AP EAPCET 2024 - 18th May Morning Shift

If the sum of two roots $\alpha, \beta$ of the equation $x^4-x^3-8 x^2+2 x+12=0$ is zero and $\gamma, \delta(\gamma>\delta)$ are its other roots, then $3 \gamma+2 \delta=$

For a set of observations, if the coefficient of variation is 25 and mean is 44 , then the variance is

If the lines $3 x+y-4=0, x-\alpha y+10=0, \beta x+2 y+4=0$ and $3 x+y+k=0$ represent the sides of a square, then $\alpha \beta(k+4)^2=$

$A$ is the point of intersection of the lines $3 x+y-4=0$ and $x-y=0$. If a line having negative slope makes an angle of $45^{\circ}$ with the line $x-3 y+5=0$ and passes through $A$, then its equation is

$2 x^2-3 x y-2 y^2=0$ represents two lines $L_1$ and $L_2$. $2 x^2-3 x y-2 y^2-x+7 y-3=0$ represents another two lines $L_3$ and $L_4$. Let $A$ be the point of intersection of lines $L_1, L_3$ and $B$ be the point of intersection of lines $...

The area of the triangle formed by the pair of lines $23 x^2-48 x y+3 y^2=0$ with the line $2 x+3 y+5=0$, is

If the points with position vectors $(\alpha \hat{\mathbf{i}}+10 \hat{\mathbf{j}}+13 \hat{\mathbf{k}}),(6 \hat{\mathbf{i}}+11 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}),\left(\frac{9}{2} \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}-8 \hat{\mathbf{k}}...

The equation $a x y+b y=c y$ represents the locus of the points which lie on

Let $P(\alpha, 4,7)$ and $Q(\beta, \beta, 8)$ be two points. If $Y Z$-plane divides the join of the points $P$ and $Q$ in the ratio $2: 3$ and $Z X$-plane divides the join of $P$ and $Q$ in the ratio $4: 5$, then length of line segment $P Q...

If the distance between the planes $2 x+y+z+1=0$ and $2 x+y+z+\alpha=0$ is 3 units, then product of all possible values of $\alpha$ is

$1+\sin x+\sin ^2 x+\sin ^3 x+\ldots \ldots+\infty=4+2 \sqrt{3}$ and $0

$ \tan 6^\circ + \tan 42^\circ + \tan 66^\circ + \tan 78^\circ = $

The maximum value of $12\sin x - 5\cos x + 3$ is

$\sin^2 16^\circ - \sin^2 76^\circ = $

By considering $1^{\prime}=0.0175$, he approximate value of $\cot 45^{\circ} 2^{\prime}$ is

If $\mathbf{f}, \mathbf{g}, \mathbf{h}$ be mutually orthogonal vectors of equal magnitudes, then the angle between the vectors $\mathbf{f}+\mathbf{g}+\mathbf{h}$ and $\mathbf{h}$ is

Let $\mathbf{a}, \mathbf{b}$ be two unit vectors. If $\mathbf{c}=\mathbf{a}+2 \mathbf{b}$ and $\mathbf{d}=5 \mathbf{a}-4 \mathbf{b}$ are perpendicular to each other, then the angle between $a$ and $b$ is

If the vectors $\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$, $\mathbf{c}=3 \hat{\mathbf{i}}+p \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ are coplanar, then $p...

If $(\alpha, \beta, \gamma)$ are the direction cosines of an angular bisector of two lines whose direction ratios are $(2,2,1)$ and $(2,-1,-2)$, then $(\alpha+\beta+\gamma)^2=$

In a regular hexagon $A B C D E F, \mathbf{A B}=\mathbf{a}$ and $\mathbf{B C}=\mathbf{b}$, then $F A=$

In the figure. If $A$ and $B$ are identical bulbs, which bulb glows brighter.

If the binding energy of the electron in a hydrogen atom is 13.6 eV . Then, energy required to remove electron from first excited state of $\mathrm{Li}^{2+}$ is

A mixture consists of two radioactive materials $A_1$ and $A_2$ with half lives of 20 s and 10 s respectively. Initially, the mixture has 40 g of $A_1$ and 160 g of $A_2$. The amount of the two in the mixture will become equal after

In the given circuit, the potential difference across $5 \mu \mathrm{~F}$ capacitor is

In an inclastic collision, after collision the kinetic energy

A wheel of angular speed $600 \mathrm{rev} / \mathrm{min}$ in is made to slow down at a rate of $2 \mathrm{rad} \mathrm{s}^{-2}$. The number of revolutions made by the wheel before coming to rest is

If the maximum and minimum voltages of an $A M$ wave are $V_{\max }$ and $V_{\min }$ respectively. Then, the modulation factor $m$ is

In a potentiometer, the area of cross-section of the wire is $4 \mathrm{~cm}^2$. The current flowing in the circuit is 1 A and the potential gradient is $7.5 \mathrm{Vm}^{-1}$. Then, the resistivity of the potentiometer wire is

Drift speed $v$ varies with the intensity of electric field $E$ as per the relation.

Energy required to remove an electron from aluminium surface is 4.2 eV . If light of wavelength $2000 \mathring{A}$ falls on the surface, the velocity of the fastest ejected electron the surface will be

Two copper wires $A$ and $B$ of lengths in the ratio $1: 2$ and diameters in the ratio $3: 2$ are stretched by foren in the ratio $3 : 1$. The ratio of the clastic potential energies stored per unit volume in the wires $A$ and $B$ is.

If the current through an inductor increases from 2A to 3A. The magnetic energy stored in the inductor increases by

The solar radiation is

Two point charges $+6 \mu \mathrm{C}$ and $+10 \mu \mathrm{C}$ kept at certain distance repel each other with a force of 30 N . If each charge is given an additional charge of $-8 \mu \mathrm{C}$, the jwo charges

In a region, the electric field is $30 \hat{\mathbf{i}}+40 \hat{\mathbf{j}} \mathrm{NC}^{-1}$, If the electric potential at the origin is zero. The electric potential at the point ( $1 \mathrm{~m}, 2 \mathrm{~m}$ ) is

216 small identical liquid drops each of surface area $A$ coalesce to form a bigger drop. If the surface tension of the liquid is $T$. The energy released in the process is

Two satellites of masses $m$ and 1.5 m are revolving around the earth with different speeds in two circular orbits of heights $R_E$ and $2 R_E$ respectively, where $R_F$ is the radius of the earth. The ratio of the minimum and maximum gravi...

Match the following． .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th...

The length of a metal bar is 20 cm and the ares of cross-section is $4 \times 10^{-4} \mathrm{~m}^2$. If one end of the rod is kept in ice at $0^{\circ} \mathrm{C}$ and the other end is kept in steamat $100^{\circ} \mathrm{C}$, the mass of ...

The work done by an ideal gas of 2 moles in increasins its volume from $V$ to 2 V at constant temperature $T$ is V . The work done by an ideal gas of 4 moles in increasits its wolume from $V$ to $8 V$ at constant temperature $\frac{T}{2}$ i...

When 403 of heat is absorbed by a monoatomic gas the increase in the internal energy of the gas is

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

The molar specific heat capacity of a diatomic gas at constant pressure is $C$. The molar specific heat capadtr of a monoatomic gas at constant volume is

Two masses $m_1$ and $m_2$ are connected by a light string passing over smooth pulley. When set free $m_1$ moves downwards by 3 m in 3 s . The ratio of $\frac{m_l}{m_2}$ is $\left(g=10 \mathrm{~ms}^{-2}\right)$

Three blocks of masses $2 \mathrm{~m}, 4 \mathrm{~m}$ and 6 m are placed as shown in figure. If $\sin 37^{\circ}=\frac{3}{5}, \sin 53^{\circ}=\frac{4}{5}$, the acceleration of the system is

A magnet suspended in a uniform magnetic field is heated, so as to reduce its magnetic moment by $19 \%$. By doing this, the time period of the magnet approximately

Object is projected such that it has to attain maximum range. Another body is projected to reach maximum heigh. If both the objects reached the same maximum height, then the ratio of initial velocities

second after projection，a projectile is travelling in a direction inclined at $45^{\circ}$ to horizontal．After two more seconds，it is travelling horizontally．Then，the magnitude of velocity of the projectile is $\left(g=10 \mathrm{~ms}^{-2}\...

Ball is projected at an angle of $45^{\circ}$ with the horizontal．It passes through a wall of height $h$ at a horizontal distance $d_1$ from the point of profection and strikes the ground at a distance $d_1+d_2$ from the point of projection...

A current carrying coil experiences a torque due to a magnetic field. The value of the torque is $80 \%$ of the maximum possible torque. The angle between the magnetic field and the normal to the plane of the coil is