TG EAPCET 2025 (Online) 2nd May Morning Shift

If the points $A(2,3), B(3,2)$ form a triangle with a variable point $p\left(t, t^2\right)$, where $t$ is a parameter, then the equation of the locus of the centroid of $\triangle A B C$ is

If $(h, k)$ is the new origin to be chosen to eliminate first degree terms from the equation $S \equiv 2 x^2-x y-y^2-3 x+3 y=0$ by translation and if $\theta$ is the angle with which the axes are to be rotated about the origin in anti-clock...

A line $L$ perpendicular to the line $5 x-12 y+6=0$ makes positive intercept on the $Y$-axis. If the distance from the origin to the line $L$ is 2 units and the angle made by the perpendicular drawn from the origin to the line $L$ with posi...

If a line $L$ passing through a point $A(2,3)$ intersects another line $4 x-3 y-19=0$ at the point $B$ such that $A B=4$, then the angle made by the line $L$ with positive $X$-axis in anti-clockwise direction is

A variable straight-line $L$ with negative slope passes through the point $(4,9)$ and cuts the positive coordinate axes in $A$ and $B$. If $O$ is the origin, then the minimum value of $O A+O B$ is

If $4 x^2+12 x y+9 y^2+2 g x+2 f y-1=0$ represent a pair of parallel lines, then

The shortest distance between the lines
$$ \begin{aligned} & \mathbf{r}=(3 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})+t(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}) \text { and } \\ & \mathbf{r}=(\hat{\mathbf{i}}+2 \...

If $A(0,3,4), B(1,5,6), C(-2,0,-2)$ are the vertices of a $\triangle A B C$ and the bisector of angle $A$ meets the side $B C$ at $D$, then $A D=$

If the direction cosines of two lines satisfy the equation $2 l+m-n=0, l^2-2 m^2+n^2=0$ and $\theta$ is the angle between the lines, then $\cos \theta=$

If the equation of the plane passing through the points $(2,1,2),(1,2,1)$ and perpendicular to the plane $2 x-y+2 z=1$ is $a x+b y+c z+d=0$, then $\frac{a+b}{c+d}=$

$\alpha, \beta$ are the roots of the equation $\sin ^2 x+b \sin x+c=0$. If $\alpha+\beta=\frac{\pi}{2}$, then $b^2-1=$

The general solution of the equation $\sqrt{6-5 \cos x+7 \sin ^2 x}-\cos x=0$ also satisfies the equation

If $\sin A=-\frac{60}{61}, \cot B=-\frac{40}{9}$ and neither $A$ and $B$ is in 4th quadrant, then $6 \cot A+4 \sec B=$

The period of the function $f(x)=\frac{2 \sin \left(\frac{\pi x}{3}\right) \cos \left(\frac{2 \pi x}{5}\right)}{3 \tan \left(\frac{7 \pi x}{2}\right)-5 \sec \left(\frac{5 \pi x}{3}\right)}$ is

If $A+B+C=4 S$, then $\sin (2 S-A)$
\(+\sin (2 S-B)+\sin (2 S-C)-\sin 2 S=\)

If $1^{\circ}=0.0175$ radians, then the approximate value of $\sec 58^{\circ}$ is

The position vectors of two points $A$ and $B$ are $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $7 \hat{\mathbf{i}}-\hat{\mathbf{k}}$ respectively. The point $P$ with position vector $-2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5...

The point of intersection of the line joining the points $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and the plane passing through the points $\hat{\mathbf{i}}, 2 \hat{\mathbf...

If $\mathbf{a}$ and $\mathbf{b}$ are two vectors such that $|\mathbf{a}|=5,|\mathbf{b}|=12$ and $|\mathbf{a}-\mathbf{b}|=13$, then $|2 \mathbf{a}+\mathbf{b}|=$

If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ are two vectors, then $(\mathbf{a}+2 \mathbf{b}) \times(3 \mathbf{a}-\mathbf{b})$

The frequency of an alternating voltage is 50 Hz . The time taken for instantaneous voltage to increase from zero to half of its peak voltage is

If the difference in the frequencies of the first and second lines of Lyman series of hydrogen atom is $f$, then the difference in frequencies of the first and second lines of Balmer series of hydrogen atom is

The average energy of a neutron produced in the fission of ${ }_{92}^{235} \mathrm{U}$ is

If $96.875 \%$ of a radioactive substance decays in 10 days, then the half life of the substance is (in days)

As shown in the figure, a dielectric of constant $K$ is placed between the plates of a parallel plate capacitor and is charged to a potential $V$ using a battery. If the dielectric is pulled out after disconnecting the battery from the capa...

Two blocks of masses in the ratio $m: n$ are connected by a light inextensible string passing over a frictionless fixed pulley. If the system of the blocks is released from rest, then the acceleration of the centre of mass of the system of ...

A particle is acted upon by a force of constant magnitude such that its velocity and acceleration are always perpendicular to each other, then its

For commercial telephonic communication, the frequency range adequate for speech signals is

The drift speed of electrons in a material is found to be $0.3 \mathrm{~ms}^{-1}$ when an electric field of $2 \mathrm{Vm}^{-1}$ is applied across it. The electron mobility (in $\mathrm{m}^2 \mathrm{~V}^{-1} \mathrm{~s}^{-1}$ ) in the mater...

The power of an electric motor is 242 W when connected to a 220 V supply. When the motor is operated at 200 V , the current drawn by it is

Photons of energy 4.5 eV are incident on a photosensitive material of work function 3 eV . The de-Broglie wavelength associated with the photoelectrons emitted with maximum kinetic energy is nearly

If a brass sphere of radius 36 cm is submerged in a lake at a depth where the pressure is $10^7 \mathrm{~Pa}$, then the change in the radius of the sphere is
(Bulk modulus of brass $=60 \mathrm{GPa}$ )

The plane of a circular coil of resistance $7.5 \Omega$ is placed perpendicular to a uniform magnetic field. The flux $\phi$ (in weber) through the coil varies with time $t$ (in second) as $\phi=2 t^2+3 t-2$. The induced power in the coil a...

The dielectric constant of a medium is 8 and its relative permeability is 200 . If an electromagnetic wave of frequency 100 MHz travels in this medium, then its wavelength is

For any fixed distance, the electromagnetic force between two protons is $10^n$ times of the gravitational force between them. Then, $n=$

A thin spherical shell of radius $R$ and surface charge density $\sigma$ is placed in a cube of side $5 R$ with their centers coinciding. The electric flux through one face of the cube is $\left(\varepsilon_0=\right.$ Permittivity of free s...

The work done in blowing a soap bubble of diameter 3 cm is (surface tension of soap solution $=0.035 \mathrm{Nm}^{-1}$ )

If the terminal velocity of a metal sphere of mass 8 g falling through a liquid is $3 \mathrm{cms}^{-1}$, then the terminal velocity of another sphere of mass 64 g made of the same metal falling through same liquid is

If a body is projected vertically from the surface of the Earth with a speed of $8000 \mathrm{~ms}^{-1}$, then the maximum height reached by the body is
(Radius of the Earth $=6400 \mathrm{~km}$ and acceleration due to gravity $=10 \mathrm{...

The length of a metal rod is 20 cm and its area of cross-section is $4 \mathrm{~cm}^2$. If one end of the rod is kept at a temperature of $100^{\circ} \mathrm{C}$ and the other end is kept in ice at $0^{\circ} \mathrm{C}$, then the mass of ...

The heat required to convert 8 g of ice at a temperature of $-20^{\circ} \mathrm{C}$ to steam at $100^{\circ} \mathrm{C}$ is [specific heat capacity of ice $=2100 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, specific heat capacity of water $=4200 \...

Two moles of a gas at a temperature of $327^{\circ} \mathrm{C}$ expands adiabatically such that its volume increases by $700 \%$. If the ratio of the specific heat capacities of the gas is $\frac{4}{3}$, then the work done by the gas is (Un...

The molar specific heat of a monoatomic gas at constant pressure is
(Universal gas constant $=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

A man of mass 60 kg is standing in a lift moving up with a retardation of $2.8 \mathrm{~ms}^{-2}$. The apparent weight of the man is

If the magnetic susceptibility of a substance is 0.6 , then the ratio of permeability of the substance and permeability of free space is

A helicopter flying horizontally with a velocity of $288 \mathrm{~km} / \mathrm{h}$ drops a bomb. If the line joining the point of dropping the bomb and the point where bomb hits the ground makes an angle $45^{\circ}$ with the horizontal, t...

The driver of a bus moving with a velocity of $72 \mathrm{~km} / \mathrm{h}$ observes a boy walking across the road at a distance of 50 m in front of the bus and decelerates the bus at $5 \mathrm{~ms}^{-2}$ by applying brakes and is just ab...

The initial and final velocities of a body projected vertically from the ground are $20 \mathrm{~ms}^{-1}$ and $18 \mathrm{~ms}^{-1}$ respectively. The maximum height reached by the body is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2...

A proton and an alpha particle moving with equal speeds enter normally into a uniform magnetic field. The ratio of times taken by the proton and the alpha particle to make one complete revolution in the magnetic field is

A solenoid of length 50 cm and radius 10 cm has two closely wound layers of windings 100 turns each. If a current of 2.5 A is passing through the windings, the magnetic field (in $10^{-4} \mathrm{~T}$ ) at a point 5 cm from the axis is