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Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

The product of the numbers $5623$ and $6$ in the scale of eight is:

  1. $41672$
  2. $33738$
  3. $42562$
  4. $45262$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To multiply 5623 (base 8) by 6 (base 8): 3*6=18 (decimal) = 22 (base 8), write 2 carry 2. 2*6=12 + 2 = 14 (decimal) = 16 (base 8), write 6 carry 1. 6*6=36 + 1 = 37 (decimal) = 45 (base 8), write 5 carry 4. 5*6=30 + 4 = 34 (decimal) = 42 (base 8). Result is 42562.

Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

Number name for $123,080,603$ is:

  1. one two three eighty thousand six hundred three

  2. one hundred twenty three million eight thousand six hundred three

  3. one hundred twenty three million eighty thousand six hundred three

  4. one twenty three million eighty thousand six hundred
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By using International number system the naming of the number $123,080,603$ is:

one hundred twenty three million eighty thousand six hundred three.

Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

Express in international number system.
$81,894,650$

  1. Eighty one million,eight hundred ninety four thousand six hundred fifty.

  2. Eighty million,eight hundred ninety four thousand six hundred fifty.

  3. Eight hundred one million,eight hundred ninety four thousand six hundred fifty.

  4. Eighty one million,eight ninety four thousand six hundred .
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let us convert the given numerals into words as follows:

$81,000,000=$Eighty one million
$894,000=$Eight hundred ninety four thousand
$600=$Six hundred
$50=$Fifty

Now, combine the numbers in words as shown below:

Eighty one million,eight hundred ninety four thousand six hundred fifty.

Hence, the International number system is eighty one million,eight hundred ninety four thousand six hundred fifty.
Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

Express as International number system.
$3,45,90,430$

  1. Thirty four million,five hundred ninety thousand hundred thirty.

  2. Thirty four million,five hundred nine thousand four hundred thirty.

  3. Thirty million,five hundred ninety thousand four hundred thirty.

  4. Thirty four million,five hundred ninety thousand four hundred thirty.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let us convert the given numerals into words as follows:

$34,000,000=$Thirty four million
$590,000=$Five hundred ninety thousand
$400=$Four hundred
$30=$Thirty

Now, combine the numbers in words as shown below:

Thirty four million,five hundred ninety thousand four hundred thirty.

Hence, the International number system is thirty four million,five hundred ninety thousand four hundred thirty.
Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

Express in Inernational number system:
Thirteen lakh five  thousand two hundred nine.

  1. Thirty four million,five hundred ninety thousand four hundred thirty.

  2. One million three hundred five thousand two hundred nine.

  3. One million three hundred five hundred two hundred nine.

  4. One three hundred five thousand two hundred nine.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let us first convert the given number in words into numerals as follows:

Thirteen lakh$=13,00,000$
Five thousand$=5,000$
Two hunderd$=200$
Nine$=9$

Now, add the numerals as shown below:

$1300000+5000+200+9=1305209$

Therefore, the required number is $13,05,209$.

Now, to convert the number in International number system, we write the number as follows:

$1,000,000=$One million
$305,000=$Three hundred five thousand
$200=$Two hundred
$9=$Nine

Now, combine the numbers in words as shown below:

One million three hundred five thousand two hundred nine.

Hence, the International number system is one million three hundred five hundred two hundred nine.
Multiple choice maths solids volume of a sphere surface area and volume of sphere surface areas and volumes surface areas and volumes of solids problems involving volume of combined solids application of surface area and volume of solids

If the circumference of the inner edge of a hemispherical bowl is $\displaystyle\frac{132}{7}:cm$, then what is the capacity?

  1. $12\pi\:cm^3$
  2. $18\pi\:cm^3$
  3. $24\pi\:cm^3$
  4. $36\pi\:cm^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle2\pi r=\frac{132}{7}\implies r=3$

$\therefore$ Capacity $\displaystyle=\frac{2}{3}\pi r^3=18\pi$

Multiple choice maths solids volume of a sphere surface area and volume of sphere surface areas and volumes surface areas and volumes of solids problems involving volume of combined solids application of surface area and volume of solids

The side of a cube is equal to diameter of the sphere. The ratio of volumes 
of cube and sphere is

  1. $\frac{11}{12}$
  2. $\frac{22}{11}$
  3. $\frac{11}{21}$
  4. $\frac{21}{11}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the sides of cube be $s$ and radius of sphere be $r$

then $s=2r=(2r)^3=8r^3$
Volume of a cube$=s^3$
Volume of a sphere$=\cfrac{4}{3}\pi r^3$
Ratio of volume of cube and sphere$=\cfrac{8r^3}{\cfrac{4}{3}\pi r^3}$
$=\cfrac{8r^3}{\cfrac{4}{3}\times \cfrac{22}{7} r^3}\=\cfrac{21}{11}$