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

The probability distribution of a random variable \( X \) is given below:
\[ \begin{array}{|c|c|c|c|c|c|} \hline X = x & 10 & 20 & 30 & 40 & 50 \\ \hline P(X = x) & k & 2k & 3k & 4k & 5k \\ \hline \end{array} \] Then, \( P(X = 50) - \dfrac{P(X < 30)}{P(X > 20)} \) = ...........
If \( X \) is a continuous random variable with the probability density function \[ f(x) = \begin{cases} K(1 - x^3), & \text{if } 0 < x < 1 \\ 0, & \text{otherwise} \end{cases} \] Then, the value of \( K \) is ..........
The complex-valued function \( f(z) = iz - |z|^2 \) is analytic at ...........
Convert the non-linear equation \( xy' + y = x^4 y^3 \) into a linear one using the transformation \( z = y^{-2} \).
The linear equation is ...........
If \( A = \begin{pmatrix} -3 & 2 \\ 1 & 0 \end{pmatrix} \) is a \( 2 \times 2 \) matrix, then \( A \) satisfies the relation ...........
Let \( i \) be an imaginary number such that \( i = \sqrt{-1} \). Let \( a \) and \( b \) be real numbers satisfying \( a^2 + b^2 = 1 \).
Then, the eigenvalues of the matrix \[ \begin{bmatrix} -a & b \\ b & a \end{bmatrix} \] are ...........
If \( \sin x \) is a solution of the differential equation \[ \dfrac{d^4 y}{dx^4} + 2 \dfrac{d^3 y}{dx^3} + 6 \dfrac{d^2 y}{dx^2} + 2 \dfrac{dy}{dx} + 5y = 0, \] then the general solution is ...........
The directional derivative of \( f(x, y, z) = xyz \) at the point \( (1, 2, 3) \) in the direction of the vector \( 2\hat{i} + \hat{j} - 2\hat{k} \) is ...........
Suppose \( R_1 \) and \( R_2 \) are reflexive relations on a set \( A \). Which of the following statements is correct?
In how many ways can a chairperson, a secretary, and a treasurer be chosen from a group of 10 people, if each person can hold only one position?
The ratio of the ages of A and B is 5:3. After 6 years, their ages will be in the ratio 6:4. What is the current age of A?
The integration factor of \( \frac{dy}{dx} + 2xy = e^{-x^2} \)

The rank of matrix \(\begin{bmatrix} k & -1 & 0 \\[0.3em]  0 & k & -1 \\[0.3em] -1 & 0 & k \end{bmatrix}\) is 2, for \( k = \)

If \(A = \begin{bmatrix} 4 & 2 \\[0.3em] -3 & 3 \end{bmatrix}\), then \(A^{-1} =\)

If \(P(A) = \frac{7}{11}\), \( P(B) = \frac{6}{11} \), and \( P(A \cup B) = \frac{8}{11} \), then \( P(A|B) = \) ?}

If \( \text{div}~\vec{F} \) of any vector \( \vec{F} \) is zero, then it is
If \( f(z) \) is analytic at \( z_0 \), then it is
If \( \bar{x} = 4 \), \( \bar{y} = 8 \), \( \sigma_x = 2 \), \( \sigma_y = 3 \), and \( r = 0.3 \), then the line of regression of \( y \) on \( x \) is
The general solution of \( z = px + qy + p^2q^2 \) is
One of the two events must occur. The chance of one is \( \frac{2}{3} \) of the other, then odds in favour of the other are
Particular integral of the partial differential equation \( \frac{\partial^2 z}{\partial x^2} - 2 \frac{\partial^2 z}{\partial x \partial y} + \frac{\partial^2 z}{\partial y^2} = 2x \cos y \) is
Matrix \( A \) has \( x \) rows and \( x + 5 \) columns. Matrix \( B \) has \( y \) rows and \( 11 - y \) columns. Both \( AB \) and \( BA \) exist, then
The minimum value of the function \( x^2 + y^2 + z^2 \) if \( x + y + z = 3a \)
A train moving at a speed of 63 km/hr enters a railway station and crosses the platform in 20 sec. If the length of the train is 100 m, what is the length of the platform?

The eigenvalues of \(\begin{bmatrix} 0 & -i \\[0.3em]i & 0 \end{bmatrix}\)are ____ .