Speed and Basic Mathematics Quiz
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Questions and Answers

What is the speed of an object in m/sec which travels 100 meters in 5 seconds?

  • 15 m/sec
  • 20 m/sec (correct)
  • 10 m/sec
  • 25 m/sec

    • If A is 67% of B, what is the ratio A:B?

  • 3:4
  • 67:100 (correct)
  • 56:100
  • 2:3

    • What is the prime number next to 100?

  • 102
  • 104
  • 101 (correct)
  • 103

    • What is the mean of the numbers 3, 9, and 12?

    <p>8</p> Signup and view all the answers

    If marked price = Rs100 and discount = 20%, what is the selling price?

    <p>Rs.80</p> Signup and view all the answers

    What is a triangle having two sides equal called?

    <p>Isosceles triangle</p> Signup and view all the answers

    What is the value of x if x^2 = 36?

    <p>±6</p> Signup and view all the answers

    If A:B = 3:4, how much percentage is A of B?

    <p>75%</p> Signup and view all the answers

    What is the formula to calculate the area of a quadrilateral?

    <p>𝑑 × (𝑝1 + 𝑝2)/2</p> Signup and view all the answers

    Which formula correctly gives the area of a kite?

    <p>𝑑1 × 𝑑2 / 2</p> Signup and view all the answers

    What is Heron's formula for the area of a triangle?

    <p>√(s × (s − 𝑎) × (s − 𝑏) × (s − 𝑐))</p> Signup and view all the answers

    What is the formula for the area of an equilateral triangle?

    <p>√3 / 4 × 𝑎²</p> Signup and view all the answers

    What is the value of Sin(30°)?

    <p>1/2</p> Signup and view all the answers

    What is the value of Cos(60°)?

    <p>1/2</p> Signup and view all the answers

    What is the value of Sin(45°)?

    <p>√2/2</p> Signup and view all the answers

    What is the value of Tan(30°)?

    <p>1/√3</p> Signup and view all the answers

    What is the name of a quadrilateral having opposite sides equal?

    <p>Parallelogram</p> Signup and view all the answers

    Which quadrilateral has all angles equal?

    <p>Square</p> Signup and view all the answers

    What quadrilateral has diagonals that bisect each other at right angles?

    <p>Square</p> Signup and view all the answers

    What type of quadrilateral is defined by having a pair of opposite sides parallel?

    <p>Trapezium</p> Signup and view all the answers

    Which of these is a characteristic of a kite?

    <p>One diagonal bisects the other at right angles</p> Signup and view all the answers

    What is the name of the quadrilateral that has all sides and angles equal?

    <p>Square</p> Signup and view all the answers

    In which quadrilateral do the diagonals bisect each other?

    <p>Parallelogram</p> Signup and view all the answers

    What is a defining feature of a concave quadrilateral?

    <p>At least one angle is greater than 180 degrees</p> Signup and view all the answers

    What is the point of intersection of the medians of a triangle called?

    <p>Centroid</p> Signup and view all the answers

    What is 20% of Rs 2000?

    <p>Rs 400</p> Signup and view all the answers

    What is the size of the exterior angle of a regular hexagon?

    <p>60°</p> Signup and view all the answers

    If (x-8)² = 100, what is the minimum value of x?

    <p>-2</p> Signup and view all the answers

    What is the total surface area of a cube with side length 3 cm?

    <p>54 sq.cm</p> Signup and view all the answers

    What is the least number that exactly divides 24, 18, and 12?

    <p>6</p> Signup and view all the answers

    What is the difference between the boiling point and freezing point of a liquid that boils at 73°C and freezes at -27°C?

    <p>100°C</p> Signup and view all the answers

    What is a polygon with 9 sides called?

    <p>Nonagon</p> Signup and view all the answers

    What is the formula for the volume of a solid cylinder?

    <p>$ ext{π} r^2 h$</p> Signup and view all the answers

    Which formula represents the total surface area of a cone?

    <p>$ ext{π} r( r + l)$</p> Signup and view all the answers

    What is the formula used to calculate the surface area of a sphere?

    <p>$4 ext{π} r^2$</p> Signup and view all the answers

    How many kilograms are in one quintal?

    <p>100 kg</p> Signup and view all the answers

    What is the formula for the volume of a solid pyramid?

    <p>$ rac{1}{3} imes ext{base area} imes ext{height}$</p> Signup and view all the answers

    Which formula calculates the total surface area of a cube?

    <p>$6l^2$</p> Signup and view all the answers

    What is the formula for finding the area of a trapezium?

    <p>$ rac{1}{2} (b_1 + b_2) h$</p> Signup and view all the answers

    What is the area of a square when given the length of its diagonal?

    <p>$d^2$</p> Signup and view all the answers

    Study Notes

    Speed Calculation and Basic Mathematics

    • Speed is calculated as distance divided by time; for 100 meters in 5 seconds, speed = 100/5 = 20 m/sec.
    • A dozen consists of 12; thus, 15 dozens have 15 × 12 = 180 objects.
    • A hexagon has 12 edges when not sharpened, given its six sides.

    Number Theory and Fractions

    • The largest number formed with four 1s is 1111.
    • The largest number formed with two 9s is 99.
    • If A is 67% of B, the ratio A:B is 67:100.
    • A:B = 3:4 means A is 75% of B.
    • The prime number next to 100 is 101.
    • The mean of numbers 3, 9, and 12 is calculated as (3+9+12)/3 = 8.

    Percentages and Money

    • To find the percent of 0.07, multiply by 100: 0.07 × 100 = 7%.
    • Rs.60 is 20% of Rs.300.
    • If 10% of a number is 2, then the number is 20.
    • 5% of 100 is equal to 5.
    • The marked price can be found by adding discount to selling price: MP = SP + Discount = 185 + 15 = Rs.200.

    Geometry Concepts

    • An isosceles triangle has two equal base angles.
    • The sum of the interior angles of a triangle is 180°.
    • A triangle with three equal sides is called an equilateral triangle.
    • Total surface area of a cylinder: (2\pi r(r + h)).
    • Volume of a cylinder: (\pi r^2 h).
    • Surface area of a sphere: (4\pi r^2).
    • Volume of a sphere: (\frac{4}{3}\pi r^3).
    • The area of a triangle can be computed using Heron’s formula.

    Sets and Relations

    • A set with no elements is called an empty or null set.
    • A singleton set contains one element.
    • Disjoint sets have no common elements, while overlapping sets share some elements.

    Statistics and Angles

    • The median is the middle value in a sorted data set.
    • Angles in a linear pair sum to 180°; if one angle is 68°, the other is 112°.
    • The exterior angle of any triangle is equal to the sum of the two opposite interior angles.

    Advanced Geometry and Algebra

    • Total surface area of a cube: (6l^2).
    • Volume of a cone: (\frac{1}{3} \pi r^2 h).
    • The value of (x) when (x^2 = 36) is ±6.
    • The minimum value of (x) from ((x - 8)^2 = 100) is -2.

    Origins and Definitions

    • Euclid is known as the father of Geometry.
    • A polygon with 7 sides is called a heptagon; for 9 sides, it’s a nonagon.
    • The least number that exactly divides 24, 18, and 12 is 2.

    Sequences and Patterns

    • For sequences like 61, 52, 63, 94, 46, the next term is 18.
    • To find the product in a specific pattern (like (2@3=35)), follow the defined operation.

    Miscellaneous Calculations

    • The area of a circle can be derived from the formula (A = \pi r^2).
    • In problems involving temperature scales, the difference between boiling and freezing points can be calculated accordingly.

    This study guide reflects important mathematical principles, geometry formulas, and number theory concepts necessary for mastering the topics presented.

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    Test your knowledge on speed calculations, number theory, and basic mathematical concepts. This quiz covers topics such as distance, time, fractions, percentages, and geometry principles. Challenge yourself and see how well you understand these fundamental math concepts!

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