TS EAMCET 2023 (Online) 13th May Evening Shift

The set of all values of $x$ for which the inequalities $x^2-7 x+10 \geq 0$ and $2 x+3-x^2>0$ hold simultaneously is

If $3 x=1+\frac{5}{8}+\frac{5}{8} \cdot \frac{9}{13}+\frac{5}{16}+\ldots$, then $x^4+4 x^3+6 x^2+4 x=$

If $M$ and $\sigma^2$ represent respectively the mean deviation from the mean and the variance for the data $1,3,5,7$, $11,13,17,19,23$, then $3\left(\sigma^2-M\right)=$

If $X$ is a Poisson variate satisfying the condition $3 P(X=2)=P(X=4)$, then $P(X=6)=$

If the lines $4 x+3 y-k=0,2 x+y+3=0$ and $3 x+2 y+k=0$ are concurrent, then the perpendicular distance from the point of concurrency of these lines to the line $3 x+4 y+2=0$ is

Let the angle between the lines $x-2 y+3=0$ and $k x-y+2=0$ be $45^{\circ}$. If $k_1, k_2\left(k_1>k_2\right)$ are two distinct real values of $k$, then $k_1-2=$

Two points $P(a, 2)$ and $Q(1, b)$ lie on either side of the line $2 x-3 y+1=0$. If $P$ is the point of intersection of the lines $4 x+3 y+k=0$ and $3 x+4 y+k=0$, then the range of $b$ is

Let $A(1,3)$ and $B(2,5)$ be two points and $C(h, k)$ be a point such that $B C$ is perpendicular to $A C$. If $\angle C A B=\angle C B A$, then $h=$

Let the line $2 x-3 y-1=0$ intersect the curve $x^2+2 x y+5 y^2+2 x+3 y-1=0$ in distinct points $A$ and $B$. If ' $O$ ' is the origin, then $\cos \angle A O B=$

A plane $\pi$ passing through the point $(1,1,1)$ is perpendicular to the line joining the points $(6,3,2)$ and $(1,-4,-9)$. If $a x+b y+c z-23=0$ is the equation of the plane $\pi$, then $a+b-c=$

If the image of the point $(1,-2,1)$ with respect to the line passing through the points $B(1,1,2)$ and $C(2,2,1)$ is $(l, m, n)$, then $l^2+m^2+n^2=$

$A(1,2,3), B(2,3,1)$ and $C(3,1,2)$ are three points. If the point $P$ divides $A B$ in the ratio $1: 2$ and the point $Q$ divides $B C$ in the ratio $-2: 3$, then the distance between $P$ and $Q$ is

$\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7} \cos \frac{\pi}{14} \cos \frac{3 \pi}{14} \cos \frac{5 \pi}{14}=$

\(\sin 6^{\circ}+\sin 54^{\circ}+\sin 126^{\circ}+\cos 156^{\circ}=\)

If $\tan \alpha=\frac{-12}{5}, \cot \beta=\frac{7}{24}, \alpha$ does not belong to second quadrant and $\beta$ does not belong to first quadrant, then $\sqrt{13} \sin \frac{\alpha}{2}+\cos \frac{\beta}{2}+\tan \frac{\alpha}{2} \cot \frac{\b...

Let $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, \mathbf{b}=6 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\mathbf{c}=3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-12 \hat{\mathbf{k}}$ be three vectors. If $\m...

The volume of the tetrahedron with $\hat{\mathbf{i}}-\lambda \hat{\mathbf{j}}+\hat{\mathbf{k}}$, $\lambda \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}$ as coterminous ed...

Let $\mathbf{a}, \mathbf{b}, \mathbf{c}$ be three non-coplanar vectors and $L$ be the line passing through the points $\mathbf{a}-\mathbf{b}+\mathbf{c}$ and $\mathbf{b}-\mathbf{c}$. If $\pi$ is a plane passing through the points $2 \mathbf{...

Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ and $\mathbf{c}=\hat{\mathbf{i}}-4 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ be three vectors. Let $\mathb...

II. If the points with position vectors $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{k}}$, $\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}$ are co...

An alternating emf given by the equation $E=200 \sin (50 \pi t)$ (where, $E$ is in volts and $t$ is in seconds) is applied across a series combination of an inductor and a resistor having inductive reactance $40 \Omega$ and resistance $30 \...

The radius of a nucleus of mass number 27 is $R$. Which of the following is true about a nucleus whose radius is $2 R$ ?

The nucleus ${ }_{50}^{120} X$ undergoes the series of reactions given below:
\({ }_Z^A X \xrightarrow{\alpha \text {-decay }} P \xrightarrow{\beta^{-} \text {-decay }} Q \xrightarrow{\alpha \text {-decay }} R\)
The number of neutrons in ...

Two blocks of masses 2 kg and 1 kg are tied to the ends of a string which passes over a light frictionless pulley. The blocks are held at the same horizontal level and then released suddenly. The distance traversed by their centre of mass i...

A car is travelling with linear velocity $v$ on a circular road of radius $r$. If its velocity is increasing at a rate of $a \mathrm{~ms}^{-2}$, then the resultant acceleration will be

A telephonic communication service is working at a carrier frequency of 20 GHz . Only $20 \%$ of it is utilised for transmission. If each channel requires a bandwidth of 5 kHz , then the number of telephonic channels that can be transmitted...

If the masses of three wires of same material are in the ratio of $1: 2: 3$ and their lengths are in the ratio of $3: 2: 1$, then electrical resistances of these wires are in the ratio

As shown in the figure, in a Wheatstone's bridge, three resistances $P, Q$ and $R$ are connected in the three arms and the fourth arm is formed by two resistances $S_1$ and $S_2$ connected in parallel. The condition for the bridge to be bal...

A photon released by the transition of an electron from the second excited state to the ground state of Hydrogen atom is incident on the surface of a metal of work function 3.1 eV . The de-Broglie wavelength of the most energetic electron e...

Consider two black bodies $A$ and $B$ having equal surface area. On the surface of $A, n$ photons of frequency $f$ are incident perpendicularly in a time $t$. On the surface of $B$, $2 n$ photons of frequency $3 f$ are incident perpendicula...

The self inductance of a coil depends on

A conducting circular coil is place in a uniform magnetic field with the magnetic field initially directed perpendicular to the plane of the coil. In step $A$, the coil is rotated from its initial position by $60^{\circ}$ about its diameter...

The speed of electromagnetic waves in a medium is $1.5 \times 10^8 \mathrm{~ms}^{-1}$. If relative permittivity of that medium is 2 , then its magnetic susceptibility is (speed of light in vacuum is $3 \times 10^8 \mathrm{~ms}^{-1}$ ).

Two conducting spheres of radii $r_1$ and $r_2$ are charged to the same surface charge density. The ratio of electric fields near their surfaces is

The ratio of relative strengths of the gravitational force and the electromagnetic force between two charged particles is

Two electric charges $+2 \mu \mathrm{C}$ and $-4 \mu \mathrm{C}$ are separated by a distance 3 m in air. At a point $P$ located on the line joining the two charges and in between them, the electric potential is zero. Then the electric field...

The angle of contact is $120^{\circ}$ when a cylindrical rod is vertically placed in a liquid. If the same rod is placed horizontally in the liquid, then the angle of contact is

In a well the pressure at a point 10 m below the surface of water is $\left(g=10 \mathrm{~ms}^{-2}\right)$

The ratio of orbital velocity of a body near to the surface of a planet and escape velocity of a body from the surface of the same planet is

When some amount of heat energy is supplied to a monatomic gas, the percentage of heat energy used for increasing the internal energy of the gas $(\gamma=5 / 3)$ is

The average energy possessed by an oscillator at a temperature 300 K is (Boltzmann constant $=1.38 \times 10^{-23} \mathrm{JK}^{-1}$ )

The length of a metal rod at $30^{\circ} \mathrm{C}$ is 30 cm . If its temperature is raised to $105^{\circ} \mathrm{C}$, its length is increased by 0.027 cm . Then, the coefficient of linear expansion of the metal is

If the reading in Fahrenheit scale is twice the reading in Celsius scale, then the reading in Fahrenheit scale is

The heat energy required to convert 10 kg of ice at $-10^{\circ} \mathrm{C}$ into water at $0^{\circ} \mathrm{C}$ is (specific heat capacity of ice $=0.5 \mathrm{calg}^{-1}$ and latent heat of fusion of ice $=80 \mathrm{calg}^{-1}$ )

Two blocks of masses $w_1$ and $w_2$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with an acceleration $g$, then the tension in the string will be

The period of oscillation of a bar magnet at a place is 2 s . At the same place, the period of oscillation of another identical bar magnet whose magnetic moment is 4 times so that of first magnet is

A bird flies with a velocity $(t-2) \mathrm{ms}^{-1}$ along a straight line, where $t$ is the time in seconds. The distance covered by it in a time of 4 seconds is

A closely wound solenoid of 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm . If the current carried is 8 A , then the magnitude of the magnetic field inside the solenoid near its centre is appr...

A current $i$ flows in an infinitely long, straight and thin walled pipe, then

A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black, then