List of top Questions asked in AP EAPCET

Let \( \vec{a}, \vec{b} \) be non-collinear vectors, with \( |\vec{a}| = 2\sqrt{2} \), \( |\vec{b}| = 3 \), and the angle between them is \( 45^\circ \). Then the lengths of the diagonals of the parallelogram whose adjacent sides are \( \vec{5a} + \vec{2b} \) and \( \vec{a} - \vec{3b} \) are:
Two vertices of a triangle are at \( -\vec{i} + 3\vec{j} \) and \( 2\vec{i} + 5\vec{j} \). Its orthocenter is at \( \vec{i} + 2\vec{j} \). If the position vector of the third vertex is \( a\vec{i} + b\vec{j} \), then \( (a, b) = \):
Identify the correct statements from the following:
The formula of Calgon is \( \text{Na}_6(\text{PO}_3)_6 \)
(II) Exhausted permutit is regenerated by aqueous KCl solution.
(III) Calcium stearate is soluble in water.
(IV) In ice crystals, each oxygen is surrounded by four oxygen atoms.
Identify the species which does **not** exist:
A person writes letters to 6 friends and addresses envelopes. In how many ways can the letters be placed so that at least two go to wrong envelopes?
In a plane there are 37 straight lines of which 13 pass through point A and 11 pass through point B. Moreover, no three lines (apart from the lines passing through A and B) pass through same point and no two lines are parallel. What is the number of points of intersection of the straight lines?
Identify the major product from the following reaction sequence.
major product from the following reaction sequence.
Person A can solve 90% of the problems given in the book and Person B can solve 70%. Then the probability that atleast one of them will solve the problem selected at random from the book is
A true statement among the following identities is
The no. of positively and negatively charged sols respectively in the following are TiO$_2$, blood, CdS, Cu, Ag, Clay, SiO$_2$, Fe$_2$O$_3$
The least distance from origin to a point on the line $y = x + 3$ which lies at a distance of 2 units from $(0,3)$ is
If $f(x) = \cot^{-1}\left( \dfrac{x^n + x^{-n}}{2} \right)$, then $f'(1) = $
Hydrolysis of nucleic acid gives nitrogenous base sugar and ________
A hydrogen atom is excited to \( n = 4 \). Find the potential energy of the electron in excited state.
Given: $$ \frac{2x^2 + 1}{x^3 - 1} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + x + 1} $$ Find the value of $ 7A + 2B + C $
A light from Paschen series of hydrogen atom is able to eject photoelectrons from a metal. Then the work function of the metal is
Identify the major product formed from the following:
the major product formed from the following
The rms speed of oxygen at room temperature is about \(500 \, \text{m/s}\). The rms speed of hydrogen at the same temperature is about
x% (w/v) solution of urea is isotonic with 4% (w/v) solution of non-volatile solute of molar mass 120 g mol-1. The value of x is
Which of the following equations are correct?
(A) U =H−PV
(B) G =H−TS
(C) U =q+W
If \(A = \begin{bmatrix}x & 2 & 1 \\ 2 & x & 1 \\ 2 & 1 & 0\end{bmatrix}\) and \(\det(A) = 125\), then \(x =\)
Which of the following compounds do not have sp$^3$ carbon atom(s)?
I. Acetone\quad II. Acetic acid\quad III. Buta-1,3-diene\quad IV. Propyne\quad V. Naphthalene
In quadrilateral ABCD, $\vec{AB} = \vec{a},\ \vec{BC} = \vec{b},\ \vec{DA} = \vec{a} - \vec{b}$. M is midpoint of BC and X lies on DM such that $\vec{DX} = \dfrac{4}{5}\vec{DM}$. Then the points A, X and C:
In a triangle \( ABC \), if \( a : b : c = 4 : 5 : 6 \), the ratio of radius of the circumcircle to that of the incircle is:
Identify the ortho and para directing groups towards aromatic electrophilic substitution reactions from the following list: -OH, -CN, COOH, -OCH3, -NHCOCH3, -CHO