List of top Mathematics Questions asked in AP EAPCET

If \( \det(AB) = \det(A)\det(B) \) and \( A \) is a non-singular matrix of order \( 3 \times 3 \), then \( \det(\text{adj}(A)) \) is:

Let \( S = \{ z \in \mathbb{C} : |z - 1 + i| = 1 \} \) represents:

If \( \left| \frac{z - 2}{z} \right| = 2 \), then the greatest value of \( |z| \) is:

One of the 15th roots of \( -1 \) is:

The product of the four values of \( \left( 1 + i\sqrt{3} \right)^{3/4} \) is:

If one root of the equation \( ax^2 + bx + c = 0 \) is twice another root, then the equation \( ax^2 + bx + c = 0 \) is:

If \( \alpha \) and \( \beta \) are the roots of \( x^2 - ax - b = 0 \), and \( \alpha^2 + \beta^2 \) and \( \alpha^3 + \beta^3 \) are the roots of \( Ax^2 + Bx + C = 0 \), then \( C = \ldots \)

If \( -1 \) is a twice repeated root of the equation \( ax^3 + bx^2 + cx + 1 = 0 \), then \( ax^3 + bx^2 + cx + 1 = 0 \) represents:

The minimum value of \( f(x) = \frac{x^2 - 2x + 3}{x^2 - 4x + 7} \) is:

If \( C_j = \binom{n}{j} \), then \( C_0 C_t + C_1 C_{t+1} + C_2 C_{t+2} + \dots + C_n = \)

The coefficient of the highest power of \( x \) in the expansion of \[ \left( x + \sqrt{x^2 - 1} \right)^3 + \left( x - \sqrt{x^2 - 1} \right)^8 \text{ is:} \]

The number of non-negative integral solutions of \( x_1 + x_2 + x_3 + x_4 = 10 \) is:

The number of six-digit natural numbers that can be formed with the digits 2, 3, 4, 0, 5, 6, 7, 8 is:

If \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), where \( a, b, c, d \in \{-1, 1\} \), then the number of singular matrices in \( A \) is:

If \( \cot x \cot y = a \) and \( x + y = \frac{\pi}{6} \), then the quadratic equation satisfying \( \cot x \) and \( \cot y \) is:

If \( \tan A + \tan B = x \) and \( \cot A + \cot B = y \), then \( \tan(A + B) = \)

Evaluate: \[ \frac{1}{\cos 290^\circ} + \frac{1}{\sqrt{3} \sin 250^\circ} \]

If \[ \left| 1 - \cos \left( \frac{\pi}{2} - \alpha \right) + \sin \left( \frac{3\pi}{2} - \alpha \right) \right| \left[ 1 - \sin \left( \frac{3\pi}{2} - \alpha \right) - \cos \left( \frac{\pi}{2} - \alpha \right) \right] = a + b \sin \left( \frac{\pi}{4} + \alpha \right) \] then \( a^2 + b^2 = \)

The range of the expression: \[ \frac{1}{\sin^2x + 3\sin x \cos x + 5\cos^2x} \] is:

If \( \cosh x = \frac{5}{4} \), then \( \tanh 3x = \)

In \( \triangle ABC \), if \( \sin B = \sin C \) and \( 3 \cos B = 2 \cos C \), then \( \triangle ABC \) is:

If \( \triangle ABC \) is a right-angled isosceles triangle and \( \angle C = 90^\circ \), then \( r = \frac{1}{5} \) is:

In \( \triangle ABC \), if \[ a \cos^2 \frac{C}{2} + \cos^2 \frac{A}{2} = \frac{3b}{2}, \] then \( a + c : b \) is:

If \[ \frac{x + 2}{x^2 - 3} \text{ is one of the partial fractions of } \frac{3x^3 - x^2 - 2x + 17}{x^4 + x^2 - 12}, \text{ then the other partial fraction of it is:} \]

If \( 7i - 4j - 5k \) is the position vector of vertex A of a tetrahedron ABCD and \( -i + 4j - 3k \) is the position vector of the centroid of the triangle BCD, then the position vector of the centroid of the tetrahedron ABCD is: