Indian Mathematical Calculus for Transportation

Description: Indian Mathematical Calculus for Transportation Quiz
Number of Questions: 16
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Who is considered the father of Indian mathematical calculus?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Madhava of Sangamagrama


Correct Option: D
Explanation:

Madhava of Sangamagrama is credited with developing the fundamental concepts of calculus, including the idea of the derivative and the integral, centuries before their formalization in Europe.

What is the name of the series developed by Madhava of Sangamagrama to approximate the value of π?

  1. Madhava series

  2. Gregory series

  3. Leibniz series

  4. Taylor series


Correct Option: A
Explanation:

The Madhava series is an infinite series that can be used to approximate the value of π. It is given by the formula: π = 4 * (1 - 1/3 + 1/5 - 1/7 + ...).

Which Indian mathematician developed a method for finding the area of a triangle using calculus?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Nilakantha Somayaji


Correct Option: D
Explanation:

Nilakantha Somayaji developed a method for finding the area of a triangle using calculus in the 15th century. His method is based on the idea of dividing the triangle into an infinite number of small triangles and then summing their areas.

What is the name of the theorem that states that the area under a curve can be found by integrating the function that defines the curve?

  1. Fundamental Theorem of Calculus

  2. Mean Value Theorem

  3. Cauchy's Integral Theorem

  4. Stokes' Theorem


Correct Option: A
Explanation:

The Fundamental Theorem of Calculus is a fundamental theorem in calculus that establishes a relationship between differentiation and integration. It states that the area under a curve can be found by integrating the function that defines the curve.

Which Indian mathematician developed a method for finding the volume of a solid of revolution using calculus?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Srinivasa Ramanujan


Correct Option: D
Explanation:

Srinivasa Ramanujan developed a method for finding the volume of a solid of revolution using calculus in the early 20th century. His method is based on the idea of dividing the solid into an infinite number of thin disks and then summing their volumes.

What is the name of the method developed by Srinivasa Ramanujan for finding the volume of a solid of revolution?

  1. Ramanujan's Method

  2. Cavalieri's Principle

  3. Disk Method

  4. Shell Method


Correct Option: A
Explanation:

Ramanujan's Method is a method for finding the volume of a solid of revolution developed by Srinivasa Ramanujan in the early 20th century. It is based on the idea of dividing the solid into an infinite number of thin disks and then summing their volumes.

Which Indian mathematician developed a method for finding the center of mass of a region using calculus?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Gangesha Upadhyaya


Correct Option: D
Explanation:

Gangesha Upadhyaya developed a method for finding the center of mass of a region using calculus in the 14th century. His method is based on the idea of dividing the region into an infinite number of small pieces and then summing their masses and moments.

What is the name of the method developed by Gangesha Upadhyaya for finding the center of mass of a region?

  1. Gangesha's Method

  2. Centroid Method

  3. Moment Method

  4. Composite Method


Correct Option: A
Explanation:

Gangesha's Method is a method for finding the center of mass of a region developed by Gangesha Upadhyaya in the 14th century. It is based on the idea of dividing the region into an infinite number of small pieces and then summing their masses and moments.

Which Indian mathematician developed a method for finding the moment of inertia of a region using calculus?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Bhaskara I


Correct Option: D
Explanation:

Bhaskara I developed a method for finding the moment of inertia of a region using calculus in the 7th century. His method is based on the idea of dividing the region into an infinite number of small pieces and then summing their masses and distances from a given axis.

What is the name of the method developed by Bhaskara I for finding the moment of inertia of a region?

  1. Bhaskara's Method

  2. Moment of Inertia Method

  3. Parallel Axis Theorem

  4. Perpendicular Axis Theorem


Correct Option: A
Explanation:

Bhaskara's Method is a method for finding the moment of inertia of a region developed by Bhaskara I in the 7th century. It is based on the idea of dividing the region into an infinite number of small pieces and then summing their masses and distances from a given axis.

Which Indian mathematician developed a method for finding the work done by a force using calculus?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Jyeshtadeva


Correct Option: D
Explanation:

Jyeshtadeva developed a method for finding the work done by a force using calculus in the 16th century. His method is based on the idea of dividing the path of the force into an infinite number of small segments and then summing the products of the force and the displacement along each segment.

What is the name of the method developed by Jyeshtadeva for finding the work done by a force?

  1. Jyeshtadeva's Method

  2. Work-Energy Theorem

  3. Principle of Virtual Work

  4. Lagrange's Equations


Correct Option: A
Explanation:

Jyeshtadeva's Method is a method for finding the work done by a force developed by Jyeshtadeva in the 16th century. It is based on the idea of dividing the path of the force into an infinite number of small segments and then summing the products of the force and the displacement along each segment.

Which Indian mathematician developed a method for finding the velocity and acceleration of a moving object using calculus?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Narayana Pandit


Correct Option: D
Explanation:

Narayana Pandit developed a method for finding the velocity and acceleration of a moving object using calculus in the 14th century. His method is based on the idea of dividing the time interval into an infinite number of small intervals and then summing the products of the force and the displacement along each interval.

What is the name of the method developed by Narayana Pandit for finding the velocity and acceleration of a moving object?

  1. Narayana Pandit's Method

  2. Kinematic Equations

  3. Newton's Laws of Motion

  4. Lagrange's Equations


Correct Option: A
Explanation:

Narayana Pandit's Method is a method for finding the velocity and acceleration of a moving object developed by Narayana Pandit in the 14th century. It is based on the idea of dividing the time interval into an infinite number of small intervals and then summing the products of the force and the displacement along each interval.

Which Indian mathematician developed a method for finding the trajectory of a projectile using calculus?

  1. Aryabhata

  2. Bhaskara II

  3. Brahmagupta

  4. Sridhara Acharya


Correct Option: D
Explanation:

Sridhara Acharya developed a method for finding the trajectory of a projectile using calculus in the 12th century. His method is based on the idea of dividing the trajectory into an infinite number of small segments and then summing the products of the force and the displacement along each segment.

What is the name of the method developed by Sridhara Acharya for finding the trajectory of a projectile?

  1. Sridhara Acharya's Method

  2. Projectile Motion Equations

  3. Newton's Laws of Motion

  4. Lagrange's Equations


Correct Option: A
Explanation:

Sridhara Acharya's Method is a method for finding the trajectory of a projectile developed by Sridhara Acharya in the 12th century. It is based on the idea of dividing the trajectory into an infinite number of small segments and then summing the products of the force and the displacement along each segment.

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