List of top Questions asked in AP EAPCET- 2022

Evaluate \( \int \frac{\cos(\sec^2 x) - 2022}{\cos^{2022} x} dx = f(x) + C \Rightarrow f\left( \frac{\pi}{4} \right) = \)
Let \( z \) and \( w \) be two complex numbers such that \( \bar{z} + i\bar{w} = 0 \) and \( \text{Arg}(zw) = \pi \). Then \( \text{Arg}(z) = \)
For the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \), if the length of the transverse axis is 8 and the distance between the foci is \( 2\sqrt{41} \), then the length of its latus rectum is:
Find the length of the intercept made by the line $ x + 1 = 0 $ between the lines: $$ 3x + 2y = 5 \quad \text{and} \quad 3x + 2y = 3 $$
If the solution of \( \frac{dy}{dx} = y \log_e 0.5 = 0 \), \( y(0) = 1 \), and \( y(x) \to k \) as \( x \to \infty \), then \( k = \)
The number of real values of \( m \) such that the equation \[ x^2 + (2m + 1)x + m = 0 \] has equal roots is:
In a triangle ABC, $r_1 \cot \dfrac{A}{2} + r_2 \cot \dfrac{B}{2} + r_3 \cot \dfrac{C}{2} = $ ?
The range of the data set: \( 35, 12, 21, 24, 15, 7, 16, 12, 30, 32, 13, 17 \) is:
Assertion (A): \( I_n = \int \cot^n x \, dx \), then \( I_6 + I_4 = -\frac{\cot^5 x}{5} \)
Reason (R): \( \int \cot^n x \, dx = \frac{-\cot^{n-1} x}{n - 1} - \int \cot^{n - 2} x \, dx \)
Evaluate the limit: \[ \lim_{x \to \infty} \frac{A + e^{mx}}{x + Ae^{mx}} \]
The number of solutions of the equations \[ x + y + z = 1,\quad x^2 + y^2 + z^2 = 1,\quad x^3 + y^3 + z^3 = 1 \] is:
Which of the following functions is differentiable at \( x = 0 \)?
If \( \int e^{\sqrt{x}} / \sqrt{x} (x + \sqrt{x}) dx = e^{\sqrt{x}}[Ax + B\sqrt{x} + C] + K \), then \( A + B + C = \):
If \( y^2+z^2=3yz, z^2+x^2=8zx, x^2+y^2=4xy \), then the value of \( \frac{x^2}{yz} + \frac{y^2}{zx} + \frac{z^2}{xy} \) is
If $4^x - 3^{x - \frac{1}{2}} = 3^{x + \frac{1}{2}} - 2^{2x - 1}$, then the value of $x$ is:
An ellipse has lengths of major and minor axes as 6 and 2 respectively. If the center is at \( (5,6) \) and the major axis lies along the line \( x - y + 1 = 0 \), then the equation of the ellipse is:
What is the sum of the first \( n \) terms of the series, whose \( k \)-term is \( k! \cdot k \)?
Suppose a parabola passes through $(0, 4)$, $(1, 9)$ and $(4, 5)$ and has its axis parallel to the $y$-axis. Then the equation of the parabola is
Suppose a triangle is formed by $x + y = 10$ and the coordinate axes. Then the number of points $(x, y)$ where $x$ and $y$ are natural numbers, lying inside the triangle is
Equation of tangent to the curve \( y = x + \frac{4}{x^2} \) which is parallel to x-axis is
If $a$, $b$, $c$ are respectively the $5^{\text{th}$, $8^{\text{th}}$, $13^{\text{th}}$ terms of an arithmetic progression, then}
$\begin{vmatrix} a & 5 & 1 \\ b & 8 & 1\\ c & 13 & 1 \end{vmatrix} = $
If a and b are respectively the order and degree of a differential equation \( y^2(y'')^2 + 3x(y')^{1/3} + x^2y^2 = \sin x \), then
\( \int_0^1 \alpha^k x^k dx = \)
The point on the curve $ y = x^2 + 4x + 3 $ that is closest to the line $ y = 3x + 2 $ is:
If \( \lim_{x \to 0} x^2 \left( \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}} \right) = k \), and \( \lim_{x \to 0} x^2 \left( \frac{e^{kx} - e^{-kx}}{e^{kx} + e^{-kx}} \right) = 1 \), then: