5th

6th

7th

8th

Brahmasphuta Siddhanta

Khandakhadyaka

Aryabhatiya

Surya Siddhanta

To provide a comprehensive guide to astronomy and mathematics

To explain the principles of Hindu astrology

To develop new mathematical techniques

To calculate the positions of the planets

The development of the decimal system

The discovery of the zero

The invention of the negative numbers

The development of the quadratic equation

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a}$

$x = \frac{-b \pm \sqrt{b^2 - 2ac}}{2a}$

$x = \frac{-b \pm \sqrt{b^2 + 2ac}}{2a}$

The development of the trigonometric functions

The discovery of the irrational numbers

The invention of the calculus

The development of the concept of infinity

$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$

$\sin \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$

$\sin \theta = \frac{\text{opposite}}{\text{adjacent}}$

$\sin \theta = \frac{\text{hypotenuse}}{\text{adjacent}}$

$\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$

$\cos \theta = \frac{\text{opposite}}{\text{hypotenuse}}$

$\cos \theta = \frac{\text{opposite}}{\text{adjacent}}$

$\cos \theta = \frac{\text{hypotenuse}}{\text{adjacent}}$

$\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$

$\tan \theta = \frac{\text{adjacent}}{\text{opposite}}$

$\tan \theta = \frac{\text{hypotenuse}}{\text{opposite}}$

$\tan \theta = \frac{\text{hypotenuse}}{\text{adjacent}}$

He developed a new model for the solar system

He discovered the existence of other planets

He calculated the distance between the Earth and the Sun

He predicted the occurrence of eclipses

He used a mathematical model to calculate the positions of the Sun and Moon

He observed the positions of the Sun and Moon over time

He consulted ancient texts to find records of past eclipses

He used a combination of all of the above methods

He is considered to be one of the greatest mathematicians of all time

His work had a profound influence on the development of mathematics in India

His work was translated into Arabic and Latin and had a major impact on the development of mathematics in Europe

All of the above

A theorem that gives a formula for the area of a cyclic quadrilateral

A theorem that gives a formula for the volume of a sphere

A theorem that gives a formula for the surface area of a sphere

A theorem that gives a formula for the circumference of a circle

An identity that relates the sine and cosine functions

An identity that relates the sine and tangent functions

An identity that relates the cosine and tangent functions

An identity that relates all three trigonometric functions

A rule for solving quadratic equations

A rule for solving cubic equations

A rule for solving quartic equations

A rule for solving quintic equations