List of top Questions asked in AP EAPCET

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
The eccentric angle of a point on the ellipse $x^2 + 3y^2 = 6$ lying at a distance of 2 units from its centre is
If $f(x) = \cot^{-1}\left( \dfrac{x^n + x^{-n}}{2} \right)$, then $f'(1) = $
If a function \( f \) satisfies \( f(x+1) + f(x-1) = \sqrt{2}f(x) \), then \( f(x+2) + f(x-2) = \)
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 \( (a, b) = \):
Let \( A = (1, -2, 3) \), \( B = (3, 1, -3) \), \( C = (-3, 1, 3) \) be the vertices of triangle \( ABC \). If \( \cos \theta = \frac{\vec{AB} \cdot \vec{AC}}{|\vec{AB}||\vec{AC}|} \), then \( \cos A \) is:
A true statement among the following identities is
A cricket ball of mass 50 g and velocity 50 cm/s is stopped in 0.5 s. What is the force applied?
Toroid has 4900 turns, \( I = 12\ \text{A} \), average radius = \( 24.5\ \text{cm} \). Find magnetic field inside core.
Given: $$ 3f(\cos x) + 2f(\sin x) = 5x $$ Find: $$ f'(\cos x) + f'(\sin x) $$
Identify the species which does **not** exist:
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?
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
Identify the correct statements from the following. (i). For adiabatic process, $\Delta U = W_{adiabatic$} (ii). Work is a path function. (iii). Volume is an extensive property.
At 25$^\circ$C, the solubility product of MCl is $1 \times 10^{-10}$. What is its molar solubility in 0.1 M NaCl solution at same temperature?
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$_3$
Which of the following represents correct order of oxidizing power of halogens with water
Hydrolysis of nucleic acid gives nitrogenous base sugar and ________
Identify the major product from the following reaction sequence.
major product from the following reaction sequence.
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
Which of the following equations are correct?
(A) U =H−PV
(B) G =H−TS
(C) U =q+W
If $(1 + \tan1^\circ)(1 + \tan2^\circ)\dots(1 + \tan45^\circ) = 2^n$, then $n =$ ?
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:
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