List of top Questions asked in AP EAMCET

If the circles $ x^2 + y^2 + 2ax + 2y - 8 = 0 $ and $ x^2 + y^2 - 2x + ay - 14 = 0 $ intersect orthogonally, then the distance between their centers is:

If $ A = \left[\begin{array}{ccc} 83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79 \end{array} \right] $, then $\text{det} (A - A^T) = $:

If the inverse point of the point $ (-1, 1) $ with respect to the circle $ x^2 + y^2 - 2x + 2y - 1 = 0 $ is $ (p, q) $, then $ p^2 + q^2 = $

The density of $\beta$-Fe is 7.6 g/cm$^3$. It crystallizes in a cubic lattice with $ a = 290 $ pm.
What is the value of $ Z $? ($ Fe = 56 $ g/mol, $ N_A = 6.022 \times 10^{23} $ mol$^{-1}$)

The maximum value of \[ 12 \sin x - 5 \cos x + 3 \] is:

If $x^2 + 5ax + 6 = 0$ and $x^2 + 3ax + 2 = 0$ have a common root, then that common root is:

Find the equation of a line passing through the intersection of $ 3x + y - 4 = 0 $ and $ x - y = 0 $, and making a $ 45^\circ $ angle with $ x - 3y + 5 = 0 $.

A spring of spring constant $ 200 \, {N/m} $ is initially stretched by $ 10 $ cm from the unstretched position. The work to be done to stretch the spring further by another $ 10 $ cm is:

In $ \triangle ABC $, if $ a = 13 $, $ b = 14 $, and $ \cos \frac{C}{2} = \frac{3}{\sqrt{13}} $, then $ 2r_1 = $:

If $ l, m, n $ are the direction cosines of a line that is perpendicular to the lines having the direction ratios $ (1,2,-1) $ and $ (-2,1,1) $, then $ (l+m+n)^2 $ =

If $ y = f(x) $ is a thrice differentiable function and a bijection, then \[ \frac{d^2x}{dy^2} \left(\frac{dy}{dx}\right)^3 + \frac{d^2y}{dx^2} = ? \]

A car travelling at 80 kmph can be stopped at a distance of 60 m by applying brakes. If the same car travels at 160 kmph and the same braking force is applied, the stopping distance is:

If $ Q(h, k) $ is the inverse point of $ P(1,2) $ with respect to the circle $ x^2 + y^2 - 4x + 1 = 0 $, then $ 2h + k $ is:

Evaluate: \[ \cosh^{-1} 2 \]

If the system of equations: $$ a_1 x + b_1 y + c_1 z = 0, \quad a_2 x + b_2 y + c_2 z = 0, \quad a_3 x + b_3 y + c_3 z = 0 $$ has only the trivial solution, then the rank of the matrix: \[\left[ \begin{array}{ccc} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{array} \right] \] is

Evaluate $ \cosh (\log 4) $:

Given the partial fraction decomposition: \[ \frac{4x^2 + 5}{(x - 2)^4} = \frac{A}{(x - 2)} + \frac{B}{(x - 2)^2} + \frac{C}{(x - 2)^3} + \frac{D}{(x - 2)^4} \] then the value of \[ \sqrt{\frac{A}{C} + \frac{B}{C} + \frac{D}{C}} \] is:

The range of the real-valued function $ f(x) = \sin^{-1} \left( \frac{1 + x^2}{2x} \right) + \cos^{-1} \left( \frac{2x}{1 + x^2} \right) $ is:

In a triangle ABC, if $ r : R = 1 : 3 : 7 $, then $ \sin(A + C) + \sin B = $

2.644 g of metal (M) was deposited when 8040 coulombs of electricity was passed through molten MF$_2$ salt. What is the atomic mass of M? (F = 96500 C mol$^{-1}$)

The set of all values of $k$ for which the inequality $x^2 - (3k+1)x + 4k^2 + 3k - 3>0$ is true for all real values of $x$ is

If $\sec \theta + \tan \theta = \frac{1}{3}$, then the quadrant in which $2\theta$ lies is:

Among the 4-digit numbers formed using the digits $ 0, 1, 2, 3, 4 $ when repetition of digits is allowed, the number of numbers which are divisible by 4 is:

At 300 K, $ \Delta_r G^\circ $ for the reaction $ A(g) \rightleftharpoons B(g) $ is $ -11.5 $ kJ mol$^{-1}$. The equilibrium constant at 300 K is approximately: $(R = 8.314 \text{ J mol}^{-1} \text{ K}^{-1})$

A slab consists of two identical plates of copper and brass. The free face of the brass is at $ 0^\circ C $ and that of copper at $ 100^\circ C $. If the thermal conductivities of brass and copper are in the ratio $ 1:4 $, then the temperature of the interface is: