TS EAMCET 2022 (Online) 18th July Evening Shift

If a line $L$ is common to the pairs of lines $6 x^2-x y-12 y^2=0$ and $15 x^2+14 x y-8 y^2=0$ then the combined equation the other two lines is

The centroid of the triangle formed by the lines $x-3 y+3=0, x+3 y+3=0 x+y-1=0$ is

If $L$ is a line passing through the point $(-1,1)$ and parallel to the common line of the pairs of lines $6 x^2-x y-12 y^2=0$ and $15 x^2+14 x y-8 y^2=0$, then the equation of pair of lines joining the origin to the points of intersection ...

If the slope of one of the lines represented by $5 x^2+\frac{40}{3} x y+k y^2=0$ is 3 , then the angle between the pair of lines is

If the line $2 x-3 y+4=0$ divides the line segment joining the points $A(-2,3)$ and $B(3,-2)$ in the ratio $m: n$, then the point which divides $A B$ in the ratio $-4 m: 3 n$ is

If the lines $L_1 \equiv 2 x+y+3=0, L_2 \equiv k x+2 y-3=0$ and $L_3 \equiv 3 x-2 y+1=0$ are concurrent then the cosine of the acute angle between the lines $L_2=0$ and $2 x-5 y+7=0$ is

If $Q$ is the image of the point $P(1,1)$ with respect to the straight line $x+y+1=0$, then the length of the perpendicular drawn from $Q$ to the line $3 x-4 y+3=0$ is

Let $A=(3,4,0), B=(4,4,4), C=(-6,2,3)$ and $D=(1,1,2)$. If $\theta$ is the acute angle between the lines $A B$ and $C D$, then $\cos \theta=$

A plane containing two lines whose direction ratios are $(-1,2,1)$ and $(1,3,2)$ passes through the point $(2,1, k)$. If this plane also passes through the point $(3,-1,4)$, then $k=$

If the points $A(1,3,5), B(2,4,6), C(4,5, k)$ form a right angled triangle then the number of possible values of $k$ is

Let a plane $P$ has the points $\hat{\mathbf{i}}, \hat{\mathbf{j}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$. Let $L$ be the line through the point $A$ and parallel to the vector $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\math...

Let $\pi_1^{\prime}$ be the plane passing through the point $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and perpendicular to the vector $a \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\pi_2$ be the plane passing t...

\(\frac{e^{4 x}+e^{-4 x}+14}{4\left(e^x-e^{-x}\right)^2}=\)

If $A+B+C=\frac{3 \pi}{2}$, then $4 \sin A \sin B \sin C+\cos 2 A+\cos 2 B+\cos 2 C=$

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

If $\cos x+\cos y=p, \sin x+\sin y=q$, then $\cos \left(\frac{x-y}{2}\right)=$

If $A(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}), B(\lambda \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}), C(-4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})$ and $D(-\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat...

If $3 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, 7 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}, \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $-7 \hat{\mathbf{i}}-17 \hat{\mathbf{j}}+16 \hat{\mathbf{k}}...

Let $\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{b}$ be two vectors such that $\mathbf{a} \cdot \mathbf{b}=1$, $\cos (\mathbf{a} \cdot \mathbf{b})=\frac{1}{3}$ and the components of $\mathbf{b}$ w.r.t. $(\hat...

If $\mathbf{a}$ and $\mathbf{b}$ are two vectors such that $\mathbf{a}=2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+p \hat{\mathbf{k}}$, $|\mathbf{b}|=7, \mathbf{a} \cdot \mathbf{b}=4$ and $|\mathbf{a} \times \mathbf{b}|=5 \sqrt{17}$, then $p=$

A $2 \mu \mathrm{~F}$ capacitor is charged to 50 V by a battery. The battery is removed after capacitor if fully charged. At time $t=0$, a 10 mH coil is connected in series with the capacitor. The maximum rate at which the current changes i...

Consider a nucleus ${ }_{30}^{60} \mathrm{X}$. Its approximate density is (take, $1 \mathrm{amu}=1.6 \times 10^{-27} \mathrm{~kg}, R_0=1.2 \times 10^{-15} \mathrm{~m}$ )

Which of the following interaction is responsible for beta decay?

If the series limit frequency of Balmer series is $v_B$, then the series limit frequency of the Brackett series is

The equivalent capacitance between points $A$ and $B$ is

A moving particle collides with a stationary particle of mass $\frac{1}{n}$ times the mass of moving particle, the fraction of its kinetic energy transferred to the stationary particle is

A message signal of frequency 15 kHz is used to modulate a carrier of frequency $v_c$. If the side bands produced are 1515 kHz and 1485 kHz , then $v_c$ is

A cylindrical metallic wire is stretched to increase its length in such a way that the metallic wire changes its resistance by $6 \%$. The percentage increase in its length is

The resistivity of a material is found to be $10^8 \Omega-\mathrm{m}$, then the material would be

Find the current in the three resistors as shown in the following figure?

