List of top Mathematics Questions asked in AP EAPCET

If there exists a $ k^{th} $ order non-singular sub-matrix in a matrix $ P $ of order $ m \times n $, then the rank $ (\rho) $ of $ P $

If $ A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix} $ and $ B = \begin{bmatrix} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \end{bmatrix} $, then which one of the following is True?

In a matrix $ A $, if all the sub matrices of $ k^{th} $ order are singular and there is one non-singular sub matrix of order $ r $ $ (r<k) $, then the rank $ (\rho) $ of the matrix $ A $

Let $ f: \mathbb{R} \rightarrow \mathbb{R} $ be a function defined by $ f(x) = \frac{2x+1}{3} $. If $ \alpha $ is an element in the domain of $ f $ whose image is $ \frac{1}{\alpha} $, then the sum of all possible values of such $ \alpha $ is

Consider the following statements (A) and (B): \[ \text{(A):} \quad \int_a^b \frac{d}{dx} \left( f(x) \right) dx = \frac{d}{dx} \int_a^b f(x) dx \] \[ \text{(B):} \quad \frac{d}{dx} \left( \int f(x) dx \right) = f(x) + C \] Which one of the following is True?

Let $ [t] $ represent the greatest integer not exceeding $ t $. The number of discontinuous points of $ [10^t] $ in $ (0, 10) $ is:

Let $ f(x) = \frac{x}{\sqrt{1- x}}$ + $\frac{\sqrt{1- x}}{x}$. If $ \lim_{x _ 1^-} f(x) = l $ and $ \lim_{x \to m} f(x) = \frac{5}{2} $, then the set of all possible finite values of $ l $ and $ m $ is

Let $ x + y + 1 = 0 $ and $ x - y + 4 = 0 $ be the asymptotes of a hyperbola $ H $. If $ (1, 1) $ is a point on $ H $, then the length of the latus rectum of $ H $ is

If $ P(2, 3) $ and $ Q(-1, 2) $ are conjugate points with respect to the circle $ x^2 + y^2 + 2gx + 3y - 2 = 0 $ then the radius of the circle is

If a straight line is equally inclined at an angle $ \theta $ with all the three coordinate axes, then $ \tan \theta =$

The number of straight lines that can be drawn through the point $ (-3, 4) $, which are at a distance of 5 units from the point $ (2, -8) $, is:

If $ O $ is the origin and $ P, Q $ are points on the line $ 3x + 4y + 15 = 0 $ such that $ OP = OQ = 9 $, then the area of $ \triangle OPQ $ is:

The vector equation of any plane passing through the line of intersection of the planes $ \bar{r} \cdot \bar{n}_1 = q_1 $ and $ \bar{r} \cdot \bar{n}_2 = q_2 $ is given by $ \bar{r} \cdot (\bar{n}_1 + \lambda \bar{n}_2) = q_1 + \lambda q_2 $ for $ \lambda \in \bar{R} $. The vector equation of a plane passing through the point $ 2\bar{i} - 3\bar{j} + \bar{k} $ and the line of intersection of the planes $ \bar{r} \cdot (\bar{i} - 2\bar{j} + 3\bar{k}) = 5 $, $ \bar{r} \cdot (3\bar{i} + \bar{j} - 2\bar{k}) = 7 $ is

Let $ \bar{a}, \bar{b}, \bar{c} $ be three non-coplanar vectors. Then the point of intersection of the line joining the points $ \mathbf{a} + \bar{b} + \bar{c} $, $ \bar{a} - \bar{b} + 3\bar{c} $ and the line joining the points $ 2\bar{a} - \bar{b} + \bar{c} $, $ \bar{a} - 2\bar{b} + 4\bar{c} $ is

In $ \triangle ABC $, the expression $ \frac{a}{s-a} + \frac{b}{s-b} + \frac{c}{s-c} $ is equivalent to:

In $ \triangle ABC $, if $ r = 1 $, $ R = 4 $, and $ \Delta = 8 $, then \[ \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} = \]

If $ \cos A + \cos B + \cos C = 0 $ and $ \sin A + \sin B + \sin C = 0 $, then $ \cos(A - B) = $

If $ P = \tan 15^\circ + \cot 15^\circ $, $ Q = \tan 22\frac{1}{2}^\circ + \cot 22\frac{1}{2}^\circ $, and $ R = \sin 54^\circ + \sin 18^\circ $, then their ascending order is

The greatest term in the expansion of $ (1+x)^{15} $, when $ x = \frac{1}{2} $ is

When $ x $ is so small that its square and its higher powers may be neglected, then the value of $ \frac{(1 + \frac{3}{4}x)^{-4} \sqrt{(3 + x)}}{\sqrt{(3 - x)^3}} $ is approximately equal to

If $ 3 + i $ and $ 2 - \sqrt{3} $ are the roots of the equation $ f(x) = a_0 + a_1 x + a_2 x^2 + ... + a_n x^n $, where $ a_0, a_1, ..., a_n \in \mathbb{Z} $, then the least value of $ n $ and the value of $ a_0 $ are respectively:

If the roots of the equation \[ 6x^3 - 11x^2 + 6x - 1 = 0 \] are in harmonic progression, then the roots of \[ x^3 - 6x^2 + 11x - 6 = 0 \] will be in

If $ z_1 = 2 + 3i $, $ z_2 = 4 - 5i $, and $ z_3 $ are three points in the Argand plane such that $ 5z_1 + xz_2 + yz_3 = 0 $ (where $ x, y \in \mathbb{R} $) and $ z_3 $ is the midpoint of the line segment joining the points $ z_1 $ and $ z_2 $, then find $ x + y $.

If $ 1, \omega, \omega^2 $ are the cube roots of unity, then the roots of the equation $ 8z^3 - 12z^2 + 6z - 28 = 0 $ are:

The rank of the matrix \[ \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & -2 \\ 1 & -1 & 4 \\ 2 & 2 & 8 \\ \end{pmatrix} \] is