TG EAPCET 2024 (Online) 10th May Morning Shift

If $M_1$ is the mean deviation from the mean of the discrete data $44,5,27,20,8,54,9,14,35$ and $M_2$ is the mean deviation from the median of the same data, then $M_1-M_2=$

The mean of a binomial variate $X \sim B(n, p)$ is 1 . If $n>2$ and $P(X=2)=\frac{27}{128}$, then the variance of the distribution is

If $Q$ and $R$ are the images of the point $P(2,3)$ with respect to the lines $x-y+2=0$ and $2 x+y-2=0$ respectively, then $Q$ and $R$ lie on

$(0, k)$ is the point to which the origin is to be shifted by the translation of the axes so as to remove the first degree terms from the equation $a x^2-2 x y+b y^2-2 x+4 y+1=0$ and $\frac{1}{2} \tan ^{-1}(2)$ is the angle through which th...

If the distance from a variable point $P$ to the point $(4,3)$ is equal to the perpendicular distance from $P$ to the line $x+2 y-1=0$, then the equation of the locus of the point $P$ is

The line $2 x+y-3=0$ divides the line segment joining the points $A(1,2)$ and $B(-2,1)$ in the ratio $a: b$ at the point $C$. If the point $C$ divides the line segment joining the points $P\left(\frac{b}{3 a},-3\right)$ and $Q\left(-3,-\fra...

If $(2,-1)$ is the point of intersection of the pair of lines $2 x^2+a x y+3 y^2+b x+c y-3=0$, then $3 a+2 b+c=$

$\beta$ is the angle made by the perpendicular drawn from origin to the line $L \equiv x+y-2=0$ with the positive $X$-axis in the anticlockwise direction. If $a$ is the $X$-intercept of the line $L=0$ and $p$ is the perpendicular distance f...

$A(2,3, k), B(-1, k,-1)$ and $C(4,-3,2)$ are the vertices of $\triangle A B C$. If $A B=A C$ and $k>0$, then $\triangle A B C$ is

If $a, b$ and $c$ are the intercepts made on $X, Y, Z$-axes respectively by the plane passing through the points $(1,0,-2),(3,-1,2)$ and $(0,-3,4)$, then $3 a+4 b+7 c=$

A plane $\pi_1$ passing through the point $3 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ is perpendicular to the vector $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and another plane $\pi_2$ passing through the point...

The equation that is satisfied by the general solution of the equation $4-3 \cos ^2 \theta=5 \sin \theta \cos \theta$ is

If $\tan A+\tan B+\cot A+\cot B=\tan A \tan B-\cot A \cot B$ and $0^{\circ} < A+B<270^{\circ}$, then $A+B=$

$\tan A=\frac{-60}{11}$ and $A$ does not lie in the 4th quadrant. $\sec B=\frac{41}{9}$ and $B$ does not lie in the 1st quadrant. If $\operatorname{cosec} A+\cot B=K$, then $24 K=$

The approximate value of $\sec 59^{\circ}$ obtained by taking $1^{\circ}$ $=0.0174$ and $\sqrt{3}=1.732$ is

If $\cos ^2 84^{\circ}+\sin ^2 126^{\circ}-\sin 84^{\circ} \cos 126^{\circ}=K$ and $\cot A+\tan A=2 K$, then the possible values of $\tan A$ are

The position vector of the point of intersection of the line joining the points $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and the line joining the points $2 \hat{\mathbf{i}}+\...

$\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\mathbf{c}=2 \hat{\mathbf{k}}-\hat{\mathbf{i}}$ are three vectors and $\mathbf{d}$ is a unit vector perpendicular to $\mathbf{c}$. If $\ma...

If $\mathbf{a}=4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\mathbf{b}=6 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ are two vectors, then the magnitude of the component of $\mathbf{b}$ parallel to $\mathbf{a}$...

$P$ and $Q$ are the points of trisection of the segment $A B$. If $2 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $4 \hat{\mathbf{i}}+\hat{\mathbf{j}}-6 \hat{\mathbf{k}}$ are the position vectors of $A$ and $B$ respectively, ...

An inductor and a resistor are connected in series to an AC source of 10 V . If the potential difference across the inductor is 6 V , then the potential difference across the resistor is

The operation of a nuclear reactor is said to be critical when the value of neutron multiplication factor $K i s$

The ratio of the centripetal accelerations of the electron in two successive orbits of hydrogen is $81: 16$. Due to ${ }^3$ transition between these two states, the angular momentum of the electron changes by ( $h=$ Planck's constant)

An $\alpha$-particle of energy $E$ is liberated during the decay of a nucleus of mass number 236. The total energy released in this process is

A $10 \mu \mathrm{~F}$ capacitor is charged by a 100 V battery. It is disconnected from the battery and is connected to another uncharged capacitor of capacitance $30 \mu \mathrm{~F}$. During this process, the electrostatic energy lost by t...

