List of top Mathematics Questions asked in AP EAPCET

If \( \cosh(x - \log 3) = \sinh x \), then \( x = \):
In \( \triangle ABC \), if \( 3\sin A + 4\cos B = 6 \) and \( 4\sin B + 3\cos A = 1 \), then the angle \( C \) is:
If \( \sin\left(x + \frac{\pi}{3}\right) + \sin\left(x - \frac{\pi}{3}\right) = 1 \), then the value of \( x \) in the interval \( [0, \pi] \) is:
The sides of a triangle \( ABC \) are given by \( a = 3 \), \( b = 5 \), and \( c = 3 \). Then \( \cos A = \)
In triangle \( ABC \), if \( a = 2 \), \( b = 3 \) and \( \sin A = \frac{2}{3} \), then \( \angle B = \):
In a triangle \( ABC \), if \( a : b : c = 4 : 5 : 6 \), the ratio of radius of the circumcircle to that of the incircle is:
PQRS is a quadrilateral and \( \vec{PQ} = \vec{a} \), \( \vec{QR} = \vec{b} \), \( \vec{SP} = \vec{a} - \vec{b} \).
\( M \) is the midpoint of \( QR \), and \( X \) lies on \( \vec{SM} \) such that \( \vec{SX} = \frac{4}{5} \vec{SM} \).
If \( \vec{SM} = m(4\vec{a} - \vec{b}) \), and \( \vec{SX} = n(4\vec{a} - \vec{b}) \), then \( m + n = \):
If \( \frac{4x^3 + 16x + 7}{(x^2 + 4)^2} = \frac{Ax + B}{x^2 + 4} + \frac{Cx + D}{(x^2 + 4)^2} \), then the number of non-zero values among \( A, B, C, D \) is:
The smallest integer \( n \) such that \[ \frac{1}{\sin 45^\circ \sin 46^\circ} + \frac{1}{\sin 47^\circ \sin 48^\circ} + \cdots + \frac{1}{\sin 133^\circ \sin 134^\circ} = \frac{1}{\sin(n^\circ)} \]
Evaluate: \( 1 + \cot^2 30^\circ - \sec^2 45^\circ \)
Simplify: \( \sin(x + y) \sec x \sec y = \)
Let \( P_1, P_2, \ldots, P_{15} \) be 15 points on a circle. The number of distinct triangles formed by points \( P_i, P_j, P_k \) such that \( i + j + k \ne 15 \), is:
What is the sum of the first \( n \) terms of the series, whose \( k \)-term is \( k! \cdot k \)?
Which of the following quadratic equations whose real roots \( x_1, x_2 \) satisfy the conditions \( x_1^2 + x_2^2 = 5 \), \( 3(x_1^5 + x_2^5) = 11(x_1^3 + x_2^3) \)?
The range of the function \( f(x) = \frac{x^2 + x + 1}{x^2 - x + 1} \) is:
The remainder when the polynomial \( 2x^5 - 3x^4 + 5x^3 - 3x^2 + 7x - 9 \) is divided by \( x^2 - x - 3 \) is:
If \( 1, \omega, \omega^2 \) are the cube roots of unity, then evaluate: \[ (2 - \omega)^2 (2 - \omega^2)^2 (2 - \omega^{10})^2 (2 - \omega^{11})^2 \]
If \( ^nC_{r-1} = 36 \), \( ^nC_r = 84 \), and \( ^nC_{r+1} = 126 \), then the value of \( nr^2 \) is:
The total number of positive integral solutions \((x, y, z)\) of \( xyz = 24 \) is:
Let \( f(x) = x^2 + \frac{1}{x^2} \) and \( g(x) = x - \frac{1}{x} \) for \( x \in \mathbb{R} \setminus \{-1, 0, 1\} \). Then, the local minimum of \( \frac{f(x)}{g(x)} \) is:
Let \( z = x + iy \) be a complex number with \( x, y \in \mathbb{Z} \). Then the area (in square units) of the rectangle whose vertices are the roots of the equation \( \bar{z} \cdot z^3 + z \cdot \bar{z}^3 = 350 \) is:
Let \( A = \begin{bmatrix} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{bmatrix} \) and \( B = \begin{bmatrix} 0 & 0 & n \\ 0 & n & 0 \\ n & 0 & 0 \end{bmatrix} \). Then \( A^2 + B^2 + AB = \)
Let \( z \) and \( w \) be two complex numbers such that \( \bar{z} + i\bar{w} = 0 \) and \( \text{Arg}(zw) = \pi \). Then \( \text{Arg}(z) = \)
If the complex numbers \( z_1, z_2, 0 \) are vertices of an equilateral triangle, then \( z_1^2 + z_2^2 = \)
If \(A = \begin{bmatrix}x & 2 & 1 \\ 2 & x & 1 \\ 2 & 1 & 0\end{bmatrix}\) and \(\det(A) = 125\), then \(x =\)