List of top Questions asked in AP EAPCET

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 \( x = \) ?
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?
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 $
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:
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
In a Binomial distribution $B(n, p)$, if the mean and variance are 15 and 10 respectively, then the value of the parameter $n$ is
In a triangle ABC, if $a \ne b$, then \[ \frac{a\cos A - b\cos B}{a\cos B - b\cos A} + \cos C = ? \]
If $ \sin\theta + \csc\theta = 4 $, then find: $$ \sin^2\theta + \csc^2\theta = ? $$
In any triangle ABC, \( \frac{\cos 2A}{a^2} - \frac{\cos 2B}{b^2} = \)
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?
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
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 \(4e^2 = \)
\( \int \sqrt{x+\sqrt{x^2+2}} \ dx = \)
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
Which of the following molecules is eliminated during peptide bond formation?
The relative basic strength of the compounds is correctly shown in the option:
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:
A short bar magnet produces a magnetic field of \(6.4 \times 10^{-5}\) T at a distance of 20 cm from the center of the magnet on the normal bisector of the magnet. The magnetic field produced by this magnet at a distance of 40 cm on the axis is