List of top Questions asked in AP EAPCET

If \( \overline{a} = \overline{i} - 2\overline{j} - 3\overline{k} \), \( \overline{b} = -2\overline{i} + 3\overline{j} + 4\overline{k} \), \( \overline{c} = 5\overline{i} - 4\overline{j} + 3\overline{k} \), and \( \overline{d} = 3\overline{i} + \overline{j} + 5\overline{k} \) are four vectors, then \( (\overline{a} \times \overline{b}) \cdot (\overline{c} \times \overline{d}) = \)
The general solution of the differential equation \( \left(x - (x + y)\log(x + y)\right) dx + x\,dy = 0 \) is:
\( \sum_{k=1}^{n} k(k+1)(k+2)...(k+r-1) = \)
The number of all five-letter words (with or without meaning) having at least one repeated letter that can be formed by using the letters of the word INCONVENIENCE is:
An alcohol X $\mathrm{C_5H_{12}O}$ on dehydration gives Y (major product). Reaction of Y with HBr gave Z ($\mathrm{C_5H_{11}Br}$, major product). Z undergoes nucleophilic substitution in two steps. What are X and Y?
The synthetic detergents of the following are
synthetic detergents of the following are
A ray of light incidents at an angle of \(60^\circ\) on the first face of a prism. The angle of the prism is \(30^\circ\) and its second face is silvered. If the light ray inside the prism retraces its path after reflection from the second face, then the refractive index of the material of the prism is
If \( Q \) is the inverse point of \( P(-1, 1) \) with respect to the circle \( x^2 + y^2 - 2x + 2y = 0 \), then the line containing \( Q \) is:

Match the following: 



 

Sucrose when boiled with dilute HCl gives two functional isomers X and Y. X gives monocarboxylic acid with bromine water but not Y. The number of --OH groups in cyclic structure of X is
The number of molecules having lone pair of electrons on central atom in the following is: BF$_3$, SF$_4$, SiCl$_4$, XeF$_4$, NCl$_3$, XeF$_6$, PCl$_5$, HgCl$_2$, SnCl$_2$
If \( \sqrt{x-xy} + \sqrt{y-xy} = 1 \), then \( \frac{dy}{dx} = \)
In solving a system of linear equations \(AX = B\) by Cramer's rule, in the usual notation, if \[ \Delta_1 = \begin{vmatrix} -11 & 1 & -7\\ -4 & 1 & -2 \\ 5 & 1 & 1 \end{vmatrix} \quad \text{and} \quad \Delta_3 = \begin{vmatrix} 4 & 1 & -11 \\ 3 & 1 & -4 \\ 4 & 1 & 5 \end{vmatrix}, \quad \text{then } X = ? \]
A particle of mass $8~\mu g$ collides with another stationary particle of mass $4~\mu g$. If the collision is perfectly elastic and one dimensional, the ratio of de Broglie wavelengths after collision is
The angle made by a line \(L\) with positive X-axis measured in the positive direction is \(\frac{\pi}{6}\) and the intercept made by \(L\) on Y-axis is negative. If \(L\) is at a distance 5 units from the origin, then the perpendicular distance from the point \(\left(1,-\sqrt{3}\right)\) to the line \(L\) is?
The equation of the circle touching the lines \(|x-2| + |y-3| = 4\) is?
If the lines \(x+y-2=0\), \(3x-4y+1=0\) and \(5x+ky-7=0\) are concurrent at \((\alpha, \beta)\), then equation of the line concurrent with the given lines and perpendicular to \(kx+y-k=0\) is
The angle between the tangents drawn from the point (2, 2) to the circle \(x^2 + y^2 + 4x + 4y + c = 0\) is \(\cos^{-1} \left( \frac{7}{16} \right)\). If two such circles exist, then the sum of values of \(c\) is
Let \( A_1 \) be the area of the given ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \). Let \( A_2 \) be the area of the region bounded by the curve which is the locus of mid point of the line segment joining the focus of the ellipse and a point P on the given ellipse, then \( A_1 : A_2 = \)
If a proton and an alpha particle are accelerated through the same potential difference, then the ratio of their de Broglie wavelengths is:
The radius of fourth orbit in \( He^+ \) ion is \( R_1 \) pm and radius of third orbit in \( Li^{2+} \) ion is \( R_2 \) pm. The value of \( (R_1 - R_2) \) in pm is:
A student has probability \(\dfrac{2}{3}\) of getting distinction in a test. Out of 5 tests, the probability that he gets distinction in at least 3 tests is
For a positive real number p, if the perpendicular distance from a point \( -\vec{i} + p\vec{j} - 3\vec{k} \) to the plane \( \vec{r} \cdot (2\vec{i} - 3\vec{j} + 6\vec{k}) = 7 \) is 6 units, then p =
If the slope of the tangent drawn at any point \((x, y)\) on a curve is \(x + y\), then the equation of that curve is
If \( y = \operatorname{Sin}^{-1} \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} \) and \( -\frac{3\pi}{2}<x<-\frac{\pi}{2} \), then \( \frac{dy}{dx} \) is: