List of top Questions asked in AP EAMCET- 2024

If \[ \int \frac{1}{1 - \cos x} \, dx = \tan \left( \frac{x}{4} + \beta \right) + c, \] then one of the values of $ \frac{\pi}{4} - \beta $ is:

$ C_1 $ is the circle with centre at $ (0,0) $ and radius 4, $ C_2 $ is a variable circle with centre at $ (\alpha, \beta) $ and radius 5. If the common chord of $ C_1 $ and $ C_2 $ has slope $ \frac{3}{4} $ and of maximum length, then one of the possible values of $ \alpha + \beta $ is:

Evaluate the integral: \[ I = \int \frac{1}{x^2\sqrt{1 + x^2}} \,dx. \]

For real values of $ x $ and $ a $, if the expression $ \frac{x+a}{2x^2 - 3x + 1} $ assumes all real values, then:

Evaluate the integral: \[ \int \frac{1}{x^5 \sqrt{x^5+1}} dx. \]

Find the sum of the first 10 terms of the sequence $ 2.5 + 5.9 + 8.13 + 11.17 + \cdots \ to \ 10 \ terms =$:

If the roots of $\sqrt{\frac{1 - y}{y}} + \sqrt{\frac{y}{1 - y}} = \frac{5}{2}$ are $\alpha$ and $\beta$ ($\beta > \alpha$) and the equation $(\alpha + \beta)x^4 - 25\alpha \beta x^2 + (\gamma + \beta - \alpha) = 0$ has real roots, then a possible value of $y$ is:

If the origin is shifted to remove the first degree terms from the equation $2x^2 - 3y^2 + 4xy + 4x + 4y - 14 = 0$, then with respect to this new co-ordinate system, the transformed equation of $x^2 + y^2 - 3xy + 4y + 3 = 0$ is

If the line $2x - 3y + 5 = 0$ is the perpendicular bisector of the line segment joining $1, -2$ and $(a, b)$, then $a + b =$

Evaluate the integral $ \int \frac{dx}{x(x^4 + 1)} $:

Evaluate the integral \[ \int \frac{\sin^6 x}{\cos^8 x} \, dx. \]

The sum of the rational terms in the binomial expansion of $ \left( \sqrt{2} + 3^{1/5} \right)^{10} $ is:

The general solution of $ \cot \frac{x}{2} - \cot x = \csc \frac{x}{2} $ is:

If $ AB = 2i + 3j - 6k $, $ BC = 6i - 2j + 3k $ are the vectors along two sides of a triangle ABC, then the perimeter of triangle ABC is:

If $ y = x + \sqrt{2} $ is a tangent to the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $, then equations of its directrices are:

If $ \int_0^{2\pi} (\sin^4 x + \cos^4 x) \, dx = K \int_0^\pi \sin^2 x \, dx + L \int_0^\frac{\pi}{2} \cos^2 x \, dx $ and $ K, L \in \mathbb{N} $, then the number of possible ordered pairs $ (K, L) $ is}

If $ Z = x + iy $ is a complex number, then the number of distinct solutions of the equation \[ z^3 + \bar{z} = 0 \] is:

If set $ A $ contains 8 elements, then the number of subsets of $ A $ which contain at least 6 elements is:

The point (a, b) is the foot of the perpendicular drawn from the point (3, 1) to the line x + 3y + 4 = 0. If (p, q) is the image of (a, b) with respect to the line 3x - 4y + 11 = 0, then $\frac{p}{a} + \frac{q}{b} = $

If $ A = [a_{ij}]$ where $ 1 \leq i, j \leq n $ with $ n \geq 2 $ and $ a_{ij} = i + j $ is a matrix, then the rank of $ A $ is:

Evaluate the integral $ \int_{-\frac{1}{24}}^{\frac{1}{24}} \sec(x) \log\left(\frac{1-x}{1+x}\right) \, dx $:

The square root of $ 7 + 24i $ is:

Evaluate the integral: \[ \int \sin^4 x \cos^4 x \, dx. \]

If both the roots of the equation $ x^2 - 6ax + 2 - 2a + 9a^2 = 0 $ exceed 3, then:

8 teachers and 4 students are sitting around a circular table at random. The probability that no two students sit together is: