List of top Mathematics Questions asked in AP EAPCET

If \( f(x) = x e^{x(1-x)}, \, x \in \mathbb{R} \), then \( f(x) \) is:
After the roots of the equation $6x^3 + 7x^2 - 4x - 2 = 0$ are diminished by $h$, if the transformed equation does not contain $x$ term, then the product of all possible values of $h$ is
The number of solutions of the equation $\sqrt{3x^2 + x + 5} = x - 3$ is
The general solution of the differential equation \( \frac{dy}{dx} = \frac{x+y}{x-y} \) is
Three dice are thrown simultaneously and the sum of the numbers is noted. If A = getting sum greater than 14 and B = getting sum divisible by 3, then \(P(A \cap B) + P(A \cup B) =\)
$f(x)$ is an $n^{th}$ degree polynomial satisfying $f(x) = \frac{1}{2}\left[f(x)f\left(\frac{1}{x}\right) + f\left(\frac{f(x)}{x}\right)\right]$. If $f(2) = 33$, then the value of $f(3)$ is
If \( \frac{1}{2} \leq \frac{x^2+x+a}{x^2-x+a} \leq 2 \ \forall x \in \mathbb{R} \), then \( a = \)
If the normal drawn at the point $$ P \left(\frac{\pi}{4}\right) $$ on the ellipse $$ x^2 + 4y^2 - 4 = 0 $$ meets the ellipse again at $ Q(\alpha, \beta) $, then find $ \alpha $.
Let \(z_1 = 3 + 4i\) and \(z_2 = 1 - 2i\). Then the argument of \(\frac{z_1}{z_2}\) is:
An item is tested on a device for its defectiveness. The probability that such an item is defective is 0.3. The device gives an accurate result in 8 out of 10 such tests. If the device reports that an item tested is not defective, then the probability that it is actually defective is
The quadratic equation whose roots are \[ l = \lim_{\theta \to 0} \left( \frac{3\sin\theta - 4\sin^3\theta}{\theta} \right) \] \[ m = \lim_{\theta \to 0} \left( \frac{2\tan\theta}{\theta(1-\tan^2\theta)} \right) \] is:
If \( y = \operatorname{Sin}^{-1} \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} \) and \( -\frac{3\pi}{2}<x<-\frac{\pi}{2} \), then \( \frac{dy}{dx} \) is:
If $P_n$ denotes the product of the binomial coefficients in the expansion of $(1 + x)^n$, then find \[ \frac{P_{n+1}}{P_n}. \]
If \( A \) and \( B \) are both \( 3 \times 3 \) matrices, then which of the following statements are true? \[ \begin{cases}
If A and B are the values such that $(A + B)$ and $(A - B)$ are not odd multiples of $\frac{\pi}{2}$ and $2\tan(A+B) = 3 \tan(A-B)$, then $\sin A \cos A =$
If \( \frac{1}{2} \sin^{-1} \left( \frac{3\sin 2\theta}{5+4\cos 2\theta} \right) = \tan^{-1 x \) then \( x = \)}
If $\alpha$ is the maximum value and $\beta$ is the minimum value of $\cos^2 \frac{x{4} + \sin \frac{x}{4}$, $x \in \mathbb{R}$, then $\alpha-\beta=$}
The sum of all integers between 1 and 100 (both inclusive) which are divisible by 5 or 13 is
Lines \(L_1\) and \(L_2\) have slopes 2 and \(-\frac{1}{2}\) respectively. If both \(L_1\) and \(L_2\) are concurrent with the lines \(x - y + 2 = 0\) and \(2x + y + 3 = 0\), then the sum of the absolute values of the intercepts made by the lines \(L_1\) and \(L_2\) on the coordinate axes is?
If the power of the point \( (1,6) \) with respect to the circle \( x^2+y^2+4x-6y-a=0 \) is \( -16 \), then \( a \) is:
Let 'a' be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation \( x^3 - ax^2 + ax - 1 = 0 \) is identical with this cubic equation, then 'a' =
Evaluate the integral: \[ I = \int_0^{3\pi/2} \frac{\cos^5 x}{\cos^3 x+\sin^3 x}dx \]
Two roots of the equation $ax^4 + bx^3 + cx^2 + dx + e = 0$ are positive and equal. If the product of the other two real roots is 1, then
If \( (2k - 1)x^2 - 2(3k - 2)x + 4k>0 \) for every \( x \in \mathbb{R} \), then the sum of all possible integral values of \( k \) is:
On a line with direction cosines l, m, n, \( A(x_1, y_1, z_1) \) is a fixed point. If \( B=(x_1+4kl, y_1+4km, z_1+4kn) \) and \( C=(x_1+kl, y_1+km, z_1+kn) \) (\(k>0\)) then the ratio in which the point B divides the line segment joining A and C is