TS EAMCET 2022 (Online) 19th July Morning Shift

The mean deviation from the mean for the observations $1,3,5,7,11,13,17,19,23$ is

The distance between the points of concurrency of the two families of straight lines given by $x+(5 \lambda+1) y+1-3 \lambda=0$ and $(5 \mu+2) x-3 y+3+6 \mu=0$ is

If $\alpha x^2+2 \gamma x y+\beta y^2=0$ is the equation of pair of lines passing through the origin and perpendicular to the pair of lines $b h x^2+a b x y+a h y^2=0(a \neq 0, b \neq 0)$, then $\alpha \beta / \gamma^2=$

$\frac{x^2}{a}+\frac{x y}{h}+\frac{y^2}{b}=0(a \neq 0, h \neq 0, b \neq 0)$ represents two coincident lines if

If the lines joining the origin to the points of intersection of the line $x+y=k$ and the curve $x^2+y^2-2 x-4 y+2=0$ are at right angles, then the sum of all the possible values of $k$ is

If the line $2 x-y-4=0$ divides the line segment joining the points $(2,-1)$ and $(1,-4)$ at the point $(a, b)$ in the ratio $m: n$, then $4\left(a-b\left(\frac{m}{n}\right)^2\right)=$

The orthocentre of the triangle formed by the points $(1,3),(-3,5)$ and $(5,-1)$ is

Let the line $L$ drawn perpendicular to the lines $2 x-3 y+4=0$ and $6 x-9 y+7=0$ meet them at $A$ and $B$, respectively. If $P(\mathrm{l}, \mathrm{l})$ is a point on $L$, then the ratio in which $P$ divides $A B$ is

Let $L$ be a line passing through a point $A$ and parallel to the vector $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$. Let $-7 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}$ be the position vector of a point $P$ on $L$...

A bisector of the angle between the normals of the planes $4 x+3 y=5$ and $x+2 y+2 z=4$ is along the vector

If $A(1,2,3), B(2,-3,1), C(3,2,-1)$ are three vertices of a tetrahedron $A B C D$ and $G\left(\frac{5}{2}, \frac{3}{2}, \frac{9}{4}\right)$ is its centroid, then the point which divides $G D$ in the ratio $1: 2$ is

Let $6 x-3 y+2 z-6=0$ be the given plane. If $a, b$ and $c$ are the intercepts made by the plane on $X, Y$ and $Z$-axes, respectively; $l, m$ and $n$ are the direction cosines of a normal drawn to the plane and $p$ is the perpendicular dist...

Let $D$ be the foot of the perpendicular drawn from the point $A(2,0,3)$ to the line joining the points $B(0,4,1)$ and $C(-2,0,4)$. Then, the ratio in which $D$ divides $B C$ is

If $|\sin \alpha-\cos \alpha|=\frac{3}{4}$, then $|\sec 2 \alpha-\tan 2 \alpha|=$

If $\frac{1}{\sin 45^{\circ} \sin 46^{\circ}}+\frac{1}{\sin 46^{\circ} \sin 47^{\circ}}+\ldots$ up to 45 terms $=\frac{1}{\sin x^{\circ}}$, then $\sin \left(\frac{\pi}{2} x\right)=$

If $\sinh x=\frac{-1}{2}$, then $\tanh 2 x=$

Let the vectors $\mathbf{A B}=2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{A C}=2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ be two sides of a $\triangle A B C$. If $G$ is the centroid of $\triangle A B ...

If $(\alpha, \beta, \gamma)$ is a triad of real numbers satisfying $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}=\alpha(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})+\beta(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k...

If $\theta$ is the angle between the vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $a \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+b \hat{\mathbf{k}}$ and $\cos \theta=\frac{2}{3}$, then $2(a+b+3)=$

Let the volume of the tetrahedron with vertices $\hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}},-2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}},-\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+2 \hat{\...

A resistor of resistance of $100 \Omega$ is connected to an AC source $\varepsilon=10 \sin (250 \pi) t$. The energy dissipated as heat during $t=0$ to $t=1 \mathrm{~ms}$ is approximately.

The difference in the wavelength between the maximum and minimum of Balmer series (use $R_H=1 \times 10^7 \mathrm{~m}^{-1}$ )

The radius and mass number of nucleus 1 is $R_1$ and $A_1$, respectively. The radius and mass number of nucleus 2 is $R_2$ and $A_2$, respectively. If $A_2$ is larger than $A_1$ by $2 \%$, then $R_2$ is larger than $R_1$ by

A parallel plate capacitor of plate area $10 \mathrm{~cm}^2$ and plate separation 3 mm is charged to a potential difference 12 V and then the battery is disconnected. A slab of dielectric constant 3 is then inserted between the plates. The ...

Assertion (A) In an elastic collision of two billiard balls, both kinetic energy and linear momentum remain conserved.
Reason (R) During the collision of the balls, as the collision is elastic there is no exchange of energy. Therefore, both...

A merry-go-round rotating at a constant angular speed completes 9 rotations is 18 s . What is its angular speed?

The range of frequency bands used for standard AM broadcast is

A metal has $9 \times 10^{28}$ conduction electrons per $m^3$ and its resistivity is $1 \times 10^{-8} \Omega \mathrm{~m}$. If the drift speed of an electron in the metal is $1.6 \times 10^6 \mathrm{~m} / \mathrm{s}$, then its mean free pat...

The resistivity of a metal is $1 \times 10^{-8} \Omega-\mathrm{m}$. If it contains $9 \times 10^{28}$ electrons per $\mathrm{m}^3$, then the relaxation time of electrons inside the metal is nearly
(electron mass $=9 \times 10^{-31} \mathrm{...

Light strikes a metal surface causing photoelectric emission. The wavelength of incident light is 248 nm . If the stopping potential for the ejected electrons is 2.8 eV , then the work function of the metal is (take, $h c=1240 \mathrm{eV}-\...

The de-Broglie wavelength associated with an electron, accelerated through a potential difference of 121 V is about
(take, Plank's constant $=h=6.6 \times 10^{-34} \mathrm{Js}$, mass of electron $=9 \times 10^{-31} \mathrm{~kg}$ )

An object of mass 15 kg is attached to the end of a metal wire of unstretched length 1.0 m . The object is then whirled in a vertical circle with an angular velocity of $4 \mathrm{rad} / \mathrm{s}$ at the bottom of the circle. If the cross...

A wire loop of area $0.2 \mathrm{~m}^2$ has a resistance of $20 \Omega$. A magnetic field pointing normal to the loop has a magnitude of 0.25 T and is reduced to zero at a uniform rate in $10^{-4} \mathrm{~s}$. What is induced emf and resul...

About $20 \%$ of the power of a 100 W bulb is converted to visible radiation. Assuming that the radiation is emitted isotropically and neglecting reflection, the average intensity of visible radiation at a distance of 5 m is $\frac{\alpha}{...

Two charged particles of mass 1 g each are placed 1 m apart. If each of these possesses 1 femto coulomb of charge, then the dominant force of interaction between them is

Three charges are arranged on the vertices of a right angle triangle as shown in the figure. The magnitude of dipole moment of the combination in the unit of $\mathrm{C}-\mathrm{cm}$ is

A particle of mass $m$ and charge $q$ travelling with a velocity $v$ along the $X$-axis enters a uniform electric field $\mathbf{E}$ directed along the $Y$-axis. What will be the trajectory of the particle?

In the figure, the chamber $A$ contains a gas, movable chamber $B$ is placed on the top of the gas and it contains $n$ metal balls. The weight of chamber $B$ is supported by the gas. Chamber $C$ has vacuum. Let the gas be in equilibrium at ...

A liquid flows steadily through a cylindrical pipe having a radius $2 R$ at a point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity at point $B$ is $4 v$, what will be the velocity at point $A$ ?

A uniform sphere $A$ with radius $R$ exerts a force $F$ on a small particle $B$ situated at a distance $2 R$ from the centre of the sphere. A spherical portion of diameter $R$ is cut from the sphere $A$ as shown in the figure. If $F^{\prime...

A piece of metal has a weight of 49 g in air and 39 g in a liquid of density $1.2 \times 10^3 \mathrm{~kg} / \mathrm{m}^3 \mathrm{kept}$ at $32^{\circ} \mathrm{C}$. When the temperature of the liquid is raised to $42^{\circ} \mathrm{C}$ the...

A metal cooking pot has a base area of $0.2 \mathrm{~m}^2$ and thickness 2.0 cm . It boils water at a rate of $3.0 \mathrm{~kg} / \mathrm{min}$ when placed on a hot plate. The temperature of the part of the hot plate in contact with the pot...

A quantity of monoatomic gas undergoes a process in which pressure is changed linearly with volume. The pressure and volume are changed from initial value $\left(p_0 V_0\right)$ of final value $\left(3 p_0, 3 V_0\right)$. The heat absorbed ...

An ideal gas having initial pressure $p$, volume $V$ and temperature $T$ is allowed to expand adiabatically until its volume becomes 4 V , while its temperature falls to $\frac{T}{2}$. If the work done by the gas during the expansion is $\a...

At what temperature, an oxygen molecule has the same rms velocity as the hydrogen molecule has at 20 K ?

A motor car moving with velocity $7 \mathrm{~m} / \mathrm{s}$ stops at 10 m distance when brakes are applied. What is the relation between the resistance force $R$ and the weight $w$ of the car? (take, value of $g=9.8 \mathrm{~m} / \mathrm{...

A thin magnetic needle is placed in a magnetic field of 200 G with its axis at $30^{\circ}$ to the direction of the field. Find the magnetic moment of the needle, if it experiences a torque of 0.012 Nm in this field.

A man walking along a straight line with a velocity 6 $\mathrm{km} / \mathrm{h}$ encounters rain falling vertically down with a velocity $6 \sqrt{3} \mathrm{~km} / \mathrm{h}$. At what angle the man should hold his umbrella, so that he can ...

A particle moves along a straight line, such that its displacement $x$ varies with time $t$ as $x=\alpha t^3+\beta t^2+\gamma$, where $\alpha, \beta$ and $\gamma$ are constants, $v_1$ is the average velocity of the particle during its journ...

An aircraft is flying at a height of $h$ above the ground and at a speed of $v$. The maximum angle subtended at a ground observation point by the aircraft after time $t$ is