List of top Mathematics Questions asked in AP EAPCET

The positive value of \(a\) for which the system of linear homogeneous equations \[ x+ay+z=0, \qquad ax+2y-z=0, \qquad 2x+3y+z=0 \] has non-trivial solution is

If the system of equations \[ 2x+3y-3z=3, \qquad x+2y+\alpha z=1, \qquad 2x-y+z=\beta \] has infinitely many solutions, then \[ \frac{\alpha}{\beta}-\frac{\beta}{\alpha} = \]

If \[ A=\begin{bmatrix}3 & 4 5 & 6\end{bmatrix} \quad \text{and} \quad B=\begin{bmatrix}x & 0 0 & y\end{bmatrix}, \] where \(x,y \in \mathbb{N}\), then:

If \( A \) and \( B \) are both \( 3 \times 3 \) matrices, then which of the following statements are true?
(i) \( AB = 0 \Rightarrow A = 0 \) or \( B = 0 \)
(ii) \( AB = I_3 \Rightarrow A^{-1} = B \)
(iii) \( (A - B)^2 = A^2 - 2AB + B^2 \)

If \( A = \begin{bmatrix} 1 & 2 3 & 4 \end{bmatrix} \), then \( \text{adj}(\text{adj}(\text{adj } A)) \)

If \( A = \begin{bmatrix} a & 1 & 2 1 & 2 & b c & 1 & 3 \end{bmatrix} \) and \( \text{adj } A = \begin{bmatrix} 7 & -1 & -5 -3 & 9 & 5 1 & -3 & 5 \end{bmatrix} \), then \( a^2 + b^2 + c^2 = \)

The value of the limit \( \lim_{n \to \infty} \left( \frac{1}{1^2 + n^2} + \frac{2}{2^2 + n^2} + \frac{3}{3^2 + n^2} + \cdots + \frac{n}{n^2 + n^2} \right) \) is equal to:

The value of the integral \[ \int_{-\frac{\pi}{8}}^{\frac{\pi}{8}} \frac{\sin^4(4x)}{1 + e^{4x}} \, dx \] is equal to:

The value of the integral \[ \int_{0}^{2} x^8 \left( \frac{4}{x^2} - 1 \right)^{\frac{5}{2}} \, dx \] is equal to:

The value of the integral \[ \int_{-2}^{2} x^4 (4 - x^2)^{\frac{7}{2}} \, dx \] is equal to:

The value of the integral \( \int_{-2\pi}^{2\pi} \sin^4 x \cos^6 x \, dx \) is equal to:

The value of the integral \( \int_{0}^{\pi/2} \sin^6 x \cos^4 x \, dx \) is equal to:

The value of the integral \( \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \, dx \) is equal to:

The value of the integral \[ \int_{-\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec(2023x)}{1 + (2023)^{2023x}} \, dx \] is equal to:

The value of the integral \( \int_{-\frac{\pi}{15}}^{\frac{\pi}{15}} \frac{\cos 5x}{1 + e^{5x}} \, dx \) is equal to:

The value of the integral \(\int_{0}^{3\pi/2} \frac{\cos^3 x}{\cos^3 x + \sin^3 x} \, dx\) is:

The value of the integral \(\int_{0}^{\pi/2} \frac{\sin^{3/2} x}{\sin^{3/2} x + \cos^{3/2} x} \, dx\) is equal to:

The value of the integral \(\int_{5}^{9} \frac{\log(3x^2)}{\log(3x^2) + \log(588 - 84x + 3x^2)} \, dx\) is equal to:

The value of the integral \(\int_{0}^{\pi} \frac{x \sin x}{\sin^2 x + 2 \cos^2 x} \, dx\) is:

The value of the integral \(\int_{0}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \, dx\) is:

The value of the integral \(\int_{0}^{2} x^2 (2 - x)^5 \, dx\) is:

The value of the integral \( \int_{0}^{4} ||x - 2| - x| dx = \)

If \( [ ] \) denotes the greatest integer function, then \( \int_{1}^{2} [x^2] dx = \)

If the system of equations \( 2x + py + 6z = 8 \), \( x + 2y + qz = 5 \) and \( x + y + 3z = 4 \) has infinitely many solutions, then \( p = \)

The integral \[ \int \frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}} \, dx \] is equal to: