AP EAPCET 2024 - 19th May Evening Shift

\(2 \cdot 5+5 \cdot 9+8 \cdot 13+11 \cdot 17+\ldots \text { to } 10 \text { terms }=\)

If $m$ and $M$ denote the mean deviations about mean and about median respectively of the data $20,5,15,2$, $7,3,11$, then the mean deviation about the mean of $m$ and $M$ is

If a variable straight line passing through the point of intersection of the lines $x-2 y+3=0$ and $2 x-y-1=0$ intersects the $X, Y$-axes at $A$ and $B$ respectively, then the equation of the locus of a point which divides the segment $A B$...

Point $(-1,2)$ is changed to $(a, b)$, when the origin is shifted to the point $(2,-1)$ by translation of axes, Point $(a, b)$ is changed to $(c, d)$, when the axes are rotated through an angle of $45^{\circ}$ about the new origin, $(c, d)$...

The area (in sq units) of the triangle formed by the lines $6 x^2+13 x y+6 y^2=0$ and $x+2 y+3=0$ is

The point $(a, b)$ is the foot of the perpendicular drawn from the point $(3,1)$ to the line $x+3 y+4=0$. If $(p, q)$ is the image of $(a, b)$ with respect to the line $3 x-4 y+11=0$, then $\frac{p}{a}+\frac{q}{b}=$

A ray of light passing through the point $(2,3)$ reflects on $Y$-axis at a point $P$. If the reflected ray passes through the point $(3,2)$ and $P=(a, b)$, then $5 b=$

A line $L$ passes through the points $(1,2,-3)$ and $(\beta, 3,1)$ and a plane $\pi$ passes through the points $(2,1,-2)$, $(-2,-3,6),(0,2,-1)$. If $\theta$ is the angle between the line $L$ and plane $\pi$, then $27 \cos ^2 \theta=$

The shortest distance between the skew lines $\mathbf{r}=(-\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})+t(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})$ and $\mathbf{r}=(7 \hat{\mathbf{i}}+4 \hat{\mathbf{k}})+s(\hat{\...

If $A(1,2,0), B(2,0,1), C(-3,0,2)$ are the vertices of $\triangle A B C$, then the length of the internal bisector of $\angle B A C$ is

The perpendicular distance from the point $(-1,1,0)$ to the line joining the points $(0,2,4)$ and $(3,0,1)$ is

The general solution of
$$ \begin{aligned} & 4 \cos 2 x-4 \sqrt{3} \sin 2 x+\cos 3 x-\sqrt{3} \sin 3 x \\ & \qquad+\cos x-\sqrt{3} \sin x=0 \end{aligned} $$

The smallest positive value (in degrees) of $\theta$ for which $\tan \left(\theta+100^{\circ}\right)=\tan \left(\theta+50^{\circ}\right) \tan (\theta) \tan \left(\theta-50^{\circ}\right)$ is valid, is

The general solution of $2 \cos ^2 x-2 \tan x+1=0$ is

Statement $(\mathrm{S} 1) \sin 55^{\circ}+\sin 53^{\circ}-\sin 19^{\circ}-\sin 17^{\circ}=\cos 2^{\circ}$
Statement (S2) Range of $\frac{1}{3-\cos 2 x}$ is $\left[\frac{1}{4}, \frac{1}{2}\right]$
Which one of the following is correct?

The value of $5 \cos \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+3$ lies between

Let $\mathbf{a} \times \mathbf{b}=7 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ and $\mathbf{a}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$. If the length of projection of $\mathbf{b}$ on $\mathbf{a}$ is

$$
\frac{8}...

Let $A B C$ be an equilateral triangle of side a. $M$ and $N$ are two points on the sides $A B$ and $A C$, respectively such that $\mathbf{A N}={ }^{\prime} K \mathbf{A C}$ and $\mathbf{A B}=3 \mathbf{A M}$. If the vectors $\mathbf{B N}$ an...

Let $\mathbf{a}$ and $\mathbf{b}$ be two non-collinear vector of unit modulus. If $\mathbf{u}=\mathbf{a}-(\mathbf{a} \cdot \mathbf{b}) \mathbf{b}$ and $\mathbf{v}=\mathbf{a} \times \mathbf{b}$, then $|\mathbf{v}|=$

If $L M N$ are the mid-points of the sides $P Q, Q R$ and $R P d$ $\triangle P Q R$ respectively, then

$$ \begin{aligned} & \mathbf{Q M}+\mathbf{L N}+\mathbf{M L}+\mathbf{R N}-\mathbf{M N}-\mathbf{Q L}= \end{aligned} $$

A series $L-C-R$ circuit is shown in the figure. Where the inductance of 10 H , capacitance $40 \mu \mathrm{~F}$ and resistance $60 \Omega$ are connected to a variable frequency 240 V source. The current at resonating frequency is

A hydrogen atom falls from $n$th higher energy orbit to first energy orbit $(n=1)$. The energy released is equal to 12.75 eV . The $n$th orbit is

The decrease in each day in the uranium mass of the material in a uranium reactor operating at a power of 12 MW is (Energy released in one ${ }_{92} \mathrm{U}^{235}$ fission is about 200 MeV )

Four condensers each of capacitance $8 \mu \mathrm{~F}$ are joined as shown in the figure. The equivalent capacitance between the points $A$ and $B$ will be

A ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just before the first bounce is $7 \mathrm{~ms}^{-1}$ and the coefficient of restitution is 0.75 , the total distance travelled ...

