AP EAPCET 2023 - 15th May Morning Shift

The variance of 20 observations is 5. If each one of the observations is multiplied by 2 , then the variance of the resulting observations is

If the area of the triangle formed by the lines $y=x+c$ and $2 x^2+5 x y+3 y^2=0$ is $\frac{1}{20}$ sq units, then $c=$

If the lines given by $\left(x^2+y^2\right) \sin ^2 \alpha=(x \cos \alpha-y \sin \alpha)^2$ are perpendicular to each other, then $\sin ^2 \alpha+\tan ^2 \alpha=$

In $\triangle A B C$ the coordinates of the vertex $A$ are $(-3,1)$. If the equation of the median through $B$ is $2 x+y-3=0$ and the equation of the bisector of $\angle C$ is $7 x-4 y-1=0$, then the equation of the side $B C$ is

The combined equation of the lines passing through the point $(3,4)$ and each making an angle $45^{\circ}$ with the line $x+y+1=0$ is-

The equal sides of an isosceles triangle are given by equations $7 x-y+3=0$ and $x+y-3=0$. If the slope $m$ of the third side is an integer, then $m=$

If the line passing through the points $(5,1, a)$ and $(3, b, 1)$ crosses the $Y Z$-plane at the point $\left(0, \frac{17}{2}, \frac{-13}{2}\right)$, then $a+b=$

$\triangle A B C$ is formed by $A(1,8,4), B(0,-11,4)$ and $C(2,-3,1)$. If $D$ is the foot of the perpendicular drawn from $A$ to $B C$, then the coordinates of $D$ are

Let $\pi_1$ be the plane determined by the vectors $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}$ and $3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$. Let $\pi_2$ be the plane determined by the vectors $\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $3 \hat{\math...

The distance between two parallel planes $a x+b y+c z+d_1=0, a x+b y+c z+d_2=0$ is given by $\frac{\left|d_1-d_2\right|}{\sqrt{a^2+b^2+c^2}}$. If the plane $2 x-y+2 z+3=0$ has the distances $\frac{1}{3}$ and $\frac{2}{3}$ units from the pla...

If $A=\frac{\pi}{24}$, then $\frac{\cos A+\cos 3 A+\cos 5 A+\cos 7 A}{\sin A+\sin 3 A+\sin 5 A+\sin 7 A}=$

If $(1+\sqrt{1+a}) \sin \alpha=(1+\sqrt{1-a}) \cos \alpha$ and $0

$\sin 21^{\circ} \cos 9^{\circ}-\cos 84^{\circ} \cos 6^{\circ}=$

If $\cos \alpha+\cos \beta=a$ and $\sin \alpha+\sin \beta=b$, then match the items given in List-A with those of their values in List-B
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If $\alpha=\log _e(2+\sqrt{3})$, then $\frac{\cosh \alpha}{1-\tanh \alpha}+\frac{\sinh \alpha}{1-\operatorname{coth} \alpha}=$

If $\sec (\theta+\alpha), \sec \theta$ and $\sec (\theta-\alpha)$ are in arithmetic progression, then $\sin ^2 \theta=$

a and b are two vectors such that a is not parallel to b. If $\mathbf{p}=(x+2 y+3) \mathbf{a}+(5 x-y+2) \mathbf{b}$ and $\mathbf{q}=(2 x+3 y+5) \mathbf{a}+(x-5 y-2) \mathbf{b}$ are two vectors such that $\mathbf{p}=2 \mathbf{q}$, then $x-2 ...

Let $\mathbf{O A}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{O B}=\hat{\mathbf{i}}-4 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\mathbf{O C}=-3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ be the position vector...

$3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-\hat{\mathbf{k}},-2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $-\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ are the position vectors of the vertices $A, B$ and $C$ of a $\tr...

If $\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}, \mathbf{b}=3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{c}=5 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}$ are three vectors, then a vector which is perpendicular to $\mathbf{a}$ and $\mat...

The frequency of AC at which $16 \mu \mathrm{~F}$ capacitor and $\frac{10}{\pi^2} \mathrm{mH}$ inductor will have same reactance is

The transition of an electron in hydrogen atom that emits a photon whose wavelength lies in the ultraviolet region of the electromgnetic spectrum is

The relation between the mean-life time $\tau$ and the half-life time $T_{1 / 2}$ of a radioactive substance is

Two square shaped metal plates of side 1 m , kept 0.01 m apart in air from a parallel plate capacitor. It is connected to a battery of 500 V . The plates of the capacitor are then immersed in an insulating oil by lowering the plates vertica...

A body falls freely from a height of 100 m on to the ground and rebounds to a maximum height of 36 m after collision. The coefficient of restitution between ground and the body is

A carrier wave of peak voltage 15 V is used to transmit a message signal. If the modulation index is $60 \%$, then the peak of voltage of the modulating signal is

Charge passing through a conductor of cross-section $0.3 \mathrm{~m}^2$ is given by $q=\left(3 t^2+5 t+2\right) \mathrm{C}$ where $t$ is in seconds. The drift velocity at $t=2 \mathrm{~s}$ is (Concentration of electrons in the conductor $=2...

When a resistance $R_1$ is connected across a cell, the current is $I_1$ and if the resistance $R_1$ is replaced by $R_2$, the current is $I_2$. Then the internal resistance of the cell is

The velocity of a particle $A$ is 3 times the velocity of proton. If the ratio of the de- Broglie wavelengths of the particle $A$ and the proton is $3: 2$, the mass of the particle $A$ is
( $m_p=$ mass of proton)

The maximum possible height of a mountain on earth is approximately
(elastic limit of mountain rock $=30 \times 10^7 \mathrm{Nm}^{-2}$, average density of mountain rock $=3 \times 10^3 \mathrm{kgm}^{-3}$, $g=10 \mathrm{~ms}^{-2}$ )

Two springs $A$ and $B$ fixed at the top and are stretched by 8 cm and 16 cm respectively, when loads of 20 N and 10 N suspended at the lower ends. The ratio of the spring constant of the springs $A$ and $B$ is

In an AC generator, if coils of $N$ turns and area $A$ is rotated at $v$ revolutions per second in a uniform magnetic field $B$, then the motional emf produced is equal to (At $t=0 \mathrm{~s}$, the coil is perpendicular to the field)

The average power output of a point source of an electromagnetic radiation is 1080 W . The maximum value of the rms value of the electric field at a distance of 3 m from the source is

The electric field ( E in $\mathrm{NC}^{-1}$ ) in a region is given by $\mathrm{E}=3 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}$. The net electric flux through a square area of side 2 m parallel to $y z$-plane is

Two thin conducting concentric shells of radii $R$ and $2 R$ are shown in the figure. The outer shell carries a charge $+Q$ and the inner shell is neutral. Then the correct statement/s is
(a) When the switch is closed, the potential on the ...

A person of height 1.65 m is standing upright. The additional external force required by blood vessel of length 1 cm , diameter 1 mm at feet to balance the pressure compared to similar blood vessel in head is (Density of blood $=1.1 \times ...

The value of acceleration due to gravity at a height of $4 R_E$ from surface of earth is
( $R_E$ is radius of earth and acceleration due to gravity on the surface of the earth $=10 \mathrm{~ms}^{-2}$ )

2 moles of a monatomic gas requires heat energy $Q$ to be heated from $30^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ at constant volume. The heat energy required to raise the temperature of 4 moles of a diatomic gas from $28^{\circ} \ma...

A vessel of volume 10 litres is filled with $\mathrm{H}_2$ gas. The total average translational kinetic energy of its molecules is $4.5 \times 10^5 \mathrm{~J}$. The pressure of hydrogen in the vessel is

A block of steel of mass 2 kg slides down a rough inclined plane of inclination of $\sin ^{-1}\left(\frac{3}{5}\right)$ at a constant speed. The temperature of the block as it slides through 80 cm , assuming that the mechanical energy lost ...

Isothermal bulk modulus of a gas at a pressure $p$ is ( $\gamma$-ratio of specific heat capacities of the gas)

The specific heat capacity of a copper block of mass $M$ is $s$. If the mass of the copper block is doubled, the specific heat capacity will be

A body is made to move up along an inclined plane of inclination $30^{\circ}$ and the coefficient of friction is 0.5 , then its retardation is
( $g$ is acceleration due to gravity)

A car of mass 1500 kg is moving with $20 \mathrm{~ms}^{-1}$ velocity. If the breaks are applied, it comes to rest in 5 s, then the retarding force is

A solenoid has a core of a material with relative permeability 400 . The windings of the solenoid are insulated from the core and carry of 4 A . If the number of turns is 500 per metre, then the magnetising field is

A stone thrown with velocity $u$ at angles $\theta$ and $\left(90^{\circ}\right.$ $-\theta$ ) with the horizontal reaches to maximum heights $H_1$ and $H_2$ respectively. Its horizontal range is

The time of flight of a vertically projected stone is 8 s . the position of the stone after 6 s from the ground is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A magnetic field intensity at the centre of a circular wire of radius 0.1 m carrying a current 0.2 A is

A wire is first bent in the form of a circular coil of 5 turns and the same wire is then bent in the form of another circular coil of 10 turns. If same current is passed in both the coils, then the ratio of the magnetic fields at their cent...

A force of $(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}) \mathrm{N}$ acts on a particle whose position vector with respect to the origin of the coordinate system is $(6 \hat{\mathbf{i}}+b \hat{\mathbf{j}}+12 \hat{\mathbf{k}}) ...