AP EAPCET 2024 - 22th May Morning Shift

$|x|<1$, The coefficient of $x^2$ in the power series expansion of $\frac{x^4}{(x+1)(x-2)}$ is

If set $A$ has 5 elements, set $B$ has 7 elements, then the number of many one functions that can be defined from $A$ to $B$ is

If $x_1, x_2, x_3, \ldots . x_n$ are $n$ observations such, that $\Sigma\left(x_i+2\right)^2=28 n$ and $\Sigma\left(x_1-2\right)^2=12 n$, then the variance is

The equation of the locus of points which are equidistant from the point $(2,3)$ and $(4,5)$ is

If the slope of one of the pair of lines represented by $2 x^2+3 x y+K y^2=0$ is 2 , then the angle between the pair of lines is

The length of $x$-intercept made by pair of lines $2 x^2+x y-6 y^2-2 x+17 y-12=0$ is

The orthocentre of the triangle formed by lines $x+y+1=0, x-y-1=0$ and $3 x+4 y+5=0$ is

The equation of the side of an equilateral triangle is $x+y=2$ and one vertex is $(2,-1)$. The length of the side is

The distance of a point $(2,3,-5)$ from the plane $\hat{\mathbf{r}} \cdot(4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})=4$ is

The orthocentre of triangle fromed by points $(2,1,5)$ $(3,2,3)$ and $(4,0,4)$ is

If $P=(0,1,2), Q=(4,-2,1)$, and $O=(0,0,0)$, then $\angle P O Q=$

If the perpendicular distance from $(1,2,4)$ to the plane $2 x+2 y-z+k=0$ is 3 , then $k=$

The general solution of the equation $\tan x+\tan 2 x-\tan 3 x=0$ is

If $M_1$ and $M_2$ are the maximum values of $\frac{1}{11 \cos 2 x+60 \sin 2 x+69}$ and $3 \cos ^2 5 x+4 \sin ^2 5 x$ respectively, then $\frac{M_1}{M_2}=$

\(4 \cos \frac{\pi}{7} \cos \frac{\pi}{5} \cos \frac{2 \pi}{7} \cos \frac{2 \pi}{5} \cos \frac{4 \pi}{7}=\)

If $\tanh x=\operatorname{sech} y=\frac{3}{5}$ and $e^{x+y}$ is an integer, then $e^{x+ y}$ =

Let $\hat{\mathbf{a}}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}, \hat{\mathbf{b}}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$. The projection d the sum of the vectors $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ on t...

In $\triangle P Q R,(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}),(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})$ and $(3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \mathbf{k})$are$\mathbf{}$ the position vectors of the ve...

If $\hat{\mathbf{f}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{g}}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$, then the projection vector of $\hat{\mathrm{f}}$ on $\hat{\mathrm{g}}$ is

If $\theta$ is the angle between $\hat{\mathbf{f}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\hat{\mathbf{g}}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+a \hat{\mathbf{k}}$ and $\sin \theta=\sqrt{\frac{24}{28}}$, then $7 a^2+...

A 50 Hz AC circuit has a 10 mH inductor and a $2 \Omega$ resistor in series. The value of capacitance to be placed in series in the circuit to make the circuit power factor as unity is

The ratio of minimum wavelength of Balmer series to maximum wavelength in Brackett series in hydrogen spectrum is

The half-life period of a radioactive element $A$ is 62 years. It decays into another stable element $B$. An archaeologist found a sample in which $A$ and $B$ are in 1:15 ratio. The age of the sample is

Eight capacitors each of capacity $2 \mu \mathrm{~F}$ are arranged as shown in figure. The effective capacitance between $A$ and $B$ is

The maximum distance between the transmitting and receiving antennas for satisfactory communication in line of sight mode is 57.6 km . If the height of the receiving antenna is 80 m , the height of the transmitting antenna is (radius of ear...

The potential difference across the ends of conductor is $\beta 0 \pm 03) \mathrm{V}$ and the current through the conductor is $(5 \pm 0.10)$ A. The error in the determination of the resistance of the conductor is

Two identical cells gave the same current through an external resistance of $2 \Omega$ regardless whether the cells are grouped in series or parallel. The internal resistance of the cells is

If $E_1=4 \mathrm{~V}$ and $E_2=12 \mathrm{~V}$, the current in the circuit and potential difference between the points $P$ and $Q$ respectively are

The surface of a metal is first illuminated with a light of wavelength 300 nm and later illuminated by another light of wavelength 500 nm . It is observed that the ratio of maximum velocities of photoelectrons in two cases is 3 . The work f...