The value of planck's constant, if the slope of the graph of stopping potential versus frequency of incident light is $4 \times 10^{-15} \mathrm{~V}$-s is (given charge of an electron $=1.6 \times 10^{-19} \mathrm{C}$ )

A swimming pool has a depth of 22 m and area $700 \mathrm{~m}^2$. Calculate fractional change $\Delta v / v$ of water at the bottom of the swimming pool, given that the bulk modulus of water is $2.2 \times 10^9 \mathrm{Nm}^{-2}, g=10 \mathr...

A flat circular coil has 100 turns of wire of radius 10 cm . A uniform magnetic field exists in a direction perpendicular to the plane of the coil and it grows at a rate of $0.1 \mathrm{~T} / \mathrm{s}$. The induced emf in the coil is

A beam of white light is incident normally on a plane surface absorbing 70\% of the light and reflecting the rest. If the incident beam carries 10 W of power, the force exerted by it on the surface is

An electromagnetic wave has its electric and magnetic fields given by
\(\mathbf{E}(t)=\mathbf{E}_m \sin (k x-\omega t) ; \quad \mathbf{B}(t)=\mathbf{B}_m \sin (k x-\omega t)\)
If the direction of $\mathbf{E}_m$ and $\mathbf{B}_m$ are in t...

A large metal plate has a surface charge density of $8.85 \times 10^{-6} \mathrm{C} / \mathrm{m}^2$. An electron having initial kinetic energy of $8 \times 10^{-17} \mathrm{~J}$ is moving towards the centre of the plate. If the electron sto...

What is the terminal velocity of a rain drop of radius 0.02 mm ?
[Note that the coefficient of viscosity of air is $1.8 \times 10^{-5} \mathrm{N} / \mathrm{m}^2$, density of water is $1000 \mathrm{~kg} / \mathrm{m}^3$. Use, $g=10 \mathrm{~m...

A hollow spherical body of outer and inner radii of 4 cm and 2 cm respectively, floats half submerged in a liquid of density $2.0 \mathrm{~g} / \mathrm{cm}^3$. The density of the material of the sphere is

A rocket is fired vertically with a speed of $4 \mathrm{~km} / \mathrm{s}$ from the earth's surface. How far from the earth does the rocket go before returning to the earth?
(Take, radius of earth $=6.4 \times 10^6 \mathrm{~m}$ and $g=10 \m...

A metal cube absorbs 2100.0 J of heat when its temperature is raised by $2^{\circ} \mathrm{C}$. If the specific heat of the metal is $900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$, then the mass of the cube is

A diatomic gas $\left(C_p=\frac{7}{2} R\right)$ does 200 J of work when it is expanded isobarically. The heat given to the gas in the process is

Statement I Gas thermometers are less sensitive than liquid thermometers.
Statement II The ratio of universal gas constant and avogadro's number is called Boltzmann's constant.
Statement III The density of a given mass of a gas at constant ...

The net work done by an ideal gas going through the cycle as shown in the $p-V$ diagram below is

A hole of diameter 5 cm is drilled in a metal sheet at $30^{\circ} \mathrm{C}$. The linear expansion of metal is $2 \times 10^{-5} \mathrm{~K}^{-1}$. The diameter of the hole when the temperature is raised to $230^{\circ} \mathrm{C}$, is eq...

A block is placed on a parabolic shape ramp given by equation, $y=\frac{x^2}{20}$. If the coefficient of static friction $\left(\mu_s\right)$ is 0.5 , then what is the maximum height above the ground at which the block can be placed without...

Assertion (A) The magnetic field lines are continuous and form closed loops.
Reason (R) Magnetic monopole does not exist.
The correct option among the following is

A small object slides down with initial velocity equal to zero from the top of a smooth hill of height $H$. The other end of the hill is horizontal and is at height $H / 2$ as shown in the figure. The horizontal distance covered by the obje...

A projectile is given an initial velocity of $(3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$ where $\hat{\mathbf{i}}$ is along the ground and $\hat{\mathbf{j}}$ is along the vertical. Assuming $g=10 \mathrm{~m} / \mathrm{s...

Assertion (A) The zero velocity of a particle at any instant always implies zero acceleration at that instant.
Reason (R) A body is momentarily at rest when it reverses its direction of motion. The correct option among the following is

A river has a steady speed of $v$. A man swims upstream at a distance of $d$ and swims back to the starting point in total time $t$. The man can swim at a speed of $2 v$ in still water. If the time taken by the man in still water is $t_0$ t...