List of top Questions asked in AP EAPCET

Let the position vectors of the vertices of triangle ABC be \(\vec{a}, \vec{b}, \vec{c}\). If a point \(P\) on the plane of triangle has a position vector \(\vec{r}\) such that \(\vec{r} - \vec{b} = \vec{a} - \vec{c}\) and \(\vec{r} - \vec{c} = \vec{a} - \vec{b}\), then \(P\) is the
The point of intersection of the lines represented by \(\vec{r} = (\hat{i} - 6\hat{j} + 2\hat{k}) + t(\hat{i} + 2\hat{j} + \hat{k})\) and \(\vec{r} = (4\hat{j} + \hat{k}) + s(2\hat{i} + \hat{j} + 2\hat{k})\) is
If the points A, B, C, D with position vectors \(\vec{i} + \vec{j} - \vec{k}, -\vec{i} + 2\vec{k}, \vec{i} - 2\vec{j} + \vec{k}, 2\vec{i} + \vec{j} + \vec{k}\) form a tetrahedron, then angle between faces ABC and ABD is
If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors and \(\vec{a} \perp \vec{b}\), and \((\vec{a} - \vec{c}) \cdot (\vec{b} + \vec{c}) = 0\), and \(\vec{c} = l\vec{a} + m\vec{b} + n(\vec{a} \times \vec{b})\), then \(n^2 =\)
If the variance of the first \(n\) natural numbers is 10 and the variance of the first \(m\) even natural numbers is 16, then \(n : m =\)
Evaluate the expression:
\[ \cos^3 \left( \frac{3\pi}{8} \right) \cos \left( \frac{3\pi}{8} \right) + \sin^3 \left( \frac{3\pi}{8} \right) \sin \left( \frac{3\pi}{8} \right) \]
If \( A + B + C = \frac{\pi}{4} \), then evaluate the expression:
\[ \sin 4A + \sin 4B + \sin 4C \]
In a triangle ABC, if \(\sin\frac{A}{2} = \dfrac{1}{4}\sqrt{\dfrac{5}{\sqrt{5}}}, a = 2, c = 5\), and \(b\) is an integer, then the area (in sq. units) of triangle ABC is
In \(\triangle ABC\), if \(a + c = 5b\), then \(\cot\dfrac{A}{2} \cdot \cot\dfrac{C}{2} =\)
If \[ \binom{p}{q} = \binom{p}{q} \quad \text{and} \quad \sum_{i=0}^m \binom{10}{i} \binom{20}{m-i} \text{ is maximum, then find } m. \]
If $a = \ln \left( \frac{1}{z^2} \right)$ and $z$ is any non-zero complex number such that $|z| = 1$, then which of the following is the correct expression for $a$?
If \( ax^2 + bx + e>0 \) for all \( x \in \mathbb{R} \) and the expressions \( cx^2 + ax + b \) and \( ax^2 + bx + c \) have their extreme values at the same point \( x \), then for the expression \( cx^2 + ax + b \), find the correct statement regarding its extreme value.
If \( x^2 - 5x + 6 \) is a factor of \( f(x) = x^4 - 17x^3 + kx^2 - 247x + 210 \), find the other quadratic factor of \( f(x) \).
What are x and y in the following set of reactions?
Which of the following is not an example of an antacid?
When ethyl bromide and \textit{n}-propyl bromide are allowed to react with Na metal in dry ether, the number of different alkanes formed is:
Consider the following sequence of reactions:
isopropyl benzene
The incorrect statement about compound \( z \) is:
Which of the following complexes exhibit geometrical isomerism?
[label=\Roman*.]
The IUPAC name of the following compound is
7-Bromo-5-ethyl-2-methyldec-5-en-4-ol
Identify the correct statements from the following (only one):
I) Sulphur sol is an example of multimolecular colloid.
II) Starch sol is an example of associated colloid.
III) Artificial rubber is an example of macromolecular colloid.
Which of the following statements is incorrect with reference to alkaline earth metals?
Consider the following statements:
Statement-I: The order of electronegativity of B, Al, In, Tl is \(B>Tl>Al>In\)
Statement-II: Boric acid is a weak protic acid
Consider the following:
Assertion (A): CO is poisonous to living beings
Reason (R): CO binds to hemoglobin forming carboxyhaemoglobin, which is less stable than oxygen-hemoglobin complex.
Consider the following reaction sequence:
Vinylbenzene \(\xrightarrow{KMnO_4 + KOH, \Delta}\) X \(\xrightarrow{NaOH + CaO, \Delta}\) Y
'Y' can also be formed from
At 273 K the maximum work done when pressure on 10 g of hydrogen is reduced from 10 atm to 1 atm under isothermal, reversible conditions is