AP EAPCET 2025 - 23rd May Morning Shift

If $x>\sqrt{3}$ and $\frac{x^2+1}{\left(x^2+2\right)\left(x^2+3\right)}$ is expanded in terms of powers of $x$, then the coefficient of $x^{-8}$ is

If $t_n=\frac{1}{4}(n+2)(n+3), n \in N$, then which one of the following is true?
Assertion (A) $\frac{1}{t_1}+\frac{1}{t_2}+\ldots+\frac{1}{t_{2003}}=\frac{2003}{3009}$
Reason (R) $\frac{1}{t_1}+\frac{1}{t_2}+\ldots+\frac{1}{t_n}=\frac{4 n...

The mean and variance of the observations $x_1, x_2, x_3 \ldots x_{15}$ are respectively 2 and 4 . If the mean and variance of the observations $y_1, y_2 \ldots, y_{10}$ are respectively 2 and 5 , then the variance of the observations $x_1,...

If the perpendicular distances from the points $(2,3)$, $(4, a)$ and $(\alpha, \beta)$ on to the line $3 x+4 y-3=0$ are equal and $4 \alpha-3 \beta+1=0$, then sum of all possible values of $a, \alpha$ and $\beta$ is

Let $A(5,4)$ and $B(5,-4)$ be two points.
If $P$ is a point in the coordinate plane such that $\sqrt{A P B}=\frac{\pi}{4}$, then the point $P$ lies on the curve

The equation of the base of an equilateral triangle is $x+y=2$ and its opposite vertex is $(2,1)$. If $m_1, m_2$ are the slopes of the other two sides and the length of its side is $a$, then $\left|m_1-m_2\right|+a \sqrt{2}=$

The triangle formed by the lines $2 x^2+x y-6 y^2=0$ and $x+y-1=0$ is

If $\left(\frac{2}{3}, 0\right)$ is the centroid of the triangle formed by the lines $4 x^2-y^2=0$ and $l x+m y+n=0$, then, $l+m+n=$

A plane $\pi$ given by $a x+b y+11 z+d=0$ is perpendicular to the planes $2 x-3 y+z=4$, $3 x+y-z=5$ and the perpendicular distance from the origin to the plane $\pi$ is $\sqrt{6}$ units. If all the intercepts made by the plane $\pi$ on the ...

If $A(2,-1,1), B(2,5,1)$ and $C(0,-2,3)$ are the vertices of a triangle. If $D$ is the point of intersection of the side $B C$ and the internal angular bisector of angle $A$, then $A D=$

The number of solutions of the equation $\sec x \cdot \cos 5 x+1=0$ in the interval $[0,2 \pi]$ is

If $\sin x-\sin y=\frac{27}{65}$ and $\cos x-\cos y=\frac{-21}{65}$, then $\sin (x+y)=$

If $A$ and $B$ are positive 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 $\alpha$ is the maximum value and $\beta$ is the minimum value of $\cos ^2 \frac{x}{4}+\sin \frac{x}{4}, x \in R$, then $\alpha-\beta=$

If the vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 4 \hat{\mathbf{i}}+p \hat{\mathbf{j}}+\hat{\mathbf{k}}$ are coplanar, then $p=$

A unit vector that is perpendicular to the vector $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and coplanar with the vectors $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\m...

A line segment $P Q$ has the length 63 and direction ratios $(3,-2,6)$. If this line makes an obtuse angle with $X$-axis, then the components of the vector $\mathbf{P Q}$ are

If $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}},-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ are the position vectors of four poin...

If the magnitudes of $\mathbf{a}, \mathbf{b}$ and $\mathbf{a}+\mathbf{b}$ are respectively 3,4 and 5 , then the magnitude of $\mathbf{a}-\mathbf{b}$ is

If the vectors $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+l \hat{\mathbf{k}},-3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-4 l \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}-\hat{\mathbf{j}}+3 / \hat{\mathbf{k}}$ form a right-angled triangle for a positive v...

If a resistor of resistance $4 \Omega$, a capacitor of capacitive reactance $6 \Omega$ and an inductor of inductive reactance $9 \Omega$ are connected in series with an AC source, then the impedance of the circuit is

Of the following, Bohr's atomic model is applicable to

The ratio of the orders of the spacings of nuclear energy levels and atomic energy levels is

If 27 indentical charged conducting spheres each of capacitance $10 \mu \mathrm{~F}$ combine to form a big sphere, then the capacitance of the big sphere is

The capacitance of a spherical capacitor is 100 pF . If the spacing between the two spheres is 1 cm , then the radius of the inner sphere of the capacitor is

A wire of length 2.5 m is fixed at one end and a box of mass 4 kg is tied at the other end. If the wire rotates in a horizontal circle about the fixed end with $\frac{2}{\pi}$ rotations per second, then the tension in the wire is

If the maximum and minimum amplitudes of a modulated wave are 25 V and 5 V respectively, then the modulation index is

When a wire is connected in the left gap of a metre bridge, the balancing point is at 40 cm from the left end of the bridge wire. If the wire in the left gap is stretched so that its length is doubled and again connected in the same gap, th...

A wire of resistance ' $R$ ' is bent in the form of a circular loop. Two points on the circle seperated by a quarter circumference are connected to a battery of emf ' $E$ ' and negligible internal resistance. The heat generated in the wire ...

If a proton and an alpha particle are accelerated through the same potential difference, then the ratio of their de-Broglie wavelengths is

If the pressure on a body is increased from 200 kPa to 250 kPa , the volume of the body decreases by $0.25 \%$. The compressibility of the material of the body is (in $\mathrm{m}^2 \mathrm{~N}^{-1}$ )

If a wheel with 24 metallic spokes each 40 cm long is rotated with a speed of $180 \mathrm{rev} / \mathrm{min}$ in a plane normal to the horizontal component of Earth's magnetic field, the emf induced between the axle and the rim of the whe...

The ratio of the magnitudes of the electric field and $10^8$ times the magnetic field of a plane electromagnetic wave is

A particle of mass 0.2 g and charge 2 C is released from rest in a uniform electric field of $20 \mathrm{NC}^{-1}$. The kinetic energy of the particle after moving a distance of 20 cm is

A mercury drop of radius 1 cm is divided into $10^6$ droplets of equal size. If surface tension of mercury is $35 \times 10^{-3} \mathrm{Nm}^{-1}$, then the change in surface energy in the process is

A mass of $6 \times 10^{24} \mathrm{~kg}$ is to be compressed in the form of a solid sphere such that the escape velocity from its surface is $3 \times 10^4 \mathrm{~ms}^{-1}$. The radius of the sphere is
(Universal gravitational constant $...

The work done to increase the volume of 2 moles of an ideal gas from V to 2 V at a constant temperature $T$ is W . The work to be done to increase the volume of 2 moles of the same gas from 2 V to 4 V at the same constant temperature $T$ is

In a Carnot engine if the work done during isothermal expansion is $25 \%$ more than the work done during isothermal compression, then the efficiency of the engine is

The internal energy of one mole of a rigid diatomic gas at absolute temperature $T$ is

Steam at $100^{\circ} \mathrm{C}$ is passed into 114 g of water at $30^o$ The mass of water present in the mixture when the temperature of the water becomes $70^{\circ} \mathrm{C}$ is
(Latent heat of steam $=540 \mathrm{cal} \mathrm{g}^{-1}...

If the given graph shows the logarithmic values of pressure ( $p$ ) and volume ( $V$ ) of an ideal gas, then the ratio of the specific heat capacities of the gas is

If the tension in the horizontal wire shown in the figure is 30 N , then the weight $W$ and tension in the wire $O A$ are respectively

Materials suitable for permanent magnets should have

If the equation of motion of a projectile is $y=A x-B x^2$, then the ratio of the maximum height reached and the range of the projectile is

The angle of projection of a projectile whose path is shown in the given figure is

If the distance travelled by a freely falling body in the last but one second of its motion is 5 m , then the last second is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A long straight wire of circular cross-section of radius ' $a$ ' is carrying a steady current. The current is distributed uniformly across the cross-section of the wire. The ratio of the magnetic fields at points $0.5 a$ and $1.5 a$ from th...

If a charged particle enters a uniform magnetic field normally with certain velocity, then the time period of revolution of the particle

A light ray falls on a rectangular glass slab as shown in the figure. If total internal reflection occurs at the vertical face of the slab at point $B$, the refractive index of glass is

A thin circular ring and a circular disc of equal mass are rolling without sliding. If their linear velocities are equal and the total kinetic energy of the disc is 6 J , then the total kinetic energy of the ring is