Two blocks of masses $m$ and $2 m$ are connected by a massless string which passes over a fixed frictionless pulley. If the system of blocks is released from rest, the speed of the centre of mass of the system of two blocks after a time of ...

A steady current is flowing in a metallic conductor of non-uniform cross-section. The physical quantity which remains constant is

The resistance between points $A$ and $C$ in the given network is

The voltage $V_0$ in the network shown is

The longest wavelength of light that can initiate photo electric effect in the metal of work function 9 eV is

If the work done in stretching a wire by 1 min is 2 J . The work necessary for stretching another wire of satrs material but with double radius of cross-section and half the length by 1 mm is

Magnetic field at a distance of $r$ from $Z$-axis is $B=B_0$ $r t \hat{\mathbf{k}}$ present in the region. $B_0$ is constant and $t$ is time. The magnitude of induced electric field at a distance of $r$ from $Z$-axis is

An electromagnetic wave travel in a medium with a speed of $2 \times 10^8 \mathrm{~ms}^{-1}$. The relative permeability of the medium is 1 . Then, the relative permittivity is

A message signal of 3 kHz is used to modulate a carric signal frequency 1 MHz , using amplitude modulation. The upper side band frequency and band width respectively are

In the following diagram, the work done in moving a point charge from point $P$ to points $A, B$ and $C$ are $W_A, W_B$ and $W_C$ respectively. Then ( $A, B, C$ are points on semi-circle and point charge $q$ is at the centre of semi-circle)...

Two particles of equal mass $m$ and equal charge $q$ are separated by a distance of 16 cm . They do not experience any force. The value of $\frac{q}{m}$ is (if $G$ is the universal gravitational constant and $g$ is the acceleration due to g...

If $S_1, S_2$ and $S_3$ are the tensions at liquid-air, solid-air and solid-liquid interfaces respectively and $\theta$ is the angle of contact at the solid-liquid interface, then

Maximum height reached by a rocket fired with a speed equal to $50 \%$ of the escape speed from the surface of the earth is ( $R=$ Radius of the earth)

One mole of a gas having $\gamma=\frac{7}{5}$ is mixed with one mole of a gas having $\gamma=\frac{4}{3}$. The value of $\gamma$ for the mixture is ( $\gamma$ is the ratio of the specific heats of the gas)

An ideal heat engine operates in Carnot cycle between $127^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$. It absorbs $5 \times 10^4 \mathrm{Cal}$ of heat at height temperature. Amount of heat converted to work is

If ambient temperature is 300 K , the rate of cooling at 600 K is $H$. In the same surroundings, the rate of cooling at 900 K is

A Carnot heat engine has an efficiency of $10 \%$. If the same engine is worked backward to obtain a refrigerator, then the coefficient of performance of the refrigerator is

The rms velocity of a gas molecules oí mass $m$ at a given temperature is proportional to

A block of mass 1.5 kg kept on a rough horizontal surface is given a horizontal velocity of $10 \mathrm{~ms}^{-1}$. If the block comes to rest after travelling a distance of 12.5 m , the coefficient of kinetic friction between the surface a...

A block of mass 18.5 kg kept on a smooth horizontal surface is pulled by a rope of 3 m length by a horizontal force of 40 N applied to the other end of the rope. If the linear density of the rope is $0.5 \mathrm{kgm}^{-1}$ and initially the...

The domain in ferromagnetic material is in the form of a cube of side $2 \mu \mathrm{~m}$. Number of atoms in that domain is $9 \times 10^{10}$ and each atom has a dipole movement of $9 \times 10^{-24} \mathrm{Am}^2$. The magnetisation of t...

In a sport event, a disc is thrown such that it reaches its maximum range of 80 m , the distance travelled in first 3 s is $\left(g=10 \mathrm{~ms}^{-2}\right)$

A 2 kg ball thrown vertically upward and another 3 kg ball projected with certain angle $\left(\theta \neq 90^{\circ}\right)$ both will have same time of flight, then this ratio of their maximum heights is

A car travelling at 80 kmph can be stopped at a distance of 60 m by applying brakes. If the same car travels at 160 kmph and the same braking force is applied, the stopping distance is

A tightly wound coil of 200 turns and of radius 20 cm carrying current 5 A . Magnetic field at the centre of the coil is