AP EAPCET 2024 - 21th May Morning Shift

Mean deviation about the mean for the following data is

$$ \begin{array}{llllll} \hline \text { Class Interval } & 0-6 & 6-12 & 12-18 & 18-24 & 24-30 \\ \hline \text { Frequency } & 1 & \,2 & \,3 & \,2 & \,1 \\ \hline \end{array} $$

If all chords of the curve $2 x^2-y^2+3 x+2 y=0$, which subtend a right angle at the origin always passing through the point $(\alpha, \beta)$, then $(\alpha, \beta)=$

Let $\alpha \in R$. If the line $(\alpha+1) x+\alpha y+\alpha=1$ passes through a fixed point $(h, k)$ for all $\alpha$, then $h^2+k^2=$

The area of the triangle formed by the lines represented by $3 x+y+15=0$ and $3 x^2+12 x y-13 y^2=0$ is

When the origin is shifted to $(h, k)$ by translation of axes, the transformed equation of $x^2+2 x+2 y-7=0$ does not contain $x$ term and constant term. Then, $(2 h+k)=$

$P$ is a variable point such that the distance of $P$ from $A$ $(4,0)$ is twice the distance of $P$ from $B(-4,0)$. If the line $3 y-3 x-20=0$ intersects the locus of $P$ at the points $C$ and $D$, then the distance between $C$ and $D$ is

Consider the tetrahedron with the vertices $A(3,2,4)$, $B\left(x_1, y_1, 0\right), C\left(x_2, y_2, 0\right)$ and $D\left(x_3, y_3, 0\right)$.If the $\triangle B C D$ is formed by the lines $y=x, x+y=6$ and $y=1$, then the centroid of the t...

If $P(2, \beta, \alpha)$ lies on the plane $x+2 y-z-2=0$ and $Q(\alpha,-1, \beta)$ lies on the plane $2 x-y+3 z+6=0$, then the direction cosines of the $P Q$ are

$A(1,2,1), B(2,3,2), C(3,1,3)$ and $D(2,1,3)$ are the vertices of a tetrahedron. If $\theta$ is the angle between the faces $A B C$ and $A B D$, then $\cos \theta=$

Let $\pi$ be the plane that passes through the point $(-2,1,-1)$ and parallel to the plane $2 x-y+2 z=0$. Then the foot of perpendicular drawn from the point $(1,2,1)$ to the plane $\pi$ is

For $a \in R-\{0\}$, if $a \cos x+a \sin x+a=2 k+1$ has a solution, then $k$ lies in the interval

If the general solution .set of $\sin x+3 \sin 3 x+\sin 5 x=1$ is $S$, then $\{\sin \alpha / \alpha \in S\}=$

If the period of the function $f(x)=\frac{\tan 5 x \cos 3 x}{\sin 6 x}$ is $\alpha$, then $f\left(\frac{\alpha}{8}\right)=$

If $\sin x+\sin y=\alpha, \cos x+\cos y+\beta$, then $\operatorname{cosec}(x+y)=$

If $P+Q+P=\frac{\pi}{4}$, then $\cos \left(\frac{\pi}{8}-P\right)+\cos \left(\frac{\pi}{8}-Q\right)+\cos$ $\left(\frac{\pi}{8}-R\right)=$

If $\theta$ is an acute angle, $\cosh x=K$ and $\sinh x=\tan \theta$, then $\sin \theta=$

$\mathbf{c}$ is a vector along the bisector of the internal angle between the vectors $\mathbf{a}=4 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ and $\mathbf{b}=12 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$. If the m...

$\mathbf{a}=\alpha \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \quad \mathbf{b}=\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{c}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ ar linearly dependent vectors and ...

If $\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \mathbf{c}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}-\hat{\mathbf{k}}$. $\mathbf{d}=2 \hat{\mathbf{i}}+\hat{\mat...

$\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ are two vectors and $\mathbf{c}$ is a unit vectors lying in the plane of $\mathbf{a}$ and $\mathbf{b}$. If $\ma...

If the energy released per fission of a ${ }_{92}^{235} \mathrm{U}$ nucleus is 200 MeV . The energy released in the fission of 0.1 kg d ${ }_{92}^{235} \mathrm{U}$ in kilowatt - hour is

The ground state energy of hydrogen atom is -13.6 eV . The potential energy of the electron in this state is

Two figures are shown as Fig. $A$ and Fig. $B$. The time constant of Fig. $A$ is $\tau_A$ and time constant of Fig. $B$ is $\tau_B$. Then

A ball falls freely from rest from a height of 6.25 m on a hard horizontal surface. If the ball reaches a heightd 81 cm after second bounce from the surface, the coefficient of restitution is

The centripetal acceleration of a particle in uniform circular motion is $18 \mathrm{~ms}^{-2}$. If the radius of the circular path is 50 cm , the change in velocity of the particle in a time of $\frac{\pi}{18} \mathrm{~s}$ is

An information signal of frequency 10 kHz is modulated with a carried wave of frequency $3.62 \mathrm{MHz}^{}$ The upper side and lower side frequencies are

A lamp is rated at $240 \mathrm{~V}, 60 \mathrm{~W}$. When in use the resistance of the filament of the lamp is 20 times that of cold filament. The resistance of the lamp when not in use is

Five equal resistances each $2 R$ connected as shown in figure. A battery of $V$ volts connected between $A$ and $B$. Then, current through $F C$ is

A blue lamp emits light of mean wavelength $4500$ Å. The lamp is rated at 150 W and $8 \%$ efficiency. Then, the number of photons are emitted by the lamp per second

The elastic energy stored per unit volume in terms of longitudinal strain $\varepsilon$ and Young's modulus $Y$ is

$X$ and $Y$ are two circuits having coefficient of mutual inductance 3 mH and resistance $10 \Omega$ and $4 \Omega$ respectively. To have induced current $60 \times 10^{-4} \mathrm{~A}$ in circuit $Y$, the amount of current to be changed i...

Which of the following produces electromagnetic waves?

A point charge $q \mathrm{C}$ is placed at the centre of a cube of a side length $L$. Then, the electric flux linked with each face of the cube is

Eight drops of mercury of equal radii and possessing equal charge combine to form a big drop. If the capacity of each drop is $C$, then capacity of the big drop is

Three equal electric charges of each charge $q$ are placed at the vertices of an equilateral triangle of side of length $L$. Then, potential energy of the system is

A large tank filled water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of the time taken for the level to fall from $h$ to $\frac{h}{2}$ and that taken for the level to fall from $\frac{h}{2}$ to 0 is

If the time period of revolution of a satellite is $T$, the its kinetic energy is proportional to

The time period of revolution of a satellite $T$ around the carth depends on the radius of the circular orbit $R$. mass of the earth $M$ and universal gravitational constant $G$. The expression for $T$, using dimensional analysis is ( $K$ ...

A slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} \mathrm{C}$ and that of copper at $100^{\circ} \mathrm{C}$. If the thermal conductivities of brass and copper are in the ratio $1: 4$,...

A monoatomic gas of $n$ moles is heated from temperature $T_1$ to $T_2$ under two different conditions, (i) at constant volume and (ii) at constant pressure. The change in internal energy of the gas is

In a Carnot engine, when the temperatures are $T_2=0^{\circ} \mathrm{C}$ and $T_1=200^{\circ} \mathrm{C}$, its efficiency is $\eta_1$ and when the temperature are $T_1=0^{\circ} \mathrm{C}$ and $T_2=-200^{\circ} \mathrm{C}$, its efficiency...

A polyatomic gas with $n$ degrees of freedom has a mean kinetic energy per molecule given by (if $N$ is Avogadro's number )

Heat energy absorbed by a system going through the cyclic process shown in the figure is

If the vertical component of the earth's magnetic field is 0.45 G at a location and angle of dip is $60^{\circ}$, then magnetic field of earth in that location is

A body of mass 1.5 kg is moving towards south with a uniform velocity of $8 \mathrm{~ms}^{-1}$. A force of 6 N is applied to the body towards east. The displacement of the body 3 s after the application of the force is

The horizontal range of a projectile projected at an angle of $45^{\circ}$ with the horizontal is 50 m . The height of the projectile when its horizontal displacement is 20 m is

An object projected upwards from the foot of a tower. The object crosses the top of the tower twice with an interval of 8 s and the object reaches foot after 16 s . The height of the tower is $\left(g=10 \mathrm{~ms}^{-2}\right)$

A rectangular loop of sides 25 cm and 10 cm carrying a current of 10 A is placed with its longer side parallel to a long straight conductor 10 cm apart carrying current 25 A . The net force on the loop is

When an electron placed in a uniform magnetic field is accelerated from rest through a potential difference $V_1$. It experiences a force $F$. If the potential difference is changed to $V_2$, the force experienced by the electron in same m...

The angle of polarisation for a medium with respect to air is $60^{\circ}$. The critical angle of this medium with respect to air is