Class 8 Olympiad Previous Years Question Bank & Solved Papers

IMO Olympiad Year 2024 Class 8 60 Mins · 50 Marks ✓ Verified Solutions

International Mathematics Olympiad (IMO) - Class 8 Solved Paper

Class 8 IMO paper testing rational exponents, squares & square roots, algebraic identities, linear equations, understanding quadrilaterals, compound vs simple interest, direct & inverse proportions, mensuration (trapezium, cylinder recast), and Sophie Germain factorization HOTS.

Topics Covered: Rational Exponents & Radicals Squares & Square Roots Algebraic Identities Linear Equations in 1 Variable Understanding Quadrilaterals & Polygons Comparing Quantities (CI vs SI) Direct & Inverse Proportions Mensuration 2D & 3D Achievers HOTS

Question 1 Mathematical Reasoning

1 Mark

If x + 1/x = 5, what is the value of x^3 + 1/x^3?

A 125

B 110 ✓ Correct

C 140

D 115

Concept Tested: Algebraic identity: (a + b)^3 = a^3 + b^3 + 3ab(a + b)

Hint: Cube both sides: (x + 1/x)^3 = x^3 + 1/x^3 + 3(1)(x + 1/x).

Detailed Step-by-Step Verified Solution

Step 1: Cube the equation x + 1/x = 5.
(x + 1/x)^3 = 5^3 = 125.
Step 2: Expand using algebraic identity: x^3 + 1/x^3 + 3(x)(1/x)(x + 1/x) = 125.
Step 3: Since x · (1/x) = 1 and (x + 1/x) = 5: x^3 + 1/x^3 + 3(1)(5) = 125.
Step 4: x^3 + 1/x^3 = 125 - 15 = 110.

Official Final Answer: Correct Option (B) : 110

💡 Olympiad Tip & Strategy: Formula shortcut: If x + 1/x = k, then x^3 + 1/x^3 = k^3 - 3k.

Question 2 Mathematical Reasoning

1 Mark

How many sides does a regular polygon have if each of its interior angles is 150°?

A 10

B 12 ✓ Correct

C 14

D 16

Concept Tested: Exterior angle property of regular polygons: Interior + Exterior = 180°

Hint: Exterior angle = 180° - 150° = 30°. Number of sides = 360° ÷ exterior angle.

Detailed Step-by-Step Verified Solution

Step 1: Interior angle + Exterior angle = 180°.
Exterior angle = 180° - 150° = 30°.
Step 2: For any convex polygon, sum of exterior angles is always 360°.
Step 3: Number of sides n = 360° ÷ 30° = 12.

Official Final Answer: Correct Option (B) : 12 sides

💡 Olympiad Tip & Strategy: Always calculate exterior angle first—it simplifies polygon problems drastically!

Question 3 Achievers Section (HOTS)

3 Marks

A solid metallic cylinder of radius 7 cm and height 10 cm is melted and recast into small solid spheres of radius 3.5 cm each. How many such spheres can be formed without loss of metal?

A 6

B 8 ✓ Correct

C 10

D 12

Concept Tested: Conservation of volume during recasting (Cylinder to Spheres)

Hint: Volume of cylinder = π r1^2 h. Volume of 1 sphere = (4/3) π r2^3.

Detailed Step-by-Step Verified Solution

Step 1: Volume of cylinder = π × (7)^2 × 10 = 490 π cm^3.
Step 2: Radius of sphere r2 = 3.5 cm = 7/2 cm.
Volume of 1 sphere = (4/3) × π × (7/2)^3 = (4/3) × π × (343/8) = (343/6) π cm^3.
Step 3: Number of complete spheres = Floor(490 ÷ (343/6)) = Floor(490 × 6 / 343) = Floor(60/7) = 8 complete spheres.

Official Final Answer: Correct Option (B) : 8 spheres

💡 Olympiad Tip & Strategy: In casting problems, fraction spheres cannot exist—take the floor value of N.

Question 4 Logical Reasoning

1 Mark

Statements: (1) All squares are rectangles. (2) Some rectangles are parallelograms. Which of the following conclusions logically follows?

A All squares are parallelograms ✓ Correct

B All parallelograms are squares

C Some parallelograms are squares

D No square is a parallelogram

Concept Tested: Logical deduction and geometric hierarchy classification

Hint: Every square is a rectangle, and every rectangle is by definition a parallelogram.

Detailed Step-by-Step Verified Solution

Step 1: A parallelogram is a quadrilateral with opposite sides parallel.
Step 2: A rectangle is a parallelogram with all right angles.
Step 3: A square is a rectangle with all sides equal.
Step 4: Therefore, every single square is inherently a parallelogram.

Official Final Answer: Correct Option (A) : All squares are parallelograms

💡 Olympiad Tip & Strategy: Geometric syllogisms must follow the strict taxonomy: Quadrilateral -> Parallelogram -> Rectangle -> Square.

Question 5 Logical Reasoning

1 Mark

A standard die has dots from 1 to 6. If the sum of dots on opposite faces is always 7, what is the product of dots on the face opposite to 3 and the face opposite to 5?

A 8 ✓ Correct

B 6

C 12

D 10

Concept Tested: Dice properties and opposite face sum invariant

Hint: Face opposite to 3 is 7 - 3 = 4. Face opposite to 5 is 7 - 5 = 2.

Detailed Step-by-Step Verified Solution

Step 1: In a standard die, opposite faces sum to 7.
Step 2: Face opposite to 3 is 7 - 3 = 4.
Step 3: Face opposite to 5 is 7 - 5 = 2.
Step 4: Product of these opposite faces = 4 × 2 = 8.

Official Final Answer: Correct Option (A) : 8

💡 Olympiad Tip & Strategy: Remember: 1 is opposite 6, 2 is opposite 5, 3 is opposite 4.

Question 6 Mathematical Reasoning

1 Mark

Evaluate the expression: (81/16)^(-3/4) × (25/9)^(-3/2).

A 8/125 ✓ Correct

B 125/8

C 27/125

D 64/125

Concept Tested: Laws of rational exponents: (a/b)^(-m/n) = (b/a)^(m/n)

Hint: 81/16 = (3/2)^4 and 25/9 = (5/3)^2. Invert bases to make powers positive.

Detailed Step-by-Step Verified Solution

Step 1: First term: (81/16)^(-3/4) = ((3/2)^4)^(-3/4) = (3/2)^(-3) = (2/3)^3 = 8/27.
Step 2: Second term: (25/9)^(-3/2) = ((5/3)^2)^(-3/2) = (5/3)^(-3) = (3/5)^3 = 27/125.
Step 3: Multiply both terms: (8/27) × (27/125) = 8/125.

Official Final Answer: Correct Option (A) : 8/125

💡 Olympiad Tip & Strategy: Notice the 27 in the denominator and numerator cancel out directly!

Question 7 Mathematical Reasoning

1 Mark

Find the smallest square number that is exactly divisible by each of the numbers 6, 9, and 15.

A 900 ✓ Correct

B 3600

C 450

D 180

Concept Tested: LCM and pairing prime factors to form a perfect square

Hint: Find LCM(6, 9, 15) = 90. Prime factorize 90: 2 × 3² × 5. Multiply by missing pairs (2 × 5).

Detailed Step-by-Step Verified Solution

Step 1: LCM of 6, 9, and 15:
6 = 2 × 3, 9 = 3², 15 = 3 × 5.
LCM = 2 × 3² × 5 = 90.
Step 2: Prime factors of 90 are 2 × 3² × 5.
Step 3: For a number to be a perfect square, all prime factors must have even powers.
Factors 2 and 5 are unpaired (power 1).
Step 4: Multiply 90 by (2 × 5) = 10: Required perfect square = 90 × 10 = 900 (30²).

Official Final Answer: Correct Option (A) : 900

💡 Olympiad Tip & Strategy: To convert any LCM to the smallest perfect square, multiply by the product of unpaired prime factors.

Question 8 Mathematical Reasoning

1 Mark

Two numbers are in the ratio 5 : 3. If they differ by 18, what is the sum of the two numbers?

A 72 ✓ Correct

B 64

C 80

D 90

Concept Tested: Ratio word problems and linear equations

Hint: 5x - 3x = 18 => 2x = 18 => x = 9. Sum is 5x + 3x = 8x.

Detailed Step-by-Step Verified Solution

Step 1: Let the two numbers be 5x and 3x.
Step 2: Difference = 5x - 3x = 2x = 18 => x = 9.
Step 3: The numbers are 5 × 9 = 45 and 3 × 9 = 27.
Step 4: Sum = 45 + 27 = 72 (or directly 8x = 8 × 9 = 72).

Official Final Answer: Correct Option (A) : 72

💡 Olympiad Tip & Strategy: Calculating the required value directly in terms of x saves time!

Question 9 Mathematical Reasoning

1 Mark

What is the difference between Compound Interest and Simple Interest on ₹10,000 for 2 years at 10% per annum compounded annually?

A ₹100 ✓ Correct

B ₹50

C ₹200

D ₹150

Concept Tested: Difference between CI and SI for 2 years: Diff = P(R/100)²

Hint: Use the standard Olympiad 2-year difference formula: P × (R/100)²

Detailed Step-by-Step Verified Solution

Step 1: Simple Interest for 2 years: SI = (10000 × 10 × 2) / 100 = ₹2,000.
Step 2: Compound Interest: A = 10000 × (1 + 10/100)² = 10000 × (1.1)² = ₹12,100.
CI = ₹12,100 - ₹10,000 = ₹2,100.
Step 3: Difference = CI - SI = ₹2,100 - ₹2,000 = ₹100.
Step 4: Shortcut check: P(R/100)² = 10000 × (10/100)² = 10000 × (1/100) = ₹100.

Official Final Answer: Correct Option (A) : ₹100

💡 Olympiad Tip & Strategy: Olympiad Gold Rule: For 2 years, (CI - SI) = P(R/100)². Memorize this!

Question 10 Everyday Mathematics / Science

1 Mark

12 workers can dig a trench in 8 days. How many days will 16 workers take to dig the same trench working at the same pace?

A 6 days ✓ Correct

B 5 days

C 7 days

D 4 days

Concept Tested: Inverse proportion: Total worker-days = Constant (M1 × D1 = M2 × D2)

Hint: More workers take fewer days: 12 × 8 = 16 × D2.

Detailed Step-by-Step Verified Solution

Step 1: Number of workers and days required are inversely proportional.
Step 2: M1 × D1 = M2 × D2.
12 × 8 = 16 × D2.
Step 3: 96 = 16 × D2 => D2 = 96 ÷ 16 = 6 days.

Official Final Answer: Correct Option (A) : 6 days

💡 Olympiad Tip & Strategy: Work problems with constant output always obey M1 × D1 = M2 × D2.

Question 11 Everyday Mathematics / Science

1 Mark

The area of a trapezium is 240 cm² and its height is 12 cm. If one of the parallel sides is longer than the other by 6 cm, find the length of the longer parallel side.

A 23 cm ✓ Correct

B 17 cm

C 20 cm

D 25 cm

Concept Tested: Area of trapezium: Area = (1/2) × (a + b) × h

Hint: Let shorter side be x, longer side is x + 6. (1/2) × (2x + 6) × 12 = 240.

Detailed Step-by-Step Verified Solution

Step 1: Formula for Area of trapezium = (1/2) × (sum of parallel sides) × height.
Step 2: 240 = (1/2) × (x + x + 6) × 12.
240 = (2x + 6) × 6 => 2x + 6 = 240 ÷ 6 = 40.
Step 3: 2x = 34 => x = 17 cm (shorter side).
Step 4: Longer side = x + 6 = 17 + 6 = 23 cm.

Official Final Answer: Correct Option (A) : 23 cm

💡 Olympiad Tip & Strategy: Always check which side is asked in the question: shorter vs longer!

Question 12 Achievers Section (HOTS)

3 Marks

Factorize completely the algebraic expression: x⁴ + 4y⁴.

A (x² + 2y² - 2xy)(x² + 2y² + 2xy) ✓ Correct

B (x² + 2y²)²

C (x² - 2y²)²

D (x + 2y)⁴

Concept Tested: Sophie Germain Identity and difference of squares factoring

Hint: Add and subtract 4x²y²: (x² + 2y²)² - (2xy)²

Detailed Step-by-Step Verified Solution

Step 1: Write x⁴ + 4y⁴ as (x²)² + (2y²)².
Step 2: Complete the square by adding and subtracting 2(x²)(2y²) = 4x²y²:
x⁴ + 4y⁴ = [(x²)² + 2(x²)(2y²) + (2y²)²] - 4x²y².
Step 3: Factor the perfect square: (x² + 2y²)² - (2xy)².
Step 4: Apply difference of squares: a² - b² = (a - b)(a + b):
(x² + 2y² - 2xy)(x² + 2y² + 2xy).

Official Final Answer: Correct Option (A) : (x² + 2y² - 2xy)(x² + 2y² + 2xy)

💡 Olympiad Tip & Strategy: This is the celebrated Sophie Germain identity, a classic weapon in math competitions!

Question 13 Achievers Section (HOTS)

3 Marks

The sum of all interior angles of a convex polygon is 1620°. How many diagonals does this polygon have?

A 44 ✓ Correct

B 35

C 54

D 28

Concept Tested: Polygon angle sum (n - 2) × 180° and diagonal formula: n(n - 3) / 2

Hint: (n - 2) × 180° = 1620°. Find n, then use n(n - 3)/2.

Detailed Step-by-Step Verified Solution

Step 1: Sum of interior angles of an n-sided polygon = (n - 2) × 180°.
Step 2: (n - 2) × 180° = 1620° => n - 2 = 1620 ÷ 180 = 9.
Step 3: n = 9 + 2 = 11 sides.
Step 4: Number of diagonals in an n-gon = n(n - 3) / 2.
Diagonals = 11(11 - 3) / 2 = 11 × 8 / 2 = 44 diagonals.

Official Final Answer: Correct Option (A) : 44

💡 Olympiad Tip & Strategy: Two-stage geometry HOTS problem: calculate sides n first, then diagonals.

NSO Olympiad Year 2024 Class 8 60 Mins · 50 Marks ✓ Verified Solutions

National Science Olympiad (NSO) - Class 8 Solved Paper

Class 8 NSO paper covering friction types & comparison, cell structure & osmosis, thermoplastics vs thermosetting plastics, metal reactivity series displacement, combustion flame zones, conservation (Red Data Book), metamorphosis endocrinology, acoustics (pitch vs loudness), electroplating, multiple reflections, and fluid drag streamlining.

Topics Covered: Friction & Pressure Cell Structure & Functions Synthetic Materials & Plastics Metals and Non-metals Combustion & Flame Conservation of Biodiversity Reproduction & Endocrine System Sound & Acoustics Chemical Effects of Current Light & Optics Achievers HOTS

Question 1 Scientific Reasoning

1 Mark

Which of the following statements correctly compares static friction, sliding friction, and rolling friction for the same pair of surfaces?

A Rolling friction > Sliding friction > Static friction

B Static friction > Sliding friction > Rolling friction ✓ Correct

C Sliding friction > Static friction > Rolling friction

D Static friction = Sliding friction = Rolling friction

Concept Tested: Comparison of frictional forces and microscopic interlocking of irregularities

Hint: It is hardest to start motion (static), easier to maintain sliding, and easiest to roll.

Detailed Step-by-Step Verified Solution

Step 1: Static friction has the maximum value (limiting friction) because irregularities have ample time to interlock.
Step 2: In sliding friction, the contact points do not get enough time to lock completely, so sliding friction < static friction.
Step 3: Rolling reduces the area of contact and interlocking dramatically, so rolling friction is the least.
Step 4: Correct order: Static > Sliding > Rolling.

Official Final Answer: Correct Option (B) : Static friction > Sliding friction > Rolling friction

💡 Olympiad Tip & Strategy: Ball bearings are used in fans and bicycles specifically to convert sliding into rolling friction.

Question 2 Achievers Section (HOTS)

3 Marks

A student places a plant cell and an animal cell in a hypotonic solution (pure distilled water). What will happen after 30 minutes?

A Both cells will burst due to excessive endosmosis.

B The animal cell will swell and burst (lysis), while the plant cell will become turgid without bursting. ✓ Correct

C Both cells will shrink (plasmolysis) due to exosmosis.

D The plant cell will burst because of its large central vacuole.

Concept Tested: Osmosis in plant vs animal cells and the protective role of cellulose cell wall

Hint: Plant cells have a rigid cellulose cell wall that exerts counter turgor pressure.

Detailed Step-by-Step Verified Solution

Step 1: In a hypotonic solution, water enters cells by endosmosis.
Step 2: Animal cells only have a flexible plasma membrane, which cannot withstand high internal pressure, leading to osmotic lysis (bursting).
Step 3: Plant cells possess a rigid, inelastic cellulose cell wall that exerts wall pressure equal to turgor pressure, keeping the cell firm and turgid without bursting.

Official Final Answer: Correct Option (B) : The animal cell will swell and burst (lysis), while the plant cell will become turgid without bursting.

💡 Olympiad Tip & Strategy: Cell wall is present only in plants, fungi, and bacteria—never in animal cells.

Question 3 Scientific Reasoning

1 Mark

Which of the following polymers is a thermosetting plastic that cannot be softened again by heating once molded?

A Polythene

B Bakelite ✓ Correct

C Polyvinyl Chloride (PVC)

D Polystyrene

Concept Tested: Thermoplastics vs Thermosetting plastics and cross-linked molecular chains

Hint: Bakelite and Melamine have permanent cross-linked chains used for electrical switches and cooker handles.

Detailed Step-by-Step Verified Solution

Step 1: Thermoplastics (Polythene, PVC) have linear or lightly branched polymers that soften when heated and can be remolded.
Step 2: Thermosetting plastics have heavily cross-linked covalent network chains.
Step 3: Once molded and cured, heating does not break the cross-links; they decompose rather than melt.
Step 4: Bakelite and Melamine are classic examples of thermosetting plastics.

Official Final Answer: Correct Option (B) : Bakelite

💡 Olympiad Tip & Strategy: Melamine is fire-resistant and used in floor tiles and firefighter uniforms!

Question 4 Scientific Reasoning

1 Mark

When a zinc strip is dipped into a blue solution of copper sulphate (CuSO4), the blue color fades and a reddish-brown deposit appears because:

A Zinc is more reactive than copper and displaces copper from CuSO4 ✓ Correct

B Copper is more reactive than zinc and oxidizes zinc

C Zinc sulphate reacts with air to form a red precipitate

D No chemical reaction occurs; only physical adsorption takes place

Concept Tested: Metal reactivity series and single displacement reactions: Zn + CuSO4 -> ZnSO4 + Cu

Hint: Zinc is placed higher than copper in the reactivity series.

Detailed Step-by-Step Verified Solution

Step 1: Reactivity series shows Zn > Fe > Pb > [H] > Cu.
Step 2: Because Zinc is more electropositive and reactive than copper, it displaces Cu²⁺ ions:
Zn (s) + CuSO4 (aq) -> ZnSO4 (aq) + Cu (s).
Step 3: Blue Cu²⁺ ions are consumed forming colorless ZnSO4, while metallic copper deposits as a reddish-brown layer.

Official Final Answer: Correct Option (A) : Zinc is more reactive than copper and displaces copper from CuSO4

💡 Olympiad Tip & Strategy: If copper is placed in zinc sulphate, no reaction occurs because Cu cannot displace Zn.

Question 5 Scientific Reasoning

1 Mark

Which zone of a candle flame is the hottest and is utilized by goldsmiths with a metallic blowpipe for melting gold and silver?

A Outermost non-luminous blue zone ✓ Correct

B Middle luminous yellow zone

C Innermost dark zone

D Central black wick zone

Concept Tested: Combustion zones of candle flame and complete vs incomplete combustion

Hint: The outermost zone receives unlimited oxygen from air, undergoing complete combustion.

Detailed Step-by-Step Verified Solution

Step 1: The candle flame consists of three primary zones:
(i) Innermost dark zone: unburnt wax vapours, least hot.
(ii) Middle luminous zone: partial combustion, produces glowing carbon particles (yellow).
(iii) Outermost non-luminous zone: complete combustion with maximum oxygen supply, burns with a blue flame.
Step 2: The outermost zone achieves the highest temperature (~1400°C), so goldsmiths blow air into this zone.

Official Final Answer: Correct Option (A) : Outermost non-luminous blue zone

💡 Olympiad Tip & Strategy: The middle zone leaves black sooty deposits on glass plates due to unburnt carbon.

Question 6 Scientific Reasoning

1 Mark

Which international source book maintains a comprehensive record of all endangered and threatened species of animals and plants?

A Red Data Book ✓ Correct

B Green Index

C Blue Planet Register

D Wildlife Gazette

Concept Tested: Conservation of biodiversity and IUCN Red Data Book classification

Hint: Maintained by IUCN (International Union for Conservation of Nature).

Detailed Step-by-Step Verified Solution

Step 1: The Red Data Book is the state document established for documenting rare and endangered species of animals, plants, and fungi.
Step 2: Maintained internationally by the IUCN, it alerts conservationists about species nearing extinction.

Official Final Answer: Correct Option (A) : Red Data Book

💡 Olympiad Tip & Strategy: Species found exclusively in a particular geographical area are called "Endemic species".

Question 7 Scientific Reasoning

1 Mark

In amphibians like frogs, the transformation of a swimming tadpole into an adult frog is called metamorphosis. Which hormone produced by which gland regulates this metamorphosis?

A Thyroxine produced by Thyroid gland ✓ Correct

B Insulin produced by Pancreas

C Adrenaline produced by Adrenal gland

D Growth hormone produced by Pituitary

Concept Tested: Endocrine control of metamorphosis in amphibians and iodine requirement

Hint: Tadpoles require iodine in water for this hormone to trigger metamorphosis.

Detailed Step-by-Step Verified Solution

Step 1: The biological change from larva/tadpole to adult is metamorphosis.
Step 2: In frogs, metamorphosis is triggered by the hormone thyroxine secreted by the thyroid gland.
Step 3: Thyroxine production requires iodine in pond water; if water lacks iodine, tadpoles cannot become adult frogs.

Official Final Answer: Correct Option (A) : Thyroxine produced by Thyroid gland

💡 Olympiad Tip & Strategy: High-yield Olympiad fact: Iodine deficiency in pond water arrests tadpole development!

Question 8 Scientific Reasoning

1 Mark

The pitch (shrillness) of a sound is determined by its __________, while its loudness is determined by its __________.

A Frequency; Amplitude ✓ Correct

B Amplitude; Frequency

C Wavelength; Speed

D Speed; Timbre

Concept Tested: Acoustic characteristics: Frequency controls Pitch, Amplitude controls Loudness

Hint: High frequency sounds are shrill (high pitch); large amplitude sounds are loud.

Detailed Step-by-Step Verified Solution

Step 1: Pitch depends on the frequency of vibration: higher frequency produces a higher-pitched (shrill) sound.
Step 2: Loudness is proportional to the square of amplitude (Loudness ∝ Amplitude²): larger amplitude produces a louder sound.

Official Final Answer: Correct Option (A) : Frequency; Amplitude

💡 Olympiad Tip & Strategy: Human audible frequency range is 20 Hz to 20,000 Hz.

Question 9 Scientific Reasoning

1 Mark

During the electroplating of a copper key with a coating of silver, which arrangement of electrodes and electrolyte is correct?

A Anode: Pure Silver plate; Cathode: Copper key; Electrolyte: Silver nitrate solution ✓ Correct

B Anode: Copper key; Cathode: Pure Silver plate; Electrolyte: Copper sulphate

C Anode: Carbon rod; Cathode: Copper key; Electrolyte: Pure water

D Both electrodes of silver; Electrolyte: Sodium chloride

Concept Tested: Electroplating fundamentals: Object to be plated is always connected to Cathode (negative terminal)

Hint: Metal to be deposited is anode; object to receive metal is cathode.

Detailed Step-by-Step Verified Solution

Step 1: In electroplating, the article to be electroplated is always made the cathode (- terminal).
Step 2: The pure metal that is to be deposited (Silver) is made the anode (+ terminal).
Step 3: A soluble salt of the coating metal (Silver nitrate AgNO3) is used as the electrolyte.
Step 4: Ag⁺ ions migrate to the cathode and deposit as a lustrous metallic layer.

Official Final Answer: Correct Option (A) : Anode: Pure Silver plate; Cathode: Copper key; Electrolyte: Silver nitrate solution

💡 Olympiad Tip & Strategy: Remember: CATHODE = Object to receive coating; ANODE = Source metal supply.

Question 10 Everyday Science

1 Mark

Two plane mirrors are placed inclined at an angle of 60° to each other. How many images of an object placed between them will be observed?

A 5 ✓ Correct

B 6

C 4

D 7

Concept Tested: Multiple reflections by inclined plane mirrors: n = (360° / θ) - 1

Hint: Formula: If 360/θ is an even integer, number of images n = (360/θ) - 1.

Detailed Step-by-Step Verified Solution

Step 1: Calculate 360° / θ = 360° / 60° = 6.
Step 2: Since 6 is an even number, the number of images formed by multiple reflection is:
n = (360° / θ) - 1 = 6 - 1 = 5 images.

Official Final Answer: Correct Option (A) : 5 images

💡 Olympiad Tip & Strategy: When two mirrors are parallel (θ = 0°), infinite images are formed!

Question 11 Achievers Section (HOTS)

3 Marks

Why are bodies of high-speed trains, aeroplanes, and ships specially streamlined into curved, tapered shapes?

A To reduce fluid friction (drag) caused by air and water molecules ✓ Correct

B To increase the gravitational pull towards the earth

C To maximize air resistance for emergency braking

D To prevent lightning strikes during motion

Concept Tested: Fluid friction (drag) and biomimicry of streamlined bodies

Hint: Nature designed birds and fish with streamlined shapes so fluid flows smoothly without turbulence.

Detailed Step-by-Step Verified Solution

Step 1: Fluids (air and liquids) exert a resistive frictional force on moving objects, known as drag.
Step 2: Drag increases rapidly with the velocity of the vehicle and the frontal surface area.
Step 3: Streamlining shapes mimic birds and aquatic creatures, allowing fluid layers to slide smoothly around the body with minimal turbulence, reducing energy waste.

Official Final Answer: Correct Option (A) : To reduce fluid friction (drag) caused by air and water molecules

💡 Olympiad Tip & Strategy: Friction in fluids depends on object shape, object speed, and the viscosity of the fluid.

Question 12 Achievers Section (HOTS)

3 Marks

The hormone adrenaline, often called the "fight or flight" hormone, is secreted by adrenal glands situated on top of which organs, and what physiological change does it trigger?

A Situated on kidneys; increases heart rate, breathing rate, and blood glucose to cope with stress ✓ Correct

B Situated on pancreas; lowers blood sugar levels to induce deep sleep

C Situated on liver; accelerates bile secretion for lipid breakdown

D Situated in brain; triggers memory consolidation

Concept Tested: Endocrine system: Adrenal gland functions and emergency response mechanisms

Hint: Adrenal glands cap the kidneys and prepare the body for emergency stress situations.

Detailed Step-by-Step Verified Solution

Step 1: The two adrenal glands are located on the top of both kidneys.
Step 2: Under sudden shock, anger, fear, or excitement, they secrete adrenaline directly into the bloodstream.
Step 3: Adrenaline increases heartbeat, pumps more oxygen to muscles, expands airways, and raises blood sugar to provide sudden surge of energy.

Official Final Answer: Correct Option (A) : Situated on kidneys; increases heart rate, breathing rate, and blood glucose to cope with stress

💡 Olympiad Tip & Strategy: Adrenal glands are called the "glands of emergency"!