List of top Mathematics Questions asked in AP EAMCET

Evaluate the integral: $ I = \int e^{2x+3} \sin 6x \, dx $.

Let $[r]$ denote the largest integer not exceeding $r$, and the roots of the equation $ 3z^2 + 6z + 5 + \alpha(x^2 + 2x + 2) = 0 $ are complex numbers whenever $ \alpha > L $ and $ \alpha < M $. If $ (L - M) $ is minimum, then the greatest value of $[r]$ such that $ Ly^2 + My + r < 0 $ for all $ y \in \mathbb{R} $ is:

If a variable straight line passing through the point of intersection of the lines x - 2y + 3 = 0 and 2x - y - 1 = 0 intersects the X and Y axes at A and B respectively, then the equation of the locus of a point which divides the segment AB in the ratio -2 : 3 is:

In $ \triangle ABC $, if $ (r_2 - r_1)(r_3 - r_1) = 2r_2r_3 $, then $ 2(r + R) = $:

If m and M denote the mean deviations about mean and about median respectively of the data 20, 5, 15, 2, 7, 3, 11, then the mean deviation about the mean of m and M is:

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:

The descending order of magnitude of the eccentricities of the following hyperbolas is:
A. A hyperbola whose distance between foci is three times the distance between its directrices.
B. Hyperbola in which the transverse axis is twice the conjugate axis.
C. Hyperbola with asymptotes $ x + y + 1 = 0, x - y + 3 = 0 $.

If the line with direction ratios \[ (1, a, \beta) \] is perpendicular to the line with direction ratios \[ (-1,2,1) \] and parallel to the line with direction ratios \[ (\alpha,1,\beta), \] then $ (\alpha, \beta) $ is:

The equation of the circle touching the circle $$ x^2 + y^2 - 6x + 6y + 17 = 0 $$ externally and to which the lines $$ x^2 - 3xy - 3x + 9y = 0 $$ are normal is:

If 7 and 8 are the lengths of two sides of a triangle and $ a $ is the length of its smallest side. The angles of the triangle are in AP and $ a $ has two values $ a_1 $ and $ a_2 $ satisfying this condition. If $ a_1<a_2 $, then $ 2a_1 + 3a_2 = $:

For $ \lambda, \mu \in \mathbb{R} $, the lines \[ (x - 2y - 1) + \lambda (3x + 2y - 11) = 0 \] and \[ (3x + 4y - 11) + \mu (-x + 2y - 3) = 0 \] represent two families of lines. If the equation of the line common to both families is given by \[ ax + by - 5 = 0, \] then $ 2a + b = $ ?

If $ 4x - 3y - 5 = 0 $ is a normal to the ellipse $ 3x^2 + 8y^2 = k $, then the equation of the tangent at point (-2,m) is:

If all the letters of the word ‘SENSELESSNESS’ are arranged in all possible ways and an arrangement among them is chosen at random, then, the probability that all the E’s come together in that arrangement is:

Evaluate $$ \cot \left( \sum_{n=1}^{50} \tan^{-1} \left( \frac{1}{1 + n + n^2} \right) \right).= $$

If $y = \tan^{-1} \frac{x}{1+2x^2} + \tan^{-1} \frac{x}{1+6x^2} + \tan^{-1} \frac{x}{1+12x^2}$, then $\left(\frac{dy}{dx}\right)_{x=\frac{1}{2}} =$

Let $E_1$ and $E_2$ be two independent events of a random experiment such that
$P(E_1) = \frac{1}{2}, \quad P(E_1 \cup E_2) = \frac{2}{3}$.
Then match the items of List-I with the items of List-II: