List of top Questions asked in Tamil Nadu Common Entrance Test

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:
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:
The value of the integral \[ \iiint\limits_{0}^{a, b, c} e^{x+y+z} \, dz \, dy \, dx \] is:
The area between the parabolas \( y^2 = 4 - x \) and \( y^2 = x \) is given by:
The complete integral of the partial differential equation \( pz^2 \sin^2 x + qz^2 \cos^2 y = 1 \) is:
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 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:
If the system of equations: \[ 3x + 2y + z = 0, \quad x + 4y + z = 0, \quad 2x + y + 4z = 0 \] is given, then:

The degree of static indeterminacy for the frame shown in the figure is 

As per IS 456 : 2000, Limit state of collapse – flexure, the maximum strain in reinforcing bars under tension at failure shall not be less than ……… , where \( f_y \) is the characteristic strength of steel and \( E_s \) is the Modulus of elasticity of steel.

As per IS800-2007, the minimum centre-to-centre bolt spacing measured in the direction of stress is ……. , where \( d \) is the nominal diameter of bolt.

The net section strength of a tension member …………. with the increase in ductility of steel.

Consider the following statements:
1. ‘Relative compaction’ is not the same as ‘relative density’.
2. Vibroflotation is not effective in the case of highly cohesive soils.
3. ‘Zero air void line’ and ‘100\% saturation line’ are not identical.
Of these statements:
Consider the following statements:
1. Constant head permeameter is best suited for determination of coefficient of permeability of highly impermeable soils.
2. Coefficient of permeability of a soil mass decreases with an increase in viscosity of the pore fluid.
3. Coefficient of permeability of a soil mass increases with an increase in temperature of the fluid.
Of these statements:

What will be the unit weight of a fully saturated soil sample having water content of 38% and grain specific gravity of 2.65?

The hydraulic efficiency of an impulse turbine is maximum when the velocity is …………. of the jet velocity.

The dimensions of Chezy’s coefficient \( C \) in [MLT] notation system are:
In the preservation process of timber, the surface is burnt and the burnt part acts as a protective coating is named as

The bulking of the sand is increased in volume from 20% to 40% of various sand and moisture content ranges from ……… to ……….. percent.

A fixed beam of uniform cross-section carries a point load \( P \) at the mid-span. If the moment of inertia of the middle half portion is reduced to half its previous value, then the fixed end moments will
What will happen if the frequency of power supply in a pure capacitor is doubled?
Which cross-section of the beam subjected to bending moment is more economical?
Which one of the following represents an open thermodynamic system?