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BEU 1st Sem Maths Important Questions 2024 – CSE, Electrical & Civil

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Preparing for the BEU 1st Sem Maths Important Questions 2024 – CSE, Electrical & Civil, this page guide covers the most important questions, based on the latest syllabus and PYQs. Access the model paper, high-weightage topics, and key questions to boost your preparation and score better.

SECTION A: Short Answer Type Questions

(1) Find the rank of the matrix. (PYQ) $$ \begin{bmatrix} 3 & 2 & -1 \\ 4 & 2 & 6 \\ 7 & 4 & 5 \end{bmatrix} $$

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BEU 1st Sem Maths Important Questions, math electrical, math civil, beu maths pyq, math cse

(2). Define the Jacobian and write its formula for transformation from Cartesian to polar coordinates. (High Weightage)

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BEU 1st Sem Maths Important Questions, math electrical, math civil, beu maths pyq, math cse

(3). State and prove Rolle’s Theorem. (PYQ)

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(4). Expand $$ f(x) = \frac{1}{1 + x^2} $$ using Taylor Series about x = 0. (PYQ)

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BEU 1st Sem Maths Important Questions, math electrical, math civil, beu maths pyq, math cse

(5). Write the formula and condition for applying Simpson’s 1/3 Rule. (High Weightage)

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BEU 1st Sem Maths Important Questions, math electrical, math civil, beu maths pyq, math cse

(6). State Parseval’s theorem for Fourier series. (PYQ)

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BEU 1st Sem Maths Important Questions, math electrical, math civil, beu maths pyq, math cse

(7). Define and explain linearly independent vectors. (High Weightage)

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BEU 1st Sem Maths Important Questions, math electrical, math civil, beu maths pyq, math cse
SECTION B: Long Answer Type Questions
Q1. Linear Algebra – I

(a) Use Gauss-Jordan method to find inverse of:(PYQ) $$ A = \begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix} $$

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(a) Use Gauss-Jordan method to find inverse of:(PYQ) $$ A = \begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix} $$

(b) Determine the value of p such that the rank of matrix is 3. (PYQ) $$ \begin{bmatrix} 1 & 1 & -1 & 0 \\ 4 & 4 & -3 & 1 \\ p & 2 & 2 & 2 \\ 9 & 9 & p & 3 \end{bmatrix} $$

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(b) Determine the value of p such that the rank of matrix is 3. (PYQ) $$ \begin{bmatrix} 1 & 1 & -1 & 0 \\ 4 & 4 & -3 & 1 \\ p & 2 & 2 & 2 \\ 9 & 9 & p & 3 \end{bmatrix} $$
Q2. Linear Algebra – II

(a) Verify Cayley-Hamilton theorem for:$$ A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{bmatrix} $$and hence find $ A^{-1} $. (PYQ)

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(a) Verify Cayley-Hamilton theorem for:$$ A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{bmatrix} $$and hence find $ A^{-1} $. (PYQ)
(a) Verify Cayley-Hamilton theorem for:$$ A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{bmatrix} $$and hence find $ A^{-1} $. (PYQ)

(b) Find eigenvectors and eigenvalues of: (PYQ)$$ \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix} $$

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(b) Find eigenvectors and eigenvalues of: (PYQ)$$ \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix} $$
(b) Find eigenvectors and eigenvalues of: (PYQ)$$ \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix} $$
(b) Find eigenvectors and eigenvalues of: (PYQ)$$ \begin{bmatrix} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix} $$
Q3. Calculus & Multivariable Calculus

(a) Obtain the Fourier series of $ f(x) = \pi x $ on $ (0, 2) $ and show:(PYQ) $$ \frac{1}{1^2} + \frac{1}{3^2} + \frac{1}{5^2} + \cdots = \frac{\pi^2}{8} $$

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(a) Obtain the Fourier series of $ f(x) = \pi x $ on $ (0, 2) $ and show:(PYQ) $$ \frac{1}{1^2} + \frac{1}{3^2} + \frac{1}{5^2} + \cdots = \frac{\pi^2}{8} $$
(a) Obtain the Fourier series of $ f(x) = \pi x $ on $ (0, 2) $ and show:(PYQ) $$ \frac{1}{1^2} + \frac{1}{3^2} + \frac{1}{5^2} + \cdots = \frac{\pi^2}{8} $$

(b) Using Beta and Gamma functions, evaluate: $$ \iiint x^{l-1} y^{m-1} z^{n-1} \, dx\,dy\,dz $$ over the region $ x + y + z \le 1, \quad x,y,z \ge 0 $. (PYQ)

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(b) Using Beta and Gamma functions, evaluate: $$ \iiint x^{l-1} y^{m-1} z^{n-1} \, dx\,dy\,dz $$ over the region $ x + y + z \le 1, \quad x,y,z \ge 0 $. (PYQ)
Q4. Numerical Methods + Vector Calculus

(a) Use Runge-Kutta 4th order method to solve: $$ \frac{dy}{dx} = \frac{y – x}{y + x}, \quad y(0) = 1, \quad h = 0.5 $$(PYQ)

Solution: Runge-Kutta 4th Order Method Solution

Given:

The differential equation: $$ \frac{dy}{dx} = \frac{y – x}{y + x}, \quad y(0) = 1 $$ with step size ( h = 0.5 ).

Method:

The RK4 method computes: $$ y_{i+1} = y_i + \frac{1}{6}(k_1 + 2k_2 + 2k_3 + k_4) $$ where: $$ k_1 = h \cdot f(x_i, y_i) $$ $$ k_2 = h \cdot f\left(x_i + \frac{h}{2}, y_i + \frac{k_1}{2}\right) $$ $$ k_3 = h \cdot f\left(x_i + \frac{h}{2}, y_i + \frac{k_2}{2}\right) $$ $$ k_4 = h \cdot f\left(x_i + h, y_i + k_3\right) $$

$ Compute ( k_1 )$

$At ( x_0 = 0 ), ( y_0 = 1 )$: $$ k_1 = 0.5 \cdot \frac{1 – 0}{1 + 0} = 0.5 \cdot 1 = 0.5 $$

$ Compute ( k_2 )$

$At ( x = 0.25 ), ( y = 1 + \frac{0.5}{2} = 1.25 )$: $$ k_2 = 0.5 \cdot \frac{1.25 – 0.25}{1.25 + 0.25} = 0.5 \cdot \frac{1}{1.5} \approx 0.333333 $$

$Compute ( k_3 )$

At $( x = 0.25 ), ( y = 1 + \frac{0.333333}{2} \approx 1.166666)$: $$ k_3 = 0.5 \cdot \frac{1.166666 – 0.25}{1.166666 + 0.25} = 0.5 \cdot \frac{0.916666}{1.416666} \approx 0.323529 $$

$Compute ( k_4 )$

At$ ( x = 0.5 ), ( y = 1 + 0.323529 \approx 1.323529 )$: $$ k_4 = 0.5 \cdot \frac{1.323529 – 0.5}{1.323529 + 0.5} = 0.5 \cdot \frac{0.823529}{1.823529} \approx 0.2258 $$

Combine for $( y(0.5) )$

$$ y(0.5) = 1 + \frac{1}{6}(0.5 + 2 \times 0.333333 + 2 \times 0.323529 + 0.2258) $$ $$ = 1 + \frac{1}{6}(2.039524) \approx 1.3399 $$

Final Answer:

$$ \boxed{y(0.5) \approx 1.340} $$

(b) Evaluate the surface integral using Stokes’ theorem for: $$ \vec{F} = (3x – y)\hat{i} – 2yz^2\hat{j} – 2y^2z\hat{k} $$over the surface of sphere $ x^2 + y^2 + z^2 = 16, \quad z > 0 $. (PYQ)

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(b) Evaluate the surface integral using Stokes’ theorem for: $$ \vec{F} = (3x - y)\hat{i} - 2yz^2\hat{j} - 2y^2z\hat{k} $$over the surface of sphere $ x^2 + y^2 + z^2 = 16, \quad z > 0 $. (PYQ)
(b) Evaluate the surface integral using Stokes’ theorem for: $$ \vec{F} = (3x - y)\hat{i} - 2yz^2\hat{j} - 2y^2z\hat{k} $$over the surface of sphere $ x^2 + y^2 + z^2 = 16, \quad z > 0 $. (PYQ)
(b) Evaluate the surface integral using Stokes’ theorem for: $$ \vec{F} = (3x - y)\hat{i} - 2yz^2\hat{j} - 2y^2z\hat{k} $$over the surface of sphere $ x^2 + y^2 + z^2 = 16, \quad z > 0 $. (PYQ)
Conclusion:

In this post, we provided detailed solutions for BEU Maths PYQs for CSE / BEU B.Tech CSE Math Solved Papers​ previous year questions.BEU CSE Math 2023 PYQ with Solutions and 1st Semester Math Solved Papers are now available to help students prepare effectively for Bihar Engineering University exams Understanding these solutions will help you strengthen your core concepts and improve your exam performance. Keep practicing and exploring related topics to enhance your knowledge.

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