List of top Mathematics Questions asked in AP EAPCET

A farmer owns a triangular plot in Guntur. He measures the sides of the plot as 4 cm, 5 cm, and 7 cm. The area of the land (in sq. cm) is:

In a triangle, if \( b = 5 \), \( c = 6 \), and \( \tan\left(\frac{A}{2}\right) = \frac{1}{\sqrt{2}} \), then the side \( a = \) ?

In a triangle \( ABC \), the identity holds: \[ s \left( \frac{r_1 - r}{a} + \frac{r_2 - r}{b} + \frac{r_3 - r}{c} \right) = ? \]

If the position vectors of points \( A, B, C, D \) are: \[ \vec{A} = 7\hat{i} - 4\hat{j} + 7\hat{k},\quad \vec{B} = \hat{i} - 6\hat{j} + 10\hat{k},\quad \vec{C} = -\hat{i} - 3\hat{j} + 4\hat{k},\quad \vec{D} = 5\hat{i} - \hat{j} + 5\hat{k} \] Then the quadrilateral \( ABCD \) is:

Let \( x \in \mathbb{R} \) and \( |x|<1 \). Then \( \tanh^{-1} x = \) ?

In a triangle \( ABC \), the identity holds: \[ \tan\frac{A}{2} \tan\frac{B}{2} + \tan\frac{B}{2} \tan\frac{C}{2} + \tan\frac{C}{2} \tan\frac{A}{2} = ? \]

If \( \cos\theta - \sin\theta = \sqrt{5} \sin\theta \), then the value of \( \cos\theta + 4\sin\theta \) is:

If the equivalent partial fraction of \[ \frac{x^3}{(2x - 1)(x + 2)(x - 3)} \] is of the form \[ A + \frac{B}{2x - 1} + \frac{C}{x + 2} + \frac{D}{x - 3} \] then the value of \( A + B + C = \) ?

Simplify the expression: \[ \sec^2 x + 5 \tan x + 5 \]

Let \( \alpha, \beta \) be real numbers such that \( \pi<(\alpha - \beta)<3\pi \). If: \[ \sin \alpha + \sin \beta = \frac{-21}{65}, \quad \cos \alpha + \cos \beta = \frac{-2}{65} \] then the value of \( \cos\left( \frac{\beta - \alpha}{2} \right) \) is:

The number of real values of \( m \) such that the equation \[ x^2 + (2m + 1)x + m = 0 \] has equal roots is:

All pairs \( (x, y) \) that satisfy the inequality \[ 2\sqrt{\sin^2x - 2\sin x + 5} \cdot \frac{1}{4^{\sin^2 y}} \leq 1 \] also satisfy the equation:

Given 5 different green toys, 4 different blue toys, and 3 different red toys, how many combinations of toys can be chosen taking at least one green and one blue toy?

If \( ^{2n}C_3 : ^nC_3 = 12 : 1 \), then \( n = \) ?

There are 4 oranges, 5 apples, and 7 mangoes in a fruit basket. The number of ways of selecting at least one fruit from among the fruits in the basket is:

If \( ^9C_3 + ^9C_5 = ^{10}C_r \) for some \( r \in \mathbb{N} \), then \( r = \) ?

The number of solutions of the equations \[ x + y + z = 1,\quad x^2 + y^2 + z^2 = 1,\quad x^3 + y^3 + z^3 = 1 \] is:

If \( \alpha, \beta \) are the roots of \( x^2 - 10x - 8 = 0 \), with \( \alpha>\beta \), and \( a_n = \alpha^n - \beta^n \), then the value of: \[ \frac{a_{10} - 8a_8}{5a_9} \] is:

Evaluate: \[ \sum_{k=1}^{6} \left[ \sin\left( \frac{2\pi k}{7} \right) - i \cos\left( \frac{2\pi k}{7} \right) \right] \]

If \( (x - iy)^{1/3} = a - ib \), then the value of \( \frac{x}{2a} + \frac{y}{2b} \) is:

If \( x = -5 + 2\sqrt{-4} \), then the value of \( x^4 + 9x^3 + 35x^2 - x + 4 \) is:

If the rank of the matrix \[ A = \begin{bmatrix} 1 & 2 & 1 & -1 \\ -1 & 2 & 3 & 5 \\ 0 & 1 & k & k \end{bmatrix} \] is 2 and \( k \) is a real number, then \( k \) is a root of which of the following quadratic equations?

If the solution of the system of simultaneous equations \[ \frac{1}{x} + \frac{2}{y} - \frac{3}{z} = 1, \quad \frac{2}{x} - \frac{4}{y} + \frac{3}{z} = 1, \quad \frac{3}{x} + \frac{6}{y} - \frac{6}{z} = 4 \] is \( x = \alpha, y = \beta, z = \gamma \), then the value of \( \alpha^2 + \gamma^2 \) is:

A true statement among the following identities is:

If \( A = \begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} 8 & 0 \\7 & 1 \end{bmatrix} \), and \( A^3 = B \), then \( x = \) ?