List of top Questions asked in AP EAMCET

The diffraction pattern of a crystalline solid gave a peak at $ 2\theta = 60^\circ $. What is the distance (in cm) between the layers that gave this peak? \[ \text{(Given: Wavelength } \lambda = 1.544\text{ Å, } \sin 30^\circ = 0.5, \sin 60^\circ = 0.866, n=1) \]

A hydrocarbon containing C and H has 92.3% C. When 39 g of hydrocarbon was completely burnt in O_2, x moles of water and y moles of CO₂were formed. x moles of water is sufficient to liberate 0.75 moles of H₂ with Na metal. What is the weight (in g) of oxygen consumed?

RMS velocity of one mole of an ideal gas was measured at different temperatures. A graph of $ (u_{\text{rms}})^2 $ (on y-axis) and $ T/K $ (on x-axis) gave a straight line passing through the origin, and its slope is $ 249 \, \text{m}^2 \text{s}^{-2}\text{K}^{-1} $. What is the molar mass (in kg mol$^{-1}$) of the ideal gas? $( R = 8.3 \, \text{J mol}^{-1} \text{K}^{-1} )$

If the points with position vectors \[ (\mathbf{a}i + 10j + 13k), \quad (6i + 11j + 11k), \quad \left(\frac{9}{2}i + \beta j - 8k\right) \] are collinear, then evaluate $ (19a - 6\beta)^2 $.

Evaluate the sum: \[ \sin^2 18^\circ + \sin^2 24^\circ + \sin^2 36^\circ + \sin^2 42^\circ + \sin^2 78^\circ + \sin^2 90^\circ + \sin^2 96^\circ + \sin^2 102^\circ + \sin^2 138^\circ + \sin^2 162^\circ. \]

If $ H $ is the orthocenter of $ \triangle ABC $ and $ AH = x $, $ BH = y $, $ CH = z $, then evaluate: \[ \frac{abc}{xyz} \]

Evaluate the expression: \[ \tan 6^\circ \tan 42^\circ \tan 66^\circ \tan 78^\circ \]

The absolute value of the difference of the coefficients of $x^4$ and $x^6$ in the expansion of
$\frac{2x^2}{(x^2+1)(x^2+2)}$
is:

When a convex lens is immersed in a liquid of refractive index equal to 80% of the refractive index of the material of the lens, the focal length of the lens increases by 100%. The refractive index of the liquid is:

While solving a system of linear equations $ AX = B $ using Cramer’s rule, if \includegraphics[]{6.png}

If the number of real roots of $ x^9 - x^5 + x^4 - 1 = 0 $ is $ n $, the number of complex roots having argument on imaginary axis is $ m $, and the number of complex roots having argument in the second quadrant is $ k $, then $ m.n.k $ is:

If $ (\alpha, \beta, \gamma) $ are the direction cosines of an angular bisector of two lines whose direction ratios are (2,2,1) and (2,-1,-2), then $ (\alpha + \beta + \gamma)^2 $ is:

Which of the following, on thermal decomposition, form both acidic and basic oxides along with O$_2$?
(i) NaNO3
(ii) Ca(NO3)2
(iii) Be(NO3)2
(iv) LiNO3

Impure silver ore + CN⁻ + H₂O → [X]⁻ + OH⁻
[X]⁻ + Zn → [Y]²⁺ + Ag (pure)
The co-ordination numbers of the metals in [X], [Y] are respectively:

Carrot and curd are sources for the vitamins respectively.

Number of deactivating groups among: $ -Cl, -SO_3H, -OH, -NHC_2H_5, -COOCH_3, -CH_3 $

If the pair of tangents drawn to the circle $ x^2 + y^2 = a^2 $ from the point $ (10, 4) $ are perpendicular, then $ a $ is:

The perimeter of the locus of the point $ P $ which divides the line segment $ QA $ internally in the ratio 1:2, where $ A = (4, 4) $ and $ Q $ lies on the circle $ x^2 + y^2 = 9 $, is:

The general solution of $ 4 \cos 2x - 4 \sqrt{3} \sin 2x + \cos 3x - \sqrt{3} \sin 3x + \cos x - \sqrt{3} \sin x = 0 $ is:

In $ \triangle ABC $, prove the identity: $$ a^2 \sin 2B + b^2 \sin 2A = $$

The $ n^{th} $ term of the series \[ 1 + (3+5+7) + (9+11+13+15+17) + \dots \] is:

If the ratio of the terms equidistant from the middle term in the expansion of $ (1 + x)^{12} $ is $ \frac{1}{256} $, then the sum of all the terms of the expansion $ (1 + x)^{12} $ is:

The voltage $ V_o $ in the network shown is

If $ \vec{a} = \hat{i} - \hat{j} + \hat{k} $, $ \vec{b} = \hat{i} + \hat{j} - 2\hat{k} $, $ \vec{c} = 2\hat{i} - 3\hat{j} - 3\hat{k} $, and $ \vec{d} = 2\hat{i} + \hat{j} + \hat{k} $ are four vectors, then $ (\vec{a} \times \vec{c}) \times (\vec{b} \times \vec{d}) = $:

A series LCR circuit is shown in the figure. Where the inductance of 10 H, capacitance 40 \muF and resistance 60 Ω are connected to a variable frequency 240 V source. The current at resonating frequency is.