BEU 2024 CSE Special Maths Exam | Most Repeated PYQs + Solutions

Preparing for the BEU 2024 CSE Special Maths Exam? Here you’ll find the most repeated PYQs with clear, step-by-step solutions, based on the latest syllabus — perfect for quick and smart revision.

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Q.1 Choose the correct option for any seven of the following:

(a) The value of $c$ in the Mean Value Theorem of
$$f(b) – f(a) = (b – a)f'(c)$$
for $f(x) = a_1x^3 + a_2x + a_3$ in $(a, b)$ is:
(i) $b + a$
(ii) $b – a$
(iii) $\dfrac{b + a}{2}$
(iv) $\dfrac{b – a}{2}$

Answer: (iii) $\dfrac{b + a}{2}$

(b) $\lim_{x \to 0} \frac{\sin x^2}{x}$ is equal to:
(i) $0$
(ii) $\infty$
(iii) $1$
(iv) $-1$

Answer: (i) $0$

(c) A triangle of maximum area inscribed in a circle of radius $r$ is:
(i) A right-angled triangle with hypotenuse $2r$
(ii) Is An equilateral triangle
(iii) Is An isosceles triangle of height $r$
(iv) Does not exist

Answer: (ii) Is An equilateral triangle

(d) If $u = \log\left(\frac{x^2}{y}\right)$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} = ?$ is equal to:
(i) $2u$
(ii) $3u$
(iii) $u$
(iv) $1$

Answer: (iv) $1$

(e) The Fourier series of the periodic function:
$f(x) = \begin{cases} 1, & -5 < x < 0 \end{cases}\ f(x) = \begin{cases} 3, when& 0 < x < 5 \end{cases}\. At $x = 5,

the series converges to:
(i) 0
(ii) 1
(iii) 2
(iv) 3

Answer: (iii) 2

(f) The value of $\Gamma\left(\frac{1}{2}\right)$ is:
(i) $\pi$
(ii) $\sqrt{\pi}$
(iii) $\frac{\pi}{2}$
(iv) $\frac{\sqrt{\pi}}{2}$

Answer: (ii) $\sqrt{\pi}$

(g) The value of $curl ( grad f )$, where $f = 2x^2 – 3x^2 + 4xz$, is:
(i) $4x – 6y + 8z$
(ii) $4x\hat{i} – 6y\hat{j} + 8z\hat{k}$
(iii) $0$
(iv) $3$

Answer: (iii) $0$

(h) The series
$$
1 – \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} – \frac{1}{\sqrt{4}} + \cdots
$$
is

(i) Oscillatory
(ii) Conditionally convergent
(iii) Divergent
(iv) Absolutely convergent

Answer: (ii) Conditionally convergent

(i) A square matrix $A$ is called orthogonal if:
(i) $A = A^2$
(ii) $A^1 = A^{-1}$
(iii) $AA^{-1} = I$
(iv) None of these

Answer: (iii) $AA^{-1} = I$

(j) The range rank of the matrix
$$
A = \begin{bmatrix}
2 & 3 & -1 & -1 \\
1 & -1 & -2 & -4 \\
3 & 1 & 3 & -2 \\
6 & 3 & 0 & -7
\end{bmatrix}
$$
is:

(i) 1
(ii) 2
(iii) 3
(iv) 4

Answer:

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Q.2 (a) Obtain the fourth-degree Taylor’s polynomial approximation to
$$f(x) = e^{2x}$$ about $x = 0$. Find the maximum error when $0 \leq x \leq 0.5$.

See Solution

(b) Evaluate
$$\lim_{x \to 0} \frac{(1 + x)^{\frac{1}{x}} – e}{x}$$

See Solution

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Q.3 (a) Discuss the convergence of the series:
$$
x + \frac{3^3 x^3}{3!} + \frac{4^4 x^4}{4!} + \frac{5^5 x^5}{5!} + \cdots \quad (x > 0)
$$

See Solution

(b) Test the series $\frac{x}{\sqrt{2}} – \frac{x^2}{\sqrt{5}} + \frac{x^3}{\sqrt{7}}- \cdots$ for absolute convergence and conditional convergence.

See Solution

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Q.4 (a) If $f(x) = |\cos x|$, expand $f(x)$ as a Fourier series in the interval $(-\pi, \pi)$.

See Solution

(b) Express $f(x) = x$ as a half-range cosine series in $0 < x < 2$.

See Solution

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Q.5 (a) Evaluate $\int_0^\infty e^{-ax} x^{m-1} \sin(bx) \, dx$ in terms of Gamma function.

See Solution

(b) Find the surface of the solid formed by revolving the cardioid
$$r = a(1 + \cos \theta)$$

See Solution

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Q.6 (a) If $u = f(x – y, y – z, z – x)$, prove that
$$
\frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} + \frac{\partial u}{\partial z} = 0
$$

See Solution

(b) In a plane triangle, find the maximum value of $\cos A \cdot \cos B \cdot \cos C.$

See Solution

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Q.7 (a) Find the directional derivative of
$$\phi = 5x^2 y – 5y^2 z + 2.5 z^2 x$$
at the point $P(1, 1, 1)$ in the direction of the line
$$\frac{x-1}{1} = \frac{y-2}{2} = \frac{z}{3}$$

See Solution

(b) Show that
$$\nabla \times (\nabla \times \vec{F}) = \nabla (\nabla \cdot \vec{F}) – \nabla^2 \vec{F}$$

See Solution

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Q.8 (a) Using elementary row operations, find the inverse of matrix
$$
A = \begin{bmatrix}
1 & 1 & 3 \\
1 & 3 & -3 \\
-2 & -4 & -4
\end{bmatrix}
$$

See Solution

(b) Solve the system of linear equations:
$$
\begin{aligned}
2x_1 + x_2 – x_3 + 3x_4 &= 11 \\
x_1 – 2x_2 + x_3 + x_4 &= 8 \\
4x_1 + 7x_2 + 2x_3 – x_4 &= 0 \\
3x_1 + 5x_2 + 4x_3 + 4x_4 &= 17
\end{aligned}
$$

See Solution

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Q.9 (a) Find the eigenvalues and eigenvectors of the matrix
$$
A = \begin{bmatrix}
4 & 6 & 6 \\
1 & 3 & 2 \\
-1 & -4 & -3
\end{bmatrix}
$$

See Solution

(b) Find the matrix $P$ which transforms the matrix
$$
A = \begin{bmatrix}
1 & 1 & 3 \\
1 & 5 & 1 \\
3 & 1 & 1
\end{bmatrix}
$$
to diagonal form and hence diagonalize matrix $A$.

See Solution

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Conclusion:

In this post, we provided detailed solutions for BEU Maths PYQs for CSE / BEU BEU 2024 CSE Special Maths Exam | Most Repeated PYQs + Solutions 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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 Disclaimer:

The solutions provided here are based on our best knowledge and are for educational purposes only. We encourage students to refer to their official study materials and consult their professors for further clarification.

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