The largest integer less than 7 + 24 = 31, and greater than 24 – 7 = 17, is 31 cm.

The perimeter of a semi-circle = πr + 2r (half the circumference plus the diameter). So, 3.14r + 2r = 36. Solving for r gives r ≈ 7 cm.

The passage specifically states that artificial intelligence in healthcare enables personalized treatment plans and predictive diagnostics, both of which improve patient outcomes, making “Both B and C” the correct answer.

‘Carbon Capture and Storage (CCS)’ technologies are significant in sustainable development for their ability to capture carbon dioxide emissions and store them, thereby mitigating climate change impacts. CCS technologies are used in large-scale emission sources like power plants and industrial processes, reducing the amount of CO2 released into the atmosphere, a crucial step in addressing global warming.

Let the sum invested at 5% be x. Then, the sum invested at 4% is ₹20,000 – x. The total interest = ₹850 = 5% of x + 4% of (₹20,000 – x). Solving for x gives x = ₹11,000.

The Simon Commission, appointed in 1927, was boycotted by Indian political leaders because it did not include any Indian members. The commission was seen as a symbol of British insensitivity to Indian demands, leading to widespread protests and the famous slogan “Simon Go Back.” The commission’s lack of Indian representation significantly undermined its credibility and fueled the Indian independence movement.

The assumption is that parks are beneficial for community well-being. The argument suggests that building more parks will lead to an enhancement in community well-being, implying that parks contribute positively to this aspect.

Using personal anecdotes instead of data represents the ‘Anecdotal Evidence’ fallacy, where personal stories are used in place of solid evidence or logical reasoning.

‘Cacophony’ refers to a harsh, discordant mixture of sounds. It is used to describe a situation where there is a jarring, unpleasant noise that lacks harmony. ‘Dissonance’ is the closest in meaning, indicating a lack of harmony and the presence of conflicting or clashing sounds. ‘Harmony’, ‘Melody’, and ‘Rhythm’ suggest musical coherence, which is the opposite of cacophony.

“A group of students is discussing the project” is correct. “A group” is singular, so it takes the singular verb “is.”

In a right-angled triangle (ΔABC with ∠B = 90°), by Pythagoras theorem, BC² = AC² – AB² = 15² – 9² = 225 – 81 = 144. Therefore, BC = √144 = 12 cm.

The ‘Bhagavad Gita’ is a 700-verse Hindu scripture that is part of the Indian epic Mahabharata. It is a conversation between prince Arjuna and the god Krishna, who serves as his charioteer. It addresses the moral and philosophical dilemmas faced by Arjuna on the battlefield.

When A reaches the finishing line, B has run 100 – 20 = 80 meters. The time taken by A to finish the race = 100/5 = 20 seconds. In 20 seconds, B runs 20 * 4 = 80 meters. So, A overtakes B 20 meters from the finishing line.

The relative speed with respect to the first person = (Speed of train – 2) km/hr. Since speed = distance/time, the length of the train = (Speed of train – 2) * 5/18 * 9 meters. Similarly, with respect to the second person, length = (Speed of train – 4) * 5/18 * 10 meters. Equating both and solving gives the length of the train ≈ 55 meters.

Surface area of the sphere = 4πr² = 4 * 22/7 * 7 * 7 cm². Surface area of the cube = 6 * side². Equating the two and solving for the side of the cube gives side ≈ 21 cm.

‘Oak’ is the odd one out as it is a tree, whereas Sunflower, Rose, and Tulip are all types of flowers.

The Ramsar Convention, an international treaty for wetland conservation, was signed in the Iranian city of Ramsar in 1971. This convention is aimed at conserving and using wetlands in a sustainable manner. It recognizes the ecological importance of wetlands as habitats for a wide range of flora and fauna, their role in hydrological cycles, and their significance for human communities. Countries that are parties to the convention commit to maintaining the ecological character of their wetlands of international importance.

