List of top Questions asked in AP EAPCET

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)

A square plate of 0.1 m side moves parallel to a second plate with a velocity of 0.1 m/s, both plates being immersed in water. If the viscous force is 0.002 N and the coefficient of viscosity is 0.01 Poise, distance between the plates in metre is:

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} $

Six marbles are lined Up in a straight groove made on a horizontal frictionless surface as shown below. Two similar marbles in contact, with a common velocity v collide with a row of 6 marbles from left. Which of the following is observed?

The acceleration due to gravity at a height h above the earths surface is $ 9m{{s}^{-2}}. $ If $ g=10\text{ }m{{s}^{-2}} $ on the earths surface, its value at a point at an equal distance h below the surface of the earth is

A block of mass m is connected to one end of a spring of spring constant k. The other end of the spring is fixed to a rigid support. Tile mass is released slowly so that the total energy of the system is then constituted by only the potential energy, then d is the maximum extension of the spring. Instead, if the mass is released suddenly from the same initial position, the maximum extension of the spring now is (g = acceleration due to gravity)

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 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}}) $

An ideal gas is taken through the cycle $A \to B \to C \to A$ as shown in the figure. If the net heat supplied to the gas in the cycle is $5\, J$. the magnitude of work done during the process $C \to A$ 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, $g=10 \,ms ^{-2}$ )

The focal length of a spherical mirror made of steel is $150 \,cm$. If the temperature of the mirror increases by $200\, K$, its focal length become (coefficient of linear expansion of steel $\alpha=12 \times 10^{-6 \circ} C ^{-1} .$ )

The hybridisation of atom $'X'$ with atomic number $27$ in $\left[X F _{6}\right]^{3-}$ is

The kinetic energy K of a particle of mass m moving along a circle of radius R depends on distance covered s as K= as2. Then the acceleration of particle is given by

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 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 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 car is traveling along a curved road of radius r. If die coefficient of friction between the tyres and the road is $ \mu $ , the car will skid if its speed exceeds

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

Two particles A and B initially at rest move towards each other under a mutual force of attraction. At the instant when the velocity of A is v and that of B is 2v. The velocity of centre of mass of the system is

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

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