AP EAPCET 2025 - 22nd May Evening Shift

If $A(1,0), B(0,-2)$ and $C(2,-1)$ are three fixed points, then the equation of the locus of a point $P$ such that area of $\triangle P A B$ is equal to area of $\triangle P A C$ is

The transformed equation of $3 x^2-4 x y=r^2$ when the coordinate axes are rotated about the origin through an angle of $\tan ^{-1}(2)$ in positive direction is

A line $L_1$ passing through the point of intersection of the lines $x-2 y+3=0$ and $2 x-y=0$ is parallel to the line $L_2$. If $L_2$ passes through origin and also through the point of intersection of the lines $3 x-y+2=0$ and $x-3 y-2=0$,...

If the lines $x+y-2=0,3 x-4 y+1=0$ and $5 x+k y-7=0$ are concurrent at $(\alpha, \beta)$, then equation of the line concurrent with the given lines and perpendicular to $k x+y-k=0$ is

If two sides of a triangle are represented by $3 x^2-5 x y+2 y^2=0$ and its orthocentre is $(2,1)$, then the equation of the third side is

If $a x^2+2 h x y-2 a y^2+3 x+15 y-9=0$ represents a pair of lines intersecting at $(1,1)$, then $a h=$

If $Q(\alpha, \beta, \gamma)$ is the harmonic conjugate of the point $P(0,-7,1)$ with respect to the line segment joining the points $(2,-5,3)$ and $(-1,-8,0)$, then $\alpha-\beta+\gamma=$

On a line with direction cosines $l, m, n, A\left(x_1, y_1, z_1\right)$ is a fixed point. If $B=\left(x_1+4 k l, y_1+4 k m, z_1+4 k n\right)$ and $C=\left(x_1+k l, y_1+k m, z_1+k n\right)(k>0)$, then the ratio in which the point $B$ divides...

If the line of intersection of the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$ makes an angle $\alpha$ with the positive $X$-axis, then $\cos \alpha=$

For a positive real number $p$, if the perpendicular distance from a point $-\hat{\mathbf{i}}+p \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ to the plane $\mathbf{r} \cdot(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}})=7$ is 6 units, the...

If $2 \sin x-\cos 2 x=1$, then $\left(3-2 \sin ^2 x\right)=$

If $x \neq(2 n+1) \frac{\pi}{4}$, then the general solutions of $\cos x+\cos 3 x=\sin x+\sin 3 x$ is

If $\alpha, \beta$ are the acute angles such that $\frac{\sin \alpha}{\sin \beta}=\frac{6}{5}$ and $\frac{\cos \alpha}{\cos \beta}=\frac{9}{5 \sqrt{5}}$, then $\sin \alpha=$

If $\left(\frac{\sin 3 \theta}{\sin \theta}\right)^2-\left(\frac{\cos 3 \theta}{\cos \theta}\right)^2=a \cos b \theta$, then $a: b=$

An aeroplane is flying at a constant speed, parallel to the horizontal ground at a height of 5 kms . A person on the ground observed that the angle of elevation of the plane is changed from $15^{\circ}$ to $30^{\circ}$ in the duration of 50...

The points in the argand plane represented by the complex numbers $4 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, 6 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}-\hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ ...

If the vector $\hat{\mathbf{i}}-7 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ is along the internal bisector of the angle between the vectors $\mathbf{a}$ and $-2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and the unit vector along $\ma...

If $\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+6 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{c}=3 \hat{\mathbf{j}}-\hat{\mathbf{k}}$, then $\mathbf{a} \times \mathbf{b} \times \mathbf{b...

Let $\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}$ be two vectors. If $\mathbf{c}^{\text {is }}$ vector such that $\mathbf{a} \cdot \mathbf{c}=|\mathbf{c}|,|\mathbf{c}-...

\((\mathbf{a}+2 \mathbf{b}-\mathbf{c}) \cdot(\mathbf{a}-\mathbf{b}) \times(\mathbf{a}-\mathbf{b}-\mathbf{c})=\)

A resistor of $450 \Omega$ and an inductor are connected in series to an AC source of frequency $\frac{75}{\pi} \mathrm{~Hz}$. If the power factor of the circuit is 0.6 , then the inductance connected in the circuit is

The ratio of the wavelengths of the first Lyman line and the second Balmer line of hydrogen atom is

Each nuclear fission of ${ }^{235} \mathrm{U}$ releases 200 MeV of energy. If a reactor generates 1 MW power, then the rate of fission in the reactor is

Three blocks $A, B$ and $C$ are arranged as shown in the figure such that the distance between two successive blocks is 10 m . Block $A$ is displaced towards block $B$ by 2 m and block $C$ is displaced towards block $B$ by 3 m . The distanc...

For transmitting a signal of frequency 1000 kHz , the minimum length of the antenna is

The length and area of cross-section of a copper wire are respectively 30 m and $6 \times 10^{-7} \mathrm{~m}^2$. If the resistivity of copper is $1.7 \times 10^{-8} \Omega \mathrm{~m}$, then the resistance of the wire is

If current of 80 A is passing through a straight conductor of length 10 m , then the total momentum of electrons in the conductor is
(mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$ and charge of electron $=1.6 \times 10^{-19} \mathrm{...

If the threshold wavelength of light for photoelectric emission to take place from a metal surface is $6250 \mathop {\rm{A}}\limits^{\rm{o}}$, then the work function of the metal is (Planck's constant $=6.6 \times 10^{-34} \mathrm{Js}$ )

When a wire made of material with Young's modulus $\gamma$ is subjected to a stress $S$, the elastic potential energy per unit volume stored in the wire is

A metallic disc of radius 0.3 m is rotating with a constant angular speed of $60 \mathrm{rad} \mathrm{s}^{-1}$ in a plane perpendicular to a uniform magnetic field of $5 \times 10^{-2} \mathrm{~T}$. The emf induced between a point on the ri...

If the rms value of the electric field of electromagnetic waves at a distance of 3 m from a point source is $3 \mathrm{NC}^{-1}$, then the power of the source is

Two charged conducting spheres of radii 5 cm and 10 cm have equal surface charge densities. If the electric field on the surface of the smaller sphere is $E$, then the electric field on the surface of the larger sphere is

As shown in the figure, the work done to move the charge ' $Q$ ' from point $C$ to point $D$ along the semicircle CRD is

As shown in the figure, if the values of the electric potential at three points $A, B$ and $C$ in a uniform electric field (E) are $V_A, V_B$ and $V_C$ respectively, then

An aeroplane of mass $4.5 \times 10^4 \mathrm{~kg}$ and total wing area of $600 \mathrm{~m}^2$ is travelling at a constant height. The pressure difference between the upper and lower surfaces of its wings is (Acceleration due to gravity $=1...

Two satellites $A$ and $B$ are revolving around the Earth in orbits of heights $1.25 R_E$ and $19.25 R_E$ from the surface of Earth respectively, where $R_E$ is the radius of the Earth. The ratio of the orbital speeds of the satellites $A$ ...

If the wavelengths of maximum intensity of radiation emitted by two black bodies $A$ and $B$ are $0.5 \mu \mathrm{~m}$ and 0.1 mm respectively, then ratio of the temperatures of the bodies $A$ and $B$ is

Water of mass 5 kg in a closed vessel is at a temperature of $20^{\circ} \mathrm{C}$. If the temperature of the water when heated for a time of 10 minutes becomes $30^{\circ} \mathrm{C}$, then the increase in the internal energy of the wate...

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat utilised to increase the internal energy of the gas is

If the degrees of freedom of a gas molecule is 6 , then the total internal energy of the gas molecule at a temperature of $47^{\circ} \mathrm{C}$ (in eV ) is
(Boltzmann constant $=1.38 \times 10^{-23} \mathrm{JK}^{-1}$ )

A Carnot engine $A$ working between temperatures 600 K and $T(<600 \mathrm{~K})$ and another Carnot engine $B$ working between temperatures $T(>400 \mathrm{~K})$ and 400 K are connected in series. If the work done by both the engines is sam...

A balloon with mass ' $m$ ' is descending vertically with an acceleration ' $a$ ' (where $a

A conveyor belt is moving horizontally with a velocity of $2 \mathrm{~ms}^{-1}$. If a body of mass 10 kg is kept on it, then the distance travelled by the body before coming to rest is
(The coefficient of kinetic friction between the belt a...

A short bar magnet of magnetic moment $10^4 \mathrm{JT}^{-1}$ is free to rotate in a horizontal plane. The work done in rotating the magnet slowly from the direction parallel to a horizontal magnetic field of $4 \times 10^{-5} \mathrm{~T}$ ...

The height of ceiling in an auditorium is 30 m . A ball is thrown with a speed of $30 \mathrm{~ms}^{-1}$ from the entrance such that it just moves very near to the ceiling without touching it and then it reaches the ground at the end of the...

In a wire of radius 1 mm a steady current of 2 A uniformly distributed across the cross-section of the wire is flowing. Then the magnetic field at a point 0.25 mm from the centre of the wire is

The magnetic field at the centre of a current carrying circular coil of radius $R$ is $B_c$ and the magnetic field at a point on its axis at a distance $R$ from its centre is $B_a$. The value of $\frac{B_c}{B_a}$ is

Images of same size are formed by a convex lens when an object is placed either at 20 cm or 10 cm distance from the lens. The focal length of the lens is

A solid sphere of mass 4 kg and radius 28 cm is on an inclined plane. If the acceleration of the sphere when it rolls down without sliding is $3.5 \mathrm{~ms}^{-2}$, then the acceleration of the sphere when it slides down without rolling i...

The device used for voltage regulation is