List of top Mathematics Questions asked in AP EAMCET

If \[ \int \frac{\sqrt[4]{x}}{\sqrt{x} + \sqrt[4]{x}} \, dx = \frac{2}{3} \left[ A \sqrt[4]{x^3} + B \sqrt[4]{x^2} + C \sqrt[4]{x} + D \log \left( 1 + \sqrt[4]{x} \right) \right] + K \] then $ \frac{2}{3} (A + B + C + D) = $}

The equation $ 2x^2 - 3xy - 2y^2 = 0 $ represents two lines $ L_1 $ and $ L_2 $. The equation $ 2x^2 - 3xy - 2y^2 - x + 7y - 3 = 0 $ represents another two lines $ L_3 $ and $ L_4 $. Let $ A $ be the point of intersection of lines $ L_1 $ and $ L_3 $, and $ B $ be the point of intersection of lines $ L_2 $ and $ L_4 $. The area of the triangle formed by the lines $ AB $, $ L_3 $, and $ L_4 $ is: .

The length of x-intercept made by the pair of lines $ 2x^2 + xy - 6y^2 - 2x + 17y - 12 = 0 $ is:

If $ L, M, N $ are the midpoints of the sides PQ, QR, and RP of triangle $ \Delta PQR $, then $ \overline{QM} + \overline{LN} + \overline{ML} + \overline{RN} - \overline{MN} - \overline{QL} = $:

If $ m, n $ are respectively the least positive and greatest negative integer values of such that $ (\frac{1-i}{1+i})^k = -i$, then $ m - n = $:

Evaluate the integral: \[ I = \int_{-\pi}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \,dx. \]

If the roots of the equation $ x^3 - 13x^2 + Kx - 27 = 0 $ are in geometric progression, then $ K = $:

If the coefficients of $x^5$ and $x^6$ are equal in the expansion of $ \left( a + \frac{x}{5} \right)^{65} $, then the coefficient of $x^2$ in the expansion of $ \left( a + \frac{x}{5} \right)^4 $ is:

If $ y = \frac{ax + \beta}{\gamma x + \delta} $, then $ 2y_1 y_3 = $ ?

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

If $ \theta $ is the angle between the tangents drawn from the point $ (2,3) $ to the circle $ x^2 + y^2 - 6x + 4y + 12 = 0 $, then $ \theta $ is:

Two persons A and B throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as 4 and the person who gets this result first is declared as the winner. If A starts the game, then the probability that B wins the game is:

Evaluate the limit: $$ \lim_{n \to \infty} n^4 \left[ \sum_{k=0}^{\infty} \frac{1}{(n^2 + k)^{5/2}} \right]. $$

If $ \alpha, \beta, \gamma $ are roots of the equation $ x^3 + ax^2 + bx + c = 0 $, then $ \alpha^{-1} + \beta^{-1} + \gamma^{-1} $ is:

The equation of the straight line passing through the point of intersection of the lines represented by $x^2 + 4xy + 3y^2 - 4x - 10y + 3 = 0$ and the point $(2,2)$ 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 function $ f(x) $ is given by: \[ f(x) = \begin{cases} \frac{2}{5 - x}, & x<3 \\ 5 - x, & x \geq 3 \end{cases} \] Which of the following is true

If \[ f(x) = 5 \cos^3 x - 3 \sin^3 x \quad \text{and} \quad g(x) = 4 \sin^3 x + \cos^2 x, \] then the derivative of $ f(x) $ with respect to $ g(x) $ is:

If \[ \int \log \left( 6\sin^2x + 17\sin x + 12 \right)^{\cos x} \, dx = f(x) + c \] then, \[ f\left(\frac{\pi}{2}\right) = \]

If the lines $ 3x+y-4=0 $, $ x - \alpha y + 10 = 0 $, $ \beta x + 2y + 4 = 0 $ and $ 3x + y + k = 0 $ represent the sides of a square, then find $ \alpha \beta (k+4)^2 $.

If two numbers $x$ and $y$ are chosen one after the other at random with replacement from the set of numbers $ \{1, 2, 3, \ldots, 10\} $, then the probability that $ |x^2 - y^2| $ is divisible by 6 is: