GK: Class 12 General Q&A · Page 44
3,658 free answers on GK (General) for Class 12 students, across CBSE, ICSE and State boards.
Question & Answer
Questions
- GeneralClass 12All
What is biodegradable waste? Give 10 examples
Biodegradable waste consists of organic materials that can be broken down naturally by microorganisms (bacteria, fungi) into simpler, harmless substances. These materials decompose through biological processes and return to nature. 10 Examples of Biodegradable Waste: Vegetable and fruit peels - Decompose within 1-2 weeks Leftover cooked food - Breaks down in 5-7 days Tea leaves and coffee grounds<
- GeneralClass 12All
What happens if garbage is not removed regularly?
If garbage isn't removed regularly, several serious problems occur: Health Hazards: Rotting garbage produces foul, unbearable smells that make living conditions unpleasant Decomposing food waste becomes a breeding ground for harmful organisms like bacteria and fungi Creates ideal conditions for disease-carrying pests: flies, mosquitoes, cockroaches, and rats These pests spread di
- GeneralClass 12All
What is garbage? Explain with examples
Answer: Garbage refers to all waste materials or rubbish that we discard from our homes, schools, offices, and shops. It's called 'kooda' in Hindi. Common examples include: Kitchen waste: Fruit and vegetable peels, leftover cooked food, tea leaves, eggshells Packaging materials: Plastic bags, cardboard boxes, paper wrappers, tin cans, glass bottles Paper waste: Old newspa
- GeneralClass 12All
What is the product of a rational number and its multiplicative inverse?
The product is always one (1). Formula: (p/q) × (q/p) = 1 (where p ≠ 0) Examples: 3/4 × 4/3 = 12/12 = 1 7/5 × 5/7 = 35/35 = 1 (-2/9) × (-9/2) = 18/18 = 1 Explanation: This is the defining property of multiplicative inverse (reciprocal). The reciprocal is specifically the number that, when multiplied by the original, gives one. <strong
- GeneralClass 12All
What is the sum of a rational number and its additive inverse?
The sum is always zero (0). Formula: p/q + (-p/q) = 0 Examples: 3/7 + (-3/7) = 0 -5/9 + 5/9 = 0 2/3 + (-2/3) = 0 Explanation: This is the defining property of additive inverse. The additive inverse is specifically the number that, when added to the original, gives zero.
- GeneralClass 12All
Arrange in ascending order: 2/3, 5/6, 1/2
Step 1: Find LCM(3, 6, 2) = 6 Step 2: Convert all to denominator 6 2/3 = 4/6 5/6 = 5/6 1/2 = 3/6 Step 3: Compare numerators 3/6 < 4/6 < 5/6 Answer in ascending order: 1/2 < 2/3 < 5/6
- GeneralClass 12All
How do you compare two rational numbers?
There are three methods: Method 1: Cross Multiplication For a/b and c/d: Calculate a × d and b × c If a × d > b × c, then a/b > c/d If a × d < b × c, then a/b < c/d If a × d = b × c, then a/b = c/d Method 2: Same Denominator Convert both to the same denominator (LCM) Compare numerators Method 3: D
- GeneralClass 12All
Convert 0.454545... (0.4̄5̄) to a rational number.
Step 1: Let x = 0.454545... Step 2: Since 2 digits repeat, multiply by 100 100x = 45.454545... Step 3: Subtract 100x - x = 45.454545... - 0.454545... 99x = 45 Step 4: Solve x = 45/99 Step 5: Simplify (GCD = 9) 45/99 = 5/11 Answer: 0.4̄5̄ = 5/11
- GeneralClass 12All
Convert 0.666... (repeating) to a rational number.
Step 1: Let x = 0.666... Step 2: Multiply by 10 (one repeating digit) 10x = 6.666... Step 3: Subtract original from multiplied 10x - x = 6.666... - 0.666... 9x = 6 Step 4: Solve for x x = 6/9 = 2/3 Answer: 0.666... = 2/3 Verification: 2 ÷ 3 = 0.666... ✓
- GeneralClass 12All
How do you convert a terminating decimal to a rational number?
Count the decimal places and use that as the power of 10 in the denominator. Examples: (a) 0.5 1 decimal place 0.5 = 5/10 = 1/2 (b) 0.75 2 decimal places 0.75 = 75/100 = 3/4 (c) 2.125 3 decimal places 2.125 = 2125/1000 = 17/8 (d) 0.008 3 decimal places 0.008 = 8/1000
- GeneralClass 12All
How do you represent -2/5 on a number line?
