Studying **Degree 1st Sem Maths Important Questions** is Good for your Exam Preparation. They Can Help You To Cover Maximum Syllabus In Minimum Time.

Maths Is A Difficult Subject if You Lack Knowledge About Its Understanding. In This Post We Have Compiled Some important Degree 1st Sem Maths Important Questions.

These Important Question Mentioned Here Are Extracted From Previous Year Question Papers And They Help You Learn Important Knowledge about Your Syllabus…

## Degree 1st Sem Maths Important Questions

Course | BSC (Bachelor of Science) |

Subject | Maths |

Content | Important Questions |

Semester | 1st Sem |

Provide by | Hindijankaripur |

Official Site | Hindijankaripur.com |

Telegram | https://t.me/studentcafeindia |

**Theory Question**

Explain the concept of a limit and its importance in calculus. How does the definition of continuity rely on limits?

Discuss the physical interpretation of the derivative of a function. Provide examples where derivatives are used in real-life applications.

Describe the Fundamental Theorem of Calculus and explain how it bridges the concept of differentiation and integration.

Compare and contrast various techniques of integration such as substitution, integration by parts, and partial fractions.

Define a convergent series and discuss the tests for convergence. Provide examples of conditionally convergent series.

What are vector spaces and why are they fundamental in linear algebra? Provide examples of vector spaces other than R^n.

Discuss the relationship between matrices and linear transformations. How do matrices represent linear transformations in different bases?

Explain the significance of eigenvalues and eigenvectors in solving systems of linear equations and in other applications such as stability analysis.

Define an ordinary differential equation (ODE) and discuss the methods to solve first-order ODEs.

Provide examples of how differential equations are used to model real-world phenomena in physics, engineering, or economics.

**Practical Questions**

Evaluate the limit (\lim_{x \to 2} \frac{x^2 – 4}{x – 2}).

Find the derivative of the function (f(x) = x^3 – 5x + 6) using the power rule.

Use derivatives to sketch the curve of (f(x) = x^3 – 3x^2 + 2), indicating all critical points, inflection points, and asymptotes.

Calculate the area under the curve (f(x) = 4x – x^2) from (x = 0) to (x = 4) using definite integrals.

Solve the linear system of equations (\begin{align*} 3x + 4y &= 5, \ 2x – y &= 1 \end{align*}) using matrix methods.

Determine the eigenvalues and eigenvectors of the matrix (\begin{bmatrix} 4 & 1 \ 2 & 3 \end{bmatrix}).

Use integration by parts to find the integral of (x \cdot e^x).

Determine if the series (\sum_{n=1}^\infty \frac{1}{n^2}) converges and, if so, find its sum.

Solve the differential equation (\frac{dy}{dx} + y = x), given that (y(0) = 1).

**Also Read: Degree 1st Year 1st Sem Maths Important Questions**

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