Tag: history of mathematics

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Questions Related to history of mathematics

Multiple choice vedic methods of multiplication history of mathematics maths

Two pipes $A$ and $B$ can fill a cistern in $37\dfrac {1}{2}$ minutes and $45$ minutes respectively. Both pipes are opened, the cistern will be filled just in half an hour, if the pipe $B$ is turned off after.

  1. $15\ minutes$
  2. $10\ minutes$
  3. $5\ minutes$
  4. $9\ minutes$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the capacity of cistern be $225$ units $\left (LCM\ of \dfrac {75}{2}\ and\ 45\right )$
$A$ does $= \dfrac {225}{75}\times 2 = 6\ units/ min$
$B$ does $= \dfrac {225}{45} = 5\ units/ min$.
Let pipe is turned off after $x$ minutes.
According to the question,
$6\times 30 + 5\times x = 225$
$5x = 225 - 180 = 45$
$x = 9$
After $9$ minutes, pipe $B$ is turned off.

Multiple choice vedic methods of multiplication history of mathematics maths

Two trains starts from stations $A$ and $B$ and travel towards each other at speed of $50\ km/hr$ and $60\ km/hr$ respectively. At the time of their meeting, the second train has travelled $120\ km$ more than the first. The distance between $A$ and $B$ is

  1. $990\ km$
  2. $1200\ km$
  3. $1320\ km$
  4. $1440\ km$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed of train $A = 50\ kmph$
Speed of train $B = 60\ kmph$
Since, time is constant
$Speed \propto$ Distance covered
$\dfrac {S _{A}}{S _{B}} = \dfrac {D _{A}}{D _{B}}$
$\dfrac {50}{60} = \dfrac {D _{A}}{D _{B}}\Rightarrow \dfrac {5}{6} = \dfrac {D _{A}}{D _{B}}$
Given that train $B$ has travelled $120\ km$ extra.
$6x - 5x = 120$
$x = 120$
The distance between $A$ and $B = 6x + 5x = 11x$
$= 11\times 120 = 1320$
Alternate Method:
Let train $A$ start form station $A$ and $B$ from station $B$.
Let the trains $A$ and $B$ meet after/ hours.
$\therefore$ Distance covered by train $A$ in $t$ hours $= 50t$
Distance covered by train $B$ in $t$ hours $= 60t\ km$.
According to the question,
$60t - 50t = 120$
$\Rightarrow t = \dfrac {120}{10} = 12\ hours$.
$\therefore$ Distance $AB = 50\times 12 + 60 \times 12$
$= 600 + 720 = 1320\ km$.

Multiple choice mathematicians and their contribution history of mathematics maths

Brahmagupta wrote which of the following book?

  1. Khand Khadya

  2. Siddhant Shiromany

  3. Aryabhatiya

  4. Leelavati
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta was an Indian mathematician and astronomer. He is the author of the Brahmasphuṭasiddhanta and the Khandakhadyaka.

Multiple choice mathematicians and their contribution history of mathematics maths

State the following statement is True or False
Bhaskaracharya wrote 'Leelavati' which contains description of arithmetic area, cube root,interest etc

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Lilavati is based on Arithmetic. The book contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical & geometric progressions. Many of the methods in the book on computing numbers such as multiplications, squares & progressions

Multiple choice mathematicians and their contribution history of mathematics maths

State whether the following statement is True or False.
Bodhayan theorem is also called as Sulv theorem.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The bodhayan theorem is also called as Sulv theorem which later became known as Pythagorean Theorem.

So, its a true statement.

Multiple choice mathematicians and their contribution history of mathematics maths

Authors of Sulva-Sutras knew Pythagoras Theorem much before the birth of Pythagoras, was mentioned in which book?

  1. History of Geometry

  2. History of Trigonometry

  3. History of Mathematics

  4. History of Algebra
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the 'History of mathematics' book, it is mentioned that Budhayana, the author of budhayana sulva-sutras, knew Pythagoras Theorem much before the birth of Pythagoras.

Multiple choice mathematicians and their contribution history of mathematics maths

Pythagoras Theorems statement is found in oldest Sulva Sutra known as Bodhayan Sulva Sutra

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pythagorean Theorem has been mentioned as a verse or a shloka in Baudhayana Sulbasutra. Here is the exact translation shloka in English:

"If a rope is stretched along the diagonal’s length, the resulting area will be equal to the sum total of the area of horizontal and vertical sides taken together."

Multiple choice mathematicians and their contribution history of mathematics maths

Whose work creation spread in Europe and western countries?

  1. Bodhayan

  2. Brahmagupta

  3. Varahmihir

  4. Bhaskaracharya
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Bhaskara work represents a significant contribution to mathematical and astronomical knowledge in the 12th century like the properties of zero, methods of multiplication, squaring, estimation of $\pi$ etc.

Multiple choice mathematicians and their contribution history of mathematics maths

When was Bhaskaracharya born? 

  1. $476\ A.D.$
  2. $1114\ A.D.$
  3. $598\ A.D.$
  4. $770\ A.D.$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Bhaskaracharya was born in $1114 A.D.$ He represented the peaks of mathematical knowledge in the $12^{th}$ century and was the head of the astronomical observatory at Ujjain, the leading mathematical center of ancient India.