AP EAPCET 2025 - 26th May Evening Shift

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $5 x^3-4 x^2+3 x-2=0$, then $\alpha^3+\beta^3+\gamma^3=$

$\frac{1}{3 \cdot 5}+\frac{1}{5 \cdot 7}+\frac{1}{7 \cdot 9}+\ldots$ to 24 terms $=$

The mean deviation from the median for the following data is
$$ \begin{array}{llllll} \hline x_1 & 9 & 3 & 7 & 2 & 5 \\ \hline f_1 & 1 & 6 & 2 & 8 & 4 \\ \hline \end{array} $$

$L_1$ and $L_2$ are two lines having slopes 2 and $-\frac{1}{2}$ respectively. If both $L_1$ and $L_2$ are concurrent with the lines $x-y+2=0$ and $2 x+y+3=0$, then sum of the absolute values of the intercepts made by the lines $L_1$ and $L...

If $2 x^2+3 x y-2 y^2-5 x+2 f y-3=0$ represents a pair of straight lines, then one of the possible values of $f$ is

The lines $L_1: y-x=0$ and $L_2: 2 x+y=0$ intersect the line $L_3: y+2=0$ at $P$ and $Q$ respectively. The bisector of the angle between $L_1$ and $L_2$ divides the line segment $P Q$ internally at $R$.
Statement $I P R: R Q=2 \sqrt{2}: \sq...

If the axes are translated to the orthocentre of the triangle formed by the points $\mathrm{A}(7,5), \mathrm{B}(-5,-7)$ and $C(7,-7)$, then the coordinates of the incentre of the triangle in the new system are

The angle made by a line $L$ with positive $X$-axis measured in the positive direction is $\frac{\pi}{6}$ and the intercept made by $L$ on $Y$-axis is negative. IF $L$ is at a distance of 5 units from the origin, then the perpendicular dist...

If the direction ratio of two lines $L_1$ and $L_2$ are given by $(1,-2,2)$ and $(-2,3,-6)$ respectively, then the direction ratios of the line which is perpendicular to the linesh and $L_2$ are

Line $L_1$ passes through the point $\hat{\mathbf{i}}+\hat{\mathbf{j}}$ and $\hat{\mathbf{k}}-\hat{\mathbf{i}}$. Line $L_2$ passes through the point $\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and is parallel to the vector $\hat{\mathbf{i}}+\hat...

The point in the $X Y$ - plane which is equidistant from the points $A(2,0,3), B(0,3,2)$ and $C(0,0,1)$ has the coordinates

If the image of the point $A(1,1,1)$ with respect to the plane $4 x+2 y+4 z+1=0$ is $B(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma=$

The number of solutions of the equation $4 \cos 2 \theta \cos 3 \theta=\sec \theta$ in the interval $[0,2 \pi]$ is

If $A$ and $B$ are the values such that $(A+B)$ and $(A-B)$ are not odd multiples of $\frac{\pi}{2}$ and $2 \tan (A+B)=3 \tan (A-B)$, then $\sin A \cos A=$

If $\cos ^3 80^{\circ}+\cos ^3 40^{\circ}-\cos ^3 20^{\circ}=k$, then $\frac{4 k}{3}=$

$$ \begin{aligned} & \left(4 \cos ^2 \frac{\pi}{20}-1\right)\left(4 \cos ^2 \frac{3 \pi}{20}-1\right) \\ & \left(4 \cos ^2 \frac{5 \pi}{20}+1\right)\left(4 \cos ^2 \frac{7 \pi}{20}-1\right)\left(4 \cos ^2 \frac{9 \pi}{20}-1\right)= \end{ali...

Let $(x, y) \in R \times R$ and $\mathbf{a}=x \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=6 \hat{\mathbf{i}}-y\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ be two vectors. If
$$ |\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot...

$\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, \mathbf{c}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$ are three vectors. If $\mathbf{r}$ is a ve...

$\mathbf{a} \cdot \mathbf{b}$ and $\mathbf{c}$ are the position vectors of three non-collinear points on a plane. If
$$ \alpha=[\mathbf{a b c}] \text { and } \mathbf{r}=\mathbf{a} \times \mathbf{b}-\mathbf{c} \times \mathbf{b}-\mathbf{a} \t...

If $P=(\mathbf{a} \times \hat{\mathbf{i}})^2+(\mathbf{a} \times \hat{\mathbf{j}})^2+(\mathbf{a} \times \hat{\mathbf{k}})^2$ and $Q=(\mathbf{a} \cdot \hat{\mathbf{i}})^2+(\mathbf{a} \cdot \hat{\mathbf{j}})^2+(\mathbf{a} \cdot \hat{\mathbf{k}...

In a series LCR circuit, the voltages across the capacitor, resistor and inductor are in the ratio $2: 3: 6,$ if the voltage of the AC source in the circuit is 240 V , then the voltage across the inductor is

The ratio of the time periods of the revolution of the electrons in the second and third excited states of hydrogen atom is

If the surface areas of two nucleii are in the ratio $9: 47$, then the ratio of their mass number is

A capacitor of capacitance $2 \mu \mathrm{~F}$ is charged with the help of a 60 V battery. After disconnecting the battery, if this capacitor is connected in parallel with another uncharged capacitor of capacitance $l \mu \mathrm{~F}$, then...

A body of mass ' $m$ ' moving along a straight line collides with a stationary body of mass ' $2 m^{\prime}$. After collision if the two bodies move together with the same velocity, then the fraction of kinetic energy lost in the process is...

When two identical batteries of internal resistance $1 \Omega$ each are connected in series across a resistor $R$, the rate of heat produced in $R$ is $P_1$. When the same batteries are connected in parallel across $R$, the rate of heat pro...

The readings of the voltmeter and ammeter in the circuit shown in the diagram are respectively

The ratio of de-Broglie wavelengths associated with thermal neutrons at temperatures $127^{\circ} \mathrm{C}$ and $352^{\circ} \mathrm{C}$ is

The elastic potential energy stored in a copper rod of length one metre and area of cross-section $1 \mathrm{~mm}^2$ when stretched by 1 mm is
(Young's modulus of copper $=1.2 \times 10^{11} \mathrm{Nm}^{-2}$ )

When current in a coil changes from 2 A to 5 A in time of 0.3 s , if the emf induced in the coil is 40 mv , then the self inductance of the coil is

If a 10 W bulb emits electromagnetic waves uniformly in all directions, then the intensity of light at a distance 0.5 m from the source is nearly

The layer of the atmosphere that reflects low frequency (LF) electromagnetic waves during day time only is

The force between two conducting spheres of same radius having charges $+8 \mu \mathrm{C}$ and $-4 \mu \mathrm{C}$ separated by some distance in air is $F$. If the spheres are connected by a conducting wire and after some time the wire is r...

In space the electric potential varies as $V=20|\mathbf{r}|$ volt. where $\mathbf{r}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}}$ is the position vector. Then, electric field in $\left(\mathrm{NC}^{-1}\right)$ at the point $(4 ...

When the temperature increases, the viscosity of

The potential energy of a satellite of mass ' $m$ ' revolving around the Earth at a height of $R_e$ from the surface of the Earth is
( $R_e=$ Radius of Earth, $\mathrm{g}=$ acceleration due to gravity)

If the rms speed of the molecules of a diatomic gas at a temperature of 322 K is $2000 \mathrm{~ms}^{-1}$, then the gas is (Universal gas constant $=8.31 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$ )

The internal energy of 4 moles of a monoatomic gas at a temperature of $77^{\circ} \mathrm{C}$ is
( $R=$ Universal gas constant)

If a body cools from a temperature of $62^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ in 10 minutes and to $42^{\circ} \mathrm{C}$ in the next 10 minutes, then the temperature of the surroundings is

If the ratio of universal gas constant and specific heat capacity at constant volume of a gas is given by 0.67 , then the gas is

If 5.6 litres of a monoatomic gas at STP is adiabatically compressed to 0.7 litres, then the work done on the gas is nearly ( $R=$ Universal gas constant)

A sample of a ferromagnetic iron in the shape of a cube of side $1.0 \mu \mathrm{~m}$ contains $8.7 \times 10^{28}$ atoms per cubic metre and the magnetic dipole moment of each iron atom is $93 \times 10^{-24} \mathrm{Am}^2$. Then, the maxi...

If a body of mass 2 kg moving with initial velocity of $4 \mathrm{~ms}^{-1}$ is subjected to a force of 3 N for a time of 2 s normal to the direction of its initial velocity, then the resultant velocity of the body is

If the velocity at the maximum height of a projectile projected at an angle of $45^{\circ}$ is $20 \mathrm{~ms}^{-1}$, then the maximum height reached by the projectile is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

If the horizontal range of a body projected with a velocity ' $u$ ' is 3 times the maximum height reached by it, then the range of the body is
( $g=$ Acceleration due to gravity)

The displacement $(x)$ and time $(t)$ graph of a particle moving along a straight line is shown in the figure. The average velocity of the particle in the time of 10 s is

The magnetic field at the centre of a long solenoid having 400 turns per unit length and carrying a current ' $i$ ' is $6.24 \times 10^{-2} \mathrm{~T}$. The magnetic field at the centre of another long solenoid having 200 turns per unit le...

If a proton of kinetic energy 8.35 MeV enters a uniform magnetic field of 10 T at right angles to the direction of the field, then the force acting on the proton is
(Mass of proton $=1.67 \times 10^{-27} \mathrm{~kg}$ and Charge of proton $...

When an object is placed infront of a convex mirror at a distance ' $u$ ' from the pole of the mirror such that the size of the image is ' $n$ ' times that of the object. Then, the object distance ' $u=$

A solid sphere and a solid cylinder have same mass and same radius. The ratio of the moment of inertia of the solid sphere about its diameter and the moment of inertia of the solid cylinder about its axis is