TS EAMCET 2022 (Online) 19th July Evening Shift

There are $n$ observations and all of them are negative numbers. The ascending order of these observations is $x_1, x_2, \ldots . x_n$. If the signs of the first term and last term in that order are changed, then the range of the data is

The equation of the pair of straight lines passing through the point $(2,3)$ and perpendicular to the pair of lines $3 x^2-4 x y+5 y^2=0$ is $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$, then $a+b+c+f+g+h=$

Let $\alpha, \beta$ and $\gamma$ be three non-zero real constants and $a, b$ and $c$ be three arbitrary real numbers which satisfy $\alpha a+\beta b+\gamma c=0$. Then, the point of concurrence of the family of lines $a x+b y+c=0$ is

For $a, b, c \in R$, if $6 a^2-3 b^2-c^2+7 a b-a c+4 b c=0$ and $|a|+|b| \neq 0$, then all the lines given by $a x+b y+c=0$ are

If a straight line $L$ passing through the point $(5,-3)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3} x+y-9=0$ and $L$ intersects $X$-axis, then the equation of $L$ is

If the algebraic sum of the perpendicular distances from the points $(2,0),(0,2)$ and $(1,1)$ to a variable line is zero, then the variable line always passes through a fixed point. The coordinates of that point are

If $\theta$ is the acute angle between the pair of lines $H \equiv a x^2-x y+b y^2=0, \tan \theta=5$ and $(1,-1)$ is a point on $H=0$, then $a^2+a b+b^2=$

If $f(x, y)=0$ is the combined equation of the lines joining the origin to the points where the line $4 x-6 y-2=0$ meets the curve $3 x^2-4 x y+5 y^2-2 x+y-6=0$, then $\frac{f(1,-1)}{f(-1,-1)}=$

$A(27,-243,81)$ is a point in space, $B, C$ and $D$ are images of $A$ with respect to $X Y, Y Z$ and $Z X$ planes respectively. If the centroid of the $\triangle B C D$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma=$

The point which lies on the plane passing through the point $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, 3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+4 \hat{\mathbf{k}},-3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}$ is

Let $A(2,5,7)$ be the image of the point $B(1,-2,3)$ with respect to a plane $\pi$. Let $C$ be the point where $A B$ meets the plane $\pi$. Let $D=(2,1,6)$. Then, the direction cosines of $C D$ are

If the angle between the planes $\mathbf{r} \cdot(11 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\alpha \hat{\mathbf{k}})=7$ and $\mathbf{r} \cdot(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})=5$ is $\frac{\pi}{2}$, then $\alpha=$

If a plane $x+y+z-5=0$ intersects the line joining $A(1,1,1)$ and $B(2,2,2)$ at $P$, then $A P: P B=$

If $\theta$ does not lie in the second quadrant and $\tan \theta=\frac{-3}{4}$, then $\tan \frac{\theta}{2}+\sin 2 \theta=$

Let $\alpha$ be the period of $3 \sin \frac{\pi x}{3}-\cos \frac{\pi x}{2}+\tan \frac{\pi x}{4}, \beta$ be the period of $\sin ^2\left(\frac{\pi}{7}+\frac{x}{4}\right)-\sin ^2\left(\frac{\pi}{7}-\frac{x}{4}\right)$, and $\gamma$ be the peri...

\(\cos ^2 76^{\circ}+\sin ^2 46^{\circ}+\sin 76^{\circ} \cos 46^{\circ}=\)

If $2 \mathbf{i}+3 \mathbf{j}-4 \mathbf{k}$ and $-\mathbf{i}+2 \mathbf{j}+\mathbf{k}$ are the two diagonals of a parallelogram, then the area of the parallelogram in square units is

If $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}$ are the position vectors of the points $\mathbf{A}$ and $\mathbf{B}$ respectively, $\mathbf{C}$ divides $\mathbf{A B}$ in the ...

If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are the non-coplanar vectors and $\mathbf{a}-2 \mathbf{b}+3 \mathbf{c},-4 \mathbf{a}+5 \mathbf{b}-6 \mathbf{c}, x \mathbf{a}-9 \mathbf{b}+z \mathbf{c}$ are collinear points, then $2 x-z=$

If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}$, then the component of $\mathbf{b}$ perpendicular to $\mathbf{a}$ is

The $Q$ value of a series $L-C-R$ circuit with $L=2 \mathrm{H}$, $C=32 \mu \mathrm{~F}, R=20 \Omega$ is

The range of the nuclear force is

Considering the Bohr's model of hydrogen atom, the ratio of velocities of electrons orbiting in the 4th orbit to that in the 9 th orbit is

What is the mass number of the nucleus having radius equal to $\frac{1}{3}$ of that of ${ }^{189} \mathrm{Os}$ ?

Particle $A$ moving with a velocity $v=10 \mathrm{~m} / \mathrm{s}$ experienced a head on collision with a stationary particle $B$ of the same mass. As a result of collision, the kinetic energy of the system decreased by $1 \%$. The speed o...

A body of mass $m$ slides down along a frictionless inclined plane from height $h$ and just completes motion in a vertical circle of radius 2 m after reaching the bottom. What is the value of $h$ ? [Use, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

Which of the following statements is not true?

Statement I The temperature coefficient of resistance for most of metals in pure form is positive.
Statement II A metal wire 2 mm in diameter carries a charge of $360 \pi \mathrm{C}$ in two hours. If the metal contains $5 \times 10^{22}$ fr...

A cylindrical resistor of radius 7.0 mm and length 4.0 cm is made of material that has a resistivity of $10^{-6} \Omega-\mathrm{m}$. If the energy is dissipated at rate 1.54 W in the resistor, then the current density is

In a photoelectric experiment, the wavelength of the light incident on the metal is changed from 200 nm to 400 nm . The decrease in the stopping potential is close to
[use $h c=1240 \mathrm{eV}$-nm, where $h=$ Planck's constant and $c$ is v...

The de-Broglie wavelength of an electron with kinetic energy of 320 eV is (take, $h=6.0 \times 10^{-34}$ SI unit, mass of electron $=m_c=9.0 \times 10^{-31} \mathrm{~kg}$, charge of an electron $=1.6 \times 10^{-19} \mathrm{C}$ )

Two wires of same length having radius of 2 mm and 1.5 mm respectively, are loaded with same weights. Extension of the second wire is double than that of the first wire. What is the ratio of the Young's modulus of the first wire to that of ...

The magnetic flux through the triangular loop shown in the figure below
Where a uniform magnetic field of strength 2 T points perpendicularly into the plane of the triangle is

A laser beam has intensity $2.1 \times 10^{15} \mathrm{~W} / \mathrm{m}^2$. The amplitude of magnetic field in the beam in approximately is

$6 \mu \mathrm{C}$ charge is placed at the centre of a cube. What will be the electric flux at each face of the cube?
\(\left[\text { Take, } \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~N}-\mathrm{m}^2 \mathrm{C}^2\right]\)

There are two thin wire rings, each of radius $R$, whose axes coincide. The charges of the rings are $q$ and $-q$. The magnitude of potential difference between the centres of the rings separated by a distance $\sqrt{3} R$ is

A metal cube of side 10 cm rests on a film of a liquid of thickness 0.2 mm . If upon applying a horizontal force $\mathbf{F}$ of magnitude 0.1 N . The cube slides with a constant speed of $0.08 \mathrm{~m} / \mathrm{s}$, then the coefficien...

Consider an increase of $1 \%$ in each of radius of artery, viscosity of blood and density of blood, respectively. The percentage change in flow rate of blood in artery is

Four particles each of mass $m$ are placed at four vertices of a rectangle having side length as $3 l_0$ and $4 l_0$. The potential energy of the system in $\frac{G m^2}{l_0}$ is

A solution consists of ether and 5.0 g of water at $0^{\circ} \mathrm{C}$. If the ether evaporates completely to freeze the water, then the mass of the ether in the solution is

Assertion (A) Heat and work are modes of energy transfer to a system resulting in change in its internal energy.
Reason (R) Heat and work in thermodynamics are state variables.
The correct option among the following is

An ideal gas at pressure $p_0$ undergoes an isothermal expansion until its volume is 8.0 times its initial volume. The gas is slowly and adiabatically compressed back to its original volume. If the adiabatic constant of the gas is $\gamma=\...

176 g of $\mathrm{CO}_2$ can change its temperature from $0^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$ by absorbing 3600 J of thermal energy. Molar specific heat of $\mathrm{CO}_2\left(\right.$ in $\left.\mathrm{J} \mathrm{mol}^{-1} \ma...

At what temperature is the root mean square rms speed of neon gas atoms is equal to the rms speed of helium gas atoms at $-33^{\circ} \mathrm{C}$ ?
(Atomic mass of $\mathrm{Ne}=20.2 \mathrm{u}$, and that of $\mathrm{He}=4.0 \mathrm{u}$ )

A constant horizontal force $\mathbf{F}$ of magnitude 10 N is applied to a block $A$ and this produces an acceleration of magnitude $20 \mathrm{~m} / \mathrm{s}^2$. If this block $A$ is then kept against another block $B$ of mass 1.5 kg as ...

The magnitude of axial field due to a bar magnet at a distance of 1 m , is found to be $5 \times 10^{-8} \mathrm{~T}$. The magnetic moment of the bar magnet is $\left(\mu_0=4 \pi \times 10^{-7}\right)$

A particle initially at origin starts moving in $X Y$ - plane has velocity component $\mathbf{v}=(6+2 t) \hat{\mathbf{i}}+(4+2 \sqrt{3 t}) \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}$. Acceleration of the particle in $\mathrm{m} / \mathrm{s}^...

Two cars, at a certain instant, are 50 km apart on a line running from south to north. The one farther north is moving west at $25 \mathrm{~km} / \mathrm{h}$. The other is moving towards north at $25 \mathrm{~km} / \mathrm{h}$. How long do ...

A bullet is fired at time $t=0$ with velocity $20 \mathrm{~m} / \mathrm{s}$ and at an initial angle of $30^{\circ}$ with the horizontal. The angle between the displacement vector and the horizontal after time 0.1 s is (assume $g=10 \mathrm{...

A rocket moves straight upward with zero initial velocity and with an acceleration $20 \mathrm{~m} / \mathrm{s}^2$. It runs out of fuel and stops accelerating at the end of 5th second. It reaches a maximum height and falls back to the earth...