List of top Questions asked in AP EAMCET

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}

In a Carnot engine, the absolute temperature of the source is 25% more than the absolute temperature of the sink. The efficiency of the engine is

If $ M_1 $ and $ M_2 $ are the maximum values of $ \frac{1}{11 \cos 2x + 60 \sin 2x + 69} $ and $ 3 \cos^2 5x + 4\sin^2 5x $ respectively, then $ \frac{M_1}{M_2} = $:

5 boys and 6 girls are arranged in all possible ways. Let $X$ denote the number of linear arrangements in which no two boys sit together, and $Y$ denote the number of linear arrangements in which no two girls sit together. If $Z$ denotes the number of ways of arranging all of them around a circular table such that no two boys sit together, then $X:Y:Z$ = ?

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 $ and $ \beta $ are two distinct negative roots of the equation $ x^5 - 5x^3 + 5x^2 - 1 = 0 $, then the equation of least degree with integer coefficients having $ \sqrt{-\alpha} $ and $ \sqrt{-\beta} $ as its roots is:

If $ \alpha, \beta $ are the roots of the equation $ x^2 - 6x - 2 = 0 $, $ \alpha > \beta $, and $ a_n = \alpha^n - \beta^n, n \geq 1 $, then the value of $ \frac{a_{10} - 2 a_8}{2 a_9} $ is:

Three blocks of masses 2 m, 4 m and 6 m are placed as shown in figure. If $ \sin 37^\circ = \frac{3}{5} $, $ \sin 53^\circ = \frac{4}{5} $, the acceleration of the system is:

One second after projection, a projectile is travelling in a direction inclined at $ 45^\circ $ to horizontal. After two more seconds it is travelling horizontally. Then the magnitude of velocity of the projectile is ( $ g = 10 $ ms$^{-2}$):

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:

If $ f(x + h) = 0 $ represents the transformed equation of $$ f(x) = x^4 + 2x^3 - 19x^2 - 8x + 60 = 0 $$ and this transformation removes the term containing $ x^3 $, then $ h $ is:

The mass % of urea solution is 6. The total weight of the solution is 1000 g. What is its concentration in mol L$^{-1}$? (Density of water = 1.0 g mL$^{-1}$)
(Given: C = 12u, N = 14u, O = 16u, H = 1u)

Find the general solution of the differential equation $ ( \sin y \cos^2 y - x \sec^2 y ) dy = (\tan y) dx $.

The set of all real values of $x$ satisfying the inequality $\frac{7x^2 - 5x - 18}{2x^2 + x - 6}<2$ is

In which of the following Galvanic cells, emf is maximum? (Given: $ E^\circ_{\text{Mg}} = -2.36 \, V $ and $ E^\circ_{\text{Cl}_2/\text{Cl}^-} = +1.36 \, V $)

If a real valued function $ f: [a, \infty) \to [b, \infty) $ is defined by $ f(x) = 2x^2 - 3x + 5 $ and is a bijection, then find the value of $ 3a + 2b $:

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 $