List of top Mathematics Questions asked in AP EAPCET

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

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

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:

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

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

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

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

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 = $ ?

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) $=

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 = $ ?

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 = $:

The differential equation formed by eliminating arbitrary constants $ A $ and $ B $ from the equation \[ y = A \cos 3x + B \sin 3x \] is:

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

The number of ordered pairs $ (x, y) $ satisfying the equations: \[ \sin x + \sin y = \sin (x + y) \quad \text{and} \quad |x| + |y| = 1. \]

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 $ T = 2\pi \sqrt{\frac{L}{g}} $, $ g $ is a constant and the relative error in $ T $ is $ k $ times to the percentage error in $ L $, then $ \frac{1}{k} = $ ?

Let $ \overline{X} $ and $ \overline{Y} $ be the arithmetic means of the runs of two batsmen A and B in 10 innings respectively, and $ \sigma_A, \sigma_B $ are the standard deviations of their runs in them. If batsman A is more consistent than B, then he is also a higher run scorer only when