AP EAPCET 2023 - 15th May Evening Shift

Assertion (A) The difference of the slopes of the lines represented by $y^2-2 x y \sec ^2 \alpha+\left(3+\tan ^2 \alpha\right)$ $\left(-1+\tan ^2 \alpha\right) x^2=0$ is 4
Reason (R) The difference of the slopes represented by $a x^2+2 h x ...

The lines $p\left(p^2+1\right) x-y+q=0$ and
$\left(p^2+1\right)^2 x+\left(p^2+1\right) y+2 q=0$ are perpendicular to a line $L$ for

If $2 x^2-3 x y+y^2=0$ represents two sides of a triangle and $x+y-1=0$ is its third side, then the distance between the orthocentre and the circumcentre of that triangle is

If a line is moving between the coordinate axes such that the sum of the intercepts made by it on the coordinate axes is always 12, then the equation of that line which forms a triangle of maximum area with the coordinate axes is

Let $P=(-1,0), Q=(0,0)$ and $R=(3,3 \sqrt{3})$ be three Points. Then, the equation of the bisector of the $\angle P Q R$ is

The diagonals $A C$ and $B D$ of a rhombus $A B C D$ intersect at the point $(3,4)$. If $B D=2 \sqrt{2}, A=(1,2), B=(\alpha, \beta)$, $C(5,6), D=(\gamma, \delta)$ and $\alpha<\delta<\gamma<\beta$, then $\beta+\gamma-\delta=$

Let $A B C D$ be a tetrahedron in which the coordinates of each of its vertices are in arithmetic progression with same common difference. If the centroid $G$ of the tetrahedron is $(2,3, k)$, then the distance of $G$ from the origin is

If $S$ is the set of all real values of ' $a$ ' such that a plane passing through the points $\left(-a^2, 1,1\right),\left(1,-a^2, 1\right)$ and $\left(1,1,-a^2\right)$ also passes through the point $(-1,-1,1)$, then $S=$

The distance of a point $\mathbf{a}$ from the plane $\mathbf{r} \cdot \mathbf{m}=q$ is given by $\frac{|\mathbf{a} \cdot \mathbf{m}-9|}{|\mathbf{m}|}$. If the distance of the point $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ fr...

If $A(3,-1,11), B(0,2,3)$ and $C(4,8,11)$ are three points, then the coordinates of the foot of the perpendicular drawn from the point $A$ to the line joining the points $B$ and $C$ is

If $\cot x \cot y=a$ and $x+y=\frac{\pi}{6}$, then the quadratic equation satisfying $\cot x$ and $\cot y$ is

If $\cos h x=\frac{5}{4}$, then $\tan h 3 x=$

The range of $\frac{1}{\sin ^2 x+3 \sin x \cos x+5 \cos ^2 x}$ is

If $\tan A+\tan B=x$ and $\cot A+\cot B=y$, then $\tan (A+B)=$

\(\frac{1}{\cos 290^{\circ}}+\frac{1}{\sqrt{3} \sin 250^{\circ}}=\)

$$ \begin{aligned} & \text { If }\left[1-\cos \left(\frac{\pi}{2}+\alpha\right)+\sin \left(\frac{3 \pi}{2}+\alpha\right)\right]^2 +\left[1-\sin \left(\frac{3 \pi}{2}-\alpha\right)-\cos \left(\frac{3 \pi}{2}+\alpha\right)\right]^2 \\ & =a+b ...

Let $(\mathbf{a}, \mathbf{b})$ denote the angle between vectors $\mathbf{a}$ and $\mathbf{b}$. If $\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}, \mathbf{a} \cdot \mathbf{b}=4$ and $(\mathbf{a}, \mathbf{b})=\cos ^{-1}\...

If $7 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ is the position vector of the vertex $A$ of a tetrahedron $A B C D$ and $-\hat{\mathbf{i}}+4 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ is the position vector of the centroid of the $\...

Let $\mathbf{O A}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{O B}=-2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$ be the position vectors of two points $A$ and $B$. If $C$ is a point on the bisector $\an...

If $\mathbf{a}$ and $\mathbf{b}$ are two vectors such that $|\mathbf{a}|=|\mathbf{b}|=\sqrt{14}$ and $\mathbf{a} \cdot \mathbf{b}=-7$, then $\frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{a} \cdot \mathbf{b}|}=$

An inductor and a resistor are connected in series to an AC source. If the power factor of the circuit is 0.5 , the ratio of the resistance of the resistor and the reactance of the inductor is

The centripetal acceleration $a$ of an electron in an orbit of hydrogen and the principal quantum number $n$ of the orbit are related by

The radius of the nucleus of an atom whose mass number is 125 is

Two capacitors of capacity $4 \mu \mathrm{~F}$ and $6 \mu \mathrm{~F}$ are connected in series to a 500 V battery. The potential difference across $4 \mu \mathrm{~F}$ capacitor is

Two particles of masses 5 g and 3 g are separated by a distance of 40 cm . The centre of mass of the system of these two particles

A block of mass $m$ and charge $q$ is connected to a point owith an inextensible string. This system is on a horizontal table. An electric field $E$ is applied perpendicular to the string and in the plane of the horizontal table. The tensio...

Bandwidth of an optical fibre is

The drift velocity of electrons in a conducting wire connected to a cell is $v_d$. If the length of the wire is doubled and area of cross-section is halved, then the drift velocity of electrons becomes

In the given circuit, if the current flowing through $5 \Omega$ resistor is 0.5 A , then the value of $E$ is

The de-Broglie wavelength of the most energetic photoelectrons emitted from a photosensitive metal of work function $\phi$, when light frequency $v$ incidents on it is $\lambda$. Then, $v=$

A spherical ball of volume $2000 \mathrm{~cm}^3$ is subjected to a hydraulic pressure of 15 atm . If the change in volume is $5 \times 10^{-2} \mathrm{~cm}^3$, the bulk modulus of the material of the spherical ball is
$$ \left(1 \mathrm{~at...

The Lenz's law is associated with

The relation between permittivity of free space, the permeability of free space and speed of light is

The device used to detect infrared radiations is

The net electric flux due to a uniform electric field of $3 \times 10^3 \hat{\mathrm{i}} \mathrm{NC}^{-1}$ through a cube of side 20 cm oriented such that its faces are parallel to the coordinate planes is

The gauge pressure at a depth of 50 m in a sea is (Density of sea water is $1025 \mathrm{~kg} \mathrm{~m}^{-3}$ and $g=10 \mathrm{~ms}^{-2}$ )

The orbital velocity of a body near the surface of a planet $A$ is equal to escape velocity of a body from the planet $B$. If the masses of planets $A$ and $B$ are same, the ratio of their radii is

The emissivity of a perfect black body is increased to 16 times by increasing its temperature. If the initial temperature is $T$, then final temperature of that black body is

The number of rotational degrees of freedom of a monatomic molecule is

The temperature of the sink of a Carnot's engine is 300 K and the efficiency of the engine is 0.25 . If the temperature of the source of the engine is increased by 100 K , the efficiency of the engine increased by

The specific heat capacity of a monatomic gas at constant volume is $x \%$ of its specific heat capacity at constant pressure. Then, $x=$

A monatomic gas of volume $V$ and pressure $p$ expands isothermally to a volume $27 V$ and then compressed adiabatically to a volume $V$. The final pressure of the gas is

A block of mass 5 kg moving on a rough surface with a velocity of $4 \mathrm{~ms}^{-1}$ is stopped by the friction in 2 seconds. Then, the coefficient of friction between the contact surfaces is
(Acceleration due to gravity $=10 \mathrm{~ms...

The following is not the method of reducing friction

Among the following the unit of permeability is NOT represented by

One of the following substances having the tendency to move from stronger region to the weaker region of the magnetic field is

A truck moving with a constant velocity $12 \mathrm{~ms}^{-1}$ crosses a car moving from rest with uniform acceleration $2 \mathrm{~ms}^{-2}$. The distance the car has to travel from the starting point to cross the truck again is

The magnetic force $q[\mathbf{v} \times \mathbf{B}]$ is

The magnifying power of a telescope with tube length 60 cm is 5 . Then, the focal length of its eye piece is

The angular speed of a rigid body rotating about a fixed axis is $(8-2 t) \mathrm{rad} \mathrm{s}^{-1}$. The angle through which the body rotates before it comes to rest is