List of top Questions asked in AP EAMCET

If
\[ \frac{x-1}{3+i}+\frac{y-1}{3-i}=i, \] then the true statement among the following is

The number of integer solutions of the equation
\[ |1-i|^x=2^x \] is

If \(f(x)=ax^2+bx+c\) for some \(a,b,c\in \mathbb{R}\) with \(a+b+c=3\) and
\[ f(x+y)=f(x)+f(y)+xy \quad \forall x,y\in \mathbb{R}, \] then
\[ \sum_{n=1}^{10} f(n)= \]

Let
\[ A= \begin{bmatrix} 5 & \sin^2\theta & \cos^2\theta \\ -\sin^2\theta & -5 & 1 \\ \cos^2\theta & 1 & 5 \end{bmatrix} \] Then, the maximum value of \(\det(A)\) is

If \(f(x)=\sqrt{2-x^2}\) and \(g(x)=\log(1-x)\) are two real valued functions, then the domain of the function \((f+g)(x)\) is

For \(i=1,2,3\) and \(j=1,2,3\), if
\[ a_i^2+b_i^2+c_i^2=1 \] and
\[ a_ia_j+b_ib_j+c_ic_j=0 \quad \forall \; i\neq j \] and
\[ A= \begin{bmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{bmatrix} \] then \(\det(AA^T)=\)

If
\[ A=\frac{1}{7} \begin{bmatrix} 3 & -2 & 6 \\ -6 & -3 & 2 \\ -2 & 6 & 3 \end{bmatrix}, \] then

If
\[ A= \begin{bmatrix} \alpha^2 & 5 \\ 5 & -\alpha \end{bmatrix} \] and
\[ \det(A^{10})=1024, \] then \(\alpha=\)

The range of the real valued function \(f(x)=\sqrt{\dfrac{x^2+2x+8}{x^2+2x+4}}\) is

Potential energy of a body of mass $1\, kg$ free to move along X-axis is given by $U(x) = \left( \frac{x^2}{2} - x \right) J .$ If the total mechanical energy of the body is $2\, J$. then the maximum speed of the body is (Assume only conservative force acts on the body)

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

If only $\frac{1}{51}^{th}$ ot the main current is to be passed through a galvanometer then the shunt required is $R_1$ and if only $\frac{1}{11}^{th}$ of the main voltage is to be developed across the galvanometer, then the resistance required is $R_2$. Then $\frac{R_2}{R_1} =$

The walls of a closed cubical box of edge $60\, cm$ are made of material of thickness $1\, mm$ and thermal conductivity $4 \times 10^{-4} \; cal \; s^{-1} \; cm^{-1} {^{\circ}C^{-1}}$. The interior of the box is maintained $1000 \; {^{\circ}C}$ above the outside temperature by a heater placed inside the box and connected across $400\, V\, DC$ supply. The resistance of the heater 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

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? $\left(N_{A}=6.0 \times 10^{23} mol ^{-1}\right)$

Acetic acid on heating with $ {NH_3}$ forms $A$. When $A$ reacts with $ {LiAlH_4}$ followed by hydrolysis gives $B$. When $B$ is heated with chloroform in $KOH$ medium gives $C$. What are $B$ and $C$ respectively?

$\cos ^{2} 5^{\circ}-\cos ^{2} 15^{\circ}-\sin ^{2} 15^{\circ}+\sin ^{2} 35^{\circ}$ $+\cos 15^{\circ} \sin 15^{\circ}-\cos 5^{\circ} \sin 35^{\circ}=$

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 the set of acidic oxides.

If $\begin{vmatrix}a+b+2c&a&b\\ c&2a+b+c&b\\ c&a&a+2b+c\end{vmatrix} = 2 $, then $a^3 + b^3 + c^3 - 3abc$ =

If $\cos \theta \neq 0$ and $\sec \theta - 1 = ( \sqrt{2} - 1 ) \tan \theta $ then $\theta $ =

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 velocity of an object moving in a straight line path is given as a function of time by $v = 6t - 3t^2$. where $v$ is in $ms^{-1} , t $ is in $s$. The average velocity of the object between $t = 0$ and $t = 2s$ is

Which of the following reactions can be used to prepare diborane? I) $ {BF_3 + LiAlH_4 ->[ether]}$ II) $ {BF_3 + NaH ->[450 k]}$ III) $ {Na_2B_4O_7 + H_2O -> }$ IV) $ { NaBH_4 + I_2 ->}$

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