AP EAPCET 2024 - 23th May Morning Shift

The $n$th term of the series $1+(3+5+7)+(9+11+13+15+17)+\ldots$ is

If the mean of the data $7,8,9,7,8,7, \lambda$ and 8 is 8 , then variance of the data is equal to

The locus of the mid-point of the portion of the line $x \cos \alpha+y \sin \alpha=p$ intercepted by the coordinate axes, where $p$ is a constant, is

The origin is shifted to the point $(2,3)$ by translation of axes and then the coordinate axes are rotated about the origin through an angle $\theta$ in the counter - clockwise sense. Due to this if the equation $3 x^2+2 x y+3 y^2-18 x-22 y...

If the straight line passing through $P(3,4)$ makes an angle $\frac{\pi}{6}$ with the positive $X$-axis in anti-clockwise direction and meets the line $12 x+5 y+10=0$ at $Q$, then the length of the segment $P Q$ is

The equation of the perpendicular bisectors of the sides $A B$ and $A C$ of $\triangle A B C$ are $x-y+5=0$ and $x+2 y=0$ respectively, If the coordinates of $A$ are $(1,-2)$, then the equal of the line $B C$ is

The combined equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve $x^2+y^2+x y+x+3 y+1=0$ and the line $x+y+2=0$ is

A pair of lines drawn through the origin forms a right angled isosceles triangle with right angle at the origin with the line $2 x+3 y=6$. The area (in sq units) of the triangle thus formed is

If the direction cosines of lines are given by $l+m+n=0$ and $m n-2 l m-2 n l=0$, then the acute angle between those lines is

If the angle $\theta$ between the line $\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$ and the plane $2 x-y+\sqrt{\lambda} z+4=0$ is such that $\sin \theta=\frac{1}{3^{\prime}}$ then the value of $\lambda=$

The length of the internal bisector of angle $A$ in $\triangle A B C$ with vertices $A(4,7,8), B(2,3,4)$ and $C(2,5,7)$ is

The general solution of $\cot \frac{x}{2}-\cot x=\operatorname{cosec} \frac{x}{2}$ is

\(\tan ^2 \frac{\pi}{16}+\tan ^2 \frac{2 \pi}{16}+\tan ^2 \frac{3 \pi}{16}+\tan ^2 \frac{4 \pi}{16}\)
$+\tan ^2 \frac{5 \pi}{16}+\tan ^2 \frac{6 \pi}{16}+\tan ^2 \frac{7 \pi}{16}$ is equal to

If $A B$ and $C$ are the angles of a triangle, then $\frac{\sin A+\sin B+\sin C}{\sin ^2 \frac{A}{2}-\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}-1}$ is equal to

$$ \begin{aligned} & \sin ^2 18^{\circ}+\sin ^2 24^{\circ}+\sin ^2 36^{\circ}+\sin ^2 42^{\circ}+\sin ^2 78^{\circ} \\ & +\sin ^2 90^{\circ}+\sin ^2 96^{\circ}+\sin ^2 102^{\circ}+\sin ^2 138^{\circ}+\sin ^2 162^{\circ} \text { is } \\ & \t...

If $\mathbf{A B}=2 \mathbf{i}+3 \mathbf{j}-6 \mathbf{k}, \mathbf{B C}=6 \mathbf{i}-2 \mathbf{j}+3 \mathbf{k}$ are the vectors along two sides of a $\triangle A B C$. Then, perimeter of $\triangle A B C$ is

The orthogonal projection vector of $a=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ on $\mathbf{b}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ is

A unit vector perpendicular to the vectors $a=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{b}=3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ is

If the vectors $a \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+b \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}+c \hat{\mathbf{k}}$ $(a \neq b \neq c \neq 1)$ are coplanar, then $\frac{1}{1...

If $\mathbf{a}=-4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{b}=\sqrt{2} \hat{\mathbf{i}}-\sqrt{2} \hat{\mathbf{j}}$ are two vectors, then angle between the vectors $2 \mathbf{a}$ and $\frac{\mathbf{b}}{2}$ is

An alternating current is given by $i=(3 \sin \omega t+4 \cos \omega t) \mathrm{A}$. The rms current will be

In a nuclear reactor, the fuel is consumed at the rate of $1 \times 10^{-3} \mathrm{gs}^{-1}$. The power generated in kW is

Energy levels $A, B$ and $C$ of a certain atom corresponding to increasing values of energy i.e $E_A < E_B < E_C$. If $\lambda_1, \lambda_2$ and $\lambda_3$ are the wavelengths of a photon corresponding to the transitions shown then.

A soccer ball of mass 250 g is moving horizontally to the left with a speed $22 \mathrm{~ms}^{-1}$. This ball is kicked towards right with a velocity $30 \mathrm{~ms}^{-1}$ at an angle $53^{\circ}$ with the horizontal in upward direction. A...