‘Waste-to-Energy Technologies’ are significantly impacting waste management and energy production by converting waste materials into renewable energy. This approach reduces landfill use and generates energy from resources that would otherwise be wasted. Waste-to-energy methods, such as incineration or anaerobic digestion, provide a dual benefit of managing waste and contributing to renewable energy generation.

Both solutions should be considered. Solution A excels in cost-effectiveness and efficiency, while Solution B brings innovation. A blend or reassessment of both could provide a balanced approach.

Let the original price be ₹100. The new price is ₹125. To keep expenditure the same, the reduction in consumption should be such that 125% of the new consumption equals 100%. The new consumption must be 100/125 = 80% of the original, indicating a 20% reduction.

The Dandi March, led by Mahatma Gandhi in 1930, was primarily against the British monopoly on salt. This non-violent protest was part of the larger Civil Disobedience Movement against British rule. The Salt Law imposed by the British prohibited Indians from collecting or selling salt, forcing them to buy it from the British at a high price. Gandhi’s march from Sabarmati Ashram to Dandi and the act of making salt from seawater were symbolic challenges to this unjust law, galvanizing widespread support across India for the independence movement.

Merging the best elements of both solutions leverages the strengths of each, demonstrating a critical thinking approach that values comprehensive solutions.

Let the shares of A, B, and C be 2x, 3x, and 5x, respectively. Since B gets ₹3000 more than A, 3x – 2x = ₹3000, so x = ₹3000. C’s share = 5x = 5 * ₹3000 = ₹15,000.

Bonus = 20% of ₹10,000 = ₹2,000. So, basic salary + bonus = ₹10,000 + ₹2,000 = ₹12,000. Commission = 5% of ₹12,000 = ₹600. Therefore, total salary = ₹12,000 + ₹600 = ₹12,600.

“Not only does he play the guitar, but he also sings” is correct. It uses the correlative conjunctions “not only… but also” with proper subject-verb agreement.

The coding pattern involves moving each letter one position forward in the alphabet. Thus, ‘SNOW’ is coded as ‘TNPX’.

The perimeter of a square = 4 * side. So, side = 64 / 4 = 16 meters. The diagonal of a square = side * √2 = 16 * √2 meters.

Both the distance flown and the time taken are necessary to calculate the average speed of a flight, as speed is defined as distance divided by time.

The order of finishing is: Jack (first, as he finishes before Maria and after Peter), Maria (second, as she finishes after Jack but before Tom), Tom (third, as he finishes after Maria but before Peter), and Peter (last). Therefore, Jack won the race.

The conclusion is valid. Since all birds fly and a sparrow is a bird, it logically follows that a sparrow can fly.

‘To bite the bullet’ means to endure a painful or otherwise unpleasant situation with courage and without showing fear. This phrase likely originates from the practice of having soldiers bite on a bullet during surgery without anesthetic. It’s about facing hardship head-on, not about avoiding, taking risks, or delaying decisions.

The Indian National Army (INA) in World War II was led by Subhas Chandra Bose. The INA was an armed force formed by Indian nationalists in 1942 in Southeast Asia during World War II. Its aim was to secure Indian independence from British rule. The INA allied with the Axis powers and played a significant role in

‘To hit the nail on the head’ means to describe exactly what is causing a situation or problem. It implies a high degree of accuracy or aptness in making a statement or observation. The phrase is often used when someone has correctly identified the most important aspect of an issue or situation. It’s not about creating problems, starting tasks, or missing the point, but about being accurate and correct.

E is at the far left since B is to the right of E. Given B is also to the left of D, the order is E, B, D, and with C right of A, A and C are the last two in the line, making E the far-left person.

If the cost price is ₹100, the marked price is ₹125. A 10% discount on ₹125 is ₹12.5, so the selling price is ₹112.5. The profit is ₹12.5, which is 12.5% of the cost price.

Area covered by the road parallel to length = 60 * 5 = 300 m². Area covered by the road parallel to breadth = 40 * 5 = 200 m². But the intersection area (5 * 5) is counted twice, so total area = 300 + 200 – 25 = 475 m².