The elongation of copper wire of cross-sectional area $3.5 \mathrm{~mm}^2$, in the figure shown, is
\(\left(Y_{\text {Copper }}=10 \times 10^{10} \mathrm{Nm}^{-2} \text { and } g=10 \mathrm{~ms}^{-2}\right)\)

A coil of inductance $L$ is divided into 6 equal parts. All these are connected in parallel. The resultant inductance of this combination is

The structure of solids is investigated by using

A neutral ammonia $\mathrm{NH}_3$ in its vapour state has electric dipole moment of magnitude $5 \times 10^{-30} \mathrm{C}-\mathrm{m}$. How far apart are the molecules centres of positive and negative charge?

If four charges $q_1=+1 \times 10^{-8} \mathrm{C}, q_2=-2 \times 10^{-8} \mathrm{C}$, $q_3=+3 \times 10^{-8} \mathrm{C}$ and $q_4=+2 \times 10^{-8} \mathrm{C}$ are kept at the four corners of a square of side 1 m , then the electric potenti...

Water is flowing in streamline manner in a horizontal pipe. If the pressure at a point where cross-sectional area is $10 \mathrm{~cm}^2$ and velocity $1 \mathrm{~ms}^{-1}$ is 2000 Pa , then the pressure of water at another point where the c...

A satellite moving round the earth in a circular orbit has kinetic energy $E$. Then, the minimum amount of energy to be added so that it escapes from the earth.

A metal ball of mass 100 g at $20^{\circ} \mathrm{C}$ is dropped in 200 g of water at $80^{\circ} \mathrm{C}$. If the resultant temperature is $70^{\circ} \mathrm{C}$, then the ratio of specific heat of the metal to that of water is

The efficiency of a heat engine that works between the temperatures where Celsius-Fahrenheit scales coincides and Kelvin-Fahrenheit scales coincides is (approximately)

Initially the pressure of 1 mole of an ideal gas is $10^5 \mathrm{Nm}^{-2}$ and its volume is 16 L . When it is adiabatically compressed, its final volume is 2 L . Work-done on the gas is $\left[\right.$ molar specific heat at constant volu...

The ratio of kinetic energy of a diatomic gas molecule at a high temperature to that of NTP is

An ideal gas is taken around $A B C A$ as shown in the $P^{\prime \prime}$ diagram. The work done during the cycle is

A 100 kg cannon fires a ball of 1 kg horizontally from a cliff of height 500 m . It falls on the ground at a distance of 400 m from the bottom of the cliff. The recoil velocity of the gun is (Acceleration due to gravity $=10 \mathrm{~ms}^{-...

A block of mass 5 kg is placed on a rough horizontal surface having coefficient of friction 0.5 . If a horizontal force of 60 N is acting on it, then the acceleration of the block is (Acceleration due ot gravity, $g=10 \mathrm{~ms}^{-2}$ )

The relation between the horizontal displacement $x$ (in metre) and the vertical displacement $y$ (in metre) of a projectile is $y=3 x-0.8 x^2$. The time of flight of the projectile is (Acceleration due to gravity, $g=10 \mathrm{~ms}^{-2}$ ...

A boy weighing 50 kg finished long jump at a distance of 8 m . Considering that he moved along a parabolic path and his angle of jump is $45^{\circ}$, his initial KE is

Two toroids with number of turns 400 and 200 have average radii respectively 30 cm and 60 cm . If they carry the same current, the ratio of magnetic fields in these two toroids is

Three rings, each with equal radius $r$ are placed mutually perpendicular to each other and each having centre at the origin of coordinate system. $I$ is current passing through each ring. The magnetic field value at the common centre is

A person can see objects clearly when they lie between 40 cm and 400 cm from his eye. In order to increase the maximum distance of distant vision to infinity the type of lens and power of correction lens required respectively, are

The moment of inetia of a rod about an axis passing through its centre and perpendicular to its length is $\frac{1}{12} M L^2$, where $M$ is the mass and $L$ is the length of the rod. The rod is bent in the middle, so that the two halves ma...

A uniform rod of length $2 L$ is placed with one end in contact with the earth and is then inclined at an angle $\alpha$ to the horizontal and allowed to fall without slipping at contact point. When it becomes horizontal, its angular veloci...