List of top Questions asked in AP EAMCET

If all the letters of the word MASTER are permuted in all possible ways and words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word MASTER is:

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 = $

If $ A = [a_{ij}]$ where $ 1 \leq i, j \leq n $ with $ n \geq 2 $ and $ a_{ij} = i + j $ is a matrix, then the rank of $ A $ is:

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:

Let $ |\mathbf{a}| = 2, |\mathbf{b}| = 3 $ and the angle between $ \mathbf{a} $ and $ \mathbf{b} $ be $ \frac{\pi}{3} $. If a parallelogram is constructed with adjacent sides $ 2\mathbf{a} + 3\mathbf{b} $ and $ \mathbf{a} - \mathbf{b} $, then its shorter diagonal is of length:

cos 6° sin 24° cos 72° =

If set $ A $ contains 8 elements, then the number of subsets of $ A $ which contain at least 6 elements 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:

If $ Z = x + iy $ is a complex number, then the number of distinct solutions of the equation \[ z^3 + \bar{z} = 0 \] is:

If real parts of $ \sqrt{-5 - 12i} $, $ \sqrt{5 + 12i} $ are positive values, the real part of $ \sqrt{-8 - 6i} $ is a negative value. If \[ a + ib = \frac{\sqrt{-5 - 12i} + \sqrt{5 + 12i}}{\sqrt{-8 - 6i}} \] then $ 2a + b $ is:

The range of the real valued function $ f(x) = \frac{15}{3 \sin x + 4 \cos x + 10} $ is:

The square root of the independent term in the expansion of \[ \left( \frac{2x^2}{5} + \frac{5}{\sqrt{x}} \right)^{10} \] is:

The equilibrium constant for the dissociation of HI at 773 K is:

200 g of 20\% w/w urea solution is mixed with 400 g of 40\% w/w urea solution. What is the weight percentage (w/w \%) of resultant solution?

If the sum of two roots $ \alpha, \beta $ of the equation \[ x^4 - x^3 - 8x^2 + 2x + 12 = 0 \] is zero and $ \gamma, \delta $ ($ \gamma\delta $) are its other roots, then $ 3\gamma + 2\delta $ 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 \[ \frac{d^2x}{dy^2} \left(\frac{dy}{dx}\right)^3 + \frac{d^2y}{dx^2} = ? \]

If a function $ f: \mathbb{R} \to \mathbb{R} $ is defined by $ f(x) = x^3 - x $, then $ f $ is:

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:

In a spring-block system as shown in the figure, if the spring constant $ K = 9 \, {N/m} $, then the time period of oscillation is:

Point (-1, 2) is changed to (a, b) when the origin is shifted to the point (2, -1) by translation of axes. Point (a, b) is changed to (c, d) when the axes are rotated through an angle of 45$^{\circ}$ about the new origin. (c, d) is changed to (e, f) when (c, d) is reflected through y = x. Then (e, f) = ?