TS EAMCET 2023 (Online) 13th May Morning Shift

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+4 x^2-9 x-36=0$ and $\alpha<\beta<\gamma$, then $\alpha+2 \beta+3 \gamma=$

If the sum of two particular roots of the equation $x^4-4 x^3-7 x^2+22 x+24=0$ is equal to the sum of the remaining two roots, then the sum of the cubes of all the roots of this equation is

If $x^2+3 x-2 k=0$ and $x^2-2 x-7 k=0$ have a non-zero common root, then the positive root of the equation $k x^2+(k+2) x-(k+1)=0$ is

If the variance of the data $2,3,5,8,12$ is $\sigma^2$ and the mean deviation from the median for this data is $M$, then $\sigma^2-M=$

If $\alpha$ is the angle made by the perpendicular drawn from origin to the line $3 x-4 y+5=0$ with positive $X$-axis in positive direction and $a x+b y=1$ is the equation of a line passing through the point $(1,-1)$ with $\tan \alpha$ as i...

Let the line $L_1$ passing through the point of intersection of the lines $2 x+3 y-5=0$ and $4 x-5 y+7=0$ divide the line segment joining the points $(2,3)$ and $(1,-1)$ in the ratio $2: 1$. If the equation of $L_1$ is $a x+b y=1$, then $33...

If $L_1$ is a line passing through the point $P(4,-3)$ and perpendicular to the line $3 x-4 y+k=0$ then the distance of $P$ from the line $5 x-3 y-2=0$ measured along the line $L_1$ is

Let $A(4,3,5), B(1,-2,1), C(3,2,1)$ be the vertices of a $\triangle A B C$. If the internal bisector of $\angle B A C$ meet the side $B C$ at $D$, then $C D=$

Let $A B C$ be a triangle and $A=(1,2)$. If $x-3 y-5=0$ the and $x+5 y-9=0$ are the perpendicular bisectors of the sides $A B$ and $B C$ respectively, then the length of the side $A C$ is

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

Let the direction cosines of two lines satisfy the equations $3 l+2 m+n=0$ and $2 m n-3 n l+5 l m=0$. If $\theta$ is the angle between these two lines, then $\cos \theta=$

A plane $\pi$ passing through the point $3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ is parallel to the plane which passes through the point $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and perpendicular to the vector ...

$(1,-2,1)$ is a point on a plane $\pi$ and $\pi$ is parallel to the plane $x-y-z=0$. If the equation of $\pi$ is $a x+b y+c z-2=0$, then $b-2 c=$

If $A+B+C+D=2 \pi$, then $\cos A-\cos B+\cos C-\cos D=$

If $\cosh x=\frac{4}{3}$, then $3 \cosh x+3^2 \cosh 2 x+3^3 \cosh 3 x=$

If $540^{\circ}<\theta<630^{\circ}$ and $\tan \theta=5 / 12$, then
\(\frac{\cos \frac{\theta}{2}-5 \sin \frac{\theta}{2}}{\sqrt{-(12 \sec \theta+5 \operatorname{cosec} \theta)}}=\)

If $\cot \theta=-\frac{2}{3}$ and $\theta$ does not lie in the 4 th quadrant, then $\frac{(5 \sin \theta+\cos \theta)^2}{\tan \theta+\cot \theta}=$

Let $\mathbf{a}=\lambda \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{b}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}$ and $\mathbf{c}=\lambda \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ be three ...

Let $\mathbf{O A}=\hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{O B}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{O C}=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ be the position vectors...

If the vectors $\mathbf{B C}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{C D}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ represent two adjacent sides of a parallelogram ABCD and $\theta$ is the angle betw...

A series $L-C-R$ circuit is connected to an AC source of voltage $150 \sin (80 \pi t)$ volt. If the resistance of the resistor in the circuit is $25 \Omega$ and the impedance in the circuit is $75 \Omega$, the average power dissipated per c...

$\alpha$-decay of a parent nucleus $X$ results in a daughter nucleus $Y$. If $m_x, m_y$ and $m_\alpha$ are the masses of the parent nucleus, the daughter nucleus and the $\alpha$-particles respectively, then the net kinetic energy gained in...

In hydrogen spectrum, the shortest and longest wavelengths of Balmer series are $\lambda_1$ and $\lambda_2$ respectively. The Rydberg constant of hydrogen is

In the nuclear fission of one nucleus of $\mathrm{U}^{235}$ the energy released is 188 MeV . The energy released in the nuclear fission of 235 g of $\mathrm{U}^{235}$ is nearly
(Avogadro number $=6.02 \times 10^{23} \mathrm{~mol}^{-1}$ )

The displacement current through the plates of a parallel plate capacitor of capacitance $30 \mu \mathrm{~F}$ is $150 \mu \mathrm{~A}$. The capacitor is charged by a source of varying potential at the rate of

The effective capacitance between points $A$ and $B$ shown in the figure is

A body falls freely from a height $h$ on a fixed horizontal plane and rebounds. If $e$ is the coefficient of restitution, the total distance travelled before it comes to rest is

A block of mass $M$ moving on a frictionless horizontal surface collides with a spring of spring constant $K$, as shown in the figure. If the spring compresses by a length $L$, then the maximum momentum of the block after the collision is

Two blocks of equal masses are tied to the ends of a light string. The string passes over a mass less pulley fixed on frictionless surface as shown in the figure. The acceleration of the centre of mass of the blocks is ( $g=$ acceleration d...

The loss of strength of a signal while propagating through a medium is known as

The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled, then

In a meter bridge experiment the ratio of the left gap resistance to the right gap resistance is $2: 3$. The balance length from left end is

In a galvanometer, $5 \%$ of the total current in the circuit passes through it. If the resistance of the galvanometer is $G$, the shunt resistance $S$ connected to the galvanometer is

The de-Broglie wavelength of a particle moving with a speed of $0.8 c$ is equal to the wavelength of a photon. If $c$ is speed of the photon in vacuum, the ratio of the energy of the photon and the kinetic energy of the particle is

The length of four wires $A, B, C$ and $D$ made of same materials are $1 \mathrm{~m}, 2 \mathrm{~m}, 3 \mathrm{~m}$ and 4 m respectively. The radii of the wires $A, B, C$ and $D$ are $0.2 \mathrm{~mm}, 0.4 \mathrm{~mm}$, 0.6 mm and 0.8 mm r...

An aeroplane is travelling horizontally towards west with a speed of $540 \mathrm{kmh}^{-1}$. The wing span of the plane is 20 m . If the horizontal component of the earth's magnetic field at the location is $2.5 \sqrt{3} \times 10^{-4} \ma...

The flux of the electric field $\mathbf{E}=24 \hat{\mathbf{i}}+30 \hat{\mathbf{j}}+28 \hat{\mathbf{k}} \mathrm{NC}^{-1}$ through an area of $20 \mathrm{~m}^2$ on the $Y Z$-plane is

A vessel having small hole in the bottom has to hold water without leakage, if water is poured into if upto a height of 7 cm . Then the radius of the hole is (surface tension of water is $0.07 \mathrm{Nm}^{-1}$, angle of contact is $0^{\cir...

A liquid is taken in a long vertical cylindrical vessel and the cylinder is rotated about its vertical axis as shown in figure. During rotation, the liquid rises along its sides. If the radius of vessel is 0.05 m and speed of rotation is $1...

The percentage increase in the energy for an artificial satellite to shift it from an orbit of radius $r$ to an orbit of radius $3 r / 2$ is

Gravitational forces operate among which of the following?

Air is filled at $60^{\circ} \mathrm{C}$ in a vessel of open mouth. The vessel is heated to a temperature $f^{\circ} \mathrm{C}$ so that $1 / 4$ th of the air is escaped from the vessel. Assuming air as ideal gas and the volume of the vesse...

For an ideal gas at a temperature of $27^{\circ} \mathrm{C}$ and at constant pressure, the coefficient of volume expansion is nearly

The temperature of 100 g of water is to be raised from $24^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$ by adding steam at $100^{\circ} \mathrm{C}$ to it. The mass of the steam required in this process is (latent heat of steam is $540 \ma...

Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and same volume $V$. The mass of the gas in $A$ is $m_A$ and that in $B$ is $m_B$. The gas in each cylinder is now allowed to ...

A body of weight 50 N is placed on a horizontal surface as shown in the figure. The minimum force required to move the body is 28.28 N . The frictional force and the normal reaction are respectively

materials suitable for permanent magnets, must have which of the following properties?

The expression for the magnetic energy stored in a solenoid of length $L$, in terms of magnetic field $B$ and area $A$ is

A stone projected from the ground with a velocity $50 \mathrm{~ms}^{-1}$ at an angle of $30^{\circ}$ with the horizontal crosses a wall after a time of 3 s . Then the horizontal distance beyond the wall that the stone strikes the ground is ...

A body starts rest with uniform acceleration. If its velocity after $n^{\text {th }}$ second (last second) is $v$ then its displacement in the last two seconds is