List of top Mathematics Questions asked in AP EAPCET

Let $ A(1,2), B(3,4) $ and $ C(k,6) $ be three points such that the area of triangle $ ABC $ is 5 square units. The possible values of $ k $ are:

If the tangent to the curve $ y = ax^2 + bx + c $ at the point $ (1,1) $ is parallel to the x-axis, and the curve passes through the point $ (2,3) $, then find the value of $ a + b + c $:

Let \[ f(x) = x^4 - 4x^3 + 6x^2 + k \] \text{If $f(x) \geq 0$ for all real $x$, then the value of $k$ is:}

A rectangular garden has a length that is 3 meters more than its width. If the area of the garden is 88 square meters, what is the width of the garden?

Bag A contains 3 white and 4 red balls, bag B contains 4 white and 5 red balls, and bag C contains 5 white and 6 red balls. If one ball is drawn at random from each of these three bags, then the probability of getting one white and two red balls is:

Evaluate the limit: \[ \lim_{x \to 1} \frac{x + x^2 + x^3 + \dots + x^n - n}{x - 1}. \]

Evaluate the expression: \[ \frac{\sin 1^\circ + \sin 2^\circ + \dots + \sin 89^\circ}{2(\cos 1^\circ + \cos 2^\circ + \dots + \cos 44^\circ) + 1} =\]

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

Evaluate the integral \[ I = \int_{-1}^{1} \left( \sqrt{1 + x + x^2} - \sqrt{1 - x + x^2} \right) \, dx \]

If $ 5 \sinh x - \cosh x = 5 $, then one of the values of $ \tanh x $ is:

If \[ 3f(x) - 2f\left(\frac{1}{x}\right) = x, \] then $ f'(2) $ is:

If the line segment joining the points $ (1,0) $ and $ (0,1) $ subtends an angle of $ 45^\circ $ at a variable point $ P $, then the equation of the locus of $ P $ is:

Let $ f(x) = 3 + 2x $ and $ g_n(x) = (f \circ f \circ \dots \text{n times}) (x) $. If for all $ n \in \mathbb{N} $, the lines $ y = g_n(x) $ pass through a fixed point $ (a, \beta) $, then $ \alpha + \beta = ? $

If $ a $ is a common root of $ x^2 - 5x + \lambda = 0 $ and $ x^2 - 8x - 2\lambda = 0 $ ($ \lambda \neq 0 $) and $ \beta, \gamma $ are the other roots of them, then $ a + \beta + \gamma + \lambda = $:

Let $ F $ and $ F' $ be the foci of the ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ (where $ b<2 $), and let $ B $ be one end of the minor axis. If the area of the triangle $ FBF' $ is $ \sqrt{3} $ sq. units, then the eccentricity of the ellipse is:

Evaluate the integral: \[ \int \frac{3x^9 + 7x^8}{(x^2 + 2x + 5x^9)^2} \,dx= \]

If $ \vec{i} - 2\vec{j} + 3\vec{k}, 2\vec{i} + 3\vec{j} - \vec{k}, -3\vec{i} - \vec{j} - 2\vec{k} $ are the position vectors of three points A, B, C respectively, then A, B, C:

The general solution of the differential equation $$ (y^2 + x + 1) \, dy = (y + 1) \, dx $$ is: