AP EAPCET 2024 - 21th May Evening Shift

In the expansion of $\frac{2 x+1}{(1+x)(1-2 x)}$ the sum of the coefficients of the first 5 odd powers of $x$ is

The condition that the roots of $x^3-b x^2+c x-d=0$ are in arithmetic progression is

If $1 \cdot 3 \cdot 5+3 \cdot 5 \cdot 7+5 \cdot 7 \cdot 9+\ldots n$ terms $=n(n+1) f(n)-3 n$, then $f(l)=$

The coefficient of variation for the frequency distribution is
$$ \begin{array}{|c|l|l|l|} \hline \boldsymbol{x}_{\boldsymbol{i}} & 4 & 3 & 1 \\ \hline \boldsymbol{f}_{\boldsymbol{i}} & 1 & 3 & 5 \\ \hline \end{array} $$

$P$ is a point on $x+y+5=0$, whose perpendicular distance from $2 x+3 y+3=0$ is $\sqrt{13}$, then the coordinates of $P$ are

Suppose the axes are to be rotated through an angle $\theta$ so as to remove the $x y$ form from the equation $3 x^2+2 \sqrt{3} x y+y^2=0$. Then, in the new coordinate system the equation $x^2+y^2+2 x y=2$ is transformed to

For $\lambda, \mu \in R,(x-2 y-1)+\lambda(3 x+2 y-11)=0$ and $(3 x+4 y-11)+\mu(-x+2 y-3)=0$ represent two families of lines. If the equation of the line common to both the families is $a x+b y-5=0$. Then, $2 a+b=$

If the pair of lines represented by $3 x^2-5 x y+P y^2=0$ and $6 x^2-x y-5 y^2=0$ have one line in common, then the sum of all possible value of $P$ is

If the plane $x-y+z+4=0$ divides the line joining the points $P(2,3,-1)$ and $Q(1,4,-2)$ in the ratio $l: m$, then $l+m$ is

If the line with direction ratios $(1, \alpha, \beta)$ is perpendicular to the line with direction ratios $(-1,2,1)$ and parallel to the line with direction ratios $(\alpha, 1, \beta)$ then $(\alpha, \beta)$ is

Angle between the planes, $\mathbf{r} \cdot(12 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})=5$ and, $\mathbf{r} \cdot(5 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})=7$ is

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

Let $P\left(x_1, y_1, z_1\right)$ be the foot of perpendicular drawn from the point $Q(2,-2,1)$ to the plane $x-2 y+z=1$. If $d$ is the perpendicular from the point $Q$ to the plane and $l=x_1+y_1+z_1$, then $l+3 d^2$ is

Number of solutions of the trigonometric equation $2 \tan 2 \theta-\cot 2 \theta+1=0$ lying in the interval $[0, \pi]$ is

Assertion (A) : If $A=10^{\circ}, B=16^{\circ}$ and $C=19^{\circ}$, then $\tan 2 A \tan 2 B+\tan 2 B \tan 2 C+\tan 2 C \tan 2 A=1$
Reason (R) : If $A+B+C=180^{\circ}, \cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}$
$$ =\cot \frac{A}{2} ...

If $A, B, C$ are the angles of triangle, then $\sin 2 A-\sin 2 B+\sin 2 C=$

If $\alpha$ is in the 3rd quadrant, $\beta$ is in the 2nd quadrant such that $\tan \alpha=\frac{1}{7}, \sin \beta=\frac{1}{\sqrt{10}}$, then $\sin (2 \alpha+\beta)=$

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are 3 vectors such that $|\mathbf{a}|=5,|\mathbf{b}|=8,|\mathbf{c}|=11$ and $\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}$, then the angle between the vectors $\mathbf{a}$ and $\mathbf{b}$ is

If $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}},-3 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ are the position vectors of three points, $A, B, C$ respectively, t...

If $\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathbf{d}$ are position vectors of 4 points such that $2 a+3 b+5 c-10 d=0$, then the ratio in which the line joining $c$ and $d$ divides the line segment joining $a$ and $\mathbf{b}$ is

A resistor of resistance $R$, inductor of inductive reactance $2 R$ and a capacitor of capacitive reactance $X_C$ are connected in series to an AC source.If the series $L-C-R$ circuit is in resonance, then the power factor of the circuit an...

The surface areas of two nuclei are in the ratio $9: 25$. The mass number of the nuclei are in the ratio

The electrostatic potential energy of the electron in an orbit of hydrogen is -6.8 eV . The speed of the electron in this orbit is ( $c$ is speed of light in vacuum)

The capacitance of an isolated sphere of radius $r_1$ is increased by 5 times, when it is enclosed by an earthed concentric sphere of radius $r_2$. The ratio of their radii is

When a parallel plate capacitor is charged up to 95 V , its capacitance is $C$. If a dielectrtic slab of thickness 2 mm is inserted between plates and distance between the plates is increased by 1.6 mm such that the same potential differenc...

The charge $q$ (in coulomb) passing through a $10 \Omega$ resistor as a function of time $t$ (in second) is given by $q=3 t^2-2 t+6$. The potential difference across the ends of the resistor at time $t=5 \mathrm{~s}$ is

A cell of emf 1.2 V and internal resistance $2 \Omega$ is connected in parallel to another cell of emf 1.5 V and internal resistance $1 \Omega$. If the like poles of the cells are connected together, the emf of the combination of the two ce...

The maximum wavelength of light which causes photoelectric emission from photosensitive metal surface is $\lambda_0$. Two light beams of wavelengths $\frac{\lambda_0}{3}$ and $\frac{\lambda_0}{9}$ incident on the metal surface. The ratio of...

A 4 kg stone attached at the end of a steel wire is being whirled at a constant speed $12 \mathrm{~ms}^{-1}$ in a horizontal circle. The wire is 4 m long with a diameter 2.0 mm and Young's modulus of the steel is $2 \times 10^{11} \mathrm{N...

The current passing through a coil of 120 turns and inductance 40 mH is 30 mA . The magnetic flux linked with the coil is

A transmitter of power 10 kW emits radio waves of wavelength 500 m . The number of photons emitted por second by the transmitter of the order of

The rms value of the electric field of an electromagnetic wave emitted by a source is $660 \mathrm{NC}^{-1}$. The average energy density of the electromagnetic wave is

The electric field intensity $E$ at a distance of 3 m from a uniform long straight wire of linear charge density $0.2 \mu \mathrm{~cm}^{-1}$ is

A spherical ball of radius $1 \times 10^{-4} \mathrm{~m}$ and of density $10^4 \mathrm{kgm}^{-3}$ falls freely under gravity through a distance $h$ before entering a tank of water. After entering water if the velocity of the ball does not c...

A particle is projected from the surface of the earth with a velocity equal to twice the escape velocity. When particle is very far from the earth. Its speed would be

The condition $d W=d Q$ holds good in the following process.

The efficiency of a Carnot engine found to increase from $25 \%$ to $40 \%$ on increasing the temperature ( $T_1$ ) of source alone through 100 K . The temperature $\left(T_2\right)$ of the sink is given by

Match the following ( $f$ is number of degrees of freedom)
$$
\begin{array}{llll}
\hline& \text { Gases } & & \frac{C_p}{C_v} \text { value } \\
\hline \text { A } & \text { Monoatomic } & \text { I } & \frac{4+f}{3+f} \\
\hline \text { B ...

A metal block is made from mixture of 2.4 kg of aluminium, 1.6 kg of brass and 0.8 kg of copper. The metal block is initially at $20^{\circ} \mathrm{C}$. If the heat supplied to the metal block is 44.4 cal . Find the final temperature of th...

An ideal gas is found to obey $p V^{\frac{3}{2}}=$ constant during an adiabatic process. If such a gas initially at temperature $T$ is adiabatically compressed to $\frac{1}{4}$ th of its volume, then its final temperature is

A block of metal 4 kg is in rest on a frictionless surface. It was targeted by a jet releasing water of $2 \mathrm{~kg} \mathrm{~s}^{-1}$ at a speed of $10 \mathrm{~ms}^{-1}$. The acceleration of the block is

A person climbs up a conveyor belt with a constant acceleration. The speed of the belt is $\sqrt{\frac{g h}{6}}$ and coefficient of friction is $\frac{5}{3 \sqrt{3}}$. The time taken by the person to reach from $A$ to $B$ with maximum possi...

At a place the horizontal component of earth's magnetic field $3 \times 10^{-5} \mathrm{~T}$ and the magnetic declination is $30^{\circ}$. A compass needle of magnetic moment $18 \mathrm{Am}^2$ pointing towards geographic north at this plac...

The maximum height attained by projectile is increased by $10 \%$ by keeping the angle of projection constant. What is the percentage increase in the time of flight ?

The velocity of a particle is given by the equation $v(x)=3 x^2-4 x$, where $x$ is the distance covered by the particle. The expression for its acceleration is

The acceleration of a particle which moves along the positive $X$-axis varies with its position as shown in the figure. If the velocity of the particle is $0.8 \mathrm{~ms}^{-1}$ at $x=0$ , then its velocity at $x=1.4 \mathrm{~m}$ is $\left...

A charged particle moving along a straight line path enters a uniform magnetic field of 4 mT at right angles to the direction of the magnetic field. If the specific charge of the charged particle is $8 \times 10^7 \mathrm{C} \mathrm{kg}^{-1...

A proton and an alpha particle moving with energies in the ratio $1: 4$ enter a uniform magnetic field of 3 T at right angles to the direction of magnetic field. The ratio of the magnetic forces acting on the proton and the alpha particle ...

The focal length of the objective lens of a telescope is 30 cm and that of its eye lens is 3 cm . It is focussed on a scale at a distance 2 m from it. The distance of objective lens from eye lens to see the clear image is

Three particles of each mass $m$ are kept at the three vertices of an equilateral triangle of side $l$. The moment of inertia of a system of the particles about any side of the triangle is