A ball of mass 1.2 kg moving with a velocity of $12 \mathrm{~ms}^{-1}$ makes one-dimensional collision with anothe stationary ball of mass 1.2 kg . If the coefficient of restitution is $\frac{1}{\sqrt{2}}$, then the ratio of the total kinet...

An alphabet $T$ made of two similar thin uniform metal plates of each length $L$ and width $a$ is placed on a horizontal surface as shown in the figure. If the alphabet is vertically inverted, the shift in the position of its centre of mass...

An aircraft executes a horizontal loop of radius 9 km at a constant speed of $540 \mathrm{kmh}^{-1}$. The wings of the aircraft are banked at an angle of (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The process of the loss of strength of a signal while propagating through a medium is

The relation between the current $i$ (in ampere) in a conductor and the time $t$ (in second) is $i=12 t+9 t^2$. The charge passing through the conductor between the times $t=2 \mathrm{~s}$ and $t=10 \mathrm{~s}$ is

A conductor of length 1.5 m and area of cross-section $3 \times 10^{-5} \mathrm{~m}^2$ has electrical resistance of $15 \Omega$.
The current density in the conductor for an electric field of $21 \mathrm{Vm}^{-1}$ is

The de-Broglie wavelength of a proton is twice the de-Broglie wavelength of an alpha particle. The ratio of the kinetic energies of the proton and the alpha particle is

A block of mass 2 kg is tied to one end of a 2 m long metal wire of $1.0 \mathrm{~mm}^2$ area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the...

A circular coil of area $200 \mathrm{~cm}^2$ and 50 turns is rotating about its vertical diameter with an angular speed of $\theta$ $40 \mathrm{rads}^{-1}$ in a uniform horizontal magnetic field of magnitude $2 \times 10^{-2} \mathrm{~T}$. ...

If the peak value of the magnetic field of an electromagnetic wave is $30 \times 10^{-9} \mathrm{~T}$, then the peak value of the electric field is

Two point charges $-10 \mu \mathrm{C}$ and $-5 \mu \mathrm{C}$ are situated on $X$-axis at $x=0$ and $x=\sqrt{2} \mathrm{~m}$. The point along the $X$-axis, where the electric field becomes zero is

A wooden cube of side 10 cm floats at the interface between water and oil with its lower surface 3 cm below the interface. If the density of oil is $0.9 \mathrm{~g} \mathrm{~cm}^{-3}$, the mass of the wooden cube is

Two stars of masses $M$ and $2 M$ that are at a distance $d$ apart, are revolving one around another. The angular velocity of the system of two stars is ( $G$-Universal gravitational constant)

37 g of ice at $0^{\circ} \mathrm{C}$ temperature is mixed with 74 g of water at $70^{\circ} \mathrm{C}$ temperature. The resultant temperature is (specific heat capacity of water $=1 \mathrm{cal} {\mathrm{g}^{-1o}} \mathrm{C}^{-1}$ and lat...

The thickness of a uniform rectangular metal plate is 5 mm and the area of each surface is $5 \mathrm{~cm}^5$. In steady state, the temperature difference between the two surfaces of the plate is $14^{\circ} \mathrm{C}$. If the heat flowing...

A vessel contains hydrogen and nitrogen gases in the ratio $2: 3$ by mass. If the temperature of the mixture of the gases is $30^{\circ} \mathrm{C}$, then the ratio of the average kinetic energies per molecule of hydrogen and nitrogen gases...

A big liquid drop splits into $n$ similar small drops under isothermal conditions, then in the process

The ratio of the specific heat capacities of a gas is 1.5 . When the gas undergoes adiabatic process, its volume is doubled and pressure becomes $p_1$. When the gas undergoes isothermal process, its volume is doubled and pressure becomes $p...

A body is projected from the ground at an angle of $\tan ^{-1}(\sqrt{7})$ with the horizontal. At half of the maximum height, the speed of the body is $n$ times the speed of projection. The value of $n$ is

A body moving with uniform acceleration, travels a distance of 25 m in the fourth second and 37 m in the sixth second. The distance covered by body in the next two seconds is

A circular coil carrying a current of 2.5 A is free to rotate about an axis in its plane perpendicular to an external field. When the coil is made to oscillate, the time period of oscillation is $T$. If the current through the coil is 10 A ...

A straight wire of length 20 cm carrying a current of $\frac{3 .}{\pi^2} \mathrm{~A}$ is bent in the form of a circle. The magnetic field at the centre of the circle is

A long straight rod of diameter 4 mm carries a steady current $i$. The current is uniformly distributed across its cross-section. The ratio of the magnetic fields at distances 1 mm and 4 mm from the axis of the rod is

A thin plano-convex lens of focal length 73.5 cm has a circular aperture of diameter 8.4 cm . If the refractive index of the material of the lens is $\frac{5}{3}$, then the thickness of the lens is nearly

When an object of height 12 cm is placed at a distance from a convex lens, an image of height 18 cm is formed on a screen. Without changing the positions of the object and the screen. If the lens is moved towards the screen, another clear i...