TG EAPCET 2025 (Online) 3rd May Morning Shift

The variance of the discrete data $3,4,5,6,7,8,10,13$ is

If a possion variate $X$ satisfies the relation $P(X=3)=P(X=5)$, then $P(X=4)=$

If $2 x^2+x y-6 y^2+k=0$ is the transformed equation of $2 x^2+x y-6 y^2-13 x+9 y+15=0$ when the origin is shifted to the point $(a, b)$ by translation of axes, then $k=$

If $\tan ^{-1}(2 \sqrt{10})$ is the angle between the lines $a x^2+4 x y-2 y^2=0$ and $a \in Z$, then the product of the slopes of given lines is

The line $L \equiv 6 x+3 y+k=0$ divides the line segment joining the points $(3,5)$ and $(4,6)$ in the ratio $-5: 4$. If the point of intersection of the lines $L=0$ and $x-y+1=0$ is $P(g, h)$, then $h=$

The lines $x-2 y+1=0,2 x-3 y-1=0$ and $3 x-y+k=0$ are concurrent. The angle between the lines $3 x-y+k=0$ and $m x-3 y+6=0$ is $45^{\circ}$. If $m$ is an integer, then $m-k=$

A straight line through the point $P(1,2)$ makes an angle $\theta$ with positive X -axis in anticlockwise direction and meets the line $x+\sqrt{3 y}-2 \sqrt{3}=0$ at $Q$. If $P Q=\frac{1}{2}$, then $\theta=$

Let $\pi_1$ be the plane determined by the vectors $\hat{\mathbf{i}}+\hat{\mathbf{j}}$. $\hat{\mathbf{i}}+\hat{\mathbf{k}}$ and $\pi_2$ be the plane determined by the vectors $\hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{k}}-\hat{\mathbf...

If $A(2,1,-1), B(6,-3,2), C(-3,12,4)$ are the vertices of a $\triangle A B C$ and the equation of the plane containing the $\triangle A B C$ is $53 x+b y+c z+d=0$, then $\frac{d}{b+c}=$

If $m: n$ is the ratio in which the point $\left(\frac{8}{5},-\frac{1}{5}, \frac{8}{5}\right)$ divides the segment joining the points $(2, p, 2)$ and $(p,-2, p)$, where $p$ is an integer than $\frac{3 m+n}{3 n}=$

If $(\alpha, \beta \gamma)$ is the foot of the perpendicular drawn from a point $(-1,2,-1)$ to the line joining the points $(2,-1,1)$ and ( $1,1-2$ ), then $\alpha+\beta+\gamma=$

If $\cos \alpha+\cos \beta+\cos \gamma=0=\sin \alpha+\sin \beta+\sin \gamma$, then $\sin 2 \alpha+\sin 2 \beta+\sin 2 \gamma=$

Number of solutions of the equation $\sin ^2 \theta+2 \cos ^2 \theta-\sqrt{3} \sin \theta \cos \theta=2$ lying in the interval ( $-\pi, \pi$ ) is

If $3 \sin \theta+4 \cos \theta=3$ and $\theta \neq(2 n+1) \frac{\pi}{2}$, then $\sin 2 \theta=$

\(\frac{\cos 15^{\circ} \cos ^2 22 \frac{1^{\circ}}{2}-\sin 75^{\circ} \sin ^2 \cdot 52 \frac{1^{\circ}}{2}}{\cos ^2 15^{\circ}-\cos ^2 75^{\circ}}\)

$16 \sin 12^{\circ} \cos 18^{\circ} \sin 48^{\circ}=$

If $\mathbf{a}=(x+2 y-3) \hat{\mathbf{i}}+(2 x-y+3) \hat{\mathbf{j}}$ and $\mathbf{b}=(3 x-2 y) \hat{\mathbf{i}} +(x-y+1) \hat{\mathbf{j}}$ are two vectors such that $\mathbf{a}=2 \mathbf{b}$, then $y-5 x=$

If $\mathbf{a}=\hat{\mathbf{i}}+\sqrt{11} \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}+\sqrt{11} \hat{\mathbf{j}}-10 \hat{\mathbf{k}}$ are two vectors, then the component of $\mathbf{b}$ perpendicular to $\mathbf{a}...

Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+p \hat{\mathbf{k}}$ be two vectors.
If $(\mathbf{a}, \mathbf{b})=60^{\circ}$, then $p=$

$7 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}, \hat{\mathbf{i}}-6 \hat{\mathbf{j}}+10 \hat{\mathbf{k}},-\hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, 5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$ are the positi...

An electric bulb, an open coil inductor, an AC source and a key are all connected in series to form a closed circuit. They key is closed and after some time an iron rod is inserted into the interior of the inductor, then

The phenomenon of physics that deals with the constitution and structure of matter at the minute scales of atoms and nuclei is

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

A radioactive material of half-life 2.5 hours emits radiation that is 32 times the safe maximum level. The time (in hours) after which the material can be handled safely is

If the number of uranium nuclei required per hour to produce a power of 64 kW is $7.2 \times 10^{18}$, then the energy released per fission is

If the rate of change in electric flux between the plates of a capacitor is $9 \pi \times 10^3 \mathrm{Vms}^{-1}$, then the displacement current inside the capacitor is

A body of mass ' $m$ ' moving with a velocity of ' $v$ ' collides head on with another body of mass ' 2 m ' at rest. If the coefficient of restitution between the two bodies is ' $~ e$ ', then the ratio of the velocities of the two bodies a...

A solid cylinder of mass 2 kg , length 40 cm and radius 10 cm is placed in contact with a solid sphere of mass 0.5 kg and radius 10 cm such that the centres of the two bodies lie along the geometrical axis of the cylinder. The distance of t...

When the receiving antenna is on the ground, the range of a transmitting antenna of height 980 m is (Radius of the Earth $=6400 \mathrm{~km}$ )

The length of a potentiometer wire is 2.5 m and its resistance is $8 \Omega$. A cell of negligible internal resistance and emf of 2.5 V is connected in series with a resistance of $242 \Omega$ in the primary circuit. The potential differenc...

The potential difference between points $C$ and $D$ of the electrical circuit shown in the figure is

20 kV electrons can produce X- rays with a minimum wavelength of

A metal rod of area of cross-section $3 \mathrm{~cm}^2$ is stretched along its length by applying a force of $9 \times 10^4 \mathrm{~N}$. If the Young's modulus of the material of the rod is $2 \times 10^{11} \mathrm{Nm}^{-2}$, the energy s...

A circular coil of area $3 \times 10^{-2} \mathrm{~m}^2, 900$ turns and a resistance of $1.8 \Omega$ is placed with its plane perpendicular to a uniform magnetic field of $3.5 \times 10^{-5} \mathrm{~T}$. The current induced in the coil whe...

If a particle of mass 10 mg and charge $2 \mu \mathrm{C}$ at rest is subjected to a uniform electric field of potential difference 160 V , then the velocity acquired by the particle is

Four electric charges $2 \mu \mathrm{C}, Q, 4 \mu \mathrm{C}$ and $12 \mu \mathrm{C}$ are placed on $X$-axis at distance $x=0,1 \mathrm{~cm}, 2 \mathrm{~cm}$ and 4 cm respectively. If the net force acting on the charge at origin is zero, th...

An air bubble rises from the bottom to the top of a water tank in which the temperature of the water is uniform. The surface area of the bubble at the top of the tank is $125 \%$ more than its surface area at the bottom of the tank. If the ...

If $W_1$ is the work done in increasing the radius of a soap bubble from ' $r$ ' to ' $2 r$ ' and $W_2$ is the work done in increasing the radius of the soap bubble from ' $2 r$ ' to ' $3 r$ ', then $W_1: W_2=$

A body is projected from the Earth's surface with a speed $\sqrt{5}$ times the escape speed $\left(V_e\right)$. The speed of the body when it escapes from the gravitational influence of the Earth is

To increase the length of a metal rod by $0.4 \%$ the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $\left.=20 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right)$

The power of a refrigerator that can make 15 kg of ice at $0^{\circ} \mathrm{C}$ from water at $30^{\circ} \mathrm{C}$ in one hour is

The pressure of a mixture of 64 g of oxygen, 28 g of nitrogen and 132 g of carbon dioxide gases in a closed vessel is $p$. Under isothermal conditions if entire oxygen is removed from the vessel, the pressure of the mixture of remaining two...

Three moles of an ideal gas undergoes a cyclic process $A B C A$ as shown in the figure. The pressure, volume and absolute temperature at points $A, B$ and $C$ are respectively $\left(p_1, V_1, T_1\right),\left(p_2, 3 V_1, T_1\right)$ and $...

A force separately produces accelerations of $18 \mathrm{~ms}^{-2}$, $9 \mathrm{~ms}^{-2}$ and $6 \mathrm{~ms}^{-2}$ in three bodies of masses $P, Q$ and $R$ respectively. If the same force is applied on a body of mass $P+Q+R$, then the acc...

The magnetic field at a point $P$ on the axis of a short bar magnet of magnetic moment $M$ is $B$. If another short bar magnet of magnetic moment 2 M is placed on the first magnet such that their axes are perpendicular and their centres coi...

If a body projected with a velocity of $19.6 \mathrm{~ms}^{-1}$ reaches a maximum height of 9.8 m , then the range of the projectile is
(Neglect air resistance)

A particle initially at rest is moving along a straight line with an acceleration of $2 \mathrm{~ms}^{-2}$. At a time of 3 s after the beginning of motion, the direction of acceleration is reversed. The time from the beginning of the motion...

The magnetic field due to a current carrying circular coil on its axis at a distance of $\sqrt{2} \mathrm{~d}$ from the centre of the coil is $B$. If $d$ is the diameter of the coil, then the magnetic field at the centre of the coil is

A square coil of side 10 cm having 200 turns is placed in a uniform magnetic field of 2 T such that the plane of the coil is in the direction of magnetic field. If the current through the coil is 3 mA , then the torque acting on the coil is...

An object of height 3.6 cm is placed normally on the principal axis of a concave mirror of radius of curvature 30 cm . If the object is at a distance of 10 cm from the principal focus of the mirror, then the height of the real image formed ...