List of top Mathematics Questions asked in AP EAPCET

A point P divides the line joining points $A(2, 3)$ and $B(10, 7)$ in the ratio 3:1 internally. What are the coordinates of point P?
A bag contains 4 red and 5 blue balls. One ball is drawn at random. What is the probability that it is red?
Let \( f(x) = \frac{1+x{1-x} \). Find the value of \( f(x) + f(-x) \):}
If $ a $ and $ b $ are the roots of the equation $ 4x^2 - 12x + 11 = 0 $, find the value of $ a^2 + b^2 $.
Find the determinant of the matrix: $$ \begin{bmatrix} 3 & 2 \\ 1 & 5 \end{bmatrix} $$
Let \( A(1,2), B(3,4) \) and \( C(k,6) \) be three points such that the area of triangle \( ABC \) is 5 square units. The possible values of \( k \) are:
If \( \tan(\theta - \phi) = \frac{3}{4} \) and \( \theta + \phi = \frac{\pi}{2} \), then the value of \[ \tan \left( \frac{\pi}{4} - \theta \right) + \tan \left( \frac{\pi}{4} - \phi \right) \] is:
If the tangent to the curve \( y = ax^2 + bx + c \) at the point \( (1,1) \) is parallel to the x-axis, and the curve passes through the point \( (2,3) \), then find the value of \( a + b + c \):
Let \[ f(x) = x^4 - 4x^3 + 6x^2 + k \] \text{If \(f(x) \geq 0\) for all real \(x\), then the value of \(k\) is:}
A rectangular garden has a length that is 3 meters more than its width. If the area of the garden is 88 square meters, what is the width of the garden?
What is the distance between the points $(3, -2)$ and $(-1, 4)$?
Imaginary part of \( \frac{(1 - i)^3}{(2 - i)(3 - 2i)} \) is:
Suppose the axes are to be rotated through an angle \( \theta \) so as to remove the \( xy \) term from the equation \(3 x^2 + 2\sqrt{3}xy + y^2 = 0 \). Then in the new coordinate system, the equation \( x^2 + y^2 + 2xy = 2 \) is transformed to:
The area of the region enclosed by the curves \[ 3x^2 - y^2 - 2xy + 4x + 1 = 0 \] and \[ 3x^2 - y^2 - 2xy + 6x + 2y = 0 \] is:
Let \( f(x) = 3 + 2x \) and \( g_n(x) = (f \circ f \circ \dots \text{n times}) (x) \). If for all \( n \in \mathbb{N} \), the lines \( y = g_n(x) \) pass through a fixed point \( (a, \beta) \), then \( \alpha + \beta = ? \)

If \( y = \tan(\log x) \), then \( \frac{d^2y}{dx^2} \) is given by: 

The square root of \( 7 + 24i \) is:
In the expansion of \(\frac{2x+1}{(1+x)(1-2x)}\), the sum of the coefficients of the first 5 odd powers of \(x\) is:
If the solution of the system of simultaneous linear equations: $$ x + y - z = 6, $$ $$ 3x + 2y - z = 5, $$ $$ 2x - y - 2z + 3 = 0 $$ is \( x = \alpha, y = \beta, z = \gamma \), then \( \alpha + \beta = ?\) 
There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is:

If \(3A = \begin{bmatrix} 1 & 2 & 2 \\[0.3em] 2 & 1 & -2 \\[0.3em] a & 2 & b \end{bmatrix}\) and \(AA^T = I\), then\(\frac{a}{b} + \frac{b}{a} =\):

The condition that the roots of \( x^3 - bx^2 + cx - d = 0 \) are in arithmetic progression is:

If \[ A = \begin{bmatrix} 1 & 0 & 2\\ 2 & 1 & 3 \\3 & 2 & 4 \end{bmatrix}, \] then evaluate \( A^2 - 5A + 6I \)=

If \( P(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e \) is a polynomial such that: \[ P(0) = 1, \quad P(1) = 2, \quad P(2) = 5, \] \[ P(3) = 10, \quad P(4) = 17, \] then find the value of \( P(5) \)=

If the origin is shifted to a point \( P \) by the translation of axes to remove the \( y \)-term from the equation \( x^2 - y^2 + 2y - 1 = 0 \), then the transformed equation of it is: