AP EAPCET 2025 - 24th May Morning Shift

The number of solutions of the equation $\sqrt{3 x^2+x+5}=x-3$ is

The set of all real values of $x$ for which $\frac{x^2-1}{(x-4)(x-3)} \geq 1$ is

The mean deviation about the mean for the following data is
$$ \begin{array}{llllll} \hline \text { Class Interval } & 0-2 & 2-4 & 4-6 & 6-8 & 8-10 \\ \hline \text { Frequency } & 1 & 3 & 4 & 1 & 2 \\ \hline \end{array} $$

The point $P(4,1)$ undergoes the following transformations in succession :
(i) origin is shifted to the point $(1,6)$ by translation of axes.
(ii) translation through a distance of 2 units along the positive direction of $X$-axis.
(iii) rot...

If the pair of lines $a x^2-7 x y-3 y^2=0$ and $2 x^2+x y-6 y^2=0$ have exactly one line in common and ' $a$ ' is an integer, then the equation of the pair of bisectors of the angles between the lines $a x^2-7 x y-3 y^2=0$ is

If the angle between the pair of lines $2 x^2+2 h x y+2 y^2-x+y-1=0$ is $\tan ^{-1}\left(\frac{3}{4}\right)$ and $h$ is a positive rational number, then the point of intersection of these two lines is

If $(h, k)$ is the image of the point $(2,-3)$ with respect to the line $5 x-3 y=2$, then $h+k=$

$L_1 \equiv a x-3 y+5=0$ and $L_2 \equiv 4 x-6 y+8=0$ are two parallel lines. If $p, q$ are the intercepts made by $L_1=0$ and $m, n$ are the intercepts made by $L_2=0$ on the $X$, $Y$-coordinate axes respectively, then the equation of the ...

If $A(1,2,3), B(2,3,-1), C(3,-1,-2)$ are the vertices of a $\triangle A B C$, then the direction ratios of the bisector of $\angle A B C$ are

The locus of a point at which the line joining the points $(-3,1,2),(1,-2,4)$ subtends a right angle, is

Let $A=(2,0,-1), B=(1,-2,0), C=(1,2,-1)$ and $D=(0,-1,-2)$ be four points.
If $\theta$ is the acute angle between the plane determined by $A, B, C$ and the plane determined by $A, C, D$, then $\tan \theta=$

Assertion (A) For the lines $\mathbf{r}=\mathbf{a}+t \mathbf{b}$ and $\mathbf{r}=\mathbf{p}+s \mathbf{q}$, if $(\mathbf{a}-\mathbf{p}) \cdot(\mathbf{b} \times \mathbf{q}) \neq 0$, then the two lines are coplanar.
Reason $(\mathrm{R})|(\math...

\(\tan \frac{2 \pi}{7} \cdot \tan \frac{4 \pi}{7}+\tan \frac{4 \pi}{7} \cdot \tan \frac{\pi}{7}+\tan \frac{\pi}{7} \cdot \tan \frac{2 \pi}{7}=\)

The sum of the solutions of $\cos x \sqrt{16 \sin ^2 x}=1$ in $(0,2 \pi)$ is

\(\sin \frac{\pi}{5}+\sin \frac{2 \pi}{5}+\sin \frac{3 \pi}{5}+\sin \frac{4 \pi}{5}=\)

\(\cos 13^{\circ} \sin 17^{\circ} \sin 21^{\circ} \cos 47^{\circ}=\)

In a right angled triangle, if the position vector of the vertex having the right angle is $-3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and the position vector of the mid-point of its hypotenuse is $6 \hat{\mathbf{i}}+2 \hat{...

If the position vectors of the vertices $A, B, C$ of a triangle are $3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 5(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})$ respec...

Let $\mathbf{a}=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}$ and $\mathbf{b}$ be two perpendicular vectors in the $X O Y$-plane. A vector $\mathbf{c}$ in the same plane and having projections 1 and 2 respectively on $\mathbf{a}$ and $\mathbf{b}$ ...

If the vectors $2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-3 \hat{\mathbf{k}},-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $p \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ are coplanar, then the unit vector in the directi...

If the voltage and current in an AC circuit are respectively $50 \sin (50 t) \mathrm{V}$ and $50 \sin \left(50 t+\frac{\pi}{4}\right) \mathrm{mA}$, then the power dissipated in the circuit is nearly

The half life of a radioactive substance is 10 minutes. If $n_1$ and $n_2$ are the number of atoms decayed in 20 and 30 minutes respectively, then $n_1: n_2=$

The ratio of energies of photons produced due to transition of an electron in hydrogen atom from second energy level to first energy level and fifth energy level to second energy level is

A parallel plate capacitor has plates of area $0.4 \pi \mathrm{~m}^2$ and spacing of 0.5 mm . If a slab of thickness 0.5 mm and dielectric constant 4.5 is introduced in between the plates of the capacitor, then the capacitance of the capaci...

The energy stored in a capacitor of capacitance $10 \mu \mathrm{~F}$ when charged to a potential of 6 kV is

In the given circuit, the potential difference across the plates of the capacitor $C$ in steady state is

A disc of mass 0.2 kg is kept floating in air without falling by vertically firing bullets each of mass 0.05 kg on the disc at the rate of 10 bullets per every second. If the bullets rebound with the same speed, then the speed of each bulle...

A body moving along a straight line collides another body of same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is 0.5 , then the ratio of the velocit...

If the ratio of the maximum and minimum amplitudes of an amplitude modulated wave is $7: 3$, then the modulation index is

The potential difference across a conducting wire of length 20 cm is 30 V . If the electron mobility is $2 \times 10^{-6} \mathrm{~m}^2 \mathrm{~V}^{-1} \mathrm{~s}^{-1}$, then the drift velocity of the electrons is

A maximum current of 0.5 mA can pass through a galvanometer of resistance $15 \Omega$. The resistance to be connected in series to the galvanometer to convert it into a voltmeter of range $0-10 \mathrm{~V}$ is

A laser produces a beam of light of frequency $5 \times 10^{14}$ Hz with an output power of 33 mW . The average number of photons emitted by the laser per second is (Planck's constant $=6.6 \times 10^{-34} \mathrm{Js}$ )

A wire is stretched 1 mm by a force $F$. If a second wire of same material, same length and 4 times the diameter of the first wire is stretched by the same force $F$, then the elongation of the second wire is

A wire of length 0.5 m and area of cross-section $4 \times 10^{-6} \mathrm{~m}^2$ at a temperature of $100^{\circ} \mathrm{C}$ is suspended vertically by fixing its upper end to the ceiling. The wire is then cooled to $0^{\circ} \mathrm{C}$...

A coil of resistance $200 \Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (in weber) linked with the coil varies with time ' $t$ ' (in second) as per the equation $\phi=50 t^2+4$, then the current induced in the coil at a...

The oscillating electric and magnetic field vectors of an electromagnetic wave are along

The sum of two point positive charges separated by a distance of 1.5 m in air is $25 \mu \mathrm{C}$. If the electrostatic force between the two charges is 0.6 N , then the difference between the two charges is

In a water tank, an air bubble rises from the bottom to the top surface of the water. If the depth of the water in the tank is 7.28 m and atmospheric pressure is 10 m of water, then the ratio of the radii of the bubble at the bottom of the ...

The time period of a simple pendulum on the surface of the Earth is $T$. If the pendulum is taken to a height equal to half of the radius of the Earth, then its time period is

If the escape velocity of a body from the surface of the Earth is $11.2 \mathrm{~km} \mathrm{~s}^{-1}$, then the orbital velocity of a satellite in an orbit which is at a height equal to the radius of the Earth is

In a container of volume $16.62 \mathrm{~m}^3$ at $0{ }^{\circ} \mathrm{C}$ temperature, 2 moles of oxygen 5 moles of nitrogen and 3 moles of hydrogen are present, then the pressure in the container is
(Universal gas constant $=8.31 \mathrm...

The temperature of water of mass 100 g is rasied from $24^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$ by adding steam to it. The mass of the steam added is
(Latent heat of steam $=540 \mathrm{cal} \mathrm{g}^{-1}$ and specific heat capac...

When 80 J of heat is supplied to a gas at constant pressure, if the work done by the gas is 20 J , then the ratio of the specific heat capacities of the gas is

A refrigerator of coefficient of performance 5 that extracts heat from the cooling compartment at the rate of 250 J per cycle is placed in a room. The heat released per cycle to the room by the refrigerator is

Two bodies $A$ and $B$ of masses 1.5 kg and 3 kg are moving with velocities $20 \mathrm{~ms}^{-1}$ and $15 \mathrm{~ms}^{-1}$ respectively. If the same retarding force is applied on the two bodies, then the ratio of the distances travelled ...

A sample of paramagnetic salt contains $2 \times 10^{24}$ atomic dipoles each of dipole moment $15 \times 10^{-23} \mathrm{JT}^{-1}$. The sample is placed under homogeneous magnetic field of 0.6 T and cooled to a temperature 4.2 K . The deg...

If the range of a body projected with a velocity of $60 \mathrm{~ms}^{-1}$ is $180 \sqrt{3} \mathrm{~m}$, then the angle of projection of the body is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

If the height of a projectile at a time of 2 s from the beginning of motion is 60 m , then the time of flight of the projectile is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A body starts from rest with uniform acceleration and its velocity at a time of ' $n$ ' seconds is ' $v$ '. The total displacement of the body in the $n$th and $(n-1)$ th seconds of its motion is

Two charged particles of specific charges in the ratio 2:1 and masses in the ratio $1: 4$ moving with same kinetic energy enter a uniform magnetic field at right angles to the direction of the field. The ratio of the radii of the circular p...