List of top Mathematics Questions asked in AP EAMCET

If \( \vec{f} = i + j + k \) and \( \vec{g} = 2i - j + 3k \), then the projection vector of \( \vec{f} \) on \( \vec{g} \) 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:
In \(\triangle ABC\), if \(4r_1 = 5r_2 = 6r_3\), then \(\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} =\)
The values of \( x \) for which the angle between the vectors \[ \mathbf{a} = x\hat{i} + 2\hat{j} + \hat{k}, \quad \mathbf{b} = -\hat{i} + 2\hat{j} + x\hat{k} \] is obtuse lie in the interval:
The length of the latus rectum of \( 16x^2 + 25y^2 = 400 \) is:
If the coefficients of the \( (2r + 6)^{th \) and \( (r - 1)^{th} \) terms in the expansion of \( (1 + x)^{21} \) are equal, then the value of \( r \) is:}
The number of different ways of preparing a garland using 6 distinct white roses and 6 distinct red roses such that no two red roses come together is:
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:
For a dataset, if the coefficient of variation is 25 and the mean is 44, find the variance.
Let \( \mathbf{a}, \mathbf{b} \) be two unit vectors. If \( \mathbf{c} = \mathbf{a} + 2\mathbf{b} \) and \( \mathbf{d} = 5\mathbf{a} - 4\mathbf{b} \) are perpendicular to each other, find the angle between \( \mathbf{a} \) and \( \mathbf{b} \).
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 \(\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} =\)
The general solution of \( \cot \frac{x}{2} - \cot x = \csc \frac{x}{2} \) is:
If \( \mathbf{f}, \mathbf{g}, \mathbf{h} \) are mutually orthogonal vectors of equal magnitudes, then find the angle between the vectors \( \mathbf{f} + \mathbf{g} + \mathbf{h} \) and \( \mathbf{h} \).
The origin is shifted to the point \( (2, 3) \) by translation of axes and then the coordinate axes are rotated about the origin through an angle \( \theta \) in the counter-clockwise sense. Due to this if the equation \( 3x^2 + 2xy + 3y^2 - 18x - 22y + 50 = 0 \) is transformed to \( 4x^2 + 2y^2 - 1 = 0 \), then the angle \( \theta = \):
If \( (a, b) \) is the midpoint of the chord \( 2x - y + 3 = 0 \) of the circle \( x^2 + y^2 + 6x - 4y + 4 = 0 \), then \( 2a + 3b = \):
If the eleventh term in the binomial expansion of \( (x + a)^n \) is the geometric mean of the eighth and twelfth terms, then the greatest term in the expansion is:
The set of all real values of \( a \) such that the function \( f(x) = x^3 + 2ax^2 + 3(a+1)x + 5 \) is strictly increasing in its entire domain is:
The length of the tangent drawn at the point \( P \left( \frac{\pi}{4} \right) \) on the curve \( x^{2/3} + y^{2/3} = 2^{2/3} \) is:
If A, B, C are the angles of a triangle, then \(\frac{\sin A + \sin B + \sin C}{\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} - 1} =\)
Evaluate the limit: \[ \lim_{x \to 0} \frac{1 - \cos x \cos 2x}{\sin^2 x} \]
If the distance between the planes \( 2x + y + z + 1 = 0 \) and \( 2x + y + z + \alpha = 0 \) is 3 units, then the product of all possible values of \( \alpha \) is:
The complex conjugate of \( (4 - 3i)(2 + 3i)(1 + 4i) \) is:
The line \( x - 2y - 3 = 0 \) cuts the parabola \( y^2 = 4ax \) at points P and Q. If the focus of this parabola is \( \left(\frac{1}{4}, k\right) \), then PQ is:
A student writes an exam with 8 true/false questions. He passes if he answers at least 6 correctly. Find the probability that he fails.
If the matrix is: 
\(\left| \begin{array}{ccc} a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c \end{array} \right|>0, \text{ then } abc>?\)