List of top Engineering Mathematics Questions asked in Tamil Nadu Common Entrance Test

The Laplace transform of a signal $X(t)$ is $$ X(s) = \frac{4s + 1}{s^2 + 6s + 3}. $$ The initial value $X(0)$ is:
If \( A \) is a \( 3 \times 3 \) matrix and determinant of \( A \) is 6, then find the value of the determinant of the matrix \((2A)^{-1}\):
If \( \nabla \phi = 2xy^2 \hat{i} + x^2z^2 \hat{j} + 3x^2y^2z^2 \hat{k} \), then \( \phi(x,y,z) \) is:
The Region of Convergence (ROC) of the signal \( x(n) = \delta(n - k), k>0 \) is:
The shortest and longest distance from the point \( (1,2,-1) \) to the sphere \( x^2 + y^2 + z^2 = 24 \) is:
The solution of the given ordinary differential equation \( x \frac{d^2 y}{dx^2} + \frac{dy}{dx} = 0 \) is:
The value of the integral \[ \iiint\limits_{0}^{a, b, c} e^{x+y+z} \, dz \, dy \, dx \] is:
The value of \( m \) so that \( 2x - x^2 + m y^2 \) may be harmonic is:
The value of \( \oint_C \frac{1}{z} dz \), where \( C \) is the circle \( z = e^{i\theta}, 0 \leq \theta \leq \pi \), is:
The area between the parabolas \( y^2 = 4 - x \) and \( y^2 = x \) is given by:
If the system of equations: \[ 3x + 2y + z = 0, \quad x + 4y + z = 0, \quad 2x + y + 4z = 0 \] is given, then:
Let \(M = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}\)The maximum number of linearly independent eigenvectors of \( M \) is:
Which of the following formula is used to fit a polynomial for interpolation with equally spaced data?
The complete integral of the partial differential equation \( pz^2 \sin^2 x + qz^2 \cos^2 y = 1 \) is:
The Laplace transform of a signal \( X(t) \) is \[ X(s) = \frac{4s + 1}{s^2 + 6s + 3}. \] The initial value \( X(0) \) is:
The only function from the following that is analytic is:
If \( A = [a_{ij}] \) is the coefficient matrix for a system of algebraic equations, then a sufficient condition for convergence of Gauss-Seidel iteration method is:
Given the inverse Fourier transform of \(f(s) = \begin{cases} a - |s|, & |s| \leq a \\ 0, & |s|>a \end{cases}\).The value of \[ \int_0^\pi \left( \frac{\sin x}{x} \right)^2 dx \] is:
For a Binomial distribution with mean 4 and variance 2, the value of \( n \) is:
A discrete random variable \( X \) has the probability mass function given by \[ p(x) = c x, \quad x = 1,2,3,4,5. \] The value of the constant \( c \) is:
For applying Simpson's \( \frac{1}{3} \) rule, the given interval must be divided into how many number of sub-intervals?
For applying Simpson's \( \frac{1}{3} \) rule, the given interval must be divided into how many number of sub-intervals?
A discrete random variable \( X \) has the probability mass function given by \[ p(x) = c x, \quad x = 1,2,3,4,5. \] The value of the constant \( c \) is:
Which of the following formula is used to fit a polynomial for interpolation with equally spaced data?
For a Binomial distribution with mean 4 and variance 2, the value of \( n \) is: