List of top Mathematics Questions asked in AP EAPCET

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 = ? $

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

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 infinite series: \[ 1 + \frac{1}{3} + \frac{1.3}{3.6} + \frac{1.3.5}{3.6.9} + \dots \text{ to } \infty = \]

Evaluate the integral: \[ I = \int_{-3}^{3} |2 - x| dx. \]

P is a point on $ x + y + 5 = 0 $, whose perpendicular distance from $ 2x + 3y + 3 = 0 $ is $ \sqrt{13} $, then the coordinates of P are:

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

If \[ a^2 x^4 + b^2 y^4 = c^6, \] then the maximum value of $ xy $ is:

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:

If $\cos \alpha + \cos \beta + \cos \gamma = \sin \alpha + \sin \beta + \sin \gamma = 0,$ then evaluate $(\cos^3 \alpha + \cos^3 \beta + \cos^3 \gamma)^2 + (\sin^3 \alpha + \sin^3 \beta + \sin^3 \gamma)^2 =$

An urn contains 3 black and 5 red balls. If 3 balls are drawn at random from the urn, the mean of the probability distribution of the number of red balls drawn is:

If $\alpha$ and $\beta$ are two double roots of the equation: $$ x^2 + 3(a + 3)x - 9a = 0 $$ for different values of $a$ (where $\alpha > \beta$), then the minimum value of the equation: $$ x^2 + \alpha x - \beta = 0 $$ is:

If $ P(A \cap B) + P(B \mid A \cap B) = $, then:

The coefficient of $ x^5 $ in the expansion of $ \left( 2x^3 - \frac{1}{3x^2} \right)^5 $ is:

If $ \vec{a}, \vec{b}, \vec{c} $ are 3 vectors such that $ |\vec{a}| = 5, |\vec{b}| = 8, |\vec{c}| = 11 $ and $ \vec{a} + \vec{b} + \vec{c} = 0 $, then the angle between the vectors $ \vec{a} $ and $ \vec{b} $ is:

If a five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4, and 5 without repetition, then the total number of ways this can be done is:

The equation of the tangent to the curve \[ y = x^3 - 2x + 7 \] at the point $ (1,6) $ is:

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 \[ \int \frac{3}{2\cos 3x \sqrt{2} \sin 2x} dx = \frac{3}{2} (\tan x)^{\beta} + \frac{3}{10} (\tan x)^4 + C \] then $ A = $ ?

A common tangent to the circle $ x^2 + y^2 = 9 $ and the parabola $ y^2 = 8x $ is

If the sum of two roots of $ x^3 + px^2 + qx - 5 = 0 $ is equal to its third root, then $ p(q^2 - 4q) = $ ?

If $ P(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e $ is a polynomial such that: \[ P(0) = 1, \quad P(1) = 2, \quad P(2) = 5, \] \[ P(3) = 10, \quad P(4) = 17, \] then find the value of $ P(5) $=

In a random experiment, two dice are thrown and the sum of the numbers appeared on them is recorded. This experiment is repeated 9 times. If the probability that a sum of 6 appears at least once is $ P_1 $ and a sum of 8 appears at least once is $ P_2 $, then $ P_1 : P_2 = $:

If $ y = x - x^2 $, then the rate of change of $ y^2 $ with respect to $ x^2 $ at $ x = 2 $ is: