List of top Mathematics Questions asked in AP EAPCET

Given: $$ 3f(\cos x) + 2f(\sin x) = 5x $$ Find: $$ f'(\cos x) + f'(\sin x) $$
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 \( f(x+2) + f(x-2) = \)
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?
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 \( (a, b) = \):
If $(1 + \tan1^\circ)(1 + \tan2^\circ)\dots(1 + \tan45^\circ) = 2^n$, then $n =$ ?
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
For $\alpha \in \left[0, \dfrac{\pi}{2} \right]$, the angle between the lines represented by
$[x \cos\theta - y] \left[ (\cos\theta + \tan\alpha)x - (1 - \cos\theta \tan\alpha)y \right] = 0$ is
The straight line passing through \( (0, 0) \) and the foot of the perpendicular from \( (2, 4) \) onto the line \( x + y - 1 = 0 \) is:
If the point \( P(\sin\alpha, \cos\alpha) \) lies inside the triangle formed by the vertices \( (0, 0), \left(\frac{\sqrt{3}}{2}, 0\right), (0, \frac{\sqrt{3}}{2}) \), then \( \alpha \) lies in the interval:
The ratio of the largest and shortest distances from the point $(2, -7)$ to the circle $x^2 + y^2 - 14x - 10y - 151 = 0$ is
Find the least distance from the point $ (10, 7) $ to the circle: $$ x^2 + y^2 - 4x - 2y - 20 = 0 $$
\( \int_{a-1}^{a} \frac{e^x(a-x)}{(x-a+1)^2} dx = \)
If \(A = \begin{bmatrix}x & 2 & 1 \\ 2 & x & 1 \\ 2 & 1 & 0\end{bmatrix}\) and \(\det(A) = 125\), then \(x =\)
In a triangle ABC, let \(\angle C = \pi/2\). If r and R are respectively inradius and circumradius of ABC, then R + r =
In a triangle \( ABC \), if \( a : b : c = 4 : 5 : 6 \), the ratio of radius of the circumcircle to that of the incircle is:
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 $
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 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?