AP EAPCET 2024 - 20th May Morning Shift

\(1+\frac{1}{3}+\frac{1 \cdot 3}{3 \cdot 6}+\frac{1 \cdot 3 \cdot 5}{3 \cdot 6 \cdot 9}+\ldots \text { to } \infty=\)

$x$ and $y$ are the arithmetic means of the runs of two batsmen $A$ and $B$ in 10 innings respectively and $\sigma_A, \sigma_B$ are the standard deviations of their runs in them. If batsman $A$ is more consistent than $B$, then he is also a...

If the origin is shifted to a point $P$ by the translationd axes to remove the $y$-term from the equation $x^2-y^2+2 y-1=0$, then the transformed equation of it is

If the slope of one line of the pair of lines $2 x^2+h x y+6 y^2=0$ is thrice the slope of the other line, then $h=$

If the equation of the pair of straight lines passing through the point $(1,1)$ and perpendicular to the pair of lines $3 x^2+11 x y-4 y^2=0$ is $a x^2+2 h x y+b y^2+2 g x+2 f y+12=0$, then $2(a-h+b-g+f-12)=$

A line $L$ intersects the lines $3 x-2 y-1=0$ and $x+2 y+1=0$ at the points $A$ and $B$. If the point $(1,2)$ bisects the line segment $A B$ and $\frac{x}{a}+\frac{y}{b}=1$ is the equation of the line $L$, then $a+2 b+1=$

A line $L$ passing through the point $(2,0)$ makes an angle $60^{\circ}$ with the line $2 x-y+3=0$. If $L$ makes an acute angle with the positive X-axis in the anti-clockwise direction, then the $Y$-intercept of the line $L$ is

The distance from a point $(1,1,1)$ to a variable plane $\pi$ is 12 units and the points of intersections of the plane $\pi$ and $X, Y, Z$ - axes are $A, B, C$ respectively, If the point of intersection of the planes through the points $A, ...

The direction cosines of two lines are connected by the relations $l+m-n=0$ and $l m-2 m n+n l=0$. If $\theta$ is the acute angle between those lines, then $\cos \theta=$

If $A(1,0,2), B(2,1,0), C(2,-5,3)$ and $D(0,3,2)$ are four points and the point of intersection of the lines $A B$ and $C D$ is $P(a, b, c)$, then $a+b+c=$

The distance of the point $O(\mathbf{O})$ from the plane $\mathbf{r}$. $(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})=5$ measured parallel to $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-6 \hat{\mathbf{k}}$ is

Let $O(\mathbf{O}), A(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}), B(-2 \hat{\mathbf{i}}+3 \hat{\mathbf{k}}), C(2 \hat{\mathbf{i}}+\hat{\mathbf{j}})$ and $D(4 \hat{\mathbf{k}})$ are position vectors of the points $O, A, B, C$ and ...

If $5 \sin h x-\cos h x=5$, then one of the values of $\tan h x$ is

The number of ordered pairs $(x, y)$ satisfying the equations $\sin x+\sin y=\sin (x+y)$ and $|x|+|y|=1$ is

If $\cos \alpha+\cos \beta+\cos \gamma=\sin \alpha+\sin \beta+\sin \gamma=0$, then $\left(\cos ^3 \alpha+\cos ^3 \beta+\cos ^3 \gamma\right)^2+\left(\sin ^3 \alpha+\sin ^3 \beta+\sin ^3 \gamma\right)^2=$

$\frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots . . .+\sin 89^{\circ}}{2\left(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ}\right)+1}=$

\(\text { } \frac{\cos 10^{\circ}+\cos 80^{\circ}}{\sin 80^{\circ}-\sin 10^{\circ}}=\)

If $\mathbf{a}$ and $\mathbf{b}$ are the two non collinear vectors, then $|\mathbf{b}|\mathbf{a}+|\mathbf{a}| \mathbf{b}$ represents

$\mathbf{u}, \mathbf{v}$ and $\mathbf{w}$ are three unit vectors. Let $\hat{\mathbf{p}}=\hat{\mathbf{u}}+\hat{\mathbf{v}}+\hat{\mathbf{w}} \cdot \hat{\mathbf{q}}=\hat{\mathbf{u}} \times(\hat{\mathbf{v}} \times \hat{\mathbf{w}})$. If $\hat{\...

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are non-coplanar vectors. If $\alpha \mathbf{d}=\mathbf{a}+\mathbf{b}+\mathbf{c}$ and $\beta \mathbf{a}=\mathbf{b}+\mathbf{c}+\mathbf{d}$, then $|\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}|=$

A full wave rectifier circuit is operating from 50 Hz mains. The fundamental frequency in the ripple output will be

A resistance of $20 \Omega$ is connected to a source of an alternating potential $V=200 \sin (10 \pi t)$. If $t$ is the time taken by the current to change from the peak value to rms value, then $t$ is (in seconds)

A nucleus with atomic mass number $A$ produces another nucleus by loosing 2 alpha particles. The volume of the new nucleus is 60 times that of the alpha particle. The atomic mass number $A$ of the original nucleus is

$\mu$-meson of charge $e$, mass $208 m_e$ moves in a circular orbit around a heavy nucleus having charge $+3 e$. The quantum state $n$ for which the radius of the orbit is same as that of the first Bohr orbit for hydrogen atom is (approxima...

Two condensers $C_1$ and $C_2$ in a circuit are joined as shown in the figure. The potential of point $A$ is $V_1$ and that of point $B$ is $V_2$. The potential at point $D$ will be

A body of mass 2 kg collides head on with another body of mass 4 kg . If the relative velocities of the bodies before and after collision are $10 \mathrm{~ms}^{-1}$ and $4 \mathrm{~ms}^{-1}$ respectively. The loss of kinetic energy of the s...

A wooden plank of mass 90 kg and length 3.3 m is floating on still water. A girl of mass 20 kg walks from one end to the other end of the plank. The distance through which the plank moves is

A carrier is simultaneously modulated by two sine waves with modulation indices of 0.3 and 0.4 , then the total modulation index is

A block has dimensions $1 \mathrm{~cm}, 2 \mathrm{~cm}$ and 3 cm . Ratio of the maximum resistance to minimum resistance between any palr of opposite faces of the block is

The value of shunt resistance that allows only $10 \%$ of main current through the galvanometer of resistance $99 \Omega$ is

A current of 6 A enters one corner $P$ of an equilateral triangle $P Q R$ having three wires of resistance $2 \Omega$ each and leaves by the corner $R$ as shown in figure. Then the currents $I_1$ and $I_2$ are respectively

An electron of mass $m$ with initial velocity $\mathbf{v}=v_0 \hat{\mathbf{i}}\left(v_0>0\right)$ enters in an electric field $\mathbf{E}=-E_0 \hat{\mathbf{i}}$
( $E_0$ is constant $>0$ ) at $t=0$. If $\lambda$ is its de-Broglie wavelength ...

When the load applied to a wire is increased from 5 kg wt to 8 kg wt . The elongation of the wire increases from 1 mm to 1.8 mm . The work done during the elongation of the wire is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The average value of electric energy density in an electromagnetic wave is where $E_0$ is peak value

Two spheres $A$ and $B$ of radii 4 cm and 6 cm are given charges of $80 \mu \mathrm{C}$ and $40 \mu \mathrm{C}$ respectively. If they are connected by a fine wire, the amount of charge flowing from one to the other is

The angle between the electric dipole moment of a dipole and the electric field strength due to it on the equatorial line is

The radius of cross-section of the cylindrical tube of a spray pump is 2 cm . One end of the pump has 50 fine holes each of radius 0.4 mm . If the speed of flow of the liquid inside the tube is $0.04 \mathrm{~ms}^{-2}$. The speed of ejectio...

The acceleration due to gravity at a height of 6400 km from the surface of the earth is $2.5 \mathrm{~ms}^{-2}$. The acceleration due to gravity at a height of 12800 km from the surface of the earth is (Radius of the earth= 6400 km )

The temperature difference across two cylindrical rods $A$ and $B$ of same material and same mass are $40^{\circ} \mathrm{C}$ and $60^{\circ} \mathrm{C}$ respectively. In steady state, if the rates of flow of heat through the rods $A$ and $...

In a cold storage ice melts at the rate of 2 kg per hour when the external temperature is $20^{\circ} \mathrm{C}$. The minimum power output of the motor used to drive the refrigerator which just prevents the ice from melting is (latent heat...

The efficiency of Carnot cycle is $\frac{1}{6}$. By lowering the temperature of sink by 65 K , it increases to $\frac{1}{3}$. The initial and final temperature of the sink are

A Carnot engine has the same efficiency between 800 K and 500 K and $x>600 \mathrm{~K}$ and 600 K . The value of $x$ is

When the temperature of a gas is raised from $27^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$. The increase in the rms velocity of the gas molecule is

Any magnetic material loses its magnetic property when it is

A projectile can have the same range $R$ for two angles of projection. Their initial velocities are same. If $T_1$ and $T_2$ are times of flight in two cases, then the product of two times of flight is directly proportional to

A body starting from rest moving with an acceleration of $\frac{5}{4} \mathrm{~ms}^{-2}$. The distance travelled by the body in the third second is

In hydrogen atom an electron is making $6.6 \times 10^{15} \mathrm{rev} / \mathrm{s}$ around the nucleus of radius $0.47 $$\mathop A\limits^o $. The magnetic field induction produced at the centre of the orbit is nearly.

When two coaxial coils having same current in same direction are brought to each other, then the value of current in both the coils

An object lying 100 cm inside water is viewed normally from air. If the refractive index of water is $\frac{4}{3}$, then the apparent depth of the object is

The moment of inertia of a solid sphere of mass 20 kg and diameter 20 cm about the tangent to the sphere is