List of top Questions asked in Andhra Pradesh Post Graduate Engineering Common Entrance Test

What is the use of the Ellingham diagram in metallurgy?
Given \( x_0 \neq 0 \), the iteration \[ x_{n+1} = \frac{1}{2} \left( -\frac{9}{x_n} + x_n \right), n \geq 0 { is a} \]
Suppose \( \sum_{n=1}^{\infty} a_n (x - 2)^n \) is convergent at \( x = -5 \), then it need not be convergent on which interval?
The set of all critical points of the function \( f(x) = |x^2 - 1| \) on \( [-2, 2] \) is ...........

The surface integral \( \int_S x^2 \, dS \) over the upper hemisphere 
\[ z = \sqrt{1 - x^2 - y^2}  \]
with radius 1 is ..........

Consider the system of equations:
\[ x + 2y - z = 3 \\ 2x + 4y - 2z = 7 \\ 3x + 6y - 3z = 9 \]
Which of the following statements is true about the system?
A cantilever beam carrying a point load at free end, BM at fixed end is:
Which is a bottom-up approach in nanotechnology?
A furnace uses 1000 kJ of fuel energy.
Useful heat output = 700 kJ.
What is the furnace efficiency?

When hydrogen peroxide is added to an acidified solution of KI, iodine (I2) is liberated. In this case, hydrogen peroxide acts as?
 

The general solution of the ordinary differential equation
\[ \frac{dy}{dx} = \log \left( x \frac{dy}{dx} - y \right) \] is ...........
If \( X \) is a normal distribution with mean \( \mu \) and variation \( \sigma^2 \), then the standard deviation and the mean of \( Z = \frac{x - \mu}{\sigma} \) are ........... , ...........
In a binomial distribution \( B(n = 10, p) \), the probability of getting exactly 4 successes equals the probability of getting exactly 6 successes. What is the mean of the distribution?
The work done during isothermal expansion of an ideal gas is:
What is the primary reason for the unique properties of nanomaterials?
In semiconductors, light is emitted when:
The monomer of poly vinyl chloride (PVC) is?
If \( A \) is a 3 \(\times\) 3 matrix with eigenvalues 1, 2, and 3, what is the trace of \( A^2 - 3A + I \)?
A direction in which the function \( f(x) = 2x + y \) remains constant at the point (1,1) is .........
Adiabatic flame temperature is highest when:
The Zeroth Law of Thermodynamics is used to define:
Glass transition temperature (\(T_g\)) in polymers marks:
According to free electron theory, electrical conductivity increases with:
A quantum dot is a nanomaterial of dimension?
A ductile material exhibits: