AP EAPCET 2024 - 22th May Evening Shift

Based on the following statements, choose the correct option.
Statement I The variance of the first $n$ even natural numbers is $\frac{n^2-1}{4}$.
Statement II The difference between the variance of the first 20 even natural numbers and the...

If the slope of one of the lines in the pair of lines $8 x^2+a x y+y^2=0$ is thrice the slope of the second line, then $a$ is equal to

$A$ line $L$ passing through the point $P(-5,-4)$ cuts the lines $x-y-5=0$ and $x+3 y+2=0$ respectively at $Q$ and $R$ such that $\frac{18}{P Q}+\frac{15}{P R}=2$, then slope of line $L$ is

The locus of a variable point which forms a triangle of fixed area with two fixed points is

The equation of a line which makes an angle of $45^{\circ}$ with each of the pair of lines $x y-x-y+1=0$ is

If the reflection of a point $A(2,3)$ in $X$-axis is $B$, reflection of $B$ in the line $x+y=0$ is $C$ and the reflection of $C$ in $x-y=0$ is $D$, then the point of intersection of the lines $C D, A B$ is

If $\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}$ are the vertices of a tetrahedron, t...

If a line $L$ makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with $Y$-axis and $Z$-axis respectively, then the angle between $L$ and another line having direction ratio $1,1,1$ is

If $l, m$ and $n$ are the direction cosines of a line that is perpendicular to the lines having the direction ratios $(1,2,-1)$ and $(1,-2,1)$, then $(l+m+n)^2$ is equal to

The foot of the perpendicular drawn from a point $A(1,1,1)$ on to a plane $\pi$ is $P(-3,3,5)$.If the equation of the plane parallel to the plane of $\pi$ and passing through the mid-point of $A P$ is $a x-y+c z+d=0$, then $a+c-d$ is equal ...

If $A=(1,2,3), B=(3,4,7)$ and $C=(-3,-2,-5)$ are three points, then the ratio in which the point $C$ divides $A B$ externally is

The values of $x$ in $(-\pi, \pi)$, which satisfy the equation $8^{1+\cos ^2 x+\cos ^4 x+\ldots \ldots}=4^3$ are

$\cos 6^{\circ} \sin 24^{\circ} \cos 72^{\circ}$ is equal to

$\tan \alpha+2 \tan 2 \alpha+4 \tan 4 \alpha+8 \cot 8 \alpha$ is equal to

If $\sinh x=\frac{\sqrt{21}}{2}$, then $\cosh 2 x+\sinh 2 x$ is equal to

$\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to

If $\cos \alpha+4 \cos \beta+9 \cos \gamma=0$ and $\sin \alpha+4 \sin \beta+9 \sin \gamma=0$, then 81 $\cos (2 \gamma-2 \alpha)-16 \cos (2 \beta-2 \alpha)$ is equal to

If the vectors $a \hat{\mathbf{i}}+\mathbf{j}+3 \hat{\mathbf{k}}, 4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$ are coplanar, then $a$ is equal to

Let $|\hat{\mathbf{a}}|=2=|\hat{\mathbf{b}}|=3$ and the angle between $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ be $\frac{\pi}{3}$.
If a parallelogram is constructed with adjacent sides $2 \hat{\mathbf{a}}+3 \hat{\mathbf{b}}$ and $\hat{\mat...

The values of $x$ for which the angle between the vectors $x^2 \hat{\mathbf{i}}+2 x \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+x \hat{\mathbf{k}}$ is obtuse lie in the interval

Which physical quantity is measured in barn?

The principle quantum number $n$ corresponding to the exited state of $\mathrm{He}^{+}$ion. If on transition to the ground state two photons in succession with wavelength $1026 \mathop {\rm{A}}\limits^{\rm{o}}$ and $304 \mathop {\rm{A}}\lim...

The space between the plates of a parallel plate capacitor is halved and a dielectric medium of relative permittivity 10 is introduced between the plates. The ratio of the final and initial capacitances of the capacitor is

A body of mass 30 kg moving with a velocity $20 \mathrm{~ms}^{-1}$ undergoes one-dimensional elastic collision with another ball of same mass moving in the opposite direction with a velocity of $30 \mathrm{~ms}^{-1}$. After collision the ve...

Two blocks of equal masses are tied with a light string passing over a massless pulley (assuming frictionless surfaces ) acceleration of centre of mass of the two blocks is $\left(g=10 \mathrm{~ms}^{-2}\right)$

Which one of the following is not classified as pulse modulation?

Resistance of a wire is $8 \Omega$. It is drawn in such a way that it experiences a longitudinal strain of $400 \%$. The final resistance of the wire is

A battery of emf 8 V and internal resistance $0.5 \Omega$ is being charged by a 120 V DC supply using a series resister of $15.5 \Omega$. The terminal voltage of 8 V batter) during charging is

In the circuit shown in the figure, neglecting the source resistance, the voltmeter and ammeter readings respectively are

Light of wavelength $4000\mathop {\rm{A}}\limits^{\rm{o}}$ is incident on a sodium surface for which the threshold wavelength of photoelectrons is $5420 \mathop {\rm{A}}\limits^{\rm{o}}$. The work function of sodium is

A wire of length 100 cm and area of cross-section $2 \mathrm{~mm}^2$ is stretched by two forces of each 440 N applied at the ends of the wire in opposite directions along the length of the wire. If the elongation of the wire is 2 mm , the Y...

A metallic wire loop of side $(l) 0.1 \mathrm{~m}$ and resistance of $1 \Omega$ is moved with a constant velocity in a uniform magnetic field of $2 \mathrm{Wm}^{-2}$ as shown in the figure. The magnetic field is perpendicular to the plane o...

The radiation of energy $E$ falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

The magnitude of an electric field which can just suspend a deuteron of mass $3.2 \times 10^{-27} \mathrm{~kg}$ freely in ari is

Two charges 5 nC and -2 nC are placed at points $( 5 cm\mathrm{~}$ $0,0)$ and $(23 \mathrm{~cm}, 0,0)$ in a region of space where there is no other external field. The electrostatic potential energy of this charge system is

Two cylindrical vessels $A$ and $B$ of different areas of cross-section kept on same horizontal plane are filled with water to the same height. If the volume of water in vessel $A$ is 3 times the volume of water in vessel $B$, then the rati...

The gravitational potential energy of a body on the surface of the earth is $E$. If the body is taken from the surface of the earth to a height equal to $150 \%$ of the radius of the earth. Its gravitational potential energy is

Two ideal gases $A$ and $B$ of same number of moles expand at constant temperatures $T_1$ and $T_2$ respectively such that the pressure of gas $A$ decreases by $50 \%$ and the pressure of gas $B$ decreases by $75 \%$. If the work done by bo...

The efficiency of a Carnot heat engine is $25 \%$ and the temperature of its source is $127^{\circ} \mathrm{C}$. Without changing the temperature of the source, if absolute temperature of the sink is decreased by $10 \%$, the efficiency of ...

Water of mass $m$ at $30^{\circ} \mathrm{C}$ is mixed with with 5 g of ice at $-20^{\circ} \mathrm{C}$. If the resultant temperature of the mixture is $6^{\circ} \mathrm{C}$, then the value of $m$ is (specific heat capacity of ice $=0.5 \ma...

When 80 J of heat is absorbed by a monoatomic gas, its volume increases by $16 \times 10^{-5} \mathrm{~m}^3$. The pressure of the gas is

The total internal energy of 2 moles of a monoatomic gas at a temperature $27^{\circ} \mathrm{C}$ is $U$. The total internal energy of 3 moles of a diatomic gas at a temperature $127^{\circ} \mathrm{C}$ is

A body of 2 kg mass slides down with an acceleration of $4 \mathrm{~ms}^{-2}$ on an inclined plane having slope of $30^{\circ}$. The external force required to take the same body up the plane with same acceleration will be (acceleration due...

The acceleration of a body sliding down the inclined plane, having coefficient of friction $\mu$ is

A boy throws a ball with a velocity $v_0$ at an angle $\alpha$ to the ground. At the same time he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of

A ball at point $O$ is at a horizontal distance of 7 m from a wall. On the wall a target is set at point $C$. If the ball is throw from $O$ at an angle $37^{\circ}$ with horizontal aiming the target $C$. But it hits the wall at point $D$ wh...

A particle starts from rest and moves in a straight line. It travels a distance $2 L$ with uniform acceleration and then moves with a constant velocity a further distance of $L$. Finally, it comes to rest after moving a distance of $3 L$ un...

A short magnet oscillates with a time period 0.1 s at a place where horizontal magnetic field is $24 \mu \mathrm{~T}$. A downward current of 18 A is established in a vertical wire kept at a distance of 20 cm east of the magnet. The new time...

Two infinite length wires carry currents 8 A and $6^{\mathrm{A}}$ respectively and are placed along $X$ and $Y$-axes respectively. Magnetic field at a point $P(0,0, C)$ will

Current flows in a conductor from east to west. The direction of the magnetic field at a point below the conductor is towards