List of top Questions asked in AP EAPCET

An iron block A of volume \( 0.25\ \text{m}^3 \) stretches a spring by 0.2 m. A new block B of volume \( 0.75\ \text{m}^3 \) is kept on a frictionless incline (30°) using same spring. Find equilibrium distance along incline.
An iron block A of volume 0.25 m3
If $(1 + \tan1^\circ)(1 + \tan2^\circ)\dots(1 + \tan45^\circ) = 2^n$, then $n =$ ?
A stick of length $r$ units slides with its ends on coordinate axes. Then the locus of the midpoint of the stick is a curve whose length is
For $\alpha \in \left[0, \dfrac{\pi}{2} \right]$, the angle between the lines represented by
$[x \cos\theta - y] \left[ (\cos\theta + \tan\alpha)x - (1 - \cos\theta \tan\alpha)y \right] = 0$ is
The straight line passing through \( (0, 0) \) and the foot of the perpendicular from \( (2, 4) \) onto the line \( x + y - 1 = 0 \) is:
If the point \( P(\sin\alpha, \cos\alpha) \) lies inside the triangle formed by the vertices \( (0, 0), \left(\frac{\sqrt{3}}{2}, 0\right), (0, \frac{\sqrt{3}}{2}) \), then \( \alpha \) lies in the interval:
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
Find the least distance from the point $ (10, 7) $ to the circle: $$ x^2 + y^2 - 4x - 2y - 20 = 0 $$
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
\( \int_{a-1}^{a} \frac{e^x(a-x)}{(x-a+1)^2} dx = \)
In a triangle ABC, let \(\angle C = \pi/2\). If r and R are respectively inradius and circumradius of ABC, then R + r =
A block of mass \(5\,\text{kg}\) starts up a \(45^\circ\) incline with an initial kinetic energy of \(100\,\text{J}\). The coefficient of friction is \(0.5\). The distance it travels before coming to rest is:
The relative basic strength of the compounds is correctly shown in the option:
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 $\dfrac{1 + \tanh x}{1 - \tanh x} =$ ?
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$_6$
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 \( y^2 = 8x \)
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 \( x = \) ?
3.1 g of a compound, 'X' (molar mass = 62 g mol$^{-1}$) is dissolved in 19.5 g of other compound, Y (molar mass = 78 g mol$^{-1}$). The ratio of mole fractions of X and Y in the solution is
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 $
What are X and Y respectively in the following reactions?
\( \text{X} + \text{D}_2\text{O} \rightarrow \text{CD}_2 + \text{P} \)
\( \text{Y} + \text{D}_2\text{O} \rightarrow \text{CD}_4 + \text{Q} \)