TS EAMCET 2023 (Online) 12th May Morning Shift

If $(x-2)$ is a common factor of the expressions $x^2+a x+b$ and $x^2+c x+d$, then $\frac{b-d}{c-a}=$

If one root of the equation $4 x^2-2 x+k-4=0$ is the reciprocal of the other, then the value of $k$ is

Two numbers $b$ and $c$ are chosen at random in succession without replacement from the set $\{1,2,3, \ldots \ldots, 9\}$. Then, the probability that $x^2+b x+c>0, \forall x \in R$ i

The sum of the roots of the equation $e^{4 t}-10 e^{3 t}+29 e^{2 t}-20 e^t+4=0$ is

The roots of the equation $x^3-14 x^2+56 x-64=0$ are in

The angle, by which the coordinate axes are to be rotated about the origin so that the transformed equation of $\sqrt{3} x^2+(\sqrt{3}-1) x y-y^2=0$ would be free from $x y$-term is

If each of the points $(a, 4),(-2, b)$ lies on the line joining the points $(2,-1)$ and $(5,-3)$, then the point $(a, b)$ lies on the line

If the slope of a straight line passing through $A(3,2)$ is $3 / 4$, then the coordinates of the two points on the same line that are 5 units away from $A$ are

The sum of the squares of the perpendicular distances of a point $(x, y, z)$ from the coordinate axes is $k$ times the square of the distance of the point from the origin Then, $k=$

If the direction cosines $(l, m, n)$ of two lines are connected by the relations $l+m+n=0$ and $l m=0$, then the angle between those lines is

Equation of the plane through the mid-point of the line segment joining the points $A(4,5,-10)$ and $B(-1,2,1)$ and perpendicular to $A B$ is

\(\sin \alpha+\cos \alpha=m \Rightarrow \sin ^6 \alpha+\cos ^6 \alpha=\)

For $0 \leq x \leq \pi$, if $81^{\sin ^2 x}+81^{\cos ^2 x}=30$, then $x=$

\(\frac{\left(1+\tan 32^{\circ}\right)}{\left(1-\tan 48^{\circ}\right)}=\)

If $\mathbf{a}$ is a vector such that $\mathbf{a} \times \hat{\mathbf{i}}=\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{a} \cdot \hat{\mathbf{i}}=1$, then equation of the line passing through the point $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\...

If the position vectors of $\mathbf{P}$ and $\mathbf{Q}$ are $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-7 \hat{\mathbf{k}}$ and $5 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ respectively, then the cosine of the angle between $P Q$ an...

The position vectors of the point $A, B$ are $\mathbf{a}, \mathbf{b}$ respectively. If the position vector of the point $C$ is $\frac{a}{2}+\frac{b}{3}$, then

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three-unit yectors such that $|\mathbf{a}+\mathbf{b}+\mathbf{c}|=1$ and $\mathbf{a}$ is perpendicular to $\mathbf{b}$. If $\mathbf{c}$ makes angles $\alpha, \beta$ with $\mathbf{a}, \mathbf{b}$ respe...

If $|\mathbf{a}|=1,|\mathbf{b}|=2,|\mathbf{a}-\mathbf{b}|^2+|\mathbf{a}+2 \mathbf{b}|^2=20$, then $(a, b)=$

The power factor of an AC circuit containing peak current 2 A and peak voltage 1 V is $1 / 2$, then the angle between voltage and current is

The energy equivalent to a mass of 1 kg is

If $S$ is the surface area of a nucleus of mass number $A$, then

If $F_1, F_2$ and $F_3$ are the relative strengths of the gravitational, the weak nuclear and the electromagnetic forces respectively, then

If an electron is moving in the 4th orbit of the hydrogen atom, then the angular momentum of the electron in SI unit is

A system consists of two particles of masses $m_1$ and $m_2$. If the particle of mass $m_1$ is moved towards the centre of mass through a distance $d$, then the distance the second particle should be moved, so as to keep the centre of mass ...

The angular speed of a particle moving in a circular path is doubled. Then, the centripetal acceleration of the particle is

A message signal of frequency 10 kHz is used to modulate a carrier wave of frequency 6 MHz , then the side band frequencies are

In the given part of a circuit, the potential at point $B$ is zero. Then, the potentials at $A$ and $C$ respectively, are

When a potentiometer is connected between the points $A$ and $B$ as shown in the circuit, balance point is obtained at 64 cm . When it is connected between $A$ and $C$, the balance point is 8 cm . If the potentiometer is connected between $...

The de-Broglie wavelength of an electron accelerated between two plates having a potential difference of 900 V is nearly

A wire of length 40 cm is stretched by 0.1 cm . The strain on the wire is

In a pair of adjacent coils, if the current in one coil changes from 10 A to 2 A in a time 0.2 s , an emf of 120 V is induced in another coil. The mutual inductance of the pair of the coils is

When a current $i$ through a solenoid is increasing at a constant rate, then the induced current is

If a plane electromagnetic wave has electric field oscillations of frequency 3 GHz , then the wavelength of the wave is (speed of light in vacuum $=3 \times 10^8 \mathrm{~ms}^{-1}$ )

A clock dial has point charges $-q,-2 q,-3 q, \ldots \ldots \ldots,-12 q$ at the positions of the corresponding numbers on the dial respectively. The time at which the hour's hand points the direction of the net electric field at the centre...

The electric potential at a place is varying as $V=\frac{1}{2}\left(y^2-4 x\right) \mathrm{V}$. Then, the electric field at $x=1 \mathrm{~m}$ and $y=1 \mathrm{~m}$ is

A solid metal sphere released in a vertical liquid column has attained terminal velocity in the downward direction. The magnitudes of viscous force, buoyant force and gravitational force acting on it are $F_V, F_B$ and $F_W$ respectively. T...

A straw of circular cross-section of radius $R$ and negligible thickness is dipped vertically into a liquid of surface tension $T$. If the contact angle between the liquid and the straw material is $53^{\circ}$. The force acting on the stra...

A ring has a mass $M$ and radius $R$. The distance of the point on its geometric axis from its centre at which the gravitational field is strongest is

The percentage of heat supplied to a diatomic ideal gas that is converted into work in an isobaric process is

Ratio of translational degrees of freedom to rotational degrees of freedom of a polyatomic linear gas molecule is

On a new temperature scale, the melting point of ice is $20^{\circ} \mathrm{X}$ and the boiling point of water is $110^{\circ} \mathrm{X}$. A temperature of $40^{\circ} \mathrm{C}$ would be indicated on this new temperature scale as

Two objects made of the same material have masses $m$ and $2 m$ and are at temperatures $2 T$ and $T$ respectively. When heat $Q$ is supplied to the object of mass $2 m$, its temperature raises to $2 T$. If the same heat is supplied to the ...

A bar magnet has coercivity $4 \times 10^3 \mathrm{Am}^{-1}$. It is placed inside a solenoid of 12 cm length and 60 turns. The current that should be passed through the solenoid to demagnetise, the bar magnet is

A bomb is dropped on an enemy post on the ground by an aeroplane flying horizontally with a velocity of $60 \mathrm{kmh}^{-1}$ at a height of 490 m . At the time of dropping the bomb, the horizontal distance of the aeroplane from the enemy ...

The relation between time $t$ and distance $x$ of a particle is $t=a x^2+b x$, where $a$ and $b$ are constants. If $v$ is the velocity of the particle, then its acceleration is

A long straight wire carries a current of 18 A . The magnitude of the magnetic field at a point 12 cm from it is

A contjucting wire $P Q$ carries a current 10 A as shown in the figure. ft is placed in a uniform magnetic field 5 T which is acting normally outside from the paper. Then, the net force experienced by it is

An empty tank has concave murror as its bottom. When sunlight falls normally on the mirror, it is focussed $\mathrm{a}_2$ height of 32 cm from the mirror. If the tank is filled with water upto a height of 20 cm , then the sunlight focusses ...

If the radius of the earth becomes $x$ times its present value, the new period of rotation in hours is