GK: Class 12 General Q&A · Page 46
3,658 free answers on GK (General) for Class 12 students, across CBSE, ICSE and State boards.
Question & Answer
Questions
- GeneralClass 12All
What is the standard form of a rational number?
A rational number p/q is in standard form when: The denominator q is positive p and q have no common divisor except 1 (they are co-prime) The fraction is in its simplest/lowest form Examples: 2/3 is in standard form -4/6 is NOT in standard form (can be simplified to -2/3) 3/-5 is NOT in standard form (denominator should be positive: -3/5)
- GeneralClass 12All
What is the relationship between rational numbers and the number line?
Every rational number corresponds to a unique point on the number line, and these points are dense (infinitely many between any two points). Representation: Positive rationals lie to the right of 0 Negative rationals lie to the left of 0 Zero is at the center Rationals can be plotted by dividing segments appropriately Example: To plot 2/5: Divide the segment from 0 to 1 into 5 equal par
- GeneralClass 12All
Can a rational number have a negative denominator?
While mathematically possible, in standard form, rational numbers are written with positive denominators. Examples: 3/-4 can be written, but should be rewritten as -3/4 -5/-7 should be rewritten as 5/7 2/-3 should be rewritten as -2/3 Rule: The negative sign, if present, is conventionally placed in the numerator or in front of the fraction.
- GeneralClass 12All
Why can't the denominator of a rational number be zero?
The denominator cannot be zero because division by zero is undefined in mathematics. Explanation: If we try to calculate 5/0, we're asking "what number multiplied by 0 gives 5?" No such number exists because any number × 0 = 0, not 5 Division by zero would break fundamental mathematical rules Therefore, q ≠ 0 is a mandatory condition for p/q to be a rational number
- GeneralClass 12All
What does p/q represent in a rational number?
In the rational number p/q: p = numerator (the top number, can be any integer) q = denominator (the bottom number, must be a non-zero integer) p/q = the ratio or fraction representing the division of p by q Conditions: q ≠ 0 (denominator cannot be zero) Both p and q must be integers q can be negative, but in standard form, it's made positive <
- GeneralClass 12All
What is the difference between rational and irrational numbers?
Rational Numbers Irrational Numbers Can be expressed as p/q (q ≠ 0) Cannot be expressed as p/q Examples: 1/2, 0.5, 5, 0.333... Examples: √2, π, √3, e Decimal form either terminates or repeats Decimal form neither terminates nor repeats Forms the set Q Forms the set R - Q </tr
- GeneralClass 12All
Is every natural number a rational number?
Yes, every natural number is a rational number, but a rational number need not be a natural number. Examples: 1 = 1/1 (natural and rational) 2 = 2/1 (natural and rational) 3 = 3/1 (natural and rational) But -2/3, 0, 1/2 are rational but not natural numbers Note: Natural numbers are {1, 2, 3, 4, ...}
- GeneralClass 12All
Are all fractions rational numbers?
Yes, every fraction is a rational number, but not every rational number needs to be expressed as a fraction in its traditional sense. Explanation: All fractions like 2/3, 5/7, -4/9 are rational numbers But rational numbers also include integers (5 = 5/1) and decimals (0.5 = 1/2) So while all fractions are rational, rational numbers encompass more than just fractions
- GeneralClass 12All
Are all integers rational numbers?
Yes, every integer is a rational number, but not every rational number is an integer. Explanation: Any integer n can be written as n/1 For example: 5 = 5/1, -3 = -3/1, 0 = 0/1 However, 1/2, 3/4, -2/5 are rational numbers but not integers
- GeneralClass 12All
Is 0 a rational number? Why?
Yes, zero (0) is a rational number because it can be expressed in the form p/q where p = 0 and q is any non-zero integer. Examples: 0 = 0/1 0 = 0/2 0 = 0/100 Since 0 divided by any non-zero number gives 0, and this fits the definition p/q, zero is rational.
- GeneralClass 12All
What is a rational number?
A rational number is any number that can be expressed as p/q, where p and q are integers and q ≠ 0. The word "rational" comes from "ratio," representing the relationship between two integers. Examples: 1/2 (one divided by two) 0.75 (which equals 3/4) 5 (which can be written as 5/1) -6.6 (which equals -66/10)
- GeneralClass 12All
How can you calculate surface tension?
Surface tension is calculated using the formula γ=FL\gamma = \frac{F}{L}γ=LF, where FFF is force and LLL is length. It measures the force acting along the surface of a liquid. This concept explains why insects can walk on water or why droplets form spheres. Surface tension calculations are common in fluid mechanics and material science.
- GeneralClass 12All
How do you know which way tension is going?
Tension always acts along the length of a rope or cable and pulls away from the object it is attached to. It never pushes. When solving problems, assume a direction first, then let the math confirm it. If the final value is negative, the actual direction is opposite to the assumption—classic physics honesty at work.
- GeneralClass 12All
How do you calculate tensile force?
Tensile force is calculated using F=σAF = \sigma AF=σA, where σ\sigmaσ is tensile stress and AAA is cross-sectional area. This relationship is crucial in material testing and design. It helps determine whether a material will stretch safely or fail under load.
- GeneralClass 12All
How do you calculate ultimate tensile strength?
Ultimate tensile strength (UTS) is calculated by dividing the maximum force a material withstands by its original cross-sectional area. UTS represents the highest stress a material can endure before failure. It is a key property used in selecting materials for construction and manufacturing.
- GeneralClass 12All
What is the process of breaking a force into its components called?
The process is called resolution of forces. It involves splitting a force into perpendicular components, usually horizontal and vertical. This technique simplifies problem-solving in physics and engineering by allowing complex forces to be analyzed using basic equations.
- GeneralClass 12All
How much force does it take to break a bolt?
The force required to break a bolt depends on its material, diameter, and tensile strength. It is calculated by multiplying the bolt’s tensile strength by its cross-sectional area. In practice, engineers rely on standardized strength ratings and safety margins. Bolts are chosen to fail only under loads far beyond normal operating conditions, because nobody likes surprise disassembly.
- GeneralClass 12All
How do you work out braking force?
Braking force is calculated using Newton’s second law: F=maF = maF=ma, where acceleration is negative due to deceleration. This calculation is essential in vehicle safety design. It helps determine stopping distances and brake system requirements.
- GeneralClass 12All
How to calculate the breaking force of a material?
Breaking force is calculated using the material’s ultimate tensile strength multiplied by its cross-sectional area. This value indicates the maximum force a material can handle before failure. Engineers use safety factors to ensure real-world loads stay well below this limit.
- GeneralClass 12All
What are the different types of tensile forces?
Tensile forces include static tension, dynamic tension, and cyclic tension. Each type describes how force is applied over time. Understanding these distinctions matters because materials behave differently under steady loads versus repeated or changing loads. Fatigue failure often results from cyclic tensile forces.