TG EAPCET 2024 (Online) 9th May Morning Shift

The equations $2 x^2+a x-2=0$ and $x^2+x+2 a=0$ have exactly one common root. If $a \neq 0$, then one of the roots of the equation $a x^2-4 x-2 a=0$ is

The sum of two roots of the equation $x^4-x^3-16 x^2+4 x+48=0$ is zero. If $\alpha, \beta, \gamma$ and $\delta$ are the roots of this equation, then $\alpha^4+\beta^4+\gamma^4+\delta^4=$

When $|x|<2$, then coefficient of $x^2$ in the power series expansion of $\frac{x}{(x-2)(x-3)}$, is

The mean deviation about the mean for the following data is
\begin{array}{c|l|l|l|l|l}
\hline \text { Class interval } & 0-2 & 2-4 & 4-6 & 6-8 & 8-10 \\\\
\hline \text { Frequency } & 1 & 3 & 5 & 3 & 1 \\\\
\hline
\end{array}

Area of the triangle bounded by the lines given by the equations $12 x^2-20 x y+7 y^2=0$ and $x+y-1=0$ is

The slope of a line $L$ passing through the point $(-2,-3)$ is not defined. If the angle between the lines $L$ and $a x-2 y+3=0(a>0)$ is $45^{\circ}$, then the angle made by the line $x+a y-4 \doteq 0$ with positive $X$-axis in the anti-clo...

$(a, b)$ is the point of concurrency of the lines $x-3 y+3=0, k x+y+k=0$ and $2 x+y-8=0$. If the perpendicular distance from the origin to the line $L=a x-b y+2 k=0$ is $p$, then the perpendicular distance from the point $(2,3)$ to $L=0$ is

If $(4,3)$ and $(1,-2)$ are the end points of a diagonal of a square, then the equation of one of its sides is

When the origin is shifted to the point $(2, b)$ by translation of axes, the coordinates of the point $(a, 4)$ have changed to $(6,8)$. When the origin is shifted to $(a, b)$ by translation of axes, if the transformed equation of $x^2+4 x y...

If the ratio of the perpendicular distances of a variable point $P(x, y, z)$ from the $X$-axis and from the $Y Z$ - plane is $2: 3$, then the equation of the locus of $P$ is

A plane $\pi$ passes through the points $(5,1,2),(3,-4,6)$ and $(7,0,-1)$. If $p$ is the perpendicular distance from the origin to the plane $\pi$ and $l, m$ and $n$ are the direction cosines of a normal to the plane $\pi$, the $|3 l+2 m+5 ...

The direction cosines of two lines are connected by the relations $l-m+n=0$ and $2 l m-3 m n+n l=0$. If $\theta$ is the angle between these two lines, then $\cos \theta=$

The number of solutions of the equation $\sin 7 \theta-\sin 3 \theta=\sin 4 \theta$ that lie in the interval $(0, \pi)$, is

If the period of the function
$f(x)=2 \cos (3 x+4)-3 \tan (2 x-3)+5 \sin (5 x)-7$ is $k$, then

If $m \cos (\alpha+\beta)-n \cos (\alpha-\beta)$ $=m \cos (\alpha-\beta)+n \cos (\alpha+\beta)$, then $\tan \alpha \tan \beta=$

If $\tan A<0$ and $\tan 2 A=-\frac{4}{3}$, then $\cos 6 A=$

A vector of magnitude $\sqrt{2}$ units along the internal bisector of the angle between the vectors $2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ is

If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are non-coplanar vectors and the points $\lambda \mathbf{a}+3 \mathbf{b}-\mathbf{c}, \mathbf{a}-\lambda \mathbf{b}+3 \mathbf{c}, 3 \mathbf{a}+4 \mathbf{b}-\lambda \mathbf{c}$ and $\mathbf{a}-6 b+...

$\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are three vectors such that $|a|=3,|b|=2 \sqrt{2},|c|=5$ and $\mathbf{c}$ is perpendicular to the plane of $\mathbf{a}$ and $\mathbf{b}$. If the angle between the vectors a and $\mathbf{b}$ is $\fra...

If $\theta$ is the angle between the vectors $4 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$, then $\sin 2 \theta=$

$\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ are the position vectors of the vertices $A, B$ and $C$ of a $\triangle ...

In a series $L-C-R$ circuit, if the current leads the source voltage, then

The half-life of a radioactive substance is 12 min . The time gap between $28 \%$ decay and $82 \%$ decay of the radioactive substance is

An element consists of a mixture of three isotopes $A, B$ and $C$ of masses $m_1, m_2$ and $m_3$, respectively. If the relative abundances of the three isotopes $A, B$ and $C$ are in the ratio $2: 3: 5$, the average mass of the element is

At room temperature, gaseous hydrogen is bombarded with a beam of electrons of 13.6 eV energy. The series to which the emitted spectral line belongs to

Three capacitors of capacitances $10 \mu \mathrm{~F}, 5 \mu \mathrm{~F}$ and $20 \mu \mathrm{~F}$ are connected in series with a 14 V DC supply. The charge on $5 \mu \mathrm{~F}$ capacitor is

The sphere $A$ of mass $m$ moving with a constant velocity hits another sphere $B$ of mass $2 m$ at rest. If the coefficient of restitution is 0.4 the ratio of the velocities of the spheres $A$ and $B$ after collision is

Four identical particles each of mass $m$ are kept at the four corners of a square of side $a$. If one of the particles is removed, the shift in the position of the centre of mass is

A car is moving on circular track banked at an angle of $45^{\circ}$. If the maximum permissible speed of the car to avoid slipping is twice the optimum speed of the car to avoid the wear and tear of the tyres, then the coefficient of stati...

The heights of the transmitting and receiving antennas are 33.8 m and 64.8 m respectively. The maximum distance between the antennas for satisfactory communication in line of sight mode is (radius of the earth $=6400 \mathrm{~km}$ )

When the temperature of a wire is increased from 303 K to 356 K , the resistance of the wire increases by $10 \%$. The temperature coefficient of resistance of the material of the wire is

Three resistors of resistances $10 \Omega, 20 \Omega$ and $30 \Omega$ are connected as shown in the figure. If the points $A, B$ and $C$ are at potentials $10 \mathrm{~V}, 6 \mathrm{~V}$ and 5 V respectively, then the ratio of the magnitude...

If Planck's constant is $6.63 \times 10^{-34} \mathrm{Js}$, then the slope of a graph drawn between cut-off voltage and frequency of incident light in a photoelectric experiment is

A steel wire of length 3 m and a copper wire of length 2.2 m are connected end to end. When the combination is stretched by a force, the net elongation is 1.05 mm . If the area of cross-section of each wire is $6 \mathrm{~mm}^2$, then the l...

Two circular coils of radii $r_1$ and $r_2\left(r_1 \ll r_2\right)$ are placed coaxially with their centres coinciding. The mutual inductance of the arrangement is

If the amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is 270 nT , the amplitude of the electric field part of the wave is

Two positive point charges are separated by a distance of 4 m in air. If the sum of the two charges is $36 \mu \mathrm{C}$ and the electrostatic force between them is 0.18 N , then the bigger charge is

The height of water level in a tank of uniform cross-section is 5 m . The volume of the water leaked in 5 s through a hole of area $2.4 \mathrm{~mm}^2$ miade at the bottom of the tank is (Assume the level of the water in the tank remains co...

Regarding fundamental forces in nature, the correct statement is

The energy required to take a body from the surface of the earth to a height equal to the radius of the earth is $W$. The energy required to take this body from the surface of the earth to a height equal to twice the radius of the earth is

The total internal energy of 4 moles of a diatomic gas at a temperature of $27^{\circ} \mathrm{C}$ is (gas constant $=831$ $\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ )

The temperatures of equal masses of three different liquids $A, B$ and $C$ are $15^{\circ} \mathrm{C}, 24^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$, respectively. The resultant temperature when liquids $A$ and $B$ are mixed is $20^{\c...

The temperature on a fahrenheit temperature scale that is twice the temperature on a celsius temperature scale is

The efficiency of a reversible heat engine working between two temperatures is $50 \%$. The coefficient of performance of a refrigerator working between the same two temperatures but in reverse direction is

The most exotic diamagnetic materials are

A body $P$ is projected at an angle of $30^{\circ}$ with the horizontal and another body $Q$ is projected at an angle of $30^{\circ}$ with the vertical. If the ratio of the horizontal ranges of the bodies $P$ and $Q$ is $1: 2$, then the rat...

A body is falling freely from the top of a tower of height 125 m . The distance covered by the body during the last second of its motion is $x \%$ of the height of the tower. Then, $x$ is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$...

A particle of charge 2 C is moving with a velocity of $(3 \hat{\mathbf{i}}+4 \hat{\mathrm{j}}) \mathrm{ms}^{-1}$ in the presence of magnetic and electric fields. If the magnetic field is $(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{...

A rectangular coil of 400 turns and $10^{-2} \mathrm{~m}^2$ area, carrying a current of 0.5 A is placed in a uniform magnetic field of IT such that the plane of the coil makes an angle of $60^{\circ}$ with the direction of the magnetic fiel...

For a combination of two convex lenses of focal lengths $f_1$ and $f_2$ to act as a glass slab, the distance of separation between them is