List of top Questions asked in AP EAPCET- 2022

The ratio of the largest and shortest distances from the point $(2, -7)$ to the circle $x^2 + y^2 - 14x - 10y - 151 = 0$ is
If $(1 + \tan1^\circ)(1 + \tan2^\circ)\dots(1 + \tan45^\circ) = 2^n$, then $n =$ ?
A bulb of power 660 W radiates uniformly in all directions. The pressure exerted by the radiation on the surface at a distance of 5 m is
Find the false statement for ideal gases:
In a parallel plate capacitor, if \(10^{12}\) electrons pass from one plate to another, a potential difference of 10 V is developed across the plates. The capacitance of the capacitor is
The value of $\dfrac{1 + \tanh x}{1 - \tanh x} =$ ?
The function $ y = x^3 - ax^2 + 48x + 7 $ is increasing for all real values of $ x $. Find the interval in which $ a $ lies:
Let \( A = \begin{bmatrix} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{bmatrix} \) and \( B = \begin{bmatrix} 0 & 0 & n \\ 0 & n & 0 \\ n & 0 & 0 \end{bmatrix} \). Then \( A^2 + B^2 + AB = \)
Find the distance between the point \( (6, 4\sqrt{3}) \) and the focus of the parabola \( y^2 = 8x \)
\( \int \sqrt{x+\sqrt{x^2+2}} \ dx = \)
If $\displaystyle \lim_{x \to 0} \dfrac{|x|}{\sqrt{x^4 + 4x^2 + 5}} = k$, $\displaystyle \lim_{x \to 0} x^4 \sin\left(\dfrac{1}{3\sqrt{x}}\right) = l$, Then $k + l = $
If \( A = \begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} 8 & 0 \\7 & 1 \end{bmatrix} \), and \( A^3 = B \), then \( x = \) ?
Match the following: List - I \quad (Type of hydride) \quad List - II \quad (Example) A) Electron precise \quad i) SiH$_4$ B) Saline \quad ii) H$_2$O C) Electron deficient \quad iii) MgH$_2$ D) Electron rich \quad iv) B$_2$H$_6$
If $P$, $Q$ are two points on the curve $y = 2x^2$ in the rectangular Cartesian coordinate system such that $\vec{OP} \cdot \vec{i} = -1$, $\vec{OQ} \cdot \vec{i} = 2$, then $\vec{OQ} - 4\vec{OP} =$
Given that $ \vec{a}, \vec{b}, \vec{c} $ are non-coplanar vectors and: $$ \vec{a} + 3\vec{b} + 4\vec{c} = x(\vec{a} - 2\vec{b} + 3\vec{c}) + y(\vec{a} + 5\vec{b} - 2\vec{c}) + z(6\vec{a} + 14\vec{b} + 4\vec{c}) $$ Find $ x + y + z $
For any real number $t$, the point $\left( \dfrac{8t}{1 + t^2}, \dfrac{4(1 - t^2)}{1 + t^2} \right)$ lies on a/an
Which of the following molecules is eliminated during peptide bond formation?
Suppose a point \( P \) moves such that: \[ BP^2 - AP^2 = 121 \] where \( A = (2, 5) \), \( B = (5, 11) \). Then the locus of \( P \) is a straight line. What is the slope of this line?
The ratio of the areas of the greatest and the smallest circles touching \((x \pm 1)^2 + (y \pm 1)^2 = 1\) is (The equation \((x \pm 1)^2 + (y \pm 1)^2 = 1\) represents four circles with radius 1, centered at (1,1), (1,-1), (-1,1), (-1,-1).)
The locus of the point of intersection on the line \( \sqrt{3}x - y - 4\sqrt{3}k = 0 \) and \( \sqrt{3}kx + ky - 4\sqrt{3} = 0 \) for different real values of k is a hyperbola H. If e is the eccentricity of H then \(4e^2 = \)
What are X and Y respectively in the following reactions?
\( \text{X} + \text{D}_2\text{O} \rightarrow \text{CD}_2 + \text{P} \)
\( \text{Y} + \text{D}_2\text{O} \rightarrow \text{CD}_4 + \text{Q} \)
Which of the following conditions are not suitable for a spontaneous reaction?
The relative basic strength of the compounds is correctly shown in the option:
A ray makes angles \( \alpha, 2\alpha, 3\alpha \) with the coordinate axes OX, OY, OZ respectively. Then possible values of \( \alpha \) are:
The total number of positive integral solutions \((x, y, z)\) of \( xyz = 24 \) is: