Answer key & explanations

Short answers for the sample questions above. Use this to self-check before generating a fresh AI-built mock test.

1. 1. A shopkeeper bought an item for ₹800 and sold it for ₹1000. What is the profit percentage?

   ▶Reveal answer

   25%

   Profit = Selling Price − Cost Price = ₹1000 − ₹800 = ₹200. Profit percentage is always calculated against the cost price, not the selling price: (200 / 800) × 100 = 25%. Using the selling price instead is the most common mistake here, and it would give a different, incorrect answer (20%).

2. 2. Find the value of x if 3x + 7 = 22.

   ▶Reveal answer

   x = 5

   Isolate the term with x first by moving the constant to the other side: 3x = 22 − 7 = 15. Then divide both sides by the coefficient of x: x = 15 / 3 = 5. Always check by substituting back: 3(5) + 7 = 22, which confirms the answer.

3. 3. The speed of light is approximately how many kilometres per second?

   ▶Reveal answer

   About 3,00,000 km/s

   The precise value is 2,99,792 km/s in a vacuum, almost universally rounded to 3 × 10⁵ km/s for quick estimation. This speed is treated as a fixed constant in physics because nothing with mass can travel faster than it, a cornerstone of Einstein's theory of relativity.

4. 4. Which planet in our solar system has the most moons?

   ▶Reveal answer

   Saturn

   Saturn currently holds the record with 146 confirmed moons, recently overtaking Jupiter. The count keeps changing as astronomers discover more small, faint moons using more powerful telescopes, so this kind of fact is worth double-checking periodically rather than treated as permanently fixed.

5. 5. What is the square root of 144?

   ▶Reveal answer

   12

   12 × 12 = 144, so 12 is the square root. Since 144 is a perfect square, its root is a whole number, unlike most numbers, whose square roots are irrational and only estimated with a calculator.

6. 6. 35% of a number is 70. Find the number.

   ▶Reveal answer

   200

   Set up the equation directly from the sentence: let the number be x, so 0.35x = 70. Dividing both sides by 0.35 gives x = 200. This 'work backward from a percentage' setup is the reverse of the far more common 'find X% of a number' question, and it trips students up specifically because the unknown is the whole, not the part.

7. 7. Solve: 5(x − 2) = 3x + 4.

   ▶Reveal answer

   x = 7

   First expand the bracket: 5x − 10 = 3x + 4. Then collect the x terms on one side and constants on the other: 5x − 3x = 4 + 10, giving 2x = 14, so x = 7. Expanding the bracket before moving any terms is what prevents the most common error, distributing the 5 incorrectly or forgetting it entirely.

8. 8. Which is the longest river in India?

   ▶Reveal answer

   The Ganga (Ganges)

   It flows entirely within India for about 2,525 km. It's worth distinguishing this from the Brahmaputra and Indus, both of which are longer overall but spend significant length outside India, which is why the qualifier 'flowing entirely within India' matters for this specific fact.

9. 9. What is the chemical symbol for gold?

   ▶Reveal answer

   Au

   From the Latin word 'aurum', meaning 'shining dawn'. Many element symbols that don't obviously match their English name come from Latin roots this way, like Fe for iron (ferrum) and Na for sodium (natrium), which is a useful pattern to recognize rather than memorizing each symbol as an unrelated fact.

10. 10. If sin 30° = 1/2, find the value of cos 60°.

    ▶Reveal answer

    1/2

    cos 60° = sin(90° − 60°) = sin 30° = 1/2. This works because sine and cosine of complementary angles (angles that add up to 90°) are always equal, a shortcut that avoids needing to look up cos 60° separately once sin 30° is already known.

11. 11. Which vitamin is produced in the human body when skin is exposed to sunlight?

    ▶Reveal answer

    Vitamin D

    It's synthesised in the skin when ultraviolet B (UVB) rays trigger a chemical reaction converting a cholesterol-based compound into vitamin D. This is why vitamin D deficiency is more common in people with limited sun exposure, regardless of diet, since the body's own production depends specifically on UVB light, not just warmth or visible light.

12. 12. State the unit of force in the SI system.

    ▶Reveal answer

    Newton (N)

    1 N = 1 kg·m/s², the force needed to give a 1 kg mass an acceleration of 1 m/s². The unit is built directly from mass and acceleration units rather than being an independently defined quantity, which is why force calculations always reduce back to these two values.

13. 13. Who was the first President of independent India?

    ▶Reveal answer

    Dr. Rajendra Prasad

    He served as the first President of India from 1950 to 1962, spanning two full terms. He's also notably the only Indian President to have served more than one term to date, which is a detail worth knowing alongside the bare fact of who he was.

14. 14. A bag contains 5 red, 3 green and 2 blue balls. What is the probability of drawing a green ball?

    ▶Reveal answer

    3/10 (0.3)

    Total balls = 5 + 3 + 2 = 10, and the favourable outcomes (green) = 3, so probability = 3/10. A common mistake is dividing by the count of a different color group by accident, writing out all three totals separately before dividing helps catch that.

15. 15. What is 15% of 200?

    ▶Reveal answer

    30

    15% of 200 = (15/100) × 200 = 30. A faster mental shortcut: 10% of 200 is 20, and 5% is half of that (10), so 15% is 20 + 10 = 30, useful for percentage calculations without a calculator.

16. 16. Which is the smallest country in the world by area?

    ▶Reveal answer

    Vatican City

    About 0.49 square kilometres, making it the smallest sovereign state in the world, entirely enclosed within the city of Rome. Its small size is often a source of confusion with Monaco, the second-smallest country, so the two are worth keeping distinct.

17. 17. Find the next number in the series: 3, 9, 27, 81, ?

    ▶Reveal answer

    243

    Each term is 3 times the one before it (a geometric progression with common ratio 3), so the next number is 81 × 3 = 243. Confirming the pattern with at least two consecutive pairs (9/3 = 3, 27/9 = 3) before extending it is what prevents guessing an arithmetic pattern by mistake.

18. 18. A car covers 150 km using 10 litres of fuel. What is its mileage in km/litre?

    ▶Reveal answer

    15 km/litre

    Mileage = distance travelled / fuel used = 150 km / 10 L = 15 km/litre. This rate stays constant only if driving conditions (speed, terrain, load) stay similar, which is why real-world mileage often differs from a single measured trip like this one.

19. 19. Which gas do plants absorb from the atmosphere during photosynthesis?

    ▶Reveal answer

    Carbon dioxide (CO₂)

    Plants absorb it through tiny pores on their leaves called stomata, then combine it with water using sunlight energy to produce glucose and oxygen. This is the reverse of respiration, which is why plants are often described as both consuming and producing gases depending on the process being discussed.

20. 20. Convert 2.5 hours into minutes.

    ▶Reveal answer

    150 minutes

    2.5 hours × 60 minutes/hour = 150 minutes. The 0.5 hours (half an hour) contributes 30 of those minutes, a quick sanity check: 2 full hours give 120 minutes, plus 30 for the half-hour, totals 150.

21. 21. Who wrote the Indian national anthem?

    ▶Reveal answer

    Rabindranath Tagore

    He wrote 'Jana Gana Mana', adopted as India's national anthem in 1950. Tagore is also the author of Bangladesh's national anthem ('Amar Shonar Bangla'), making him the only person to have written the national anthems of two different countries.

22. 22. If the perimeter of a square is 36 cm, find the length of one side.

    ▶Reveal answer

    9 cm

    Perimeter of a square = 4 × side length, so side = 36 / 4 = 9 cm. This is the reverse of the more commonly practiced direction (given the side, find the perimeter), which is why working backward from perimeter to side trips up students who've only memorized the formula in one direction.

23. 23. What is the value of pi (π) rounded to two decimal places?

    ▶Reveal answer

    3.14

    The full value is 3.14159..., an irrational number that never terminates or repeats, so it's always used as an approximation (3.14, or the fraction 22/7) in calculations rather than an exact value.

24. 24. Which organ in the human body is primarily responsible for filtering blood?

    ▶Reveal answer

    The kidneys

    They filter waste products and excess substances from the blood to form urine, processing the body's entire blood supply roughly 40 times a day. This filtering role is distinct from the liver's job, which processes toxins and nutrients rather than filtering blood volume directly, a distinction worth keeping clear since the two organs are often confused.

25. 25. A number increased by 20% becomes 60. Find the original number.

    ▶Reveal answer

    50

    Let the original number be x. Increasing it by 20% means x + 0.2x = 1.2x, and this equals 60, so x = 60 / 1.2 = 50. A common mistake is treating 60 itself as needing a 20% reduction (which gives 48, the wrong answer), rather than solving the equation forward from the original unknown.

26. 26. What is the freezing point of water in Celsius?

    ▶Reveal answer

    0 °C

    Equal to 32 °F, at standard atmospheric pressure. This value is actually one of the two fixed reference points (along with boiling point, 100 °C) that the Celsius scale itself was originally defined around, which is why it's exactly 0, not an approximation.

27. 27. Simplify: 7 × (6 − 2) ÷ 4.

    ▶Reveal answer

    7

    Following order of operations (brackets first): 7 × (6 − 2) ÷ 4 = 7 × 4 ÷ 4. Multiplication and division are then done left to right: 7 × 4 = 28, then 28 ÷ 4 = 7. Skipping the bracket step first, or doing division before multiplication out of habit, are the two most common ways this goes wrong.

28. 28. Which continent is the Sahara Desert located in?

    ▶Reveal answer

    Africa

    The Sahara is the largest hot desert in the world, spanning much of North Africa, roughly the size of the entire United States. It's often mistakenly assumed to cover all of Africa, when it actually occupies only the northern third of the continent.

29. 29. If a clock shows 3:15, what is the angle between the hour and minute hands (approximately)?

    ▶Reveal answer

    Approximately 7.5°

    The minute hand at 15 minutes points exactly at the 3 (90° from 12). The hour hand, however, has moved a quarter of the way from the 3 toward the 4 in that same 15 minutes, since it doesn't jump instantly between hour marks. Each full hour-to-hour gap is 30°, so a quarter of that gap is 7.5°, the hour hand's small offset past the 3, which is the angle between the two hands.

30. 30. Name the currency used in Japan.

    ▶Reveal answer

    The Japanese Yen (¥)

    The yen has been Japan's official currency since 1871, when it replaced a patchwork of regional currencies used under the earlier feudal system, part of Japan's broader modernization during the Meiji era.