List of top Questions asked in AP EAPCET

If the values of \( k \) for which the equation \( x^2 + 2(k+2)x + 6k + 7 = 0 \) has equal roots are \( k_1 \) and \( k_2 \), then \( k_1^2 + k_2^2 \) is:

If \( (3 + 2\sqrt{2})^{x^2 - 4} + (3 - 2\sqrt{2})^{x^2 - 4} = 6 \), then \( x^4 + x^2 + 5 = \)?

If \( A = \begin{bmatrix} i & 0 \\ 0 & -i \end{bmatrix}, B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}, C = \begin{bmatrix} 0 & i \\ -i & 0 \end{bmatrix} \), then the expression \( A^2 + B^2 + C^2 \) is:

If \( z_1 = (2, -1) \) and \( z_2 = (6, 3) \), then find the amplitude of the expression \[ \text{amp}\left(\frac{z_1 - z_2}{z_1 + z_2}\right) \]

For \( x \in \mathbb{R} \), if \( f(x) = \sqrt{\log_{10} \left( \frac{3-x}{x} \right)} \), then the domain of \( f \) is:

Let \( A = \begin{pmatrix} 0 & 3 & 5 & -7 \\ 8 & 0 & -1 & 0 \\ 6 & -1 & 0 & 0 \end{pmatrix} \) and \( X = \begin{pmatrix} x \\ y \\ z \end{pmatrix} \). If \( D = [\alpha \, \beta \, \gamma]^T \) is the solution of \( X^T B^T = A^T X \), then \( D^T A = \)

If \( f(x) = x^3 - x \) and \( g(x) = \sin(2x) \), then \( f(g\left(\frac{\pi}{12}\right)) \) is:

If the solution for the system of equations \[ x + 2y - z = 3, \ 3x - y + 2z = 1, \ 2x - 2y + 3z = 2 \] is \( ( \alpha, \beta, \gamma ) \), then find the value of \( \alpha^2 + \beta^2 + \gamma^2 \).

If the solution for the system of equations \[ x + 2y - z = 3, \ 3x - y + 2z = 1, \ 2x - 2y + 3z = 2 \] is \( ( \alpha, \beta, \gamma ) \), then find the value of \( \alpha^2 + \beta^2 + \gamma^2 \).

If \( f(x) \) is the signum function, then in terms of \( f(x) \), the constant function \( g(x)=1, \ \forall x \in \mathbb{R} \) is:

If a set \( A \) has \( n \) elements, then the number of functions defined from \( A \) to \( A \) that are not one-one is:

The set \( \{ x \in \mathbb{R} : 16(2^x)>16^{x-1} \} \) is:

If \( \alpha, \beta \) are the two real roots of the 4th roots of unity, and \( \gamma, \delta \) are the other two roots of it, then the sum of the eccentricities of the conics \( |z - \alpha| + |z - \beta| = 4 \) and \( |z - \gamma| + |z - \delta| = 6 \) is:

If \[ \begin{vmatrix} x & 4 & -1 \\ 2 & 1 & 0 \\ 0 & 2 & 4 \end{vmatrix} = 0, \text{ then find the value of } x. \]

If \( \omega, \omega^2 \) are the cube roots of unity, \( k \) is a positive integer, and \[ (1 - \omega^2)^{3k} + (1 - \omega^2 + 0)^{3k+1} + (1 + \omega - 0)^{3k+1}, \] then find \( k \).

If \( z = (1 - i^3)(x + i) \) is a purely imaginary number for \( x = x_1 \), and if \( z \) is a purely real number for \( x = x_2 \), then find \( x_1, x_2 \).

For real numbers \( a \) and \( b \), if \[ 4a + i(3a - b) = b - 6i \] and \[ z = a + \frac{b}{4}i, \] then find \[ \frac{|z|}{a}. \]

If \( \frac{17x - 2}{12x^2 - x - 20} = \frac{A}{ax + 5} + \frac{B}{3x + b} \), then \( a \cdot A + b \cdot B \) is:

Let \( \vec{a}, \vec{b}, \vec{c} \) be any three non-coplanar vectors. If \( m, n \) are scalars such that \( \vec{a} + \vec{b} = m\vec{c} \) and \( \vec{b} + \vec{c} = n\vec{a} \), then \( 3\vec{a} + 2\vec{b} + 2\vec{c} = \):

In \( \Delta ABC \), \( A, B, C \) are in arithmetic progression and \( a : c = 1 : 2 \). If \( b = 4\sqrt{3} \) cm, then the area of \( \Delta ABC \) (in sq. cm) is:

If \( 2i\hat{i} - j\hat{j} - 3j\hat{k} \) and \( -3i\hat{i} + 4j\hat{j} - 4k\hat{k} \) are the position vectors of three points A, B, and C respectively, then \( \Delta ABC \) is: