JIIT University B.Tech Question Paper

Model B.Tech Engineering Mathematics Question Paper based on the JIIT (Jaypee Institute of Information Technology) University pattern, suitable for 1st / 2nd Semester students. Call 9650308924 to hire in B.Tech Tutors. Online Study Mart Provide Online B.Tech Tuition For JIIT University. Hire the best B.Tech Tutors from Online Study Mart.

Jaypee Institute of Information Technology (JIIT), Noida

B.Tech – Engineering Mathematics

Time: 3 Hours
Maximum Marks: 70

Instructions:

All questions are compulsory.
Use of non-programmable calculator is permitted.
Assume suitable data if required and state it clearly.
Draw neat diagrams wherever necessary.

Section A (Short Answer Questions)

(10 × 2 = 20 Marks)

Find the rank of the matrix

$[1224]\begin{bmatrix} 1 & 2 \\ 2 & 4 \end{bmatrix}$

Define eigenvalues of a matrix.
Evaluate:

$dx\int e^{x} \cos x \, dx$

State Rolle’s Theorem.
Find the Laplace transform of $f (t) = 1$ .
Write the Cauchy–Riemann equations.
Define divergence of a vector field.
Find the order and degree of the differential equation:

$(d2ydx2)3+y=0\left(\frac{d^2y}{dx^2}\right)^3 + y = 0$

Define probability density function (PDF).
What is meant by orthogonal vectors?

Section B (Medium Answer Questions)

(5 × 6 = 30 Marks)

Solve the system of equations using Gauss Elimination Method:

$\\ 2x + 3y + z = 10 \\ x + 2y + 3z = 13$

Find the eigenvalues and eigenvectors of the matrix:

$[2112]\begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}$

Evaluate:

$dx\int \frac{x^2}{x^2 + 1} \, dx$

Verify Green’s Theorem for

$dy\oint (x^2 – y^2)\,dx + 2xy\,dy$

over the region bounded by $y = x$ and $y = x^2$ .

Solve the differential equation:

$dydx+y=e−x\frac{dy}{dx} + y = e^{-x}$

Section C (Long Answer Questions)

(2 × 10 = 20 Marks)

(a) Using Laplace Transform, solve:

$d2ydt2+3dydt+2y=0\frac{d^2y}{dt^2} + 3\frac{dy}{dt} + 2y = 0$

given $y (0) = 1$ , $y^{'} (0) = 0$ .
OR
(b) Find the Fourier series expansion of $f (x) = x$ in the interval $(−π,π)(-\pi, \pi)$ .

(a) Solve the partial differential equation using Charpit’s method:

$p^2 + q^2 = z$

OR
(b) Find the mean and variance of the following distribution:

x	0	1	2	3
P(x)	0.1	0.3	0.4	0.2