List of top Mathematics Questions asked in AP EAMCET

Numerically greatest term in the expansion of \( (5 + 3x)^6 \), when \( x = 1 \), is:
When two dice are thrown, the probability of getting the sum of the values on them as 10 or 11 is:
A unit vector perpendicular to the vectors \( \bar{a} = 2\bar{i} + 3\bar{j} + 4\bar{k} \) and \( \bar{b} = 3\bar{j} + 2\bar{k} \) is:
The angle subtended by the chord \( x + y - 1 = 0 \) of the circle \( x^2 + y^2 - 2x + 4y + 4 = 0 \) at the origin is: 
If \( \alpha, \beta, \gamma \) are the roots of the equation \[ x^3 + 3x^2 - 10x - 24 = 0. \] If \( \alpha(\beta + \gamma), \beta(\gamma + \alpha) \), and \( \gamma(\alpha + \beta) \) are the roots of the equation \[ x^3 + px^2 + qx + r = 0, \] then find the value of \( q \).
The cubic equation whose roots are the squares of the roots of the equation \( 12x^3 - 20x^2 + x + 3 = 0 \) is:
If the roots of the equation \[ Z^3 + iZ^2 + 2i = 0 \] are the vertices of a triangle ABC, then that triangle ABC is:
If \( \omega \) is a complex cube root of unity and if \( Z \) is a complex number satisfying \( |Z - 1| \leq 2 \) and \[ |\omega^2 Z - 1 - \omega| = a, \] then the set of possible values of \( a \) is:
The radius of the circle which cuts the circles \( x^2 + y^2 - 4x - 4y + 7 = 0 \), \( x^2 + y^2 + 4x + 6 = 0 \), and \( x^2 + y^2 + 4x + 4y + 5 = 0 \) orthogonally is:
Which of the following functions are odd? 
\[ \begin{aligned} \text{I. } & f(x) = x \left( \frac{e^x -1}{e^x +1} \right) \\[8pt] \text{II. } & f(x) = k^x + k^{-x} + \cos x \\[8pt] \text{III. } & f(x) = \log \left( x + \sqrt{x^2 +1} \right) \end{aligned} \]
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 the circles \( x^2 + y^2 + 2ax + 2y - 8 = 0 \) and \( x^2 + y^2 - 2x + ay - 14 = 0 \) intersect orthogonally, then the distance between their centers is:
If \( A = \left[\begin{array}{ccc} 83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79 \end{array} \right] \), then \(\text{det} (A - A^T) = \): 
If the lines \( 3x+y-4=0 \), \( x - \alpha y + 10 = 0 \), \( \beta x + 2y + 4 = 0 \) and \( 3x + y + k = 0 \) represent the sides of a square, then find \( \alpha \beta (k+4)^2 \).
Consider the point \( P(\alpha, \beta) \) on the line \( 2x + y = 1 \). If the points \( P \) and \( (3,2) \) are conjugate points with respect to the circle \( x^2 + y^2 = 4 \), then find \( \alpha + \beta \):
If all the letters of the word MASTER are permuted in all possible ways and words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word MASTER is:

If the inverse point of the point \( (-1, 1) \) with respect to the circle \( x^2 + y^2 - 2x + 2y - 1 = 0 \) is \( (p, q) \), then \( p^2 + q^2 = \) 

If \( A = [a_{ij}]\) where \( 1 \leq i, j \leq n \) with \( n \geq 2 \) and \( a_{ij} = i + j \) is a matrix, then the rank of \( A \) is:
The maximum value of \[ 12 \sin x - 5 \cos x + 3 \] 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:
cos 6° sin 24° cos 72° =
If set \( A \) contains 8 elements, then the number of subsets of \( A \) which contain at least 6 elements is:
If \(x^2 + 5ax + 6 = 0\) and \(x^2 + 3ax + 2 = 0\) have a common root, then that common root is:
Find the equation of a line passing through the intersection of \( 3x + y - 4 = 0 \) and \( x - y = 0 \), and making a \( 45^\circ \) angle with \( x - 3y + 5 = 0 \).
If \( Z = x + iy \) is a complex number, then the number of distinct solutions of the equation \[ z^3 + \bar{z} = 0 \] is: