TS EAMCET 2022 (Online) 18th July Morning Shift

If the line $x-y+1=0$ cuts the lines $2 x+2 y+3=0$ and $3 x+3 y+2=0$ at the points $A$ and $B$ respectively, then $A B=$

Let $A(5,-3), B(3,-2), C(-1,5)$ be three points. If $P$ is a point satisfying the condition $P A^2+2 P B^2=3 P C^2$, then a point that lies on the locus of $P$ is

$a x^2-4 x y-2 y^2=0$ represents a pair of lines. If $\theta$ is the angle between these lines, $\cos \theta=\frac{1}{5}$ and the possible values of ' $a$ ' are $a_1$ and $a_2\left(a_1

The equation $x^2-y^2+a x+b=0$ represents a pair of lines for the ordered pair $(a, b)=$

If the incentre and the circumcentre of the triangle formed by the lines $x=2,4 x+3 y+7=0$ and $y=3$ are $I$ and $S$ respectively, then $I S=$

Let $L_1, L_2$ be the lines represented by the equation $4 x^2-5 x y+3 y^2=0$. Let $L_3, L_4$ be two lines passing through the point $(4,3)$ such that $L_3$ and $L_4$ are perpendicular to $L_1$ and $L_2$ respectively. If the combined equati...

If $P$ is a point on the line parallel to the vector $2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-6 \hat{\mathbf{k}}$ and passing through the point $A$ whose position vector is $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $A P=21$...

If a line $L$ is common to the planes $x-y+z+2=0$ and $2 x+y-2 z+5=0$ then the direction cosines of the line $L$ are

The cartesian equation of the plane passing through the point $(1,-2,3)$ and perpendicular to the vector $-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$, is

Let $A(1,2,3), B(-1,4,6), C(0,-6,4)$ and $D(1,1,1)$ be the vertices of a tetrahedron, $G$ be its centroid and $G_1$ be the centroid of its face $B C D$. Then, $\frac{A G_1}{A G}=$

Let the foot of the perpendicular drawn from the point $(1,2,3)$ to a plane be $(-1,3,-2)$. Then, the perpendicular distance from the origin to the plane is

\(\frac{\sqrt{2} \cos 45^{\circ}+\cos 56^{\circ}+\cos 58^{\circ}-\cos 66^{\circ}}{\sqrt{2} \cos 28^{\circ} \cos 29^{\circ} \sin 33^{\circ}}\)

$2 \cosh (x+y) \sinh (x-y)+\sinh 2 y=$

If $A$ and $B(A>B)$ are acute angles, $\sin (A-B)=\frac{16}{65}$ and $\sin B=\frac{5}{13}$, then $\tan A+\cot A=$

If $\theta=\frac{\pi}{12}$ and $x=\log \left(\cot \left(\frac{\pi}{4}+\theta\right)\right)$, then $\cosh x=$

If $\tan A=\frac{2}{3}$, then $\sin 4 A=$

Let $\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{c}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$, $\mathbf{d}=2 \hat{\mathbf{i}}+\hat{\ma...

Let $\mathbf{a}$ be a vector in the plane containing vectors $\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{c}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$. If $\mathbf{a}$ is perpendicular to $\hat{...

If the points with position vectors $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-4 \hat{\mathbf{k}},-3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-5 \hat{\mathbf{k}}$ and $a \hat{\mathbf{i}}-2 \hat{\m...

In a $\triangle A B C, D$ and $E$ divide the sides $B C$ and $C A$ in the ratio $2: 1$ respectively. If $P$ is the point of intersection of $A D$ and $B E$, then the ratio in which $P$ divides $A D$ is

An AC current is given by the expression, $I(t)=50 \sin (200 \pi t)$ in amperes. The frequency and rms value of the current, respectively are

As the mass number $A$ increases, which of the following quantities related to a nucleus does not change?

The following figure shows a 9 V battery and 3 uncharged capacitors of capacitances $C_1=C_2=C_3=1 \mu \mathrm{~F}$. The switch is thrown to the right side until capacitor $C_1$ is fully charged, then the switch is thrown to the left. The f...

Four masses are arranged along a circle of radius 1 m as shown in the figure. The centre of mass of this system of masses is at

A TV transmission antenna is 40 m tall. How much service area is can cover, if the receiving antenna is at the ground level?
(radius of the earth $=6400 \mathrm{~km}$ )

Balancing point of a potentiometer shifts from a length of 60 cm to 40 cm by shunting the cell with a $4 \Omega$ resistance. What is the internal resistance of the cell?

A metal wire of length $L$ and radius $r$ has a resistance $R$. If a wire of the same metal of length $2 L$ and radius $3 r$ is taken, then what will be its resistance?

For photoelectric effect which of the following statements are true.
(I) The kinetic energies of the photoelectrons do not depend on the frequency of light.
(II) Photoelectric effect will always occur for highly intense light.
(III) The max...

Which of the following statements is not true?

The light emitted in the transition $n=3$ to $n=2$, (where $n$ is the principal quantum number of the state) in hydrogen is called $\mathrm{H}_\alpha$-light. Find the maximum work function that a metal can have, so that $\mathrm{H}_\alpha$-...

\(\text { Match the following. }\)


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A long solenoid has 20 turns per cm. A small loop of area $4 / \pi \mathrm{cm}^2$ is placed inside the solenoid normal to its axis. If the current carried by the solenoid changed steadily from 1.0 A to 3.0 A in 0.2 s , what is the magnitude...

An electromagnetic wave is propagating in vacuum along $-\hat{\mathbf{j}}$ direction. The magnetic field of the wave is given by $\mathbf{B}=\left(2 \times 10^{-8}\right) \cos \left[\pi \times 10^{15}\left(t+\frac{y}{c}\right)\right] \hat{\...

An electron is released from a distance of 4 m from a stationary point charge 20 nC . What will be the speed of the electron, when it is
2 m away from the point charge?
(Charge of electron $=1.6 \times 10^{-19} \mathrm{C}$, mass of electron...

A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point 20.0 m below the water level. If the rate of flow from the hole is $3.08 \times 10^{-5} \mathrm{~m}^3 / \mathrm{s}$, the...

An air bubble of radius 1 mm is at a depth of 8 cm below the free surface of a liquid column. If the surface tension and density of the liquid is $0.1 \mathrm{~N} / \mathrm{m}$ and 2000 $\mathrm{kg} / \mathrm{m}^3$, respectively, by what am...

Three particles, each of mass $M$, situated at the vertices of an equilateral triangle of side length $l$. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle whi...

1.00 kg of liquid water at $100^{\circ} \mathrm{C}$ undergoes a phase change into steam at $100^{\circ} \mathrm{C}$ at 1.0 atm (take it to be $1.00 \times 10^5 \mathrm{~Pa}$ ). The initial volume of the liquid water was $1.00 \times 10^{-3}...

An object cools from $100^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ in 10 min , when the surrounding temperature is $10^{\circ} \mathrm{C}$. Then the time taken by the object to cool from $70^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{...

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 \mathrm{~m} / \mathrm{s}$, then the rms speed of helium molecule at the same temperature is

Find the ratio of the length of a steel rod and a copper rod, if the steel rod is 4 cm longer, then the copper rod at any temperature.
(The coefficient of linear expansion for steel and copper are $1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C}...

A monoatomic gas does 100 J of work, when it is expanded isobarically. How much of heat is given to the gas in the process?

Two blocks of masses 1 kg and 2 kg connected by a light rod and the system is slipping down a rough incline angle $45^{\circ}$ with the horizontal. The frictional coefficient at both the contacts is 0.4 . If the acceleration of the system i...

A time varying force acts on a ball of mass 100 g for 2 ms . The force versus time curve is shown below. If the initial speed of the ball is $10 \mathrm{~m} / \mathrm{s}$, then the speed of ball after 2 ms is

A planet has magnetic dipole moment of $27 \times 10^{22} \mathrm{~A}-\mathrm{m}^2$. If the radius of the planet is 300 km , what would be the magnetic field at its equator? $\left(\right.$ use,$\left.\frac{\mu}{4 \pi}=10^{-7}\right)$

A projectile is launched with an initial speed of $40 \mathrm{~m} / \mathrm{s}$ at an angle $30^{\circ}$ above the ground. The projectile lands on a hillside 2.0 s later. The net displacement from where the projectile lands on hillside 2.0 ...

A body starts from the rest and acquires a velocity of $10 \mathrm{~m} / \mathrm{s}$ in 2s. What is the acceleration of the body and the distance travelled?

A bullet fired into a target losses one-third of its velocity after travelling a distance $x$ metre into the target. If the bullet comes to rest by travelling a further distance $x^{\prime}$, then the ratio $\frac{x^{\prime}}{x}$ is

A toroid has a core (non-ferro magnetic) of inner radius 24 cm and outer radius 26 cm around which 2000 turns of a wire is wound. If the current in the wire is 12 A , the magnetic field inside the core of the toroid is

A current $I=5 \mathrm{~A}$ flows along a thin wire shaped as shown in figure. The radius of curved part of the wire is equal to $R=100 \mathrm{~mm}$, the angle $2 \phi=90^{\circ}$. The magnitude of magnetic field at the point $O$ is approx...