List of top Questions asked in AP EAMCET

If a running track of 500 ft. is to be laid out enclosing a playground, the shape of which is a rectangle with a semicircle at each end, then the length of the rectangular portion such that the area of the rectangular portion is maximum is (in feet).
If \( f(0) = 0 \), \( f'(0) = 3 \), then the derivative of \( y = f(f(f(f(f(x))))) \) at \( x = 0 \) is:
If \( y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \cdots \infty}}} \), then the value of \( \frac{d^2y}{dx^2} \) at \( (\pi,1) \) is:
The function \( f(x) = |x - 24| \) is:
If \( f(x) = \left(\frac{1+x}{1-x}\right)^{\frac{1}{x}} \) is continuous at \( x = 0 \), then \( f(0) \) is:
Let \( f(x) \) be defined as: \[ f(x) = \begin{cases} 0, & x = 0 \\ 2 - x, & 0 < x < 1 \\ 2, & x = 1 \\ 1 - x, & 1 < x < 2 \\ -\frac{3}{2}, & x \geq 2 \end{cases} \] Then which of the following is true?
If \( e_1 \) and \( e_2 \) are respectively the eccentricities of the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and its conjugate hyperbola, then the line \( \frac{x}{2e_1} + \frac{y}{2e_2} = 1 \) touches the circle having center at the origin, then its radius is:
If the eccentricity of the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) is \( \sec \alpha \), then the area of the triangle formed by the asymptotes of the hyperbola with any of its tangent is:
If the ellipse \(4x^2 + 9y^2 = 36\) is confocal with a hyperbola whose length of the transverse axis is 2, then the points of intersection of the ellipse and hyperbola lie on the circle:
If the normal chord drawn at \( (2a,2a\sqrt{2}) \) on the parabola \( y^2 = 4ax \) subtends an angle \( \theta \) at its vertex, then \( \theta \) is:
If \( x - 4 = 0 \) is the radical axis of two orthogonal circles out of which one is \( x^2 + y^2 = 36 \), then the centre of the other circle is:
\( C_1 \) is the circle with centre at \( (0,0) \) and radius 4, \( C_2 \) is a variable circle with centre at \( (\alpha, \beta) \) and radius 5. If the common chord of \( C_1 \) and \( C_2 \) has slope \( \frac{3}{4} \) and of maximum length, then one of the possible values of \( \alpha + \beta \) is:
If \( x_1, x_2, x_3, \dots, x_n \) are \( n \) observations such that \( \sum (x_i + 2)^2 = 28n \) and \( \sum (x_i - 2)^2 = 12n \), then the variance is:
If \( \theta \) is the angle between \( \vec{f} = i + 2j - 3k \) and \( \vec{g} = 2i - 3j + ak \) and \( \sin \theta = \frac{\sqrt{24}}{28} \), then \( 7a^2 + 24a = \) ?
If \( \vec{f} = i + j + k \) and \( \vec{g} = 2i - j + 3k \), then the projection vector of \( \vec{f} \) on \( \vec{g} \) is:
In \( \triangle PQR \), \((4\overline{i} + 3\overline{j} + 6\overline{k} )\) and \((3\overline{i} + \overline{j} + 3\overline{k} )\) are the position vectors of the vertices P, Q, R respectively. Then the position vector of the point of intersection of the angle bisector of \( P \) with \( QR \).
Let \( \mathbf{a} = 3\hat{i} + 4\hat{j} - 5\hat{k} \), \( \mathbf{b} = 2\hat{i} + \hat{j} - 2\hat{k} \). The projection of the sum of the vectors \( \mathbf{a}, \mathbf{b} \) on the vector perpendicular to the plane of \( \mathbf{a}, \mathbf{b} \) is:
In \( \triangle ABC \), if \( A, B, C \) are in arithmetic progression, \( \Delta = \frac{\sqrt{3}}{2} \) and \( r_1 r_2 = r_3 r \), then \( R \) is:
In \( \triangle ABC \), if \( (a+c)^2 = b^2 + 3ca \), then \( \frac{a+c}{2R} \) is:
The general solution of the equation \( \tan x + \tan 2x - \tan 3x = 0 \) is:
In a triangle \( ABC \), if \( A, B, C \) are in arithmetic progression and \[ \cos A + \cos B + \cos C = \frac{1 + \sqrt{2} +\sqrt{3}}{2\sqrt{2}}, \] then \( \tan A \) is:
Evaluate the given trigonometric expression: \[ 4 \cos \frac{\pi}{7} \cos \frac{\pi}{5} \cos \frac{2\pi}{7} \cos \frac{2\pi}{5} \cos \frac{4\pi}{7} = \]
If \( M_1 \) and \( M_2 \) are the maximum values of \( \frac{1}{11 \cos 2x + 60 \sin 2x + 69} \) and \( 3 \cos^2 5x + 4\sin^2 5x \) respectively, then \( \frac{M_1}{M_2} = \):
If \( |x| < 1 \), the coefficient of \( x^2 \) in the power series expansion of \( \frac{x^4}{(x+1)(x-2)} \) is:
If \( |x| < 1 \), then the number of terms in the expansion of \( \left[ \frac{1}{2} (1.2 + 2.3x + 3.4x^2 + \dots) \right]^{-25} \) is: