AP EAPCET 2025 - 27th May Morning Shift

If $\alpha, \beta$ are the roots of $x^2-5 \gamma x-6 \delta=0$ and $\gamma, \delta$ are the roots of $x^2-5 \alpha x-6 \beta=0$, then $\alpha+\beta+\gamma+\delta=$

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+p x^2+q x+r=0$, then $(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)=$

If $\sum_{i=1}^9\left(x_i-5\right)=9$ and $\sum_{i=1}^9\left(x_i-5\right)^2=45$, then the standard deviation of the nine observations $x_1, x_2, \ldots, x_9$ is

The coordinate axes are rotated about the origin in the counter clockwise direction through an angle $60^{\circ}$. If a and $b$ are the intercepts made on the new axes by a straight line whose equation referred to the original axes is $x+y=...

The image of a point $(2,-1)$ with respect to the line $x-y+1=0$ is

If one of the lines given by the pair of lines $3 x^2-2 y^2+a x y=0$ is making an angle $60^{\circ}$ with $X$-axis, then $a=$

If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle $\frac{\pi}{4}$ with the negative $X$-axis in the negative direction, then the equation of that line is

$A$ straight line passing through the origin $O$ meets the parallel lines $4 x+2 y=9$ and $2 x+y+6=0$ at the points $P$ and $Q$ respectively. Then, the point $O$ divides the line segment $P Q$ in the ratio

Equation of the plane passing through the origin and perpendicular to the planes $x+2 y-z=1$ and $3 x-4 y+z=5$ is

Let $A(2,3,5), B(-1,3,2)$ and $C(\lambda, 5, \mu)$ be the vertices of $\triangle A B C$. If the median through the vertex $A$ is equally inclined to the coordinate axes, then

The circumradius of the triangle formed by the points $(2,-1,1),(1,-3,-5)$ and $(3,-4,-4)$ is

Statement I In the interval $[0,2 \pi]$, the number of common solutions of the equations $2 \sin ^2 \theta-\cos 2 \theta=0$ and $2 \cos ^2 \theta-3 \sin \theta=0$ is two.
Statement II The number of solutions of $2 \cos ^2 \theta-3 \sin \the...

If $\cos x+\sin x=\frac{1}{2}$ and $0

If $\sin \theta+2 \cos \theta=1$ and $\theta$ belongs to 4 th quadrant (not lying on the coordinate axes), then $7 \cos \theta+6 \sin \theta=$

If $A$ and $B$ are acute angles satisfying $3 \cos ^2 A+2 \cos ^2 B=4$ and $\frac{3 \sin A}{\sin B}=\frac{2 \cos B}{\cos A}$, then $A+2 B=$

If the position vectors of $A, B, C, D$ are $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $4 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ resp...

If $\mathbf{u}, \mathbf{v}, \mathbf{w}$ are non-coplanar vectors and $p, q$ are real numbers, then the equality $[3 \mathbf{u} p \mathbf{v} p \mathbf{w}]-[p \mathbf{v} \mathbf{w} q \mathbf{u}]-[2 \mathbf{w} q \mathbf{v} q \mathbf{u}]=0$ hol...

The set of all real values of $c$ so that the angle between the vectors $\mathbf{a}=c x \hat{\mathbf{i}}-6 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $\mathbf{b}=x \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 c x \hat{\mathbf{k}}$ is an obtuse angle...

$P$ is the circumcentre of $\triangle A B C$. If the position vectors of $A, B, C$ and $P$ are $\mathbf{a}, \mathbf{b}, \mathbf{c}, \frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{4}$ respectively, then the position vector of the orthocentre of thi...

Let $\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=3 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{c}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ be three vectors. If $\mathbf...

An AC source of internal resistance $10^3 \Omega$ is connected to a transformer. The ratio of the number of turns in the primary to the number of turns in the secondary to match the source to a load resistance of $10 \Omega$ is

The ratio of the shortest wavelengths of Bracket and Balmer series of hydrogen atom is

If the binding energy per nucleon of deuteron $\left({ }_1 \mathrm{H}^2\right)$ is 1.15 MeV and an $\alpha$-particle has a binding energy of 7.1 MeV per nucleon, then the energy released per nucleon in the given reaction is
$$ { }_1 \mathrm...

Four capacitors are connected as shown in the figure. If $C_1, C_2, C_3$ and $C_4$ are in the ratio of $1: 2: 3: 4$, then the ratio of the charges on the capacitors $C_2$ and $C_4$ is

A body falls freely on to a hard horizontal surface. If the coefficient of restitution between the surface and the body is 0.8 , then the ratio of the maximum height to which the body rises after second impact and the initial height of the ...

Two bodies of masses $M$ and $4 M$ initially at rest, start moving towards each other due to their mutual attraction. The velocity of their centre of mass when the first body attains a velocity $v_0$ is

If a stone of mass 0.5 kg tied to one end of a wire is whirled in a circular path of radius 2 m with a speed $40 \mathrm{rev} / \mathrm{min}$ in a horizontal plane, then the tension in the wire is nearly

In amplitude modulation, if a message signal of 5 kHz 2 is modulated by a carrier wave of frequency 900 kHz , then the frequencies of the side bands are

In a meter bridge, the null point is located at 20 cm from left end of the wire when resistances $R$ and $S$ are connected in the left and right gaps respectively. If the resistance $S$ is shunted with $60 \Omega$ resistance, the null point...

In the given circuit, the internal resistance of the cell is zero. If $i_1$ and $i_2$ are the readings of the ammeter when the key $(K)$ is opened and closed respectively, then $i_1: i_2=$

The de-Broglie wavelength associated with an electron accelerated through a potential difference of $\frac{200}{3} \mathrm{~V}$ is nearly

The stress-strain graph of two wires $A$ and $B$ is shown in the figure. If $Y_A$ and $Y_B$ are Young's moduli of materials of wires $A$ and $B$ respectively, then

A coil having 100 square loops each of side 10 cm is placed such that its plane is normal to a magnetic field, which is changing at a rate of $0.7 \mathrm{Ts}^{-1}$. The emf induced in the coil is

If $11 \%$ of the power of a 200 W bulb is converted to visible radiation, then the intensity of the light at a distance of 100 cm from the bulb is

If two particles $A$ and $B$ of charges $1.6 \times 10^{-19} \mathrm{C}$ and $3.2 \times 10^{-19} \mathrm{C}$ respectively are separated by a distance of 3 cm in air, then the magnitude of electrostatic force on particle $A$ due to particle...

If four charges $+12 \mathrm{nC},-20 \mathrm{nC},+32 \mathrm{nC}$ and -15 nC are arranged at the four vertices of a square of side $\sqrt{2} \mathrm{~m}$, then the net electric potential at the centre of the square due to these four charges...

If two soap bubbles each of radius 2 cm combine in vacuum under isothermal conditions, then the radius of the new bubble formed is

The escape velocity of a body from a planet of mass $M$ and radius $R$ is $14 \mathrm{~km} \mathrm{~s}^{-1}$. The escape velocity of the body from another planet having same mass and diameter 8 R (in $\mathrm{km} \mathrm{s}^{-1}$ ) is

A rectangular slab consists of two cubes of copper and brass of equal sides having thermal conductivities in the ratio $4: 1$. If the free face of brass is at $0^{\circ} \mathrm{C}$ and that of copper is at $100^{\circ} \mathrm{C}$, then th...

The efficiency of a Carnot's heat engine is $\frac{1}{3}$. If the temperature of the source is decreased by $50^{\circ} \mathrm{C}$ and the temperature of the sink is increased by $25^{\circ} \mathrm{C}$, the efficiency of the engine become...

The change in internal energy of given mass of a gas, when its volume changes from $V$ to $3 V$ at constant pressure $p$ is
( $\gamma=$ Ratio of the specific heat capacities of the gas)

A monoatomic gas at a pressure of 100 kPa expands adiabatically such that its final volume becomes 8 times its initial volume. If the work done during the process is 180 J , then the initial volume of the gas is

If a gaseous mixture consists of 3 moles of oxygen and 4 moles of argon at an absolute temperature $T$, then the total internal energy of the mixture is (neglect vibrational modes and $R=$ Universal gas constant)

The apparent weight of a girl of mass 30 kg when she is in a lift moving vertically upwards with an acceleration of $2 \mathrm{~ms}^{-2}$ is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

If the given figure shows the relation between magnetic field ( $B$-along $Y$-axis) and magnetic intensity ( $H$-along $X$-axis) of a ferromagnetic material, then the point that represents coercivity of the material is

If two bodies $A$ and $B$ are projected with same velocity but with different angles $\theta_1$ and $\theta_2$ respectively with the horizontal such that both will have same range, then the ratio of times of flight of the bodies $A$ and $B$...

If the displacement ( $s$ in metre) of a moving particle in terms of time $(t$ in second $) s=t^3-6 t^2+18 t+9$, then the minimum velocity attained by the particle is

A galvanometer having 30 divisions has a current sensitivity of $0.0625 \frac{d i \nu}{\mu A}$. If it is converted into a voltmeter to read a maximum of 6 V , then the resistance of that voltmeter is

If a wire of length ' $L$ ' carrying a current ' $i$ ' is bent in the shape of a semi-circular arc as shown in the figure, then the magnetic field at centre of the arc is

A ray of light incidents at an angle of $60^{\circ}$ on the first face of a prism. The angle of the prism is $30^{\circ}$ and its second face is silvered. If the light ray inside the prism retraces its path after reflection from the second ...