AP EAPCET 2025 - 21st May Morning Shift

The variance of ungrouped data $2,12,3,11,5,10,6,7$, is

If the distance of a variable point $P$ from a point $A(2,-2)$ is twice the distance of $P$ from $Y$-axis, then the equation of locus of $P$ is

If one of the lines represented by $a x^2+2 h x y+b y^2=0$ bisects the angle between the positive coordinates axes, then

If the transformed equation of the equation $2 x^2+3 x y-2 y^2-17 x+6 y+8=0$ after translating the coordinate axes to a new origin ( $\alpha, \beta$ ) is $a X^2+2 h X Y+b Y^2+c=0$, then $3 \alpha+c=$

If the slope of both the line given by $x^2+2 h x y+6 y^2=0$ are options and the angle between these lines is $\tan ^{-1}\left(\frac{1}{7}\right)$, then the product of the perpendiculars draw from the point $(1,0)$ to the given pair of line...

If the straight line $2 x+3 y+1=0$ bisects the angle between two other straight lines one of which is $3 x+2 y+4=0$, then the equation of the other straight line is

$P(6,4)$ is a point on the line $x-y-2=0$. If $A(\alpha, \beta)$ and $B(\gamma, \delta)$ are two points on this line lying on either side of $P$ at a distance of 4 units from $P$, then $\alpha^2+\beta^2+\gamma^2+\delta^2=$

If the equation of the plane passing through the point $(2,-1,3)$ and perpendicular to each of the planes $3 x-2 y+z=8$ and $x+y+z=6$ is $l x+m y+n z=1$, then $4 m+2 n-3 l=$

If the sum of the distances of the point $(3,4, \alpha), \alpha \in R$ from $X$-axis, $Y$-axis and $Z$-axis is minimum, then $\sec \alpha=$

$G(1,0,1)$ is the centroid of the $\triangle A B C$. If $A=(1,-4,2)$ and $B=(3,1,0)$, then $A G^2+C G^2=$

The number of solutions of the equation $2 \sin ^2 \theta-3 \cos ^2 \theta=\sin \theta \cos \theta$ lying in the intervals $(-\pi, \pi)$ is

If $\cos \alpha=\sec h \beta$, then $\beta=$

If $630^{\circ}<\theta<810^{\circ}$ and $\tan \theta=-\frac{7}{24}$, then $\cos \left(\frac{\theta}{4}\right)=$

\(\sum\limits_{k=0}^{12} \frac{1}{\sin \left((k+1) \frac{\pi}{6}+\frac{\pi}{4}\right) \sin \left(\frac{k \pi}{6}+\frac{\pi}{4}\right)}=\)

For $\theta \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ if $2 \cos \theta+\sin \theta=1$ and $7 \cos \theta+6 \sin \theta=k$, then the possible values of $k$ are

Let $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}, 5 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}},-13 \hat{\mathbf{i}}-11 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ be the position vectors of three points. $A, B$ and $C$, respecti...

If $\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$, $\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{c}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{d}=\hat{\mathbf{i}}+...

If $\mathbf{a}=\hat{\mathbf{i}}+p \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, \mathbf{b}=p \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{c}=-3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ are three vectors such that $|\mat...

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three unit vectors such that $|\mathbf{a}-\mathbf{b}|^2+|\mathbf{b}-\mathbf{c}|^2+|\mathbf{c}-\mathbf{a}|^2=15$, then $|\mathbf{a}-\mathbf{b}-\mathbf{c}|^2-4(\mathbf{b} \cdot \mathbf{c})=$

$\mathbf{a}, \mathbf{b}$ are position vectors of the point $A$ and $B$ respectively, $C$ and $D$ are points on the line $A B$ such that $\mathbf{A B}, \mathbf{A C}$ and $\mathbf{B D}, \mathbf{B A}$ are two pairs of like vectors. If $\mathbf...

The resonant frequency of an LC circuit is $f_0$. If a dielectric slab of constant 16 is inserted completely between the plates of the capacitor, then the resonant frequency is

An element $X$ of a half-life of $1.4 \times 10^9$ years decays to form another stable element $Y$. A sample is taken from a rock that contains both $X$ and $Y$ in the ratio $1: 7$. If at the time of formation of the rock $Y$ was not presen...

A capacitor of capacitance $2 \mu \mathrm{~F}$ is charged to 50 V and then disconected from the source. Later the gap between the plates of the capacitor is filled with a dielectric material. If the energy stored in the capacitor is decreas...

If the sum of heights of transmitting and receiving antennas in line of sight of communication is ' $h$ ' then the height of receiving antenna, to have the range maximum is

In a potentiometer experiment, when two cells of emfs $E_1$ and $E_2\left(E_2>E_1\right)$ are connected in series, the balancing length is 160 cm . If one of the cells is reversed, the balancing length decreases by $75 \%$. If $E_1=1.2 \mat...

A wire of resistance $100 \Omega$ is stretched, so that its length increases by $20 \%$. The stretched wire is then bent in the form of a rectangle whose length and breadth are in the ratio $3: 2$. The effective resistance between the ends ...

If an electron in the excited state falls to ground state, a photon of energy 5 eV is emitted, then the wavelength of the photon is nearly

If the linear momentum of a proton is changed by $p_0$ then the de-Broglie wavelength associated with the proton changes by $0.25 \%$. Then the initial linear momentum of the proton is

As shown in the figure, a light uniform rod $P Q$ of length 150 cm is suspended from the ceiling horizontally using two metal wires $A$ and $B$ tied to the ends of the rod. The ratios of the radii and the Young's moduli of the materials of ...

If the magnetic field inside a solenoid is $B$, then the magnetic energy stored in it per unit volume is ( $c=$ speed of light in vacuum and $\varepsilon_0$ is permittivity of free space)

In a plane electromagnetic wave, the magnetic field is given by $\mathbf{B}=3 \times 10^{-7} \sin \left(100 \pi x+10^{12} t\right) \mathrm{T}$, then the wavelength of the wave is
(In the equation $x$ is in metre and $t$ is in second)

The force between two point charges kept with a separation of 9 cm in air is 98 N . If a dielectric slab of constant 4, thickness 6 cm and another dielectric slab of constant 9 , thickness 3 cm are introduced between the two charges, then t...

Three point charges shown in the figure lie along a straight line. The energy required to exchange the position of central charge with one of the negative charges is

If water flows with a velocity of $20 \mathrm{cms}^{-1}$ in a pipe of radius 2 cm , then the flow is (The coefficient of viscosity of water is $10^{-3} \mathrm{~kg} \mathrm{~m}^{-1} \mathrm{~s}^{-1}$ and density of water is $10^3 \mathrm{~k...

An infinite number of objects each 1 kg mass are placed on the $X$-axis on both sides of $x=0$ at $\pm 1 \mathrm{~m}$, $\pm 2 \mathrm{~m}, \pm 4 \mathrm{~m}, \pm 8 \mathrm{~m} \ldots \ldots$ and so on. The magnitude of the resultant gravita...

According to Zeroth law of thermodynamics, the physical quantity which is same for two bodies in thermal equilibrium is

If a refrigerator of coefficient of performance of 5 has a freezer at a temperature of $-13^{\circ} \mathrm{C}$, then the room temperature is

If 2 moles of an ideal monoatomic gas at a temperature of $27^{\circ} \mathrm{C}$ is mixed with 4 moles of another ideal monoatomic gas at a temperature of $327^{\circ} \mathrm{C}$, then the temperature of mixture of the two gases is

An electric kettle takes 4 A current at 220 V . If the entire electric energy is converted into heat energy, then the time (in minutes) taken to increase the temperature of 1 kg of water from $34^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{...

From the figure shown for a thermodynamic system, match the curves with their respective thermodynamic processes.
( $p=$ Pressure and $V=$ volume )
$$ \begin{array}{llll} \hline & \text { Curve } & & \text { Process } \\ \hline \text { (i) ...

As shown in the figure, a force $F$ is applied on a block of mass $\sqrt{3} \mathrm{~kg}$ placed on a rough horizontal surface. The maximum value of $F$ for the block not to move is (Coefficient of static friction between the block and the
...

A ball is projected from a point with a speed $V_0$ at certain angle with the horizontal. From the same point and at the same instant, a person starts running with a constant speed $0.5 V_0$ to catch the ball. If the person catches the ball...

If bullets are fired in all possible directions from same point with equal velocity of $10 \mathrm{~ms}^{-1}$ and with an angle of projection $45^{\circ}$, then the area covered by the bullets on the ground is nearly
(Acceleration due to gr...

If a car travels $40 \%$ of the total distance with a speed $v_1$ and the remaining distance with a speed $v_2$, then average speed of the car is

The magnetic field at a distance of 10 cm from a long straight thin wire carrying a current of 4 A is

A velocity selector is to be constructed to select ions with a velocity of $6 \mathrm{~km} \mathrm{~s}^{-1}$. If the electric field used is $400 \mathrm{~V} \mathrm{~m}^{-1}$, then the magnetic field to be used is

A closely wound solenoid of 1200 turns and area of cross-section $5 \mathrm{~cm}^2$ carries a current. If the magnetic moment of the solenoid is $1.2 \mathrm{JT}^{-1}$, then the current through the solenoid is

If the far point of a short sighted person is 400 cm , then the power of the lens required to enable him to see very distant objects clearly is

If the radius of gyration of a thin circular ring about an axis passing through its centre and perpendicular to its plane is $10 \sqrt{2} \mathrm{~cm}$, then its radius of gyration about its diameter is

If a wheel starting from rest is rotating with an angular acceleration of $\pi \mathrm{rad} \mathrm{s}^{-2}$, then the number of rotations made by the wheel in the first 6 seconds time is