List of top Mathematics Questions asked in AP EAPCET

Evaluate the limit: \[ \lim_{x \to 1} \frac{\sqrt{x} - 1}{(\cos^{-1} x)^2} =\]

The sum of the order and degree of the differential equation: \[ \frac{d^y}{dx^t} = c + \left( \frac{d^y}{dx^t} \right)^{\frac{3}{2}} \] is:

$ \sin^4 \frac{\pi}{8} + \sin^4 \frac{3\pi}{8} + \sin^4 \frac{5\pi}{8} + \sin^4 \frac{7\pi}{8} = $

If the tangent drawn to the curve $(x^2+1)(y-3)=x$ at a point P, lying in the first quadrant, is a horizontal line, then the equation of the normal at the point P is

Evaluate the following expression: \[ (1+i)^{2024} + (1-i)^{2024} \]

Let $ \vec{b} = 3i - 2j + k $ and $ \vec{c} = i - j - k $ be two vectors. If $ \vec{a} $ is a vector such that $ \vec{a} + \vec{b} + \vec{c} = 0 $, then $ | \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} | $ is:

If a function defined by $ f(x) = \frac{(3^x - 1)^2}{\sin x \cdot \log(1+x)}, x \neq 0 $ is continuous at $x = 0$, then $f(0) =$ ?

In $ \Delta ABC $, if $ \angle C = 90^\circ $, then $ \left( \frac{I_1 - I_3}{I_1} \right) \left( \frac{I_2 - I_3}{I_2} \right) = $:

The number of arrangements of the word KANGAROO in which the A's do not appear together is:

If $ O $ is the origin and $ P, Q $ are points on the line $ 3x + 4y + 15 = 0 $ such that $ OP = OQ = 9 $, then the area of $ \triangle OPQ $ is:

If the solution for the system of equations \[ x + 2y - z = 3, \ 3x - y + 2z = 1, \ 2x - 2y + 3z = 2 \] is $ ( \alpha, \beta, \gamma ) $, then find the value of $ \alpha^2 + \beta^2 + \gamma^2 $.

The number of persons joining a cinema ticket counter in a minute follows a Poisson distribution with parameter 6, then the probability that at least one and at most five persons join the queue in a particular minute is

If the equation of the tangent drawn at $(h, k)$ to the hyperbola $\frac{(x - 1)^2}{1} - \frac{(y - 2)^2}{2} = 1$ is $x = 2$, then $h + k =$

If $ f(x) = \int_0^x \frac{5t^8 + 7t^6}{(t^2 + 2t + 1)^2} dt $ and $ f(0) = 0 $, then the value of $ f(1) $ is:

In $\triangle ABC$, if $\cos A + \cos C = 4 \sin^2 \frac{B}{2}$, then the ratio between the perimeter of the triangle and $(a + c)$ is

If the difference between the mean and variance of a binomial variate is $ \dfrac{5}{9} $, then the probability of getting 2 successes for an event when the experiment is conducted 5 times is:

The Cartesian form of the curve given by $ x = \frac{a}{2}\left(t + \frac{1}{t}\right) $, $ y = \frac{a}{2}\left(t - \frac{1}{t}\right) $, where $ t $ is a parameter, is:

In a matrix $ A $, if all the sub matrices of $ k^{th} $ order are singular and there is one non-singular sub matrix of order $ r $ $ (r<k) $, then the rank $ (\rho) $ of the matrix $ A $

$\int \frac{x^2}{(x^2-1)(x^2+1)} dx =$

Let $ f(x) $ be differentiable on $ \mathbb{R} $ and $ f'(m) \ne 0, m \in \mathbb{R} $. If $ \lim\limits_{x \to m} \frac{x f(m) - m f(x)}{x - m} + f'(m) = f(m) $, then $ m = $:

Let A, A' be the end points of major axis, S, S' be the foci and B, B' be the end points of minor axis of an ellipse E. If $\angle \text{BAB}' = 60^\circ$, then $\angle \text{SBS}' =$

Let $ S $ be a circle concentric with the circle $ 3x^2 + 3y^2 + x + y - 1 = 0 $. If the length of the tangent drawn from a point $ (2, -2) $ to the given circle is the radius of the circle $ S $, then the power of the point $ (2, 1) $ with respect to the circle $ S $ is

If $ \vec{a} = 2\hat{i} - 5\hat{j} + 8\hat{k} $, $ \vec{b} = 7\hat{i} - 5\hat{j} + 3\hat{k} $, and \[ (\vec{2a} - \vec{3b}) \times (\vec{4a} + \vec{b}) = x\hat{i} + y\hat{j} + z\hat{k}, \] then $ x + y + z = $

Let $A$ and $B$ be two independent events of a random experiment. If the probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occurs is $\frac{1}{3}$, then the probability of occurrence of $A$ is:

The sum of the distinct values of $ x $ for which the matrix $ A = \begin{bmatrix} 1 & 1 & x \\ 1 & x & 1 \\ x & 1 & 1 \end{bmatrix} $ has no inverse, is: