List of top Questions asked in AP EAPCET

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}

Evaluate the integral: \[ \int \operatorname{Cos}^{-1} \left( \frac{1-x^2}{1+x^2} \right) dx \]

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:

A line segment \( PQ \) has the length 63 and direction ratios \( (3, -2, 6) \). If this line makes an obtuse angle with the X-axis, then the components of the vector \( \vec{PQ} \) are:

If \(x\) is so large that terms containing \(x^{-3}\), \(x^{-4}\), \(x^{-5}\), \ldots can be neglected, then the approximate value of \[ \left(\frac{3x - 5}{4x^2 + 3}\right)^{-4/5} \] is:

Let \( g(x) = 1 + x - \lfloor x \rfloor \) and \[ f(x) = \begin{cases} -1, & x<0\\ 0, & x = 0 \\ 1, & x>0 \end{cases} \] where \( \lfloor x \rfloor \) denotes the greatest integer less than or equal to \( x \). Then for all \( x \), \( f(g(x)) = \)

If $ x - y - 3 = 0 $ is a normal drawn through the point $ (5, 2) $ to the parabola $ y^2 = 4x $, then the slope of the other normal that can be drawn through the same point to the parabola is?

If \(2\sin x - \cos 2x = 1\), then \( (3 - 2\sin^2x) = \)

Let $ A(4, 3), B(2, 5) $ be two points. If $ P $ is a variable point on the same side of the origin as that of line $ AB $ and at most 5 units from the midpoint of $ AB $, then the locus of $ P $ is:

The number of positive integers less than 10000 which contain the digit 5 at least once is

If the normal chord drawn at the point \(\left(\frac{15}{2\sqrt{2}}, \frac{15}{2\sqrt{2}}\right)\) to the parabola \(y^2 = 15x\) subtends an angle \(\theta\) at the vertex of the parabola, then \(\sin \frac{\theta}{3} + \cos \frac{2\theta}{3} - \sec \frac{4\theta}{3} =\) ?

The set of all real values of \( c \) so that the angle between the vectors
\( \vec{a} = c\hat{i} - 6\hat{j} + 3\hat{k} \) and \( \vec{b} = x\hat{i} + 2\hat{j} + 2c\hat{k} \) is an obtuse angle for all real \( x \), is:

If \( y = \log(\sec(\tan^{-1}x)) \) for \( x>0 \), then \( \frac{dy}{dx} \) at \( x = 1 \) is:

If the function $y = g(x)$ represents the slopes of the tangents drawn to the curve $y = 3x^3 - 5x^2 - 12x^2 + 18x - 3$ strictly increasing then the domain of $g(x)$ is
Identify the correct option from the following: