List of top Questions asked in AP EAPCET- 2025

If \( \left(\frac{\sin 3\theta}{\sin \theta}\right)^2 - \left(\frac{\cos 3\theta}{\cos \theta}\right)^2 = a \cos b\theta \), then \( a : b = \)

If the equation \(2\cot^{-1}(x^2 + 2x + k) = -3\tan^{-1(x^2 + 2x + k)\) has two distinct real solutions, then all the values of \(k\) lie in the interval}

If \( \alpha, \beta \) are the acute angles such that \( \frac{\sin \alpha}{\sin \beta} = \frac{6}{5} \) and \( \frac{\cos \alpha}{\cos \beta} = \frac{9}{5\sqrt{5}} \) then \( \sin \alpha = \)

If A and B are positive acute angles satisfying $3\cos^2 A + 2\cos^2 B = 4$ and $\frac{3\sin A{\sin B} = \frac{2\cos B}{\cos A}$, then A+2B=}

If \( \frac{1}{2} \sin^{-1} \left( \frac{3\sin 2\theta}{5+4\cos 2\theta} \right) = \tan^{-1 x \) then \( x = \)}

In a \( \triangle ABC \), \( A - B = 120^\circ \), \( R = 8r \), then \[ \frac{1 + \cos C}{1 - \cos C} =\ ? \]

If $ A + B + C + D = 2\pi $, then $$ \sin A + \sin B + \sin C + \sin D = ? $$

If $ \tan\left( \frac{\pi}{4} + \alpha \right) = \tan^3\left( \frac{\pi}{4} + \beta \right) $, then compute: $$ \tan(\alpha + \beta) \cot(\alpha - \beta) = ? $$

If $\sin x - \sin y = \frac{27{65}$ and $\cos x - \cos y = -\frac{21}{65}$, then $\sin(x+y)= $}

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 $\alpha-\beta=$}

In \(\triangle ABC\), the sum of the lengths of two sides is \(x\) and the product of those lengths is \(y\). If \(c\) is the length of its third side and \(x^2 - c^2 = y\), then the circumradius of that triangle is:

Evaluate \[ \int (\log 2x)^3 \, dx = ? \]

Evaluate \[ \int \frac{x + 1}{(x - 2) \sqrt{1 - x}} \, dx = ? \]

The area of the region (in sq. units) enclosed between the curves \( y = |x| \), \( y = [x] \) and the ordinates \( x = -1, x = 0, x = 1 \) is