Current sensitivities of two galvanometers $G_1$ and $G_2$ of resistances $100 \Omega$ and $50 \Omega$ are $10^8 \mathrm{div} / \mathrm{A}$ and $0.5 \times 10^5 \mathrm{div} / \mathrm{A}$ respectively. The galvanometer in which the voltage ...

The emf of a cell of internal resistance $2 \Omega$ is measured using a voltmeter of resistance $998 \Omega$. The error in the emf measured is

In a meter bridge experiment, a resistance of $9 \Omega$ is connected in the left gap and an unknown resistance greater than $9 \Omega$ is connected in right gap. If the resistance in the gaps are interchanged, the balancing point shifts by...

A photon incident on a metal of work function 2 eV produced photoelectron of maximum kinetic energy of 2 eV . The wavelength associated with the photon is

The work done on a wire of volume of $2 \mathrm{~cm}^3$ is $16 \times 10^2 \mathrm{~J}$. If the Young's modulus of the material of the wire is $4 \times 10^{12} \mathrm{Nm}^{-2}$. Then the strain produced in the wire is

In a circuit the current falls from a 14 A to 4 A in a time 0.2 ms . If the induced emf is 150 V , then the self-inductance of the circuit is

For plane electromagnetic waves propagating in the positive $z$-direction. The combination which gives the correct possible direction for $\mathbf{E}$ and $\mathbf{B}$ fields respectively is

Size of the antenna for a carrier wave of frequency 3 MHz is

125 identical charged small spheres coalesce to form a big charged sphere. If the electric potential on each small sphere is 60 mV , then the electric potential on the bigger sphere formed is

A particle of mass 0.5 g and charge $10 \mu \mathrm{C}$ is subjected to a uniform electric field of $8 \mathrm{NC}^{-1}$. If the particle is initially at rest, the velocity of the particle after a time of 5 s is

Two particles of charges 4 nC and $Q$ are kept in air with a separation of 10 cm between them. If the electrostatic potential energy of the system is $1.8 \mu \mathrm{~J}$, then $Q=$

Water flows from a tap of diameter 1.5 cm with $75 \times 10^{-5} \mathrm{~m}^3 \mathrm{~s}^{-1}$. Coefficient of viscosity of water is $10^{-3} \mathrm{~Pa}$. The flow is

The time period of revolution of a satellite close to planet's surfaces is 80 min . The time period of another satellite, which is at a height of 3 times the radius of the planet from surface is

When 2 moles of a monoatomic gas expands adiabatically from a temperature of $80^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$, the work done is $W$. The work done when 3 moles of a diatomic gas expands adiabatically from $50^{\circ} \math...

If the ratio of the absolute temperature of the sink and source of a Carnot engine is changed from $2: 3$ to $3: 4$, the efficiency of the engine change by

A gas absorbs 18 J of heat and work done on the gas is 12 J . Then, the change in internal energy of the gas

The ratio of the molar specific heat capacities of monoatomic and diatomic gases at constant pressure is

A balloon carrying some sand of mass $M$ is moving down with a constant acceleration $a_0$. The mass $m$ of sand to be removed, so that the balloon moves up with double the acceleration $a_0$ is

The relation between $\mu$ and $H$ for a specimen of iron is $\mu=\left[\frac{1.4}{H}+12 \times 10^{-4}\right] \mathrm{Hm}^{-1}$. The value of $H$ which produces flux density of 1 T will be ( $\mu=$ magnetic permeability, $H=$ magnetic inte...

Path of projectile is given by the equation $Y=P x-Q x^2$, match the following accordingly (acceleration due to gravity $=g$ )
$$ \begin{array}{llll} \hline \text { a. } & \text { Range } & \text { i } & \frac{P}{Q} \\ \hline \text { b. } &...

A bowling machine placed at a height $h$ above the earth surface releases different balls with different angles but with same velocity $10 \sqrt{3} \mathrm{~ms}^{-1}$. All these balls landing velocities make angels $30^{\circ}$ or more with...

A person walks up a stalled escalator in 90 s. When standing on the same moving escalator, he reached in 60s. The time it would take him to walk up the moving escalator will be

A diving board is at at height of $h$ from the water surface. A swimmer standing on this board thrown a stone vertically upward with a velocity $16 \mathrm{~ms}^{-1}$. It reaches the water surface in a time of 5 s . In the next 0.2 s the di...

A charge $q$ is spread uniformly over an isolated ring $R$. The ring is rotated about its natural axis with angular speed $\omega$. The magnetic dipole moment of the ring is

When a convex lens is immersed in two different liquids of refractive indices 1.25 and 1.5 , the ratio of the focal lengths of the lens is $5: 16$. The refractive index of the material of the lens is

The moment of inertia of a solid sphere about its diameter is $20 \mathrm{~kg}-\mathrm{m}^2$. The moment of inertia of a thin spherical shell having the same mass and radius about its diameter is