List of top Questions asked in AP EAPCET

If $A=\begin{bmatrix}1 & 0 \\ 0 & -1\end{bmatrix}, P=\begin{bmatrix}1 & 1 \\ 0 & 1\end{bmatrix}$ and $X=A P A^{T}$, then $A^{T} X^{50} A=$

If $[x]$ is the greatest integer less than or equal to $x$ and $|x|$ is the modulus of $x$. then the system of three equations $2x + 3 | y | + 5[z] = 0, x + |y| - 2[z] = 4, x + |y| + |z| = 1$ has

If $z= x +iy , x,y \in R , (x,y) \ne (0, -4)$ and $Arg \left( \frac{2z-3}{z+4i}\right) = \frac{\pi}{4}$ , then the locus of $z$ is

Investigate the values of $\lambda$ and $\mu$ for the system $x+2 y+3 z=6, x+3 y+5 z=9$, $2 x+5 y+\lambda z=\mu$ and match the values in List - I with the items in List - II.

List I		List II
(A)	$\lambda=8, \mu \neq 15$	1.	Infinitely many solutions
(B)	$\lambda \neq 8, \mu \in R$	2.	No solution
(C)	$\lambda=8, \mu=15$	3.	Unique solution

Consider the following lists.

List-I		List-II
(A)	$f(x) = \frac{|x+2|}{x+2} , x \ne -2 $	(I)	$[\frac{1}{3} , 1 ]$
(B)	$(x)=|[x]|,x \in [R$	(II)	Z
(C)	$h(x) = |x - [x]| , x \in [R$	(III)	W
(D)	$f(x) = \frac{1}{2 - \sin 3x} , x \in [R$	(IV)	[0, 1)
		(V)	{ -1, 1}

Which of the following is divisible by $x^{2}-y^{2}, \forall x\ne y$?

If $z = x + iy , x , y \in R$ and the imaginary part of $\frac{\bar{z} - 1}{\bar{z} - i}$ is $1$ then the locus of $z$ is

Two bodies of masses $m_1$ and $m_2$ initially at rest at infinite distance apart move towards each other under gravitational force of attraction. Their relative velocity of approach when they are separated by a distance $r$ is (G = Universal gravitational constant)

The kinetic energy of a body rotating at 300 revolutions per minute is 62.8 J. Its angular momentum $ (\text{in kg}\,{{m}^{2}}{{s}^{-1}}) $ is approximately:

A light rod of length 100 cm is suspended from the ceiling horizontally by means of two vertical wires of equal lengths tied to the ends of the rod. One of the wires is made of steel and is of area of cross- section $ 0.1\text{ }c{{m}^{2}}. $ The other wire is of brass and of area of cross-section $ 0.2\text{ }c{{m}^{2}}. $ The position from the steel wire along the rod at which a load is to be placed to produce equal stresses in both wires is ( $ {{Y}_{steel}}=20\times {{10}^{11}} $ dyne $ c{{m}^{-2}};\text{ }({{Y}_{brass}}=10\times {{10}^{11}}dyne\text{ }c{{m}^{-2}}) $

A body of mass 5 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to $ \frac{1}{10} $ th of its original velocity. Then the mass of the second body is

A long cylindrical glass vessel has a pinhole of diameter $0.2\, mm$ at its bottom. The depth to which the vessel can be lowered vertically in a deep water bath without the water entering into the vessel is (surface tension of water, $T=0.07 \,Nm ^{-1}$, acceleration due to gravity, $g=10 \,ms ^{-2}$ )

Eight drops of water of 0.6 mm radius each merge to form one big drop. If the surface tension of water is $ 0.072\text{ }N{{m}^{-1}}, $ the energy dissipated in the process is

A metal rod of length $10 \,cm$ and area of cross-section $2.8 \times 10^{-4} m ^{2}$ is covered with a non-conducting substance. One end of it is maintained at $80^{\circ} C$, while the other end is put in ice at $0^{\circ} C .$ It is found that $20\, gm$ of ice melts in $5\, min$. The thermal conductivity of the metal in $Js ^{-1} m ^{-1} K ^{-1}$ is (Latent heat of ice is $80 \,cal\, g ^{-1} .$ )

A particle is projected up from a point at an angle 9, with the horizontal direction. At any time t, if p is the linear momentum, y is the vertical displacement, x is the horizontal displacement, the graph among the following, which does not represent the variation of kinetic energy K of the projectile is

If the earth shrinks such that its density becomes 8 times to the present value, then the new duration of the day in hours will be

A body is projected horizontally from the top of a tower of height $180\, m$ with a velocity of $20 \, ms^{-1}$. If acceleration due to gravity is $10 \, ms^{-2}$ then match the following.

List-I		List-II
A	Velocity of the body after 1 second (in $ms^{-1}$)	I	5
B	Horizontal displacement of the body after 1 second (in meters)	II	20
C	Vertical displacement of the body after 1 second (in meters)	III	10
D	Vertical velocity of the body after 1 second (in $ms^{-1}$)	IV	22.4

A planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at points $A$ and $B$ are $90 \times 10^{6} km$ and $60 \times 10^{6} km$, respectively. The ratio of velocities of the planet at the points $A$ and $B$ when its velocities make angle $30^{\circ}$ and $60^{\circ}$ with major-axis of the orbit is

A semicircular plate of mass $m$ has radius $r$ and centre $c$. The centre of mass of the plate is at a distance $x$ from its centre $c$. Its moment of inertia about an axis passing through its centre of mass and perpendicular to its plane is

Iii which of the following, the solubility of $AgCl$ will be minimum?

A boy of mass 50 kg is standing on a weighing machine placed at the floor of a lift. The machine reads his weight in newtons. What is the reading of the machine, if the lift is moving Upwards with a uniform Speed of $ 10\text{ }m{{s}^{-1}}. $ $ (g=10m{{s}^{-2}}) $

A solid copper cube of $7 \,cm$ edge is subjected to a hydraulic pressure of $8000\, kPa$. The volume contraction of the copper cube is (Bulk modulus of copper = $140 \,GPa$ )

Of the vectors given below, the parallel vectors are, $ {{A}^{\to }}=6\widehat{i}+8\widehat{j} $ $ {{B}^{\to }}=210\widehat{i}+280\widehat{k} $ $ {{C}^{\to }}=5.1\widehat{i}+6.8\widehat{k} $ $ {{D}^{\to }}=3.6\widehat{i}+6\widehat{j}+48\widehat{k} $

A solid sphere of mass $100\, kg$ and radius $10\, m$ moving in a space becomes a circular disc of radius $20\, m$ in one hour. Then the rate of change of moment of inertia in the process is