AP EAPCET 2025 - 23rd May Evening Shift

The cubic equation whose roots are the squares of the roots of the equation $x^3-2 x^2+3 x-4=0$ is

Let $(a-3) x^2+12 x+(a+6)>0, \forall x \in R$ and $a \in(\ell, \infty)$. If $a$ is the least positive integral value of $a$, then the roots of $(\alpha-3) x^2+12 x+(\ell+2)=0$ are

\(1+\frac{4}{15}+\frac{4 \cdot 10}{15 \cdot 30}+\frac{4 \cdot 10 \cdot 16}{15 \cdot 30 \cdot 45}+\ldots . .+\infty=\)

Let $x_1, x_2, \ldots, x_{11}$ be the observations satisfying $\sum\limits_{i=1}^{11}\left(x_i-4\right)=22$ and $\sum\limits_{i=1}^{11}\left(x_i-4\right)^2=154$. If the mean and variance of the observations are $\alpha$ and $\beta$, then th...

$A(-2,3)$ is a point on the line $4 x+3 y-1=0$. If the points on the line that are 10 units away from the point $A$ are ( $x_1, y_1$ ) and ( $x_2, y_2$ ), then $\left(x_1+y_1\right)^2+\left(x_2+y_2\right)^2=$

If the equation of the pair of lines passing through $(1,1)$ and perpendicular to the pair of line $2 x^2+x y-y^2-x+2 y-1=0$ is $a x^2+2 h x y+b y^2+2 g x+3 y=0$, then $\frac{b}{a}=$

If $\alpha$ is the angle made by the perpendicular drawn from origin to the line $12 x-5 y+13=0$ with the positive $X$-axis in anti-clockwise direction, then $\alpha=$

If the combined equation of the lines joining the origin to the point of intersection of the curve $x^2+y^2-2 x-4 y+2=0$ and the line $x+y-2=0$ is $\left(l_1 x+m_1 y\right)\left(l_2 x+m_2 y\right)=0$, then $l_1+l_2+m_1+m_2=$

If the locus of a point which is equidistant from the coordinate axes forms a triangle with the line $y=3$, then the area of the triangle is

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin $(0,0,0)$ to a plane, then the equation of that plane is

If $A(0,1,2), B(2,-1,3)$ and $C(1,-3,1)$ are the vertices of a triangle, then the distance between its circumcentre and orthocentre is

If the direction cosines of two lines satisfy the equations $l-2 m+n=0, l m+10 m n-2 n l=0$ and $\theta$ is the angle between the lines, then $\cos \theta=$

The general solution satisfying both the equations $\sin x=-\frac{3}{5}$ and $\cos x=-\frac{4}{5}$ is

If $\sqrt{3} \cos \theta+\sin \theta>0$, then

If $\cos \theta=\frac{-3}{5}$ and $\theta$ does not lie in second quadrant, then $\tan \frac{\theta}{2}=$

$\operatorname{cosec} 48^{\circ}+\operatorname{cosec} 96^{\circ}+\operatorname{cosec} 192^{\circ}+\operatorname{cosec} 384^{\circ}=$

If $\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ and $\mathbf{b}=-\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ are two vectors, then the vector of magnitude 28 units in the direction of the vector $\mathbf...

$3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+5 \hat{\mathbf{j}}$ are the position vectors of three non-collinear points $A, B, C$ respectively. If the perpendicular drawn from ...

If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, \mathbf{b}=-2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{c}=5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $\mathbf{d}=3 \hat{\mathbf...

If $\bar{a}$ is a unit vector, then
\(|\mathbf{a} \times \hat{\mathbf{i}}|^2+|\mathbf{a} \times \hat{\mathbf{j}}|^2+|\mathbf{a} \times \hat{\mathbf{k}}|^2=\)

In a series resonant LCR circuit, for the power dissipated to become half of the maximum power dissipated, the current amplitude is

The density (in $\mathrm{kg} \mathrm{m}^{-3}$ ) of nuclear matter is of the order of

The ratio of the wavelengths of the spectral lines emitted due to transitions $3 \rightarrow 2$ and $2 \rightarrow 1$ orbits in the hydrogen atom is

One of the two identical capacitors having the same capacitance $C$, is charged to a potential $V_1$ and the other is charged to a potential $V_2$. If they are connected with their like plates together, then the decrease in the electrostati...

The co-ordinates of the centre of mass of a uniform $L$ shaped plate of mass 3 kg shown in the figure is

Ionosphere acts as a reflector for the frequency range of

A DC supply of 160 V is used to charge a battery of emf 10 V and internal resistance $1 \Omega$ by connecting a series resistance of $24 \Omega$. The terminal voltage of the battery during charging is

A part of a circuit is shown in the figure. The ratio of the potential differences between the points $A$ and $C$ and the points $D$ and $E$ is

If the de-Broglie wavelength of an electron is 2 nm , then its kinetic energy is nearly
(Planck's constant $=6.6 \times 10^{-34} \mathrm{Js}$ and mass of electron $=9 \times 10^{-31} \mathrm{~kg}$ )

If the longitudinal strain of a stretched wire is $0.2 \%$ and the Poisson's ratio of the material of the wire is 0.3 , then the volume strain of the wire is

When a current of 4 mA passes through an inductor, if the flux linked with it is $32 \times 10^{-6} \mathrm{Tm}^2$, then the energy stored in the inductor is

The waves having maximum wavelength among the following electromagnetic waves is

A solid of mass 1 kg has $6 \times 10^{24}$ atoms. If one electron is removed from every one atom of $0.005 \%$ of the atoms, then the charge gained by the solid is

If the energy stored in a spherical conductor having a charge of $12 \mu \mathrm{C}$ is 6 J , then the radius of the spherical conductor is

If two soap bubbles $A$ and $B$ of radii $r_1$ and $r_2$ respectively are kept in vacuum at constant temperature, then the ratio of masses of air inside the bubbles $A$ and $B$ is

Water flowing through a pipe of area of cross-section $2 \times 10^{-3} \mathrm{~m}^2$ hits a vertical wall horizontally with a velocity of $12 \mathrm{~ms}^{-1}$. If the water does not rebound after hitting the wall, then the force acting ...

An artificial satellite is revolving around a planet of radius $R$ in a circular orbit of radius ' $a$ '. If the time period of revolution of the satellite. $T \propto a^{3 / 2} g^x R^y$, then the values of $x$ and $y$ are respectively
[ $g...

In a Carnot engine, if the absolute temperature of the source is $25 \%$ more than the absolute temperature of the sink, then the efficiency of the engine is

The work done by 6 moles of helium gas when its temperature increases by $20^{\circ} \mathrm{C}$ at constant pressure is (Universal gas constant $=8.31 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$ )

If a heat engine and a refrigerator are working between the same two temperatures $T_1$ and $T_2\left(T_1>T_2\right)$, then the ratio of efficiency of heat engine to coefficient of performance of refrigerator is

A small quantity of water of mass ' $m$ ' at temperature $\theta^{\circ} \mathrm{C}$ is mixed with a large mass ' $M$ ' of ice which is at its melting point. If ' $s$ ' is specific heat capacity of water and ' $L$ ' is the latent heat of fu...

If the internal energy of 3 moles of a gas at a temperature of $27^{\circ} \mathrm{C}$ is 2250 R , then the number of degrees of freedom of the gas is
( $R=$ Universal gas constant)

Two blocks $A$ and $B$ of masses 2 kg and 4 kg respectively are kept on a rough horizontal surface. If same force of 20 N is applied on each block, then the ratio of the accelerations of the blocks $A$ and $B$ is (Coefficient of kinetic fri...

The work done in rotating a bar magnet which is initially in the direction of a uniform magnetic field through $45^{\circ}$ is $W$. The additional work to be done to rotate the magnet further through $15^{\circ}$ is

If a stone thrown vertically upwards from a bridge with an initial velocity of $5 \mathrm{~ms}^{-1}$, strikes the water below the bridge in a time of 3 s , then the height of the bridge above the water surface is
(Acceleration due to gravit...

A particle moving along a straight line covers the first half of the distance with a speed of $3 \mathrm{~ms}^{-1}$, the other half of the distance is covered in two equal time intervals with speeds of $4.5 \mathrm{~ms}^{-1}$ and $7.5 \math...

The magnetic moment of an electron moving in a circular orbit of radius $R$ with a time period $T$ is

A solenoid of one metre length and 3.55 cm inner diameter carries a current of 5 A . If the solenoid consists of five closely packed layers each with 700 turns along its length, then the magnetic field at its centre is

If the least distance of distinct vision for a boy is 35 cm , then the lens to be used by the boy for correcting the defect of his eye is

A circular disc of mass 20 kg and radius 1 m is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity of $2 \mathrm{rad} \mathrm{s}^{-1}$. Then, the rotational kinetic energy of the disc i...