Studying **Degree 1st Year 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 Year 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 Year 1st Sem Maths Important Questions

Course |
BSC (Bachelor of Science) |

Subject |
Maths |

Content |
Important Questions |

Semester |
1st Year 1st Sem |

Provide by |
Hindijankaripur |

Official Site |
Hindijankaripur.com |

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

**Theory Question**

Define a limit and explain the concept with an example.

State and prove the Intermediate Value Theorem.

How do you find the derivative of a function using the definition of a derivative?

Discuss the applications of derivatives in real-life scenarios.

What is the Mean Value Theorem? Provide a proof.

Explain the method of integration by parts with examples.

Solve an improper integral.

What is the determinant of a matrix? How is it calculated?

Discuss eigenvalues and eigenvectors of a matrix.

Solve a system of linear equations using matrix methods.

Explain the method of Gauss-Jordan elimination.

What is the inner product in a vector space? Provide examples.

Solve a first-order linear ODE using an integrating factor.

What is a homogeneous differential equation? Provide the method to solve it.

Discuss the method of separation of variables in solving ODEs.

Solve a second-order linear differential equation with constant coefficients.

Explain the Laplace transform and its application in solving differential equations.

What is a system of differential equations? Solve a simple system.

Discuss the stability of equilibrium solutions in differential equations.

What are partial differential equations (PDEs)? Provide examples.

Solve a simple heat equation using Fourier series methods.

**Practical Questions**

Find the derivative of the function ( f(x) = x^3 – 5x + 6 ) and determine the critical points.

Calculate the area under the curve ( y = 4x – x^2 ) from ( x = 0 ) to ( x = 4 ).

Using the limit definition, compute the derivative of ( f(x) = \sqrt{x} ) at ( x = 4 ).

Determine the convergence or divergence of the series (\sum_{n=1}^{\infty} \frac{1}{n^2} ).

Evaluate the integral (\int_0^{\pi} \sin(x) dx).

Given the matrix ( A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} ), find its inverse, if it exists.

Solve the vector equation ( \mathbf{x} + 2\mathbf{y} = \mathbf{z} ) for (\mathbf{x}) given that (\mathbf{y} = \begin{bmatrix} 1 \ -1 \end{bmatrix}) and (\mathbf{z} = \begin{bmatrix} 3 \ 1 \end{bmatrix}).

Determine whether the vectors ( \mathbf{v}_1 = \begin{bmatrix} 1 \ 0 \ 2 \end{bmatrix} ), ( \mathbf{v}_2 = \begin{bmatrix} 2 \ -1 \ 4 \end{bmatrix} ), and ( \mathbf{v}_3 = \begin{bmatrix} 0 \ 1 \ 2 \end{bmatrix} ) are linearly independent.

Find the eigenvalues of the matrix ( B = \begin{bmatrix} 0 & 1 \ -2 & -3 \end{bmatrix} ).

Compute the dot product of ( \mathbf{a} = \begin{bmatrix} 4 \ 3 \end{bmatrix} ) and ( \mathbf{b} = \begin{bmatrix} -1 \ 2 \end{bmatrix} ).

Solve the differential equation ( \frac{dy}{dx} = 3y ) with the initial condition ( y(0) = 5 ).

Find the particular solution to the differential equation ( \frac{d^2 y}{dx^2} – 5\frac{dy}{dx} + 6y = 12x ) given that ( y(0) = 0 ) and ( y'(0) = 1 ).

Apply the method of separation of variables to solve ( \frac{dy}{dx} = xy ).

Using the Laplace transform, solve the initial value problem ( \frac{d^2 y}{dx^2} + 9y = 0 ) with ( y(0) = 2 ) and ( y'(0) = 0 ).

Determine the equilibrium solutions of the differential equation ( \frac{d^2 y}{dx^2} + \frac{dy}{dx} – 6y = 0 ) and discuss their stability.

**Also Read: BSC 2nd Sem Maths Honours Important Questions**

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