List of top Mathematics Questions asked in AP EAPCET

Let \( f(x) \) be differentiable on \( \mathbb{R} \) and \( f'(m) \ne 0, m \in \mathbb{R} \). If \( \lim\limits_{x \to m} \frac{x f(m) - m f(x)}{x - m} + f'(m) = f(m) \), then \( m = \):
If \( \vec{a} = 2\hat{i} - 5\hat{j} + 8\hat{k} \), \( \vec{b} = 7\hat{i} - 5\hat{j} + 3\hat{k} \), and \[ (\vec{2a} - \vec{3b}) \times (\vec{4a} + \vec{b}) = x\hat{i} + y\hat{j} + z\hat{k}, \] then \( x + y + z = \)
A bag contains 12 two rupee coins, 7 one rupee coins and 4 fifty paise coins. If three coins are selected at random, then the probability that the sum of the values of the three coins is not an integral multiple of a rupee is
Let $ S $ be a circle concentric with the circle $ 3x^2 + 3y^2 + x + y - 1 = 0 $. If the length of the tangent drawn from a point $ (2, -2) $ to the given circle is the radius of the circle $ S $, then the power of the point $ (2, 1) $ with respect to the circle $ S $ is
Let $f:\mathbb{R} \to \mathbb{R}$ be a differentiable function such that $|f(x)-f(y)| \le 2|x-y|^{3/2} \ \forall x,y \in \mathbb{R}$. If $f(0)=1$, then $\int_0^1 f^2(x)dx=$
If \( \tan A = \tan \alpha \coth x = \cot \beta \tanh x \), then \( \tan(\alpha + \beta) = \):
The locus of a point which is at a distance of 2 units from the line \( 2x - 3y + 4 = 0 \) and at a distance of \( \sqrt{13} \) units from a point \( (5,0) \), is:
The equation of the pair of asymptotes of the hyperbola $x^2 - 2y^2 - 8x + 8y + 4 = 0$ is
If the equations \( x = t^2 + t + 1, \quad y = t^2 - t + 1 \) represent a curve \( C \) with parameter \( t \), then the Cartesian equation of \( C \) is:
The positive value of \( x \) satisfying the equation \[ \int_0^x (1 - t) \, dt = \frac{1}{2} \] is:
If \( A, B \) and \( C \) are three events of a random experiment with \( P(A) = 0.4 \), \( P(B) = 0.3 \), and \( P(A \cap B) = 0.2 \), then the probability that neither A nor B occurs is:
If matrix \( D_1 = \text{diag}(a, b, c) \), matrix \( D_2 = \text{diag}(3, 3, 3) \) and \( A \) is a skew-symmetric matrix of order 3, then
\[ \text{Tr}(D_1 D_2 A + D_2 D_1 + D_1 A + D_2 A) - \text{Tr}(D_1 + D_2) = ? \]
Let \( A(1,2) \) be the centre and 3 be the radius of a circle \( S \). Let \( B(-1, -1) \) be the centre and \( r \) be the radius of another circle \( S_1 \). If \( \frac{\pi}{3} \) is the angle between the circles \( S \) and \( S_1 \), then the number of possible values of \( r \) is:
If the sum of the coefficients of even powers of \( x \) in the expansion of \( (1 - x + x^2)^{2n} \) is 3281, then \( n \) is:
If \( \alpha, \beta, \gamma \) are the roots of \( x^3 + 2x + 5 = 0 \), then \( \sum \frac{\beta + \gamma}{\alpha^2} \) is:
In \( \triangle ABC \), if \[ \cot \frac{A}{2} : \cot \frac{B}{2} : \cot \frac{C}{2} = 3 : 7 : 9 \] then \( a : b : c = \) ?
Evaluate the integral: \[ \int_0^{\frac{\pi}{4}} \frac{\cos^2 x}{\cos^2 x + 4 \sin^2 x} \, dx \]
Evaluate the integral: \[ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1 + \sqrt{\cot x}} \, dx = \]
If the roots of the equation \( 3x^2 + 4kx + 3 = 0 \) are non-real, then \( k \) lies in the interval:
The line \( x + y = k \) meets the curve \( x^2 + y^2 - 2x - 4y + 2 = 0 \) at two points \( A \) and \( B \). If \( O \) is the origin and \( \angle AOB = 90^\circ \), then the value of \( k \) (\( k>1 \)) is
Evaluate \( \cot 16^\circ \cot 44^\circ + \cot 44^\circ \cot 76^\circ - \cot 76^\circ \cot 16^\circ \):
If \[ \frac{d}{dx}\left( \frac{x^2}{(x+2)(2x+3)} \right) = \frac{-A}{(x+2)^2} + \frac{B}{(2x+3)^2}, \] then the value of \( A + B = \):
Tangent \( L_1 = 3x - 4y - 8 = 0 \) and the chord \( L_2 = x + y - 1 = 0 \) are at a distance of 2 and \( \sqrt{2} \) units respectively from the centre of a circle \( S \). \((h, k)\) is the centre of \( S \) such that \( h^2 + k^2 = 13 \). If the midpoint of the chord \( L_2 = 0 \) is \( (\alpha, \beta) \) and the radius of the circle is \( r \), then \( \alpha + \beta + r = \):
If \( f'(x) = a \cos x + b \sin x \), \( f'(0) = 4 \), \( f(0) = 3 \), and \( f\left( \frac{\pi}{2} \right) = 5 \), then \( f(x) = \)
If A(2,3) and B(2,-3) are two points, then the equation of the locus of a point $P$ such that $PA + PB = 8$ is