List of top Questions asked in AP EAMCET

Two equally charged metal spheres $A$ and $B$ repel each other with a force of $4 \times 10^{-5}\, N$. Another identical uncharged sphere $C$ is touched to $A$ and then placed at the mid- point of the line joining the spheres $A$ and $B$. The net electric force on the sphere $C$ is

Water stands upto height $h$ behind the dam as shown in the figure. The front view of the dam gate is also shown in the adjoining figure. Density of water is $\rho$ and acceleration due to gravity is $g$. If atmospheric pressure force is also considered, then the point of application of total force acting on the dam due to water above $O$ is

One litre of $0.15\, M\, Na _{2} SO _{3}$ aqueous solution is mixed with $500\, mL$ of $0.2\, M\, K _{2} Cr _{2} O _{7}$ aqueous solution in acid medium. What is the number of moles of $K _{2} Cr _{2} O _{7}$ remaining in the solution after the reaction?

Which of the following statements are correct? I) $\ce{P_4}$ molecule is very reactive because of angular strain II) The basicity of $\ce{H_3PO_3}$ is $3$ III) In gas phase, all $\ce{P-Cl}$ bonds of $\ce{PCl_5}$ have same bond length IV) In solid state.$ \ce{PCl_5}$ exists as an ionic solid, in which anion $\ce{[PCl_6]^{-}}$ has octahedral and cation $\ce{[PCl_4]^{+}}$ has tetrahedral shape.

Which of the following structures represents cumene?

Which one of the following compounds will not show geometrical isomerism?

$XeF_4$ is square planar where as $CCl_4$ is tetrahedral because

If $1 , \omega , \omega^2$ are the cube roots of unity, then $\frac{1}{1+2\omega} + \frac{1}{2+\omega } - \frac{1}{1+\omega } =$

If $\tan \, \theta = \frac{\cos 25^{\circ} + \sin 25^{\circ} }{\cos 25^{\circ} - \sin 25^{\circ} }$ and $\theta$ is in the third quadrant, then $\theta =$

If A and B are the two real values of k for which the system of equations $x + 2y + z = 1,x + 3y + 4r = k.x + 5v + 10z = k^2$ is consistent, then $A + B =$

If a circle touches the lines $3x - 4y - 10 = 0$ and $3x - 4y + 30 = 0$ and its centre lies on the line $x + 2y = 0$ then the equation of the equation of the circle is

If $\alpha, \beta, \gamma$ are any three angles, then $\cos \, \alpha + \cos \beta - \cos \, \gamma - \cos (\alpha + \beta + \gamma) =$

If $\frac{x^{3}}{\left(2x-1\right)\left(x-1\right)^{2}} = A + \frac{B}{2x-1}+ \frac{C}{x-1}+ \frac{D}{\left(x-1\right)^{2}}$, then $2A - 3B + 4C + 5D =$

If the petrol burnt in driving a motor boat varies as the cube of the velocity, then the speed (in km hom ) of the boat going against a water flow of C kms hour so that the quantity of petrol burnt is minimum is

If $z_{1} = 1 -2i ; z_{2} = 1 + i$ and $z_{3 } = 3 + 4i,$ then $\left( \frac{1}{z_{1}} + \frac{3}{z_{2}}\right) \frac{z_{3}}{z_{2}} =$

In $\Delta ABC. a^3 . \cos (B - C) + b^3 . \cos(C - A) + c^3 . \cos (A - B) =$

In triangle ABC. if a = 3 ,b = 4,c = 6, then $\frac{\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}}{\cot A +\cot B + cot C} =$

Let $z = x + iy$ and a point $P$ represent $z$ in the Argand plane. If the real part of $\frac{z - 1}{z + i}$ is 1. then a point that lies on the locus of $P$ is

The length of the transverse common tangent of the circles $x^2 + y^2 - 2x + 4y + 4 = 0$ and $x^2 + y^2 + 4x - 2y + 1 = 0$ is

The number of rational terms in the binomial expansion of $\left(\sqrt[4]{5} + \sqrt[5]{4}\right)^{100}$ is

The number of three digit numbers in which $9$ appears only in one place is

The numerically greatest term in the binomial expansion of $(2a - 3b)^{19}$ and $a = \frac{1}{4}$ and $b = \frac{2}{3}$ is