List of top Mathematics Questions asked in AP EAMCET

The orthogonal projection vector of \( \bar{a} = 2\bar{i} + 3\bar{j} + 3\bar{k} \) on \( \bar{b} = \bar{i} - 2\bar{j} + \bar{k} \) is:
If \( \vec{a} = i\hat{i} + j\hat{j} + 3k\hat{k} \), \( \vec{b} = i\hat{i} + 2k\hat{k} \), \( \vec{c} = -3i\hat{i} + 2j\hat{j} + k\hat{k} \) are linearly dependent vectors and the magnitude of \( \vec{a} \) is \( \sqrt{14} \), then if \( \alpha, \beta \) are integers, find \( \alpha + \beta \):
If the vectors \( a\hat{i} + \hat{j} + 3\hat{k} \), \( 4\hat{i} + 5\hat{j} + \hat{k} \), and \( 4\hat{i} + 2\hat{j} + 6\hat{k} \) are coplanar, then \( a \) is:
Let \( |\mathbf{a}| = 2, |\mathbf{b}| = 3 \) and the angle between \( \mathbf{a} \) and \( \mathbf{b} \) be \( \frac{\pi}{3} \). If a parallelogram is constructed with adjacent sides \( 2\mathbf{a} + 3\mathbf{b} \) and \( \mathbf{a} - \mathbf{b} \), then its shorter diagonal is of length:
If \( \bar{a} = -4\bar{i} + 2\bar{j} + 4\bar{k} \), \( \bar{b} = \sqrt{2} \bar{i} - \sqrt{2} \bar{j} \) are two vectors, then the angle between the vectors \( 2\bar{a} \) and \( \frac{\bar{b}}{2} \) is:
If \( \vec{i} - 2\vec{j} + 3\vec{k}, 2\vec{i} + 3\vec{j} - \vec{k}, -3\vec{i} - \vec{j} - 2\vec{k} \) are the position vectors of three points A, B, C respectively, then A, B, C:
If \( \hat{i} - \hat{j} - \hat{k} \), \( \hat{i} + \hat{j} + \hat{k} \), \( \hat{i} + \hat{j} + 2\hat{k} \), and \( 2\hat{i} + \hat{j} \) are the vertices of a tetrahedron, then its volume is:
Let \( \mathbf{a} = 3\hat{i} + 4\hat{j} - 5\hat{k} \), \( \mathbf{b} = 2\hat{i} + \hat{j} - 2\hat{k} \). The projection of the sum of the vectors \( \mathbf{a}, \mathbf{b} \) on the vector perpendicular to the plane of \( \mathbf{a}, \mathbf{b} \) is:
If \( \vec{a}, \vec{b}, \vec{c} \) are 3 vectors such that \( |\vec{a}| = 5, |\vec{b}| = 8, |\vec{c}| = 11 \) and \( \vec{a} + \vec{b} + \vec{c} = 0 \), then the angle between the vectors \( \vec{a} \) and \( \vec{b} \) is:
If \( \vec{a} = \hat{i} - \hat{j} + \hat{k} \), \( \vec{b} = \hat{i} + \hat{j} - 2\hat{k} \), \( \vec{c} = 2\hat{i} - 3\hat{j} - 3\hat{k} \), and \( \vec{d} = 2\hat{i} + \hat{j} + \hat{k} \) are four vectors, then \( (\vec{a} \times \vec{c}) \times (\vec{b} \times \vec{d}) = \):
If \( \vec{f} = i + j + k \) and \( \vec{g} = 2i - j + 3k \), then the projection vector of \( \vec{f} \) on \( \vec{g} \) is:
If \( P = (0,1,2) \), \( Q = (4,-2,-1) \) and \( O = (0,0,0) \), then \( \angle POQ \) is:
If the vectors \(a\bar{i} + \bar{j} + \bar{k}\), \(\bar{i} + b\bar{j} + \bar{k}\), \(\bar{i} + \bar{j} + c\bar{k}\) (\(a \ne b \ne c \ne 1\)) are coplanar, then \(\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} =\)
If \( AB = 2i + 3j - 6k \), \( BC = 6i - 2j + 3k \) are the vectors along two sides of a triangle ABC, then the perimeter of triangle ABC is:
Evaluate the sum: \[ \tan^2 \frac{\pi}{16} + \tan^2 \frac{2\pi}{16} + \tan^2 \frac{3\pi}{16} + \tan^2 \frac{4\pi}{16} + \tan^2 \frac{5\pi}{16} + \tan^2 \frac{6\pi}{16} + \tan^2 \frac{7\pi}{16} \]
tan 9$^\circ$ - tan 27$^\circ$ - tan 63$^\circ$ + tan 81$^\circ$ =
If \[ \cos \alpha + 4 \cos \beta + 9 \cos \gamma = 0 \quad \text{and} \quad \sin \alpha + 4 \sin \beta + 9 \sin \gamma = 0, \] then \[ 81 \cos (2\gamma - 2\alpha) - 16 \cos (2\beta - 2\alpha) = ? \]
In a triangle \( ABC \), if \( A, B, C \) are in arithmetic progression and \[ \cos A + \cos B + \cos C = \frac{1 + \sqrt{2} +\sqrt{3}}{2\sqrt{2}}, \] then \( \tan A \) is:
Evaluate the given trigonometric expression: \[ 4 \cos \frac{\pi}{7} \cos \frac{\pi}{5} \cos \frac{2\pi}{7} \cos \frac{2\pi}{5} \cos \frac{4\pi}{7} = \]
Evaluate $$ \cot \left( \sum_{n=1}^{50} \tan^{-1} \left( \frac{1}{1 + n + n^2} \right) \right).= $$
In \( \triangle ABC \), if \( (a+c)^2 = b^2 + 3ca \), then \( \frac{a+c}{2R} \) is:
cos 6° sin 24° cos 72° =
In \( \triangle ABC \), prove the identity: $$ a^2 \sin 2B + b^2 \sin 2A = $$ 
The range of the real valued function \( f(x) = \frac{15}{3 \sin x + 4 \cos x + 10} \) is:
In \( \triangle ABC \), if \( A, B, C \) are in arithmetic progression, \( \Delta = \frac{\sqrt{3}}{2} \) and \( r_1 r_2 = r_3 r \), then \( R \) is: