AP EAPCET 2022 - 4th July Morning Shift

The number of real roots of the equation \(\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}=\frac{13}{6}\) is

The mean deviation about the mean for the following data.
\(5,6,7,8,6,9,13,12,15 \text { is }\)

If the lines represented by \(a x^2+2 h x y+b y^2+2 g x+2 f y+c=0\) intersect on the \(X\)-axis, which of the following is in general incorrect?

For \(\alpha \in\left[0, \frac{\pi}{2}\right]\), the angle between the lines represented by \([x \cos \theta-y] [(\cos \theta+\tan \alpha) x-(1-\cos \theta \tan \alpha) y]=0\) is

The least distance from origin to a point on the line \(y=x+3\) which lies at a distance of 2 units from \((0,3)\) is

Suppose a triangle is formed by \(x+y=10\) and the coordinate axes. Then, the number of points \((x, y)\) where \(x\) and \(y\) are natural numbers, lying inside the triangle is

Starting from the point \(A(-3,4)\), a moving object touches \(2 x+y-7=0\) at \(B\) and reaches the point \(C(0,1)\). If the object travels along the shortest path, the distance between \(A\) and \(B\) is

The point of intersection of the lines \(\mathbf{r}=2 \mathbf{b}+t(6 \mathbf{c}-\mathbf{a})\) and \(\mathbf{r}=\mathbf{a}+s(\mathbf{b}-3 \mathbf{c})\) is

If \((a, b, c)\) are the direction ratios of a line joining the points \((4,3,-5)\) and \((-2,1,-8)\), then the point \(P(a, 3 b, 2 c)\) lies on the plane

If the point \((a, 8,-2)\) divides the line segment joining the points \((1,4,6)\) and \((5,2,10)\) in the ratio \(m: n\), then \(\frac{2 m}{n}-\frac{a}{3}=\)

The \(x\)-intercept of a plane \(\pi\) passing through the point \((1,1,1)\) is \(\frac{5}{2}\) and the perpendicular distance from the origin to the plane \(\pi\) is \(\frac{5}{7}\). If the \(y\)-intercept of the plane \(\pi\) is negative ...

If \((1+\tan 1^{\circ})(1+\tan 2^{\circ}) \ldots(1+\tan 45^{\circ})=2^n,\) then \(n=\)

If the identity \(\cos ^4 \theta=a \cos 4 \theta+b \cos 2 \theta+c\) holds for some \(a, b, c \in Q\) then \((a, b, c)=\)

The value of \(\frac{\sin \theta+\sin 3 \theta}{\cos \theta+\cos 3 \theta}\) is

\(\frac{\cos \theta}{1-\tan \theta}+\frac{\sin \theta}{1-\cot \theta}=\)

If \(\operatorname{cosech} x=\frac{4}{5}\), then \(\sinh x=\)

The vectors \(3 \mathbf{a}-5 \mathbf{b}\) and \(2 \mathbf{a}+\mathbf{b}\) are mutually perpendicular and the vectors \(a+4 b\) and \(-\mathbf{a}+\mathbf{b}\) are also mutually perpendicular, then the acute angle between \(\mathbf{a}\) and $...

Let \(\mathbf{a}=x \hat{i}+y \hat{j}+z \hat{k}\) and \(x=2 y\). If \(|\mathbf{a}|=5 \sqrt{2}\) and a makes an angle of \(135^{\circ}\) with the Z-axis, then \(\mathbf{a}=\)

In quadrilateral \(A B C D, \mathbf{A B}=\mathbf{a}, \mathbf{B C}=\mathbf{b}\). \(\mathbf{D A}=\mathbf{a}-\mathbf{b}, M\) is the mid-point of \(B C\) and \(X\) is a point on DM such that, \(\mathbf{D X}=\frac{4}{5}\) DM.
Then, the points $$...

Let \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) be the position vectors of the vertices of a \(\triangle A B C\). Through the vertices, lines are drawn parallel to the sides to form the \(\Delta A^{\prime} B^{\prime} C^{\prime}\). Then, the cent...

A coil of inductance 0.1 H and resistance \(110 \Omega\) is connected to a source of 110 V and 350 Hz . The phase difference between the voltage maximum and the current maximum is

The graph of \(\ln \left(\frac{R}{R_0}\right)\) versus $\ln A$ is where \(R\) is radius of a nucleus, \(A\) is its mass number, and \(R_0\) is constant

Energy of a stationary electron in the hydrogen atom is \(E=\frac{13.6}{n^2} \mathrm{~eV}\), then the energies required to excite the electron in hydrogen atom to (a) its second excited state and (b) ionised state, respectively.

A capacitor of capacitance \(C_1=1 \mu \mathrm{F}\) is charged using a 9 V battery. \(C_1\) is, then removed from the battery and connected to capacitors \(C_2\) and \(C_3\) of \(2 \mu \mathrm{F}\) and \(3 \mu \mathrm{F}\), respectively as ...

A ball of mass 0.5 kg moving horizontally at \(10 \mathrm{~ms}^{-1}\) strikes a vertical wall and rebounds with speed \(v\). The magnitude of the change in linear momentum is found to be \(8.0 \mathrm{~kg}-\mathrm{~ms}^{-1}\). The magnitude...

Masses \(m\left(\frac{1}{3}\right)^N \frac{1}{N}\) are placed at \(x=N\), when \(N=2,3,4 \ldots \infty\). If the total mass of the system is \(M\), then the centre of mass is

A cell can supply currents of 1 A and 0.5 A via resistances of \(2.5 \Omega\) and \(10 \Omega\), respectively. The internal resistance of the cell is

Current density in a cylindrical wire of radius \(R\) varies with radial distance as \(\beta\left(r+r_0\right)^2\). The current through the section of the wire shown in the figure is

The metal which has the highest work function in the following is

Same tension is applied to the following four wires made of same material. The elongation is longest in

If the average power per unit area delivered by an electromagnetic wave is \(9240 \mathrm{~Wm}^{-2}\). then the amplitude of the oscillating magnetic field in EM wave is

The maximum number of TV signals, that can be transmitted along a co-axial cable is

A beam of light with intensity \(10^{-3} \mathrm{~Nm}^{-2}\) and cross-sectional area \(20 \mathrm{~cm}^2\) is incident on a fully reflective surface at angle \(45^{\circ}\). Then, the force exerted by the beam on the surface is

A plane electromagnetic wave travels in free space along \(Z\)-axis. At a particular point in space, the electric field along \(X\)-axis is \(8.7 \mathrm{~Vm}^{-1}\). The magnetic field along \(Y\)-axis is

Two positive point charges of \(10 \mu \mathrm{C}\) and \(12 \mu \mathrm{C}\) are placed 10 cm apart in air. The work done to bring them 6 cm closer is

An electric dipole with dipole moment \(5 \times 10^{-7} \mathrm{C}-\mathrm{m}\) is in the electric field of \(2 \times 10^4 \mathrm{NC}^{-1}\) at an angle of \(60^{\circ}\) with the direction of the electric field. The torque acting on the...

Electrostatic force between two identical charges placed in vacuum at distance of \(r\) is F. A slab of width \(\frac{r}{5}\) and dielectric constant 9 is inserted between these two charges, then the force between the charges is

Statement (A) When the temperature increases the viscosity of gases increases and the viscosity of liquids decreases.
Statement (B) Water does not wet an oily glass because cohesive force of oil is less than that of water.
Statement (C) A l...

A projectile is thrown straight upward from the earth's surface with an initial speed \(v=\alpha v_e\) where \(\alpha\) is a constant and \(v_e\) is the escape speed. The projectile travels upto a height 800 km from earth's surface, before ...

The number of vibrational degree of freedom of a diatomic molecule is

A sphere of surface area \(4 \mathrm{~m}^2\) at temperature 400 K and having emissivity 0.5 is located in an environment of temperature 200 K. The net rate of energy exchange of the sphere is (Stefan Boltzmann constant, $$\sigma=5.67 \times...

A Carnot engine operates between a source and a sink. The efficiency of the engine is \(40 \%\) and the temperature of the sink is \(27^{\circ} \mathrm{C}\). If the efficiency is to be increased to \(50 \%\), then the temperature of the sou...

A car engine has a power of 20 kW. The car makes a roundtrip of 1 h. If the thermal efficiency of the engine is \(40 \%\) and the ambient temperature is 300 K . The energy generated by fuel combustion is

Two rectangular blocks of masses 40 kg and 60 kg are connected by a string and kept on a frictionless horizontal table. If a force of 1000 N is applied on 60 kg block away from 40 kg block, then the tension in string is

A compass needle oscillates 20 times per minute at a place where the dip is \(45^{\circ}\) and the magnetic field is \(B_1\). The same needle oscillates 30 times per minute at a place where the dip is \(30^{\circ}\) and magnetic field is $$...

A projectile with speed \(50 \mathrm{~ms}^{-1}\) is thrown at an angle of \(60^{\circ}\) with the horizontal. The maximum height that can be reached is (acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\))

A car travels with a speed of \(40 \mathrm{~km} \mathrm{~h}^{-1}\). Rain drops are falling at a constant speed vertically. The traces of the rain on the side windows of the car make an angle of \(30^{\circ}\) with the vertical. The magnitud...

A car covers a distance at speed of \(60 \mathrm{~km} \mathrm{~h}^{-1}\). It returns and comes back to the original point moving at a speed of \(v\). If the average speed for the round trip is \(48 \mathrm{~kmh}^{-1}\), then the magnitude o...

Two electrons, \(e_1\) and \(e_2\) of mass \(m\) and charge \(q\) are injected into the perpendicular direction of the magnetic field \(B\) such that the kinetic energy of \(e_1\) is double than that of \(e_2\). The relation of their freque...

Two infinitely long wires each carrying the same current and pointing in \(+y\) direction are placed in the \(x y\)-plane, at \(x=-2 \mathrm{~cm}\) and \(x=1 \mathrm{~cm}\). An electron is fired with speed \(u\) from the origin making an an...