TS EAMCET 2022 (Online) 20th July Morning Shift

A line makes intercepts 5 and 7 on the coordinate axes. The axes are rotated through an angle $\theta$ in the positive direction about the origin so that the line makes equal intercepts on the new axes, then $|\tan \theta|=$

$L \equiv 7 x-y+8=0$ is one of the diagonals of a square for which $(-4,5)$ and $(3,4)$ are two vertices. Then, the coordinates of the two vertices lying on the diagonal $L=0$ are

Let $M$ be the foot of the perpendicular drawn from the point $(5,-7)$ to the line $3 x-5 y+1=0$. Then, the perpendicular distance from $M$ to the line $2 x+5 y-3=0$ is

The line $x+2 y=k$ meets the curve $2 x^2-2 x y+3 y^2+2 x-y-1=0$ at two points $A$ and $B$. Let $O$ be the origin. If the line segments $O A$ and $O B$ are perpendicular to each other, then $k=$

$B(2,3), C(5,-2), D(1,-1)$ are three points. If $A$ is a variable point such that the area of the quadrilateral $A B C D$ is 10 sq. units, then the locus of $A$ is

Let $A B C$ be a triangle. Let a point $P$ divide $A B$ in the ratio $1: 2$ internally and a point $Q$ divide $B C$ in the ratio $1: 2$ internally. Let $D$ be the point of intersection of $A Q$ and $C P$. If the area of the $\triangle A B C...

$A(1,1,1), B(1,-4,3), C(2,-2,0)$ and $D(8,1,4)$ are the vertices of a tetrahedron. $G_1, G_2, G_3$ and $G_4$ are the centroids of the faces $A B C, B C D, C D A$ and $D A B$. Then, the centroid of the tetrahedron having $G_1, G_2, G_3$ and ...

If a plane passing through the points $(2,3,0),(0,-5,2)$ and ( $-2,0,3$ ) meets the $X, Y$ and $Z$-axes in $A, B$ and $C$ respectively, then $A=$

If $\mathbf{r} \cdot(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})=5, \mathbf{r} \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})=7$ are two planes and $(16,-9,0)$ is a point common to both the planes, then the vector e...

Let $A(2,3,-1), B(4,1,0), C(-1,-1,1)$ be the vertices of a $\triangle A B C$. Let $D$ be the point where the bisector of $B A C$ meet the side $B C$. Then, the direction ratios of $A D$ are

Let $L$ be a line passing through the points $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+8 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+6 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$. Let $P$ be a plane passing through $-5 \hat{\mathbf{i}}+19 \hat{\mathbf{j}...

If $\sin (A+B) \sin (A-B)+\cos (A+B) \cos (A-B) =\frac{1}{2}$ and $0

If $A+B+C=\frac{\pi}{2}$, then $\sqrt{2} \cos \left(\frac{\pi}{4}-A\right)$
\(+\sqrt{2} \cos \left(\frac{\pi}{4}-B\right)+\sqrt{2} \cos \left(\frac{\pi}{4}-C\right)+1=\)

\(\frac{1}{\sin 250^{\circ}}+\frac{\sqrt{3}}{\cos 290^{\circ}}=\)

If $\sinh x=\tan A$, then $|\tanh x|=$

\(\frac{\sinh (x+y)+\sinh (x-y)}{\cosh (x+y)-\cosh (x-y)}=\)

Let $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ be three unit vectors satisfying $|\mathbf{a}-\mathbf{b}|^2+|\mathbf{a}-\mathbf{c}|^2=10$. Then,
Statement (I): $|\mathbf{a}+2 \mathbf{b}|^2+|2 \mathbf{a}+\mathbf{c}|^2=2$
Statement (II) : $|2 a...

Let $A B C$ be a triangle and $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ be the position vectors of $A, B$ and $C$ respectively. If $D$ divides $B C$ in the ratio $2: 3$ internally and $E$ divides $C A$ in the ratio $2: 1$ internally, then t...

If $2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ are the position vectors of the vertices $A, B, C$ of a triangle respectively, then a uni...

A capacitor of capacitance $100 \mu \mathrm{~F}$ and a coil of resistance $20 \Omega$ and inductance 12.5 mH are connected in series with a $220 \mathrm{~V}, \frac{200}{\pi} \mathrm{~Hz}, \mathrm{AC}$ source. The maximum value of instantane...

The energy of an electron in the fourth excited state of the hydrogen atom is

Estimate the approximate volume of aluminium nucleus $(A=27)$, use $\binom{R_0 \simeq 1.0 \times 10^{-15} \mathrm{~m}}{\pi \simeq 3}$

Which of the following statements is true?

A carrier wave of peak voltage 10 V is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of $80 \%$ ?

Statement I Specific resistance depends on nature of material and independent of temperature of the material. Statement II A wire of resistance $6 \Omega$ is drawn out, so that its new length is four times its original length. The resistanc...

Find the mobility of electron in a wire, if its average collision time is $9.1 \times 10^{-15} \mathrm{~s}$. (Charge of electron $=1.6 \times 10^{-19} \mathrm{C}$ and mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$ )

Which of the following has the largest de-Broglie wavelength?

Statement I By increasing the potential difference between cathode and anode continuously in a photoelectric experiment, the photocurrent always increases continuously.
Statement II If two photons $A$ and $B$ of energies 2.5 eV and 3.5 eV r...

One end of a steel rod of radius 10.0 mm and length 50.0 cm is clamped on a horizontal table. The other end of the rod is pulled with a force of magnitude 10.0 $\times \pi \mathrm{kN}$. This force is uniform across the flat surface of the r...

A metal disc of radius 30 cm rotates with a constant angular velocity $\omega=100 \mathrm{rad} / \mathrm{s}$ about its axis. Find the magnitude of potential difference between the centre and the rim of the disc of the external uniform magne...

On a particular day, the sun delivers an average power of $\left(\frac{6}{\pi} \times 10^3\right) \frac{\mathrm{W}}{\mathrm{m}^2}$ to the top of earth's atmosphere. Find the amplitude of magnetic field for the electromagnetic waves above at...

A sphere-1 with redius $R$ has charge $q$. Sphere-2 with radius $3 R$ is far from sphere-1 and is initially uncharged. If the two spheres are now connected with a thin conducting wire, then the ratio $\frac{\sigma_1}{\sigma_2}$ of the surfa...

Two charges are $+10 \mu \mathrm{C}$ and $-10 \mu \mathrm{C}$ are separated by 10 cm . The magnitude of force acting on another charge $5 \mu \mathrm{C}$ placed at the mid-point of the line joining the two charges will be (use, $\frac{1}{4 ...

A venturimeter has a pipe diameter of 4 cm and a throat diameter of 2 cm . Velocity of water in the pipe section is $10 \mathrm{~m} / \mathrm{s}$. The pressure drop, between pipe section and the throat section is (use, density of water $=10...

A soap bubble of initial radius $R$ is to be blown up. The surface tension of the soap film is $T$. The surface energy needed to double the diameter of the bubble is

Let the escape speed of an object on the earth's surface be $v_0$. The object is projected out with speed $5 v_0$. The speed of the object far away from the earth will be

When a gas expands adiabatically, its volume is doubled while its absolute temperature is decreased by a factor of 2 . The value of the adiabatic constant is

An amount of 700 J of heat is transferred to a diatomic gas allowing it to expand with the pressure held constant. The work done on the gas is

Assertion (A) The zeroth law of thermodynamics leads to the concept of temperature.
Reason (R) The zeroth law states that two systems in thermal equilibrium with a third system are in thermal equilibrium with each other.
The correct option ...

Find the difference in temperature between the water at the top and the bottom of 20 m high waterfall assuming 10\% of the energy of fall is spent in heating the water (use, specific heat capacity of water $=4000 \mathrm{~J} \mathrm{kg}^{-1...

Two metal rods $A$ and $B$ each of length 50 cm can diameter 4.0 mm are joined together at temperature $30^{\circ} \mathrm{C}$. What is the change in length of the combined rod at $230^{\circ} \mathrm{C}$ ? (Given, linear expansion coeffici...

At time $t=0$, a force $F=\alpha t$, where $t$ is time in seconds, is applied to a body of mass 1 kg , resting on a smooth horizontal plane. If the direction of the force makes an angle of $45^{\circ}$ with the horizontal, then the velocity...

An iron bar having a cross-sectional area of $2 \times 10^{-5} \mathrm{~m}^2$ and magnetising field of $2400 \mathrm{~A} / \mathrm{m}$ produce a magnetic flux $2.4 \pi \times 10^{-5} \mathrm{~Wb}$. What will be the value of permeability $\m...

Statement I An object subjected to velocities $\mathbf{v}_1$ and $\mathbf{v}_2$ has a resultant velocity with magnitude $|\mathbf{v}|=\left|\mathbf{v}_1\right|+\left|\mathbf{v}_2\right|$.
Statement II The magnitude of displacement is either...

For a projectile, if $\alpha$ is the angle of projection, $R$ is the range, $h$ is the maximum height, $t$ is the time of flight then

A ball projected up passes the same height $H$ at 2 s and 10 s . The value of $H$ is (use, $g=9.8 \mathrm{~m} / \mathrm{s}^2$ )

Two towns $X$ and $Y$ are connected by a regular bus service. A bus leaves in either direction at every $t=T$ minutes. A man moving with same speed in the direction $X$ to $Y$ find that a bus goes past him every $t=t_1$ minutes in the direc...

A current carrying loop $A B C D$ has two circular arcs $A D$ and $B C$ with radius 1 cm and 2 cm respectively, as shown in the figure. The two arcs $A D$ and $B C$ subtend a common angle $30^{\circ}$ at the centre $O$. If the current flowi...

Three parallel wires $a, b$ and $c$ carrying currents $i_a, i_b$ and $i_c$ as shown in the figure are placed next to each other.

The magnitude force on a length $l$ of the wire $a$, if $d_2=2 d_1, i_b=i_a$ and $i_c=4 i_a$ is