List of top Mathematics Questions asked in AP EAMCET

If a real valued function \( f: [a, \infty) \to [b, \infty) \) is defined by \( f(x) = 2x^2 - 3x + 5 \) and is a bijection, then find the value of \( 3a + 2b \):
The number of 5-digit odd numbers greater than 40,000 that can be formed by using 3, 4, 5, 6, 7, 0 such that at least one of its digits must be repeated is:
Two persons A and B throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as 4 and the person who gets this result first is declared as the winner. If A starts the game, then the probability that B wins the game is:
If \( f(x) = \sqrt{x - 1 \) and \( g(f(x)) = x + 2\sqrt{x} + 1 \), then \( g(x) \) is:}
If the pair of tangents drawn to the circle \( x^2 + y^2 = a^2 \) from the point \( (10, 4) \) are perpendicular, then \( a \) is:
The perimeter of the locus of the point \( P \) which divides the line segment \( QA \) internally in the ratio 1:2, where \( A = (4, 4) \) and \( Q \) lies on the circle \( x^2 + y^2 = 9 \), is:
The general solution of \( 4 \cos 2x - 4 \sqrt{3} \sin 2x + \cos 3x - \sqrt{3} \sin 3x + \cos x - \sqrt{3} \sin x = 0 \) is:
In \( \triangle ABC \), prove the identity: $$ a^2 \sin 2B + b^2 \sin 2A = $$ 
The \( n^{th} \) term of the series \[ 1 + (3+5+7) + (9+11+13+15+17) + \dots \] is:
If \( (r, \theta) \) denotes \( r (\cos \theta + i \sin \theta) \). If \[ x = (1, \alpha), \quad y = (1, \beta), \quad z = (1, \gamma) \] and \( x + y + z = 0 \), then \[ \sum \cos (2\alpha - \beta - \gamma) = \]
If the ratio of the terms equidistant from the middle term in the expansion of \( (1 + x)^{12} \) is \( \frac{1}{256} \), then the sum of all the terms of the expansion \( (1 + x)^{12} \) is:
If there are 6 alike fruits, 7 alike vegetables, and 8 alike biscuits, then the number of ways of selecting any number of things out of them such that at least one from each category is selected, is:
If \( \vec{a} = \hat{i} - \hat{j} + \hat{k} \), \( \vec{b} = \hat{i} + \hat{j} - 2\hat{k} \), \( \vec{c} = 2\hat{i} - 3\hat{j} - 3\hat{k} \), and \( \vec{d} = 2\hat{i} + \hat{j} + \hat{k} \) are four vectors, then \( (\vec{a} \times \vec{c}) \times (\vec{b} \times \vec{d}) = \):
The number of ways of arranging 2 red, 3 white, and 5 yellow roses of different sizes into a garland such that no two yellow roses come together is:
Let \( \alpha \in \mathbb{R} \). If the line \( (a + 1)x + \alpha y + \alpha = 1 \) passes through a fixed point \( (h, k) \) for all \( a \), then \( h^2 + k^2 = \):
There are 2 bags each containing 3 white and 5 black balls and 4 bags each containing 6 white and 4 black balls. If a ball drawn randomly from a bag is found to be black, then the probability that this ball is from the first set of bags is:
Find the sum of the first 10 terms of the sequence \( 2.5 + 5.9 + 8.13 + 11.17 + \cdots \ to \ 10 \ terms =\):
If \[ \cos \alpha + 4 \cos \beta + 9 \cos \gamma = 0 \quad \text{and} \quad \sin \alpha + 4 \sin \beta + 9 \sin \gamma = 0, \] then \[ 81 \cos (2\gamma - 2\alpha) - 16 \cos (2\beta - 2\alpha) = ? \]
The determinant of the matrix $$ \begin{bmatrix} a & b & c \\ a^2 & b^2 & c^2 \\ 1 & 1 & 1 \end{bmatrix} $$ is not equal to: 
If \( A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix} \) and \( \alpha^2 + \beta A = 21 \) for some \( \alpha, \beta \in \mathbb{R} \), then find \( \alpha + \beta \):
If \( Z \) is a complex number such that \( |Z| \leq 3 \) and \( -\frac{\pi}{2} \leq \text{arg } Z \leq \frac{\pi}{2} \), then the area of the region formed by the locus of \( Z \) is:
If \( A \subseteq \mathbb{Z} \) and the function \( f: A \to \mathbb{R} \) is defined by \[ f(x) = \frac{1}{\sqrt{64 - (0.5)^{24+x- x^2} }} \] then the sum of all absolute values of elements of \( A \) is:
The independent term in the expansion of \( (1 + x + 2x^2) \left( \frac{3x^2}{2} - \frac{1}{3x} \right)^9 \) is:
The number of ways of selecting 3 numbers that are in GP from the set \( \{1, 2, 3, \dots, 100\} \) is:
It is given that in a random experiment, events A and B are such that \( P(A) = \frac{1}{4} ,P(A|B) = \frac{1}{2} \) and \( P(B|A) = \frac{2}{3} \). Then \( P(B) \) is: