List of top Questions asked in AP EAMCET

If the circle S = 0 cuts the circles x² + y² - 2x + 6y = 0, x² + y² - 4x - 2y + 6 = 0, and x² + y² - 12x + 2y + 3 = 0 orthogonally, then the equation of the tangent at (0, 3) on S = 0 is:

At 240.55 K, for one mole of an ideal gas, a graph of $ P $ (on y-axis) and $ V^{-1} $ (on x-axis) gave a straight line passing through the origin. Its slope (m) is 2000 J mol$^{-1}$. What is the kinetic energy (in J mol$^{-1}$) of the ideal gas?

The locus of a variable point which forms a triangle of fixed area with two fixed points is:

What are X and Y respectively in the following reaction sequence?

If the area of the triangle formed by the straight lines $-15x^2 + 4xy + 4y^2 = 0$ and $x = a$ is $200 \, {sq. units}$, then $|a| =$

An object is placed at a distance of 18 cm in front of a mirror. If the image is formed at a distance of 4 cm on the other side, then the focal length, nature of the mirror and nature of the image are respectively:

0.1 mole of H$_3$PO$_3$ is present in 500 mL of solution. The normality of it is:

In the extraction of iron, the reaction which occurs at 900-1500 K in blast furnace is

If $ \alpha, \beta $ ($\alpha<\beta$) are the values of $ x $ such that the determinant of the matrix \[ \begin{bmatrix} x - 2 & 0 & 1 \\ 1 & x + 3 & 2 \\ 2 & 0 & 2x - 1 \end{bmatrix} \] is zero (i.e., the matrix is singular), then the value of $ 2\alpha + 3\beta + 4\gamma $ is:

If $ A = \begin{bmatrix} 2 & 3 \\ 1 & k \end{bmatrix} $ is a singular matrix, then the quadratic equation having the roots $ k $ and $ \frac{1}{k} $ is:

If the mean deviation about the mean is $m$ and the variance is $\sigma^2$ for the following data, then $m + \sigma^2 =$ % Data table \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 7 & 9 \\ \hline f & 4 & 24 & 28 & 16 & 8 \\ \hline \end{array} \]

P is a variable point such that the distance of P from A(4,0) is twice the distance of P from B(-4,0). If the line $ 3y - 3x - 20 = 0 $ intersects the locus of P at the points C and D, then the distance between C and D is:

In $ \triangle ABC $, if $ AB:BC:CA = 6:4.5 $, then $ R : r = $

A solid is dissolved in 1 L water. The enthalpy of its solution ($\Delta H_{{sol}}^\circ$) is 'x' kJ/mol. The hydration enthalpy ($\Delta H_{{hyd}}^\circ$) for the same reaction is 'y' kJ/mol. What is lattice enthalpy ($\Delta H_{{lattice}}^\circ$) of the solid in kJ/mol?

60 cm$^3$ of SO$_2$ gas diffused through a porous membrane in $ x $ minutes. Under similar conditions, 360 cm$^3$ of another gas (molar mass 4 g mol$^{-1}$) diffused in $ y $ minutes. The ratio of $ x $ and $ y $ is:

The equation of the circle whose diameter is the common chord of the circles $x^2 + y^2 - 6x - 7 = 0$ and $x^2 + y^2 - 10x + 16 = 0$ is:

The real valued function $ f: \mathbb{R} \to \left[ \frac{5}{2}, \infty \right) $ defined by $ f(x) = \left| 2x + 1 \right| + \left| x - 2 \right| $ is:

Evaluate the integral: $ I = \int e^{2x+3} \sin 6x \, dx $.

Let $[r]$ denote the largest integer not exceeding $r$, and the roots of the equation $ 3z^2 + 6z + 5 + \alpha(x^2 + 2x + 2) = 0 $ are complex numbers whenever $ \alpha > L $ and $ \alpha < M $. If $ (L - M) $ is minimum, then the greatest value of $[r]$ such that $ Ly^2 + My + r < 0 $ for all $ y \in \mathbb{R} $ is:

If a variable straight line passing through the point of intersection of the lines x - 2y + 3 = 0 and 2x - y - 1 = 0 intersects the X and Y axes at A and B respectively, then the equation of the locus of a point which divides the segment AB in the ratio -2 : 3 is:

In $ \triangle ABC $, if $ (r_2 - r_1)(r_3 - r_1) = 2r_2r_3 $, then $ 2(r + R) = $:

Given below are two statements
Statement - I: For isothermal irreversible change of an ideal gas, \[ q = -w = P_{\text{ext}}(V_{\text{final}} - V_{\text{initial}}) \] Statement - II: For adiabatic change, \[ \Delta U = W_{\text{adiabatic}} \] The correct answer is:

If the ratio of the absolute temperature of the sink and source of a Carnot engine is changed from 2:3 to 3:4, the efficiency of the engine changes by:

If m and M denote the mean deviations about mean and about median respectively of the data 20, 5, 15, 2, 7, 3, 11, then the mean deviation about the mean of m and M 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: