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Multiple choice multiplication and division vedic methods of multiplication vedic mathematics history of mathematics maths

Which of the following statements is CORRECT?

  1. The product of $\dfrac{231}{119}$ and $\dfrac{117}{118}$ is greater than $\dfrac{231}{119}$
  2. The product of $\dfrac{17}{25}$ and $\dfrac{117}{225}$ is greater than $\dfrac{17}{25}$
  3. The product of $\dfrac{1735}{2001}$ and $\dfrac{2734}{2724}$ is greater than $\dfrac{1735}{2001}$
  4. $\dfrac{1}{3}$ of $\dfrac{4}{5}$ is greater than $\dfrac{3}{4}$ of $\dfrac{8}{7}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Option $[A]$  :  $\dfrac{117}{118}<1$.  
The product of any number with a number less than $1$ is less than that number.
So,  $\dfrac{231}{119}\times\dfrac{117}{118}<\dfrac{231}{119}$.

$\Rightarrow[A]$ is not correct.

Option $[B]$  :  $\dfrac{117}{225}<1$
The product of any number with a number less than $1$ is less than that number.
So,  $\dfrac{17}{25}\times\dfrac{117}{225}<\dfrac{17}{25}$.
$\Rightarrow[B]$ is not correct.

Option $[C]$  :  $\dfrac{2734}{2724}>1$
The product of any number with a number greater than $1$ is greater than that number.
So,  $\dfrac{1735}{2001}\times\dfrac{2734}{2724}>\dfrac{1735}{2001}$.
$\Rightarrow[C]$ is correct.

Option $[D]$  :
$\dfrac{1}{3}\times\dfrac{4}{5}=\dfrac{4}{15}\approx0.267$   and   $\dfrac{3}{4}\times\dfrac{8}{7}=\dfrac{6}{7}\approx0.857$.
But  $0.857>>0.267$.
So, $[D]$ is not correct.


$\therefore$  The correct answer is  $[C]$.

Multiple choice multiplication and division vedic methods of multiplication vedic mathematics history of mathematics maths

A board 7 feet 9 inches long is divided into 3 equal parts. What is the length of each part? 

  1. 2 feet 9 inches

  2. 2 feet 7 inches

  3. 2 feet 12 inches

  4. 2 feet 3 inches
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Length of board $=\text{7 feet 9 inches}$

$=(7\times 12+9)$ inches       $[\because \text{1 feet = 12 inches}]$
$=93 inches$
Number of parts to be cut $3$
$\therefore $ Length of each part $=(93+3) \text{inches}$
$=\text{31 inches}$
$=\text{2feet 7 inches}$

Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

Simplify: $( 16x ^{16} )^{\dfrac{3}{4}}$

  1. $8 x^{16}$
  2. $2 x^{12}$
  3. $8 x^{12}$
  4. $2 x^{16}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
${\left( 16{x}^{16} \right)}^{\cfrac{3}{4}} = {\left( {2}^{4} {x}^{16} \right)}^{\cfrac{3}{4}}$
$\Rightarrow \; = {\left( {2}^{4} \right)}^{\cfrac{3}{4}} {\left( {x}^{16} \right)}^{\cfrac{3}{4}}$

$\Rightarrow \; = {2}^\left( {4 \times \cfrac{3}{4}} \right)  {x}^\left({16 \times \cfrac{3}{4}} \right)$

$\Rightarrow \; = {2}^{3} \times {x}^{12}$

$\Rightarrow \; = 8{x}^{12}$