List of top Questions asked in AP EAMCET- 2019

If $\int \cos x . \cos 2x . \cos 5x dx = A \; \sin 2x + B \sin 4x + C \sin 6x + D \sin 8x + k $ (where $k$ is the arbitrary constant of integration), then $\frac{1}{B} + \frac{1}{C} = $

In triangle $\Delta A B C$ , if $\frac{b + c}{9} = \frac{c + a}{10} = \frac{a+b}{11},$ then $\frac{\cos A + \cos B}{\cos C} = $

If $ABCD$ is a cyclic quadrilateral with $AB = 6, BC = 4, CD = 5, DA = 3$ and $\angle ABC$ = $\theta$ then $cos\, \theta$ =

If $\frac{x^{4}}{\left(x-1\right)\left(x-2\right)\left(x-3\right)} =x + k+ \frac{A}{x-1}+\frac{B}{x-2} + \frac{C}{x-3} $, then $k + A - B + C =$

If $\sqrt{1-x^{6} }+ \sqrt{1-y^{6}} =a\left(x^{3} -y^{3}\right) , $ then $ y^{2} \frac{dy}{dx} = $

If $\alpha$ and $\beta$ are the roots of $x^{2}+7 x+3=0$ and $\frac{2 \alpha}{3-4 \alpha}, \frac{2 \beta}{3-4 \beta}$ are the roots of $a x^{2}+b x+c=0$ and $GCD$ of $a, b, c$ is $1$ , then $a+b+c=$

If $\alpha , \beta , \gamma$ are the roots of $x^3 - 6x^2 + 11x - 6 = 0 $ , then the equation having the roots $\alpha^2 + \beta^2 + \gamma^2$ and $\gamma^2 + \alpha^2$ is

If $\alpha =\displaystyle\lim_{x\to0} \frac{x.2^{x}-x}{1-\cos x} $ and $ \beta =\displaystyle\lim_{x\to0} \frac{x.2^{x}-x}{\sqrt{1+x^{2} } - \sqrt{1-x^{2}} } , $ then

Let $D=R-\{0,1\}$ and $f: D \rightarrow D, g: D \rightarrow D$ and $h: D \rightarrow D$ be three functions defined by $f(x)=\frac{1}{x} ; g(x)=1-x$ and $h(x)=\frac{1}{1-x} .$ If $j: D \rightarrow D$ is such that $(gojof)$ $(x)=f(x)$ for all $x \in D$, then which one of the following is $j(x) ?$

If $z = x - iy $ and $z^{\frac{1}{3}} = a + ib$, then $\frac{\left(\frac{x}{a}+\frac{y}{b}\right)}{a^{2}+b^{2}} = $

An organic compound $X\left( C _{7} H _{7} Cl \right)$ when reacted with $KCN / C _{2} H _{5} OH$ gave major product $Y . Z$ is formed when $Y$ is reduced with $LiAlH _{4}$. What are $Y$ and $Z$ ?

Identify $Z$ in the following sequence of reactions. $\ce{ C_2 H_4 Br_2 ->[(i) Alc.KOH][(ii) NaNH_2] X ->[Red\, hot][Fe \,tube\, 873 K] Y ->[(CH_3CO)_2 O/\Delta][Anhyd. AlCl_3] Z}$

In the first order thermal decomposition of $C _{2} H _{5} I (g) \longrightarrow C _{2} H _{4}(g)+ HI (g)$, the reactant in the beginning exerts a pressure of $2$ bar in a closed vessel at $600 \,K$. If the partial pressure of the reactant is $0.1$ bar after $1000$ minutes at the same temperature the rate constant in $\min ^{-1}$ is $(\log 2=0.3010)$

At $T( K )$, copper (atomic mass $=63.5\, u$ ) has fcc unit cell structure with edge length of $x \mathring {A}$. What is the approximate density of $Cu$ in $g \,cm ^{-3}$ at that temperature? $\left(N_{A}=6.0 \times 10^{23} mol ^{-1}\right)$

The maximun value of the applied force $F$ such that the block as shown in the arrangement does not move is (Acceleration due to gravity, $g=10 \,ms ^{-2}$ )

In a $p$ - type semiconductor the donor level is at $50 \,meV$ above the valence band. To produce one electron, the maximum wavelength of light photon required is (Planck's constant, $h=6.6 \times 10^{-34} \,Js$ and speed of light in vacuum, $c=3 \times 10^{8} \,ms ^{-1}$ )

For a particle executing simple harmonic motion, the displacement-time $(x - t)$ graph is as shown in the figure. The acceleration of the particle at $t = \frac{4}{3} s$ is

The speed of a particle changes from $\sqrt{5} \,ms^{- 1}$ to $2 \sqrt{5} \; ms^{-1}$ in a time If the magnitude of change in its velocity is $5 \; ms^{-1}$, the angle between the initial and final velocities of the particle is

The number of moles of solute present in the solutions of $I, II$ and $III$ is respectively I. $500 \,mL$ of $0.2\, M\, NaOH$ II. $200 \,mL$ of $0.1 \,N \,H _{2} SO _{4}$ II. $6 g$ of urea in $1 \,kg$ of water

Which one of the following has maximum number of hybrid orbitals ?

Noble metals like gold and platinum are soluble in which of the following mixtures?

$KMnO _{4}$ oxidises $S _{2} O _{3}^{2-}$ to $SO _{4}^{2-}$ in medium $x$ and $NO^{-}_2$ to $NO^{-}_3$ in medium $y, x$ and $y$ are respectively

$KO _{2}$, reacts with water to form $A, B$ and $C .$ $B$ forms $C$ when it reacts with iodine in basic medium. What are $B$ and $C$ respectively?

Identify the set of acidic oxides.

The non-biodegradable waste formed in fertilizer industries is