Step 1: Identify position -2/5 is negative, so it lies to the LEFT of 0 It's between -1 and 0 Step 2: Divide the segment Divide the space between -1 and 0 into 5 equal parts Each part represents 1/5 Step 3: Mark the point Count 2 parts from 0 towards the left Mark this point as -2/5 Visual: -1 -4/5 -3/5 -
- GeneralClass 12All
Find five rational numbers between 1/3 and 1/2
Method 1: Common Denominator Convert to same denominator with enough space: 1/3 = 10/30 1/2 = 15/30 Five numbers between 10/30 and 15/30: 11/30, 12/30, 13/30, 14/30, 15/30 Simplified: 11/30, 2/5, 13/30, 7/15, 1/2 Wait, we need numbers BETWEEN 1/3 and 1/2, so: 11/30, 2/5, 13/30, 7/15 (not including 15/30 which equals 1/2) Better answer with more space:</st
- GeneralClass 12All
How many rational numbers lie between two rational numbers?
Infinitely many rational numbers exist between any two rational numbers. This is called the dense property of rational numbers. Example: Between 1/2 and 1: Using the mean method: (1/2 + 1)/2 = 3/4 (1/2 + 3/4)/2 = 5/8 (3/4 + 1)/2 = 7/8 So: 1/2 < 5/8 < 3/4 < 7/8 < 1 This process can continue forever, finding more numbers each time. General method:</stro
- GeneralClass 12All
What is the distributive property for rational numbers?
Multiplication distributes over addition. Formula: a × (b + c) = (a × b) + (a × c) Example: 2/3 × (1/4 + 1/5) Method 1 (add first): = 2/3 × (5/20 + 4/20) = 2/3 × 9/20 = 18/60 = 3/10 Method 2 (distribute): = (2/3 × 1/4) + (2/3 × 1/5) = 2/12 + 2/15 = 1/6 + 2/15 = 5/30 + 4/30 = 9/30 = 3/10 Both methods give 3/10 ✓
- GeneralClass 12All
Simplify: [(2/5) ÷ (3/7)] × (4/9)
Step 1: Solve division first (2/5) ÷ (3/7) = (2/5) × (7/3) = 14/15 Step 2: Multiply by 4/9 (14/15) × (4/9) = (14 × 4)/(15 × 9) = 56/135 Check for simplification: GCD(56, 135) = 1 Already in simplest form. Answer: 56/135
- GeneralClass 12All
Find the reciprocal of: (a) 7/9 (b) -3 (c) 1
(a) Reciprocal of 7/9: Flip the fraction: 9/7 Verification: 7/9 × 9/7 = 63/63 = 1 ✓ (b) Reciprocal of -3: Write as fraction: -3 = -3/1 Flip: -1/3 Verification: -3 × (-1/3) = 3/3 = 1 ✓ (c) Reciprocal of 1: 1 = 1/1 Flip: 1/1 = 1 Verification: 1 × 1 = 1 ✓
- GeneralClass 12All
What property is shown by: (2/3 × 4/5) × 1/2 = 2/3 × (4/5 × 1/2)?
This demonstrates the Associative Property of Multiplication. Definition: For any three rational numbers a, b, and c: (a × b) × c = a × (b × c) The grouping of multiplication doesn't matter; the result is the same. Verification: Left side: (2/3 × 4/5) × 1/2 = (8/15) × 1/2 = 8/30 = 4/15 Right side: 2/3 × (4/5 × 1/2) = 2/3 × (4/10) = 2/3 × 2/5
- GeneralClass 12All
Divide: (5/6) ÷ (10/9)
Step 1: Convert to multiplication by reciprocal (5/6) ÷ (10/9) = (5/6) × (9/10) Step 2: Multiply (5 × 9)/(6 × 10) = 45/60 Step 3: Simplify (GCD = 15) 45/60 = 3/4 Answer: 3/4
- GeneralClass 12All
Multiply: (2/3) × (9/4) × (1/6)
Method: Multiply all numerators and all denominators (2 × 9 × 1)/(3 × 4 × 6) = 18/72 Simplify: GCD(18, 72) = 18 18/72 = 1/4 Answer: 1/4 Smart approach: Cancel before multiplying: (2/3) × (9/4) × (1/6) = (2 × 9 × 1)/(3 × 4 × 6) = (1 × 3 × 1)/(3 × 2 × 3) [cancel
- GeneralClass 12All
What is the multiplicative identity for rational numbers?
The multiplicative identity is 1 (or 1/1). Property: For any rational number p/q: (p/q) × 1 = p/q Examples: 3/5 × 1 = 3/5 -7/9 × 1 = -7/9 1 × 4/11 = 4/11 One is called the multiplicative identity because multiplying any number by 1 gives back the same number.