List of top Mathematics Questions asked in AP EAMCET

If \( \alpha, \beta, \gamma \) are the roots of the determinant equation: \[ \begin{vmatrix} 1-x & -2 & 1
-2 & 4-x & -2
1 & -2 & 1-x \end{vmatrix} = 0 \] then \( \alpha \beta + \beta \gamma + \gamma \alpha \) is:
The set of all real values of \(x\) satisfying the inequality \(\frac{7x^2 - 5x - 18}{2x^2 + x - 6}<2\) is
In \( \triangle PQR \), \((4\overline{i} + 3\overline{j} + 6\overline{k} )\) and \((3\overline{i} + \overline{j} + 3\overline{k} )\) are the position vectors of the vertices P, Q, R respectively. Then the position vector of the point of intersection of the angle bisector of \( P \) with \( QR \).
Let \( [P] \) denote the greatest integer \( \leq P \). If \( 0 \leq a \leq 2 \), then the number of integral values of \( a \) such that \( \lim_{x \to a} [x^2] - [x]^2 \) does not exist is:
Find the general solution of the differential equation \( ( \sin y \cos^2 y - x \sec^2 y ) dy = (\tan y) dx \).
Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be defined by \( f(x + y) = f(x) + 12y \), for all \( x, y \in \mathbb{R} \). If \( f(1) = 6 \), then the value of \( \sum_{r=1}^n f(r) \) is:
A point moves on the curve \( y = x^3 - 3x^2 + 2x - 1 \) and its y-coordinate increases at a rate of 6 units per second. When the point is at (2,-1), the rate of change of its x-coordinate is:
A box \( P \) contains one white ball, three red balls and two black balls. Another box \( Q \) contains two white balls, three red balls and four black balls. If one ball is drawn at random from each one of the two boxes, then the probability that the balls drawn are of different color is
If \( (a, b) \) and \( (c, d) \) are the internal and external centres of similitude of the circles \[ x^2 + y^2 + 4x - 5 = 0 \] and \[ x^2 + y^2 - 6y + 8 = 0 \] respectively, then \( (a + d)(b + c) \) is:
Find the domain of \( f(x) \) given: \[ \int \frac{\sin x \cos x}{\sqrt{\cos^4 x - \sin^4 x}} dx = -\frac{f(x)}{2} + C. \] then domain of f{x) is
The area of the triangle formed by the pair of lines \( 23x^2 - 48xy + 3y^2 = 0 \) with the line \( 2x + 3y + 5 = 0 \) is:
Evaluate: \[ \lim_{x \to 0} \left[ \frac{1}{x} - \frac{1}{e^x - 1} \right] \]
If the pair of lines represented by \[ 3x^2 - 5xy + P y^2 = 0 \] and \[ 6x^2 - xy - 5y^2 = 0 \] have one line in common, then the sum of all possible values of \( P \) is:
The area of the triangle formed by the lines represented by \( 3x + y + 15 = 0 \) and \( 3x^2 + 12xy - 13y^2 = 0 \) is:
The values of \( x \) for which the angle between the vectors \[ \mathbf{a} = x\hat{i} + 2\hat{j} + \hat{k}, \quad \mathbf{b} = -\hat{i} + 2\hat{j} + x\hat{k} \] is obtuse lie in the interval:
Let \( f(x) = \begin{cases 1 + \frac{2x}{a}, & 0 \le x \le 1
ax, & 1<x \le 2 \end{cases} \). If \( \lim_{x \to 1} f(x) \) exists, then the sum of the cubes of the possible values of \( a \) is: }
Two persons A and B throw three unbiased dice one after the other. If A gets the sum 13, then the probability that B gets a higher sum is:
If the normal chord drawn at \( (2a,2a\sqrt{2}) \) on the parabola \( y^2 = 4ax \) subtends an angle \( \theta \) at its vertex, then \( \theta \) is:
If \[ \frac{13x+43}{2x^2 + 17x + 30} = \frac{A}{2x+5} + \frac{B}{x+6} \text{ then } A + B = \]
Evaluate the integral \( \int \frac{\sin^{-1} \left(\frac{x}{\sqrt{a + x}}\right) \sqrt{a + x}}{dx} \):
If \( \theta = \sec^{-1}(\cosh u) \), then \( u = \)
Evaluate the integral: $$ \int \frac{x^3 \tan^{-1}(x^4)}{1 + x^8} \,dx. $$ 
The smallest positive value (in degrees) of \( \theta \) for which \( \tan(\theta + 100^\circ) = \tan(\theta + 50^\circ) \tan(\theta - 50^\circ) \) is valid, is:
The area (in square units) bounded by the curves \( x = y^2 \) and \( x = 3 - 2y^2 \) is:
If \(I_{n}=\int_{0}^{\pi/4}\tan^{n}x~dx,\) then \(I_{13}+I_{11}=\)