List of top Mathematics Questions asked in AP EAMCET

The equation of a line which makes an angle of \( 45^\circ \) with each of the pair of lines \[ xy - x - y + 1 = 0 \] is:
A and B throw a pair of dice alternately and they note the sum of the numbers appearing on the dice. A wins if he throws 6 before B throws 7, and B wins if he throws 7 before A throws 6. If A begins, the probability of his winning is:

Evaluate the following determinant: \( \begin{vmatrix} 1 & 1 & 1 \\ a^2 & {b^2} & {c^2} \\ {a^3} & {b^3} & {c^3} \\ \end{vmatrix} \)

The rate of change of \( x^{\sin x} \) with respect to \( (\sin x)^x \) is:
If \( P \) and \( Q \) are two \( 3 \times 3 \) matrices such that \( |PQ| = 1 \) and \( |P| = 9 \), then the determinant of adjoint of the matrix \( P . Adj \ 3Q \) is:
The value of \( 5 \cos \theta + 3 \cos \left( \theta + \frac{\pi}{3} \right) + 3 \) lies between:
Find the locus of points satisfying the equation \( axy + byz = cy \).
The domain of the real valued function \( f(x) = \sqrt{2 + x} + \sqrt{3 - x} \) is:
Define the functions \( f, g \) and \( h \) from \( \mathbb{R} \) to \( \mathbb{R} \) such that: \[ f(x) = x^2 - 1, \quad g(x) = \sqrt{x^2 + 1} \]
functions f,g and h from R to R
Consider the following statements:
If \( |x| < \frac{2}{3} \), then the fourth term in the expansion of \( (3x - 2)^{2/3} \) is:
A bag contains 6 balls. If three balls are drawn at a time and all of them are found to be green, then the probability that exactly 5 of the balls in the bag are green is:
If $$ \lim\limits_{x \to \infty} \frac{\left(\sqrt{2x+1} + \sqrt{2x-1}\right) + \left(\sqrt{2x+1} - \sqrt{2x-1}\right) P x^4 - 16} {(x+\sqrt{x^2 - 2}) + (x - \sqrt{x^2 - 2})} = 1, $$ then P = ? 
If \( y = \frac{ax + \beta}{\gamma x + \delta} \), then \( 2y_1 y_3 = \) ?
Which one of the following is false?
The point which lies on the tangent drawn to the curve \( x^4 e^y + 2 \sqrt{y} + 1 = 3 \) at the point \( (1,0) \) is:
If \( f(x) = x^x \), then the interval in which \( f(x) \) decreases is:
If Rolle’s theorem is applicable for the function \( f(x) \) defined by \( f(x) = x^3 + Px - 12 \) on \( [0,1] \), then the value of \( C \) of the Rolle's theorem is:
The number of all the values of \( x \) for which the function \[ f(x) = \sin x + \frac{1 - \tan^2 x}{1 + \tan^2 x} \] attains its maximum value on \( [0, 2\pi] \).
If \( x \notin \left[ 2n\pi - \frac{\pi}{4}, 2n\pi + \frac{3\pi}{4} \right] \) and \( n \in \mathbb{Z} \), then \[ \int \sqrt{1 - \sin 2x} \, dx = \]
Evaluate the integral: \[ \int e^x \left( \frac{x + 2}{(x+4)} \right)^2 dx. \]
If \[ \int \frac{1}{1 - \cos x} \, dx = \tan \left( \frac{x}{4} + \beta \right) + c, \] then one of the values of \( \frac{\pi}{4} - \beta \) is:
If \[ 729 \int_1^3 \frac{1}{x^3 (x^2 + 9)^2} \, dx = a + \log b, \] then \( a - b = \) ?
If \( n \geq 2 \) is a natural number and \( 0<\theta<\frac{\pi}{2} \), then \[ \int \frac{(\cos^n \theta - \cos \theta)^{1/n}}{\cos^{n+1} \theta} \sin \theta \, d\theta = \]
Evaluate the limit: $$ \lim_{n \to \infty} \frac{17^7 + 27^7 + \dots + n^{77}}{n^{78}}. $$ 

If $$ f(x) = \begin{cases} \frac{6x^2 + 1}{4x^3 + 2x + 3}, & 0 < x < 1 \\ x^2 + 1, & 1 \leq x < 2 \end{cases} $$ then $$ \int_{0}^{2} f(x) \,dx = ? $$