AP EAPCET 2024 - 20th May Evening Shift

If the roots of $\sqrt{\frac{1-y}{y}}+\sqrt{\frac{y}{1-y}}=\frac{5}{2}$ are $\alpha$ and $\beta(\beta>\alpha)$ and the equation $(\alpha+\beta) x^4-25 \alpha \beta x^2+(\gamma+\beta-\alpha)=0$ has real roots, then a possible value of $\gamm...

If $2 \cdot 4^{2 n+1}+3^{3 n+1}$ is divisible by $k$ for all $n \in N$, then $k=$

If the roots of the equation $x^3+a x^2+b x+c=0$ are in arithmetic progression. Then,

If the mean deviation about the mean is $m$ and variance is $\sigma^2$ for the following data, then $m+\sigma^2=$ .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:A...

The equation for straight line passing through the point of intersection of the lines represented by $x^2+4 x y+3 y^2-4 x-10 y+3=0$ and the point $(2,2)$ is

If the line $2 x-3 y+5=0$ is the perpendicular bisector of the line segment joining $(1,-2)$ and $(\alpha, \beta)$, then $\alpha+\beta=$

If the area of the triangle formed by the straight lines $-15 x^2+4 x y+4 y^2=0$ and $x=\alpha$ is 200 sq unit, then $|\alpha|=$

If the origin is shifted to remove the first degree terms from the equation $2 x^2-3 y^2+4 x y+4 x+4 y-14=0$, then with respect to this new coordinate system the transformed equation of $x^2+y^2-3 x y+4 y+3=0$ is

The circumcentre of the triangle formed by the lines $x+y+2=0,2 x+y+8=0$ and $x-y-2=0$ is

If $L_1$ and $L_2$ are two lines which pass through origin and having direction ratios $(3,1,-5)$ and $(2,3,-1)$ respectively, then equation of the plane containing $L_1$ and $L_2$ is

The direction cosines of the line of intersection of the planes $x+2 y+z-4=0$ and $2 x-y+z-3=0$ are

The angle between the line with the direction ratios $(2,5,1)$ and the plane $8 x+2 y-z=14$ is

The general solution of the equation $\sin ^2 \theta+3 \cos ^2 \theta=$ $5 \sin \theta$ is

If $(\alpha+\beta)$ is not a multiple of $\frac{\pi}{2}$ and $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$, then $\tan \left(\frac{\pi}{4}+\alpha\right)+4 \tan \left(\frac{\pi}{4}+\beta\right)=$

If $\sec \theta+\tan \theta=\frac{1}{3}$, then the quadrant in which $2 \theta$ lies is

If $540^{\circ} < A < 630^{\circ}$ and $|\cos A|=\frac{5}{13}$, then $\tan \frac{A}{2} \tan A=$

If $|f|=10,|g|=14$ and $|f-g|=15$, then $|f+g|=$

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three vectors such that $|\mathbf{a}|=|\mathbf{b}|=|\mathbf{c}|=\sqrt{3}$ and $(a+b-c)^2+(b+c-a)^2+(c+a-b)^2=36$, then $|2 a-3 b+2 c|=$

The angle between the diagonals of the parallelogram whose adjacent sides are $2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}, \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ is

If the points having the position vectors $-i+4 j-4 k_{\text {, }}$, $3 i+2 j-5 k,-3 i+8 j-5 k$ and $-3 i+2 j+\lambda k$ are coplanar, then $\lambda=$

An inductor and a resistor are connected in series to an AC source of voltage $144 \sin \left(100 \pi t+\frac{\pi}{2}\right) \mathrm{V}$. If the current in the circuit is $6 \sin \left(100 \pi t+\frac{\pi}{6}\right) \mathrm{A}$, then the re...

Inner shell electrons in atoms moving from one energy level to another lower energy level produce

The speed of the electron in a hydrogen atom in the $n=3$ level is(Planck's constant $=6.6 \times 10^{-34} \mathrm{Js}$ )

One mole of radium has an activity of $\frac{1}{3.7}$ kilo curie. Its decay constant is(Avagadro number $=6 \times 10^{23} \mathrm{~mol}^{-1}$ )

Three parallel plate capacitors of capacitances $4 \mu \mathrm{~F}$, $6 \mu \mathrm{~F}$ and $12 \mu \mathrm{~F}$ are first connected in series and then in parallel. The ratio of the effective capacitances in the two cases is

A particle revolving in a circular path travels the first half of the circumference in 4 s and the next half in 2 s . What is its average angular velocity?

A small disc is on the top of a smooth hemisphere of radius $R$. The smallest horizontal velocity $v$ that should be imparted to the disc, so that disc leaves the hemisphere surface without sliding down is ( there is no friction )

In amplitude modulation, the amplitude of the carrier wave is 10 V and the amplitude of one of the side bands is 2 V . Then, the modulation index is

A straight wire of resistance $R$ is bent in the shape of $f_d$ square. A cell of emf 12 V is connected between two adjacent corners of the square. The potential difference across any diagonal of the square is

In the given circuit, if the potential at point $B$ is 24 V , the potential at point $A$ is

If the kinetic energy of a particle in motion is decreased by $36 \%$, the increase in de-Broglie wavelength of the particle is

The ratio of the number of turns per unit length of two solenoids $A$ and $B$ are 1:3 and the lengths of $A$ and $B$ are in the ratio $1: 2$. If the two solenoids have same cross-sectional area, the ratio of the self-inductances of the sole...

A particle of mass 2 g and charge $6 \mu \mathrm{C}$ is accelerated from rest through a potential difference of 60 V . The speed acquired by the particle is

Three point charges $+q,+2 q$ and $+4 q$ are placed along a straight line such that the charge $+2 q$ lies at equidistant from the other two charges. The ratio of the net electrostatic force on charges $+q$ and $+4 q$ is

Two mercury drops, each with same radius $r$ merged to form a bigger drop. $T$ is the surface tension of single drop, then the surface energy of bigger drop is given by

Depth of a river is 100 m magnitude of compressibility of the water is $05 \times 10^{-9} \mathrm{~N}^{-1} \mathrm{~m}^2$. The fractional compression in water at the bottom of the river is (acceleration due to gravity $=10 \mathrm{~m} / \ma...

What is the height from the surface of earth, where acceleration due to gravity will be $1 / 4$ of that of the earth? $\left(R_E=6400 \mathrm{~km}\right)$

An ideal gas is kept in a cylinder of volume $3 \mathrm{~m}^3$ at a pressure of $3 \times 10^5 \mathrm{~Pa}$. The energy of the gas is

A certain volume of a gas at 300 K expands adiabatically until its volume is doubled. The resultant fall in temperature of the gas is nearly (The ratio of the specific heats of the gas $=1.5$ )

The efficiency of a Carnot's engine is $25 \%$. When the temperature of sink is 300 K . The increase in the temperature of source required for the efficiency to become $50 \%$ is

The absorption coefficient value of a perfect black body is

When 100 J of heat is supplied to a gas, the increase in the internal energy of the gas is 60 J . Then the gas is /can

Two objects having masses $1: 4$ ratio are at rest. When both of them are subjected to same force separately, they achieved same kinetic energy during times $t_1$ and $t_2$ respectively. Then, ratio of $\frac{t_2}{t_1}$ is

A block of metal 2 kg is in rest on a smooth plane. It is striked by a jet releasing water of $1 \mathrm{~kg} \mathrm{~s}^{-1}$ at a speed of $5 \mathrm{~m} / \mathrm{s}$, then the acceteration of the block is

An insect is crawling in a hemi-spherical bowl of radius $R$. If the coefficient of friction between the insect and bowl is $\mu$, then the maximum height to which the insect can crawl the bowl is

At a place where the magnitude of the earth's magnetic field is $4 \times 10^{-5} \mathrm{~T}$, a short bar magnet is placed with its axis perpendicular to the earth's magnetic field direction. If the resultant magnetic field at a point at ...

An object of mas $m$ is projected with an initial velocity $u$ with angle of $\theta$ with the horizontal. The average power delivered by gravity in reaching the highest point

If two stones are projected at angle $\theta$ and $\left(90^{\circ}-\theta\right)$ respectively with horizontal with a speed of $20 \mathrm{~ms}^{-1}$. If second stone rises 10 m higher than the first stone then, the angle of projection $\t...

The relation between time $t$ and displacement $x$ is $t=\alpha x^2+\beta x$, where $\alpha$ and $\beta$ are constants. If $v$ is the velocity, the retardation is

Two concentric thin circular rings of radii 50 cm and 40 cm , each carry a current of 3.5 A in opposite directions. If the two rings are coplanar, the net magnetic field due to the rings at their centre is