TG EAPCET 2024 (Online) 9th May Evening Shift

$\alpha, \beta, \gamma, 2$ and $\varepsilon$ are the roots of the equation
$$ \begin{aligned} & \alpha, \beta, \gamma+4 x^4-13 x^3-52 x^2+36 x+144=0 . \text { If } \\ & \alpha<\beta<\gamma<2<\varepsilon \text {, then } \alpha+2 \beta+3 \gam...

$\frac{1}{3 \cdot 6}+\frac{1}{6 \cdot 9}+\frac{1}{9 \cdot 12}+\ldots \ldots .$. to 9 terms $=$

The variance of the following continuous frequency distribution is


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If the origin is shifted to the point $\left(\frac{3}{2},-2\right)$ by the translation of axes, then the transformed equation of $2 x^2+4 x y+y^2+2 x-2 y+1=0$ is

$L \equiv x \cos \alpha+y \sin \alpha-p=0$ represents a line perpendicular to the line $x+y+1=0$. If $p$ is positive, $\alpha$ lies in the fourth quadrant and perpendicular distance from $(\sqrt{2}, \sqrt{2})$ to the line, $L=0$ is 5 units,...

If the ratio of the distances of a variable point $P$ from the point $(1,1)$ and the line $x-y+2=0$ is $1: \sqrt{2}$, then the equation of the locus of $P$ is

The slope of one of the pair of lines $2 x^2+h x y+6 y^2=0$ is thrice the slope of the other line, then $h=$

$(-2,-1),(2,5)$ are two vertices of a triangle and $\left(2, \frac{5}{3}\right)$ is its orthocenter. If $(m, n)$ is the third vertex of that triangle, then $m+n$ is equal to.

$L_1 \equiv 2 x+y-3=0$ and $L_2 \equiv a x+b y+c=0$ are two equal sides of an isosceles triangle. If $L_3 \equiv x+2 y+1=0$ is the third side of this triangle and $(5,1)$ is a point on $L_2=$ 0 , then $\frac{b^2}{|a c|}=$

If $\hat{\mathbf{i}}+\hat{\mathbf{j}}, \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{k}}+\hat{\mathbf{i}}, \hat{\mathbf{i}}-\hat{\mathbf{j}}, \hat{\mathbf{j}}-\hat{\mathbf{k}}$ are the position vectors of the points $A, B, C, D, E$ respec...

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

The solution set of the equation $\cos ^2 2 x+\sin ^2 3 x=1$ i

If $\cos x+\cos y=\frac{2}{3}$ and $\sin x-\sin y=\frac{3}{4}$, then $\sin (x-y)+\cos (x-y)=$

The maximum value of the function $f(x)=3 \sin ^{12} x+4 \cos ^{16} x$ is

$(3,0,2)$ and $(0,2, k)$ are the direction ratios of two lines and $\theta$ is the angle between them. If $|\cos \theta|=\frac{6}{13}$, then $k=$

If $\mathrm{a}, \mathrm{b}$ are two vectors such that $|\mathrm{a}|=3,|\mathrm{~b}|=4$, $|\mathbf{a}+\mathbf{b}|=\sqrt{37},|\mathbf{a}-\mathbf{b}|=k$ and $(\mathbf{a}, \mathbf{b})=\theta$, then $\frac{4}{13}(k \sin \theta)^2=$

$\mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \mathbf{k}, \quad \mathbf{c}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ are two vectors and $\mathbf{a}$ is a vector such that
$\cos (\mathbf{a}, \mathbf{b} \times \mathbf{c})=\sqrt...

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are non-coplanar vectors. If the three points $\lambda a-2 b+c, 2 a+\lambda b-2 \mathbf{c}$ and $4 \mathbf{a}+7 \mathbf{b}-8 \mathbf{c}$ are collinear, then $\lambda=$

$r$ is a vector perpendicular to the planet, determined by the vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}$ and $\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$, If the magnitude of the projection of $\mathbf{r}$ on the vector $2 \hat{\mathbf{i}}+\ha...

$A(3,2,-1), B(4,1,0), C(2,1,4)$ are the vertices of a $\triangle A B C$. If the bisector of $B A C$ ! intersects the side $B C$ at $D(p, q, r)$, then $\sqrt{2 p+q+r}=$

The related effort to derive the properties of a bigger, more complex system from the properties and interactions of its constituent simpler parts is

The half lives of two radioactive material $A$ and $B$ are respectively $T$ and $2 T$. If the ratio of the initial masses of the materials $A$ and $B$ is $8: 1$. Then, the time after which the ratio of the masses of the materials $A$ and $B...

The ratio of the wavelengths of radiation emitted when an electron in the hydrogen atom jumps from 4th orbit to 2 nd orbit and from 3rd orbit to 2 nd orbit is

The energy released by the fission of one uranium nucleus is 200 MeV . The number of fissions per second required to produce 128 W power is

The natural frequency of an $L-C$ circuit is 120 kHz . When the capacitor in the circuit is totally filled dielectric material, the natural frequency of the circuit decreases by 20 kHz . Dielectric constant of material is

If half of the space between the plates of a parallel plate capacitor is filled with a medium of dielectric constant 4 , the capacitance is $C_1$. If one-third of the space between the plates of the capacitor is filled with the medium of di...

Three particles $A, B$ and $C$ of masses $m, 2 m$ and $3 m$ are moving towards north, south and east respectively. If the velocities of the particles $A, B$ and $C$ are $6 \mathrm{~ms}^{-1}$. $12 \mathrm{~ms}^{-1}$ and $8 \mathrm{~ms}^{-1}$...

A 20 ton truck is travelling along a curved path of radius 240 m . If the centre of gravity of the truck above the ground is 2 m and the distance between its wheels is 1.5 m , the maximum speed of the truck with which it can travel without ...

A message signal of peak voltage 12 V is used to amplitude modulate a carrier signal of frequency 1.2 MHz . The amplitude of the side bands is

The potential difference between the ends of a straight conductor of length 20 cm is 16 V . If the drift speed of the electrons is $2.4 \times 10^{-4} \mathrm{~ms}^{-1}$, the electron mobility in $\mathrm{m}^2 \mathrm{~V}^{-1} \mathrm{~s}^{...

The potential difference $V$ across the filament of the bulb shown in the given Wheatstone bridge varies as $V=i(2 i+1)$, where $i$ is the current in ampere through the filament of the bulb. The emf of the battery $V_a$, so that the bridge ...

If the de-Broglie wavelength of a neutron at a temperature of $77^{\circ} \mathrm{C}$ is $\lambda$, then the de-Broglie wavelength of the neutron at a temperature of $1127^{\circ} \mathrm{C}$ is

If the length of a string is $P$ when the tension in it is 6 N and its length is $Q$ when the original length of the string is

A train with an axle of length 1.66 m is moving towards north with a speed of $90 \mathrm{kmh}^{-1}$. If the vertical component of the earth's magnetic field is $0.2 \times 10^{-4} \mathrm{~T}$, the emf induced across the ends of the axle o...

A plane electromagnetic wave of electric and magnetic fields $E_0$ and $B_0$ respectively incidents on a surface. If the total energy transferred to the surface in a time of $t$ is $U$, then the magnitude of the total momentum delivered to ...

Two point charges of magnitudes $-8 \mu \mathrm{C}$ and $+32 \mu \mathrm{C}$ are separated by a distance of 15 cm in air. The position of the point from $-8 \mu \mathrm{C}$ charge at which the resultant electric field becomes zero is

Water flows through a horizontal pipe of variable cross-section at the rate of $12 \pi$ litre per minute. The velocity of the water at the point, where the diameter of the pipe becomes 2 cm is

The excess pressure inside a soap bubble of radius 0.5 cm is balanced by the pressure due to an oil column of height 4 mm . If the density of the oil is $900 \mathrm{~kg} \mathrm{~m}^{-3}$, then the surface tension of the soap solution is (...

The ratio of the accelerations due to gravity at heights 1280 km and 3200 km above the surface of the earth is
(Radius of the earth $=6400 \mathrm{~km}$ )

If the temperature of a gas increased from $27^{\circ} \mathrm{C}$ to $159^{\circ} \mathrm{C}$, the increase in the rms speed of the gas molecules is

When 54 g of ice at $-20^{\circ} \mathrm{C}$ is mixed with 25 g of steam at $100^{\circ} \mathrm{C}$, then the final mixture at thermal equilibrium contains

A solid sphere at a temperature $T \mathrm{~K}$ is cut in to two hemisphere. The ratio of energies radiated by one hemisphere to the whole sphere per second is

If $d Q, d U$ and $d W$ are heat energy absorbed, change in internal energy and external work done respectively by a diatomic gas at constant pressure, then $d W: d U: d Q$ is

If a bar magnet of moment $10^{-4} \mathrm{Am}^2$ is kept in a uniform magnetic field of $12 \times 10^{-3} \mathrm{~T}$ such that it makes angle of $30^{\circ}$ with the direction of magnetic field, then the torque acting on the magnet is

A cannon placed on a cliff at a height of 375 m fires a cannon ball with a velocity of $100 \mathrm{~ms}^{-1}$ at an angle of $30^{\circ}$ above the horizontal. The horizontal distance between the cannon and the target is (Acceleration due ...

A stone is thrown vertically up from the top end of a window of height 1.8 m with a velocity of $8 \mathrm{~ms}^{-1}$. The time taken by the stone to cross the window during its downward journey is (acceleration due to gravity $=10 \mathrm{...

Two charged particles $A$ and $B$ of masses $m$ and $2 m$, charges $2 q$ and $3 q$ respectively moving with same velocity enter a uniform magnetic field such that both the particles make same angle ( $<90^{\circ}$ ) with the direction of th...

Two points $A$ and $B$ on the axis of a circular current loop are at distances of 4 cm and $3 \sqrt{3} \mathrm{~cm}$ from the centre of the loop. If the ratio of the induced magnetic fields at points $A$ and $B$ is $216: 125$, then radius o...

If you are using eye glasses of power 2 D, your near point is

A small angled prism is made of a material of refractive index $\frac{3}{2}$. The ratio of the angles of minimum deviations when the prism is placed in air and in water of refractive index $\frac{4}{3}$ is