List of top Questions asked in AP EAMCET

As shown in the figure, two blocks of masses \(m_1\) and \(m_2\) are connected to a spring of force constant \(k\). The blocks are slightly displaced in opposite directions to \(x_1, x_2\) distances and released. If the system executes simple harmonic motion, then the frequency of oscillation of the system (\(\omega\)) is:
twoblocksofmassesm1andm2
A particle of mass \( m \) at rest on a rough horizontal surface with a coefficient of friction \( \mu \) is given a velocity \( u \). The average power imparted by friction before it stops is:
The moment of inertia of a solid sphere about its diameter is 20 kg m². The moment of inertia of a thin spherical shell having the same mass and radius about its diameter is:
A person walks up a stalled escalator in 90s. When standing on the same moving escalator, he reached in 60s. The time it would take him to walk up the moving escalator will be:
The differential equation for which \( ax + by = 1 \) is the general solution is:
If \( A = \int_0^{\infty} \frac{1 + x^2}{1 + x^4} dx \) and \( B = \int_0^1 \frac{1 + x^2}{1 + x^4} dx \), then:
The solution of the differential equation \( e^x y dx + e^x dy + xdx = 0 \) is:
In each of the following options, a function and an interval are given. Choose the option containing the function and the interval for which Lagrange’s Mean Value Theorem is not applicable.
A is a point on the circle with radius 8 and center at O. A particle P is moving on the circumference of the circle starting from A. M is the foot of the perpendicular from P on OA and \( \angle POM = \theta \). When \( OM = 4 \) and \( \frac{d\theta}{dt} = 6 \) radians/sec, then the rate of change of PM is (in units/sec):
If the length of the sub-tangent at any point P on a curve is proportional to the abscissa of the point P, then the equation of that curve is (C is an arbitrary constant):
If \( y = \sinh^{-1} \left(\frac{1 - x}{1 + x} \right) \), then \( \frac{dy}{dx} \) is given by:
If \[ y = (x - 1)(x + 2)(x^2 + 5)(x^4 + 8), \] then \[ \lim\limits_{x \to -1} \left( \frac{dy}{dx} \right) = ? \]
Let \( f(x) = \begin{cases 1 + \frac{2x}{a}, & 0 \le x \le 1
ax, & 1<x \le 2 \end{cases} \). If \( \lim_{x \to 1} f(x) \) exists, then the sum of the cubes of the possible values of \( a \) is: }
Let \( [P] \) denote the greatest integer \( \leq P \). If \( 0 \leq a \leq 2 \), then the number of integral values of \( a \) such that \( \lim_{x \to a} [x^2] - [x]^2 \) does not exist is:
If \( f(x) = \begin{cases \frac{\sqrt{a^2 - ax - x^2} - \sqrt{x^2 + ax + a^2}}{\sqrt{a + x} - \sqrt{a - x}}, & x \ne 0
K, & x = 0 \end{cases} \) is continuous at \( x = 0 \), then \( K = \)}
If the angle \( \theta \) between the line \( \frac{x + 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{2} \) and the plane \( 2x - y + \sqrt{\lambda}z + 4 = 0 \) is such that \( \sin \theta = \frac{1}{3} \), then the value of \( \lambda \) is:
If \( y = x + \sqrt{2} \) is a tangent to the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \), then equations of its directrices are:
Let \( T_1 \) be the tangent drawn at a point \( P(\sqrt{2}, \sqrt{3}) \) on the ellipse \( \frac{x^2}{4} + \frac{y^2}{6} = 1 \). If \( (a, \beta) \) is the point where \( T_1 \) intersects another tangent \( T_2 \) to the ellipse perpendicularly, then \( a^2 + \beta^2 = \):
The area of the quadrilateral formed with the foci of the hyperbola \[ \frac{x^2}{16} - \frac{y^2}{9} = 1 \] and its conjugate hyperbola is (in square units):
The length of the internal bisector of angle A in \( \triangle ABC \) with vertices \( A(4,7,8) \), \( B(2,3,4) \), and \( C(2,5,7) \) is:
If \( P \) is a point which divides the line segment joining the focus of the parabola \( y^2 = 12x \) and a point on the parabola in the ratio 1:2, then the locus of \( P \) is:
If the direction cosines of two lines are given by \[ l + m + n = 0 \quad \text{and} \quad mn - 2lm - 2nl = 0, \] then the acute angle between those lines is:
If \( (1,3) \) is the midpoint of a chord of the circle \( x^2 + y^2 - 4x - 8y + 16 = 0 \), then the area of the triangle formed by that chord with the coordinate axes is:
The circumference of a circle passing through the point \( (4, 6) \) with two normals represented by \( 2x - 3y + 4 = 0 \) and \( x + y - 3 = 0 \) is:
The combined equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve \( x^2 + y^2 + xy + x + 3y + 1 = 0 \) and the line \( x + y + 2 = 0